Changeset 4944 for Tutorials


Ignore:
Timestamp:
Jun 8, 2021 5:11:43 PM (4 months ago)
Author:
vondreele
Message:
 
File:
1 edited

Legend:

Unmodified
Added
Removed
  • Tutorials/2DTexture/Texture analysis of 2D data in GSAS-II.htm

    r4938 r4944  
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     25  <o:Author>Von Dreele</o:Author>
     26  <o:LastAuthor>Von Dreele, Robert B.</o:LastAuthor>
     27  <o:Revision>7</o:Revision>
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     29  <o:Created>2021-06-08T17:35:00Z</o:Created>
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    19699 p.MsoNormal, li.MsoNormal, div.MsoNormal
    20         {margin-top:0in;
     700        {mso-style-unhide:no;
     701        mso-style-qformat:yes;
     702        mso-style-parent:"";
     703        margin-top:0in;
    21704        margin-right:0in;
    22705        margin-bottom:4.0pt;
    23706        margin-left:0in;
     707        mso-pagination:widow-orphan;
    24708        font-size:12.0pt;
    25         font-family:"Times New Roman",serif;}
     709        font-family:"Times New Roman",serif;
     710        mso-fareast-font-family:"Times New Roman";
     711        mso-fareast-theme-font:minor-fareast;}
    26712h1
    27         {mso-style-link:"Heading 1 Char";
     713        {mso-style-priority:9;
     714        mso-style-unhide:no;
     715        mso-style-qformat:yes;
     716        mso-style-link:"Heading 1 Char";
     717        mso-margin-top-alt:auto;
    28718        margin-right:0in;
     719        mso-margin-bottom-alt:auto;
    29720        margin-left:0in;
     721        mso-pagination:widow-orphan;
     722        mso-outline-level:1;
    30723        font-size:24.0pt;
    31724        font-family:"Times New Roman",serif;
     725        mso-fareast-font-family:"Times New Roman";
     726        mso-fareast-theme-font:minor-fareast;
    32727        font-weight:bold;}
    33728h2
    34         {mso-style-link:"Heading 2 Char";
     729        {mso-style-noshow:yes;
     730        mso-style-priority:9;
     731        mso-style-qformat:yes;
     732        mso-style-link:"Heading 2 Char";
     733        mso-margin-top-alt:auto;
    35734        margin-right:0in;
     735        mso-margin-bottom-alt:auto;
    36736        margin-left:0in;
     737        mso-pagination:widow-orphan;
     738        mso-outline-level:2;
    37739        font-size:18.0pt;
    38740        font-family:"Times New Roman",serif;
     741        mso-fareast-font-family:"Times New Roman";
     742        mso-fareast-theme-font:minor-fareast;
    39743        font-weight:bold;}
    40744h3
    41         {mso-style-link:"Heading 3 Char";
     745        {mso-style-noshow:yes;
     746        mso-style-priority:9;
     747        mso-style-qformat:yes;
     748        mso-style-link:"Heading 3 Char";
     749        mso-margin-top-alt:auto;
    42750        margin-right:0in;
     751        mso-margin-bottom-alt:auto;
    43752        margin-left:0in;
     753        mso-pagination:widow-orphan;
     754        mso-outline-level:3;
    44755        font-size:13.5pt;
    45756        font-family:"Times New Roman",serif;
     757        mso-fareast-font-family:"Times New Roman";
     758        mso-fareast-theme-font:minor-fareast;
    46759        font-weight:bold;}
    47760h4
    48         {mso-style-link:"Heading 4 Char";
     761        {mso-style-noshow:yes;
     762        mso-style-priority:9;
     763        mso-style-qformat:yes;
     764        mso-style-link:"Heading 4 Char";
     765        mso-style-next:Normal;
    49766        margin-top:10.0pt;
    50767        margin-right:0in;
    51768        margin-bottom:4.0pt;
    52769        margin-left:0in;
     770        mso-pagination:widow-orphan lines-together;
    53771        page-break-after:avoid;
     772        mso-outline-level:4;
    54773        font-size:13.0pt;
    55774        font-family:"Cambria",serif;
     775        mso-ascii-font-family:Cambria;
     776        mso-ascii-theme-font:major-latin;
     777        mso-fareast-font-family:"Times New Roman";
     778        mso-fareast-theme-font:major-fareast;
     779        mso-hansi-font-family:Cambria;
     780        mso-hansi-theme-font:major-latin;
     781        mso-bidi-font-family:"Times New Roman";
     782        mso-bidi-theme-font:major-bidi;
    56783        color:#4F81BD;
     784        mso-themecolor:accent1;
    57785        font-weight:bold;
    58786        font-style:italic;}
    59787h5
    60         {mso-style-link:"Heading 5 Char";
     788        {mso-style-noshow:yes;
     789        mso-style-priority:9;
     790        mso-style-qformat:yes;
     791        mso-style-link:"Heading 5 Char";
     792        mso-margin-top-alt:auto;
    61793        margin-right:0in;
     794        mso-margin-bottom-alt:auto;
    62795        margin-left:0in;
     796        mso-pagination:widow-orphan;
     797        mso-outline-level:5;
    63798        font-size:12.0pt;
    64799        font-family:"Times New Roman",serif;
     800        mso-fareast-font-family:"Times New Roman";
     801        mso-fareast-theme-font:minor-fareast;
    65802        color:#4F4FFF;
    66803        font-weight:bold;}
    67804p.MsoTitle, li.MsoTitle, div.MsoTitle
    68         {mso-style-link:"Title Char";
     805        {mso-style-noshow:yes;
     806        mso-style-priority:10;
     807        mso-style-unhide:no;
     808        mso-style-qformat:yes;
     809        mso-style-link:"Title Char";
     810        mso-style-next:Normal;
    69811        margin-top:0in;
    70812        margin-right:0in;
    71813        margin-bottom:15.0pt;
    72814        margin-left:0in;
     815        mso-add-space:auto;
     816        mso-pagination:widow-orphan;
    73817        border:none;
     818        mso-border-bottom-alt:solid #4F81BD 1.0pt;
     819        mso-border-bottom-themecolor:accent1;
    74820        padding:0in;
     821        mso-padding-alt:0in 0in 4.0pt 0in;
    75822        font-size:26.0pt;
    76823        font-family:"Cambria",serif;
     824        mso-ascii-font-family:Cambria;
     825        mso-ascii-theme-font:major-latin;
     826        mso-fareast-font-family:"Times New Roman";
     827        mso-fareast-theme-font:major-fareast;
     828        mso-hansi-font-family:Cambria;
     829        mso-hansi-theme-font:major-latin;
     830        mso-bidi-font-family:"Times New Roman";
     831        mso-bidi-theme-font:major-bidi;
    77832        color:#17365D;
    78         letter-spacing:.25pt;}
     833        mso-themecolor:text2;
     834        mso-themeshade:191;
     835        letter-spacing:.25pt;
     836        mso-font-kerning:14.0pt;}
    79837p.MsoTitleCxSpFirst, li.MsoTitleCxSpFirst, div.MsoTitleCxSpFirst
    80         {mso-style-link:"Title Char";
     838        {mso-style-noshow:yes;
     839        mso-style-priority:10;
     840        mso-style-unhide:no;
     841        mso-style-qformat:yes;
     842        mso-style-link:"Title Char";
     843        mso-style-next:Normal;
     844        mso-style-type:export-only;
    81845        margin:0in;
     846        mso-add-space:auto;
     847        mso-pagination:widow-orphan;
    82848        border:none;
     849        mso-border-bottom-alt:solid #4F81BD 1.0pt;
     850        mso-border-bottom-themecolor:accent1;
    83851        padding:0in;
     852        mso-padding-alt:0in 0in 4.0pt 0in;
    84853        font-size:26.0pt;
    85854        font-family:"Cambria",serif;
     855        mso-ascii-font-family:Cambria;
     856        mso-ascii-theme-font:major-latin;
     857        mso-fareast-font-family:"Times New Roman";
     858        mso-fareast-theme-font:major-fareast;
     859        mso-hansi-font-family:Cambria;
     860        mso-hansi-theme-font:major-latin;
     861        mso-bidi-font-family:"Times New Roman";
     862        mso-bidi-theme-font:major-bidi;
    86863        color:#17365D;
    87         letter-spacing:.25pt;}
     864        mso-themecolor:text2;
     865        mso-themeshade:191;
     866        letter-spacing:.25pt;
     867        mso-font-kerning:14.0pt;}
    88868p.MsoTitleCxSpMiddle, li.MsoTitleCxSpMiddle, div.MsoTitleCxSpMiddle
    89         {mso-style-link:"Title Char";
     869        {mso-style-noshow:yes;
     870        mso-style-priority:10;
     871        mso-style-unhide:no;
     872        mso-style-qformat:yes;
     873        mso-style-link:"Title Char";
     874        mso-style-next:Normal;
     875        mso-style-type:export-only;
    90876        margin:0in;
     877        mso-add-space:auto;
     878        mso-pagination:widow-orphan;
    91879        border:none;
     880        mso-border-bottom-alt:solid #4F81BD 1.0pt;
     881        mso-border-bottom-themecolor:accent1;
    92882        padding:0in;
     883        mso-padding-alt:0in 0in 4.0pt 0in;
    93884        font-size:26.0pt;
    94885        font-family:"Cambria",serif;
     886        mso-ascii-font-family:Cambria;
     887        mso-ascii-theme-font:major-latin;
     888        mso-fareast-font-family:"Times New Roman";
     889        mso-fareast-theme-font:major-fareast;
     890        mso-hansi-font-family:Cambria;
     891        mso-hansi-theme-font:major-latin;
     892        mso-bidi-font-family:"Times New Roman";
     893        mso-bidi-theme-font:major-bidi;
    95894        color:#17365D;
    96         letter-spacing:.25pt;}
     895        mso-themecolor:text2;
     896        mso-themeshade:191;
     897        letter-spacing:.25pt;
     898        mso-font-kerning:14.0pt;}
    97899p.MsoTitleCxSpLast, li.MsoTitleCxSpLast, div.MsoTitleCxSpLast
    98         {mso-style-link:"Title Char";
     900        {mso-style-noshow:yes;
     901        mso-style-priority:10;
     902        mso-style-unhide:no;
     903        mso-style-qformat:yes;
     904        mso-style-link:"Title Char";
     905        mso-style-next:Normal;
     906        mso-style-type:export-only;
    99907        margin-top:0in;
    100908        margin-right:0in;
    101909        margin-bottom:15.0pt;
    102910        margin-left:0in;
     911        mso-add-space:auto;
     912        mso-pagination:widow-orphan;
    103913        border:none;
     914        mso-border-bottom-alt:solid #4F81BD 1.0pt;
     915        mso-border-bottom-themecolor:accent1;
    104916        padding:0in;
     917        mso-padding-alt:0in 0in 4.0pt 0in;
    105918        font-size:26.0pt;
    106919        font-family:"Cambria",serif;
     920        mso-ascii-font-family:Cambria;
     921        mso-ascii-theme-font:major-latin;
     922        mso-fareast-font-family:"Times New Roman";
     923        mso-fareast-theme-font:major-fareast;
     924        mso-hansi-font-family:Cambria;
     925        mso-hansi-theme-font:major-latin;
     926        mso-bidi-font-family:"Times New Roman";
     927        mso-bidi-theme-font:major-bidi;
    107928        color:#17365D;
    108         letter-spacing:.25pt;}
     929        mso-themecolor:text2;
     930        mso-themeshade:191;
     931        letter-spacing:.25pt;
     932        mso-font-kerning:14.0pt;}
    109933a:link, span.MsoHyperlink
    110         {color:blue;
    111         text-decoration:underline;}
     934        {mso-style-noshow:yes;
     935        mso-style-priority:99;
     936        color:blue;
     937        text-decoration:underline;
     938        text-underline:single;}
    112939a:visited, span.MsoHyperlinkFollowed
    113         {color:purple;
    114         text-decoration:underline;}
     940        {mso-style-noshow:yes;
     941        mso-style-priority:99;
     942        color:purple;
     943        text-decoration:underline;
     944        text-underline:single;}
    115945p.MsoDocumentMap, li.MsoDocumentMap, div.MsoDocumentMap
    116         {mso-style-link:"Document Map Char";
     946        {mso-style-noshow:yes;
     947        mso-style-priority:99;
     948        mso-style-link:"Document Map Char";
    117949        margin-top:0in;
    118950        margin-right:0in;
    119951        margin-bottom:4.0pt;
    120952        margin-left:0in;
     953        mso-pagination:widow-orphan;
    121954        font-size:8.0pt;
    122         font-family:"Tahoma",sans-serif;}
     955        font-family:"Tahoma",sans-serif;
     956        mso-fareast-font-family:"Times New Roman";
     957        mso-fareast-theme-font:minor-fareast;}
    123958p
    124         {margin-right:0in;
     959        {mso-style-noshow:yes;
     960        mso-style-priority:99;
     961        mso-margin-top-alt:auto;
     962        margin-right:0in;
     963        mso-margin-bottom-alt:auto;
    125964        margin-left:0in;
     965        mso-pagination:widow-orphan;
    126966        font-size:12.0pt;
    127         font-family:"Times New Roman",serif;}
     967        font-family:"Times New Roman",serif;
     968        mso-fareast-font-family:"Times New Roman";
     969        mso-fareast-theme-font:minor-fareast;}
    128970pre
    129         {mso-style-link:"HTML Preformatted Char";
     971        {mso-style-noshow:yes;
     972        mso-style-priority:99;
     973        mso-style-link:"HTML Preformatted Char";
    130974        margin-top:0in;
    131975        margin-right:0in;
    132976        margin-bottom:4.0pt;
    133977        margin-left:0in;
     978        mso-pagination:widow-orphan;
     979        tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt;
    134980        font-size:10.0pt;
    135         font-family:"Courier New";}
     981        font-family:"Courier New";
     982        mso-fareast-font-family:"Times New Roman";}
    136983p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
    137         {mso-style-link:"Balloon Text Char";
     984        {mso-style-noshow:yes;
     985        mso-style-priority:99;
     986        mso-style-link:"Balloon Text Char";
    138987        margin-top:0in;
    139988        margin-right:0in;
    140989        margin-bottom:4.0pt;
    141990        margin-left:0in;
     991        mso-pagination:widow-orphan;
    142992        font-size:8.0pt;
    143         font-family:"Tahoma",sans-serif;}
     993        font-family:"Tahoma",sans-serif;
     994        mso-fareast-font-family:"Times New Roman";
     995        mso-fareast-theme-font:minor-fareast;}
    144996span.MsoPlaceholderText
    145         {color:gray;}
     997        {mso-style-noshow:yes;
     998        mso-style-priority:99;
     999        mso-style-unhide:no;
     1000        color:gray;}
    1461001p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing
    147         {margin-top:0in;
     1002        {mso-style-noshow:yes;
     1003        mso-style-priority:1;
     1004        mso-style-unhide:no;
     1005        mso-style-qformat:yes;
     1006        mso-style-parent:"";
     1007        margin-top:0in;
    1481008        margin-right:0in;
    1491009        margin-bottom:4.0pt;
    1501010        margin-left:0in;
     1011        mso-pagination:widow-orphan;
    1511012        font-size:12.0pt;
    152         font-family:"Times New Roman",serif;}
     1013        font-family:"Times New Roman",serif;
     1014        mso-fareast-font-family:"Times New Roman";
     1015        mso-fareast-theme-font:minor-fareast;}
    1531016p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
    154         {margin-top:0in;
     1017        {mso-style-noshow:yes;
     1018        mso-style-priority:34;
     1019        mso-style-unhide:no;
     1020        mso-style-qformat:yes;
     1021        margin-top:0in;
    1551022        margin-right:0in;
    1561023        margin-bottom:4.0pt;
    1571024        margin-left:.5in;
     1025        mso-add-space:auto;
     1026        mso-pagination:widow-orphan;
    1581027        font-size:12.0pt;
    159         font-family:"Times New Roman",serif;}
     1028        font-family:"Times New Roman",serif;
     1029        mso-fareast-font-family:"Times New Roman";
     1030        mso-fareast-theme-font:minor-fareast;}
    1601031p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
    161         {margin-top:0in;
     1032        {mso-style-noshow:yes;
     1033        mso-style-priority:34;
     1034        mso-style-unhide:no;
     1035        mso-style-qformat:yes;
     1036        mso-style-type:export-only;
     1037        margin-top:0in;
    1621038        margin-right:0in;
    1631039        margin-bottom:0in;
    1641040        margin-left:.5in;
     1041        mso-add-space:auto;
     1042        mso-pagination:widow-orphan;
    1651043        font-size:12.0pt;
    166         font-family:"Times New Roman",serif;}
     1044        font-family:"Times New Roman",serif;
     1045        mso-fareast-font-family:"Times New Roman";
     1046        mso-fareast-theme-font:minor-fareast;}
    1671047p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
    168         {margin-top:0in;
     1048        {mso-style-noshow:yes;
     1049        mso-style-priority:34;
     1050        mso-style-unhide:no;
     1051        mso-style-qformat:yes;
     1052        mso-style-type:export-only;
     1053        margin-top:0in;
    1691054        margin-right:0in;
    1701055        margin-bottom:0in;
    1711056        margin-left:.5in;
     1057        mso-add-space:auto;
     1058        mso-pagination:widow-orphan;
    1721059        font-size:12.0pt;
    173         font-family:"Times New Roman",serif;}
     1060        font-family:"Times New Roman",serif;
     1061        mso-fareast-font-family:"Times New Roman";
     1062        mso-fareast-theme-font:minor-fareast;}
    1741063p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
    175         {margin-top:0in;
     1064        {mso-style-noshow:yes;
     1065        mso-style-priority:34;
     1066        mso-style-unhide:no;
     1067        mso-style-qformat:yes;
     1068        mso-style-type:export-only;
     1069        margin-top:0in;
    1761070        margin-right:0in;
    1771071        margin-bottom:4.0pt;
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     1157        mso-themecolor:accent1;
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    2091160span.Heading5Char
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    2151177span.HTMLPreformattedChar
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    2311225span.DocumentMapChar
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     1239        mso-bidi-font-family:Tahoma;}
    2351240span.BalloonTextChar
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     1242        mso-style-noshow:yes;
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     1244        mso-style-unhide:no;
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    2371246        mso-style-link:"Balloon Text";
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     1254        mso-bidi-font-family:Tahoma;}
    2391255p.gsastext, li.gsastext, div.gsastext
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     1257        mso-style-noshow:yes;
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     1264        mso-pagination:widow-orphan;
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    2451266        punctuation-wrap:simple;
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    2471268        font-size:12.0pt;
    248         font-family:"Times New Roman",serif;}
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     1270        font-family:"Times New Roman",serif;
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     1272span.SpellE
     1273        {mso-style-name:"";
     1274        mso-spl-e:yes;}
     1275span.GramE
     1276        {mso-style-name:"";
     1277        mso-gram-e:yes;}
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     1284        font-family:"Calibri",sans-serif;
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    2521293@page WordSection1
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    254         margin:1.0in 1.0in 1.0in 1.0in;}
     1295        margin:1.0in 1.0in 1.0in 1.0in;
     1296        mso-header-margin:.5in;
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     1298        mso-paper-source:0;}
    2551299div.WordSection1
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    2571301 /* List Definitions */
    258  ol
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     1330@list l0:level6
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     1396ol
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    2601398ul
     
    2621400-->
    2631401</style>
    264 
     1402<!--[if gte mso 10]>
     1403<style>
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     1425 <o:shapedefaults v:ext="edit" spidmax="1027"/>
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     1427 <o:shapelayout v:ext="edit">
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    2651430</head>
    2661431
    267 <body lang=EN-US link=blue vlink=purple style='word-wrap:break-word'>
     1432<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in;word-wrap:
     1433break-word'>
    2681434
    2691435<div class=WordSection1>
    2701436
    2711437<h1 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
    272 0in;line-height:115%'>Texture analysis of 2D data in GSAS-II</h1>
    273 
    274 <p class=MsoNormal style='margin-bottom:0in'><BL><span style='font-family:Symbol'>·</span> 
    275 <b>A video version of this tutorial is available at <a
     14380in;line-height:115%'>Texture analysis of 2D data in GSAS-II<o:p></o:p></h1>
     1439
     1440<p class=MsoNormal style='margin-bottom:0in'><BL><span style='font-family:Symbol;
     1441mso-ascii-font-family:"Times New Roman";mso-fareast-font-family:Calibri;
     1442mso-fareast-theme-font:minor-latin'>·</span><span style='mso-fareast-font-family:
     1443Calibri;mso-fareast-theme-font:minor-latin'><span style='mso-spacerun:yes'> 
     1444</span><b>A video version of this tutorial is available at <a
    2761445href="https://anl.box.com/v/Textureanalysisof2DdatainGSAS-" target="_blank">https://anl.box.com/v/Textureanalysisof2DdatainGSAS-</a></b>
    277 </p>
    278 
    279 <p class=MsoNormal style='margin-bottom:0in'><span style='font-family:Symbol'>·</span> 
    280 Exercise files are found <a href="data/" target="_blank">here</a> </p>
     1446<o:p></o:p></span></p>
     1447
     1448<p class=MsoNormal style='margin-bottom:0in'><span class=GramE><span
     1449style='font-family:Symbol;mso-ascii-font-family:"Times New Roman";mso-fareast-font-family:
     1450Calibri;mso-fareast-theme-font:minor-latin'>·</span><span style='mso-fareast-font-family:
     1451Calibri;mso-fareast-theme-font:minor-latin'><span style='mso-spacerun:yes'> 
     1452</span>Exercise</span></span><span style='mso-fareast-font-family:Calibri;
     1453mso-fareast-theme-font:minor-latin'> files are found <a href="data/"
     1454target="_blank">here</a> <o:p></o:p></span></p>
    2811455
    2821456</BL>
     
    2881462analysis using GSAS-II employs spherical harmonics modeling, as described by
    2891463Bunge, &quot;Texture Analysis in Materials Science&quot; (1982), and
    290 implemented by Von Dreele, J. Appl. Cryst., <b>30</b>, 517-525 (1997) in GSAS.
    291 The even part of the orientation distribution function (ODF) via the general
    292 axis equation</p>
    293 
    294 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
    295 style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=357
    296 height=56
    297 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image001.png"></span></p>
     1464implemented by Von Dreele, J. Appl. <span class=SpellE>Cryst</span>., <b
     1465style='mso-bidi-font-weight:normal'>30</b>, 517-525 (1997) in GSAS. The even
     1466part of the orientation distribution function (ODF) via the general axis
     1467equation</p>
     1468
     1469<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1470   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
     1471  style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><span
     1472    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1473    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1474    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     1475    normal'><span style='font-family:"Cambria Math",serif'><m:r>h</m:r><m:r>,</m:r><m:r>y</m:r></span></i></m:e></m:d><i
     1476  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=1+</m:r></span></i><m:nary><m:naryPr><m:chr
     1477     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     1478    mso-ascii-font-family:"Cambria Math";mso-fareast-font-family:"Times New Roman";
     1479    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1480    normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i style='mso-bidi-font-style:
     1481    normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>=2</m:r></span></i></m:sub><m:sup><m:sSub><m:sSubPr><span
     1482      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1483      mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math";
     1484      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i
     1485      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i
     1486      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub></m:sSub></m:sup><m:e><m:f><m:fPr><span
     1487      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1488      mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math";
     1489      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
     1490      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r>&#960;</m:r></span></i></m:num><m:den><i
     1491      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>L</m:r><m:r>+1</m:r></span></i></m:den></m:f><m:nary><m:naryPr><m:chr
     1492       m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
     1493      "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-fareast-font-family:
     1494      "Times New Roman";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1495      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     1496      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i
     1497      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:nary><m:naryPr><m:chr
     1498         m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
     1499        "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-fareast-font-family:
     1500        "Times New Roman";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1501        mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     1502        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i
     1503        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span
     1504          style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1505          mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math";
     1506          font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     1507          style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
     1508          style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1509          style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary></m:e></m:nary><m:sSubSup><m:sSubSupPr><span
     1510      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1511      mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math";
     1512      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     1513      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1514      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1515      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><i
     1516  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(h)</m:r></span></i><m:sSubSup><m:sSubSupPr><span
     1517    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1518    mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math";
     1519    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     1520    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1521    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1522    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
     1523  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
     1524style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1525"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     1526mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shapetype
     1527 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
     1528 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
     1529 <v:stroke joinstyle="miter"/>
     1530 <v:formulas>
     1531  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
     1532  <v:f eqn="sum @0 1 0"/>
     1533  <v:f eqn="sum 0 0 @1"/>
     1534  <v:f eqn="prod @2 1 2"/>
     1535  <v:f eqn="prod @3 21600 pixelWidth"/>
     1536  <v:f eqn="prod @3 21600 pixelHeight"/>
     1537  <v:f eqn="sum @0 0 1"/>
     1538  <v:f eqn="prod @6 1 2"/>
     1539  <v:f eqn="prod @7 21600 pixelWidth"/>
     1540  <v:f eqn="sum @8 21600 0"/>
     1541  <v:f eqn="prod @7 21600 pixelHeight"/>
     1542  <v:f eqn="sum @10 21600 0"/>
     1543 </v:formulas>
     1544 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
     1545 <o:lock v:ext="edit" aspectratio="t"/>
     1546</v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:267.75pt;
     1547 height:42pt'>
     1548 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image001.png"
     1549  o:title="" chromakey="white"/>
     1550</v:shape><![endif]--><![if !vml]><img width=357 height=56
     1551src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
     1552v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    2981553
    2991554<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    3001555margin-left:0in;line-height:115%'>is used to give the intensity corrections due
    301 to texture. The two harmonic terms, <span
    302 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    303 top:3.0pt'><img width=43 height=35
    304 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image002.png"></span> and
    305 <span
    306 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    307 top:3.0pt'><img width=40 height=35
    308 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image003.png"></span>,
    309 take on values according to the crystal and sample symmetries, respectively,
    310 and thus the two inner summations are over only the resulting unique, nonzero
    311 harmonic terms. These unique terms are automatically selected by GSAS-II
    312 according to the space group symmetry and the user chosen sample symmetry. The
    313 available sample symmetries are cylindrical symmetry, 2/m, mmm and no symmetry.
    314 The choice of sample symmetry profoundly affects the selection of harmonic
    315 coefficients. For example, in the case of cylindrical sample symmetry (fiber
    316 texture) only <span
    317 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    318 top:3.0pt'><img width=39 height=35
    319 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"></span> terms
    320 are nonzero so the rest are excluded from the summations and the set of <span
    321 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    322 top:3.0pt'><img width=28 height=35
    323 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png"></span>coefficients
    324 is sufficient to describe the effect on the diffraction patterns due to
    325 texture. The crystal harmonic factor, <span
    326 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    327 top:3.0pt'><img width=43 height=35
    328 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"></span>,
    329 is defined for each reflection, h, <i>via</i> polar and azimuthal coordinates (<span
     1556to texture. The two harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1557   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1558   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1559   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1560   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1561   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1562   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     1563   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1564   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1565   normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     1566   normal'><span style='font-family:"Cambria Math",serif'><m:r>h</m:r></span></i></m:e></m:d></m:oMath><![endif]--><![if !msEquation]><span
     1567style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1568"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1569top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1570EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1571 type="#_x0000_t75" style='width:32.25pt;height:26.25pt'>
     1572 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
     1573  o:title="" chromakey="white"/>
     1574</v:shape><![endif]--><![if !vml]><img width=43 height=35
     1575src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
     1576v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     1577style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1578   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1579   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1580   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1581   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1582   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1583   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
     1584 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     1585style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1586"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1587top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1588EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1589 type="#_x0000_t75" style='width:30pt;height:26.25pt'>
     1590 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
     1591  o:title="" chromakey="white"/>
     1592</v:shape><![endif]--><![if !vml]><img width=40 height=35
     1593src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
     1594v:shapes="_x0000_i1025"><![endif]></span><![endif]>, take on values according
     1595to the crystal and sample symmetries, respectively, and thus the two inner
     1596summations are over only the resulting unique, nonz<span class=SpellE>ero</span>
     1597harmonic terms. These unique terms are automatically selected by <span
     1598style='mso-bidi-font-weight:bold'>GSAS-II</span> according to the space group
     1599symmetry and the user chosen sample symmetry. The available sample symmetries
     1600are cylindrical symmetry, 2/m, mmm and no symmetry. The choice of sample
     1601symmetry profoundly affects the selection of harmonic coefficients. For
     1602example, in the case of cylindrical sample symmetry (fiber texture) only <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1603   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1604   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1605   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1606   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1607   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1608   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:sup></m:sSubSup><i
     1609 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     1610style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1611"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1612top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1613EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1614 type="#_x0000_t75" style='width:29.25pt;height:26.25pt'>
     1615 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
     1616  o:title="" chromakey="white"/>
     1617</v:shape><![endif]--><![if !vml]><img width=39 height=35
     1618src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
     1619v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     1620style='mso-spacerun:yes'> </span>terms are nonzero so the rest are excluded
     1621from the summations and the set of <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1622   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1623   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1624   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1625   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
     1626   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1627   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>0</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
     1628style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1629"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1630top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1631EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1632 type="#_x0000_t75" style='width:21pt;height:26.25pt'>
     1633 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
     1634  o:title="" chromakey="white"/>
     1635</v:shape><![endif]--><![if !vml]><img width=28 height=35
     1636src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
     1637v:shapes="_x0000_i1025"><![endif]></span><![endif]>coefficients is sufficient
     1638to describe the effect on the diffraction patterns due to texture. The crystal
     1639harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1640   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1641   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1642   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1643   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1644   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1645   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i
     1646 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(h)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     1647style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1648"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1649top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1650EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1651 type="#_x0000_t75" style='width:32.25pt;height:26.25pt'>
     1652 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
     1653  o:title="" chromakey="white"/>
     1654</v:shape><![endif]--><![if !vml]><img width=43 height=35
     1655src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
     1656v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined for each
     1657reflection, h, <i>via</i> polar and azimuthal coordinates (<span
    3301658style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
    3311659of a unit vector coincident with h relative to the reciprocal lattice. For most
    3321660crystal symmetries, <span style='font-family:Symbol'>f</span> is the angle
    333 between h and the n-th order major rotation axis of the space group (usually
    334 the c-axis) and <span style='font-family:Symbol'>b</span> is the angle between
    335 the projections of h and any secondary axis (usually the a-axis) onto the
    336 normal plane.  In a similar way the sample harmonic factor, <span
    337 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    338 top:3.0pt'><img width=40 height=35
    339 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image003.png"></span>,
    340 is defined according to polar and azimuthal coordinates (<span
    341 style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
    342 of a unit vector coincident with the diffraction vector relative to a
    343 coordinate system attached to the external form of the sample. For example, in
    344 the case of a rolled steel plate having mmm symmetry, the polar angle, <span
    345 style='font-family:Symbol'>y</span>, is frequently measured from the normal
    346 direction (ND) and <span style='font-family:Symbol'>g</span> is then measured
    347 from the rolling direction (RD) in the TD (transverse direction) - RD plane. 
    348 Thus, the general axis equation becomes</p>
     1661between h and the n-<span class=SpellE>th</span> order major rotation axis of
     1662the space group (usually the c-axis) and <span style='font-family:Symbol'>b</span>
     1663is the angle between the projections of h and any secondary axis (usually the
     1664a-axis) onto the normal plane.<span style='mso-spacerun:yes'>  </span>In a
     1665similar way the sample harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1666   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1667   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1668   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1669   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1670   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1671   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
     1672 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     1673style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1674"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1675top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1676EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1677 type="#_x0000_t75" style='width:30pt;height:26.25pt'>
     1678 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
     1679  o:title="" chromakey="white"/>
     1680</v:shape><![endif]--><![if !vml]><img width=40 height=35
     1681src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
     1682v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined according to
     1683polar and azimuthal coordinates (<span style='font-family:Symbol'>y</span>, <span
     1684style='font-family:Symbol'>g</span>) of a unit vector coincident with the
     1685diffraction vector relative to a coordinate system attached to the external
     1686form of the sample. For example, in the case of a rolled steel plate having mmm
     1687symmetry, the polar angle, <span style='font-family:Symbol'>y</span>, is
     1688frequently measured from the normal direction (ND) and <span style='font-family:
     1689Symbol'>g</span> is then measured from the rolling direction (RD) in the TD
     1690(transverse direction) - RD plane.<span style='mso-spacerun:yes'>  </span>Thus,
     1691the general axis equation becomes</p>
    3491692
    3501693<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    351 margin-left:0in;line-height:115%'><span
    352 style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=428
    353 height=72
    354 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image007.png"></span><br>
    355 <br>
    356 </p>
     1694margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1695   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
     1696  style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><span
     1697    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1698    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1699    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     1700    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#981;</m:r><m:r>,</m:r><m:r>&#946;</m:r><m:r>,</m:r><m:r>&#968;</m:r><m:r>,</m:r><m:r>&#947;</m:r></span></i></m:e></m:d><i
     1701  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=1+</m:r></span></i><m:nary><m:naryPr><m:chr
     1702     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     1703    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     1704    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     1705    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>=2</m:r></span></i></m:sub><m:sup><m:sSub><m:sSubPr><span
     1706      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1707      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1708      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
     1709      normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i
     1710      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub></m:sSub></m:sup><m:e><m:f><m:fPr><span
     1711      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1712      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1713      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
     1714      normal'><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r>&#960;</m:r></span></i></m:num><m:den><i
     1715      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>L</m:r><m:r>+1</m:r></span></i></m:den></m:f></m:e></m:nary><m:nary><m:naryPr><m:chr
     1716     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     1717    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     1718    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     1719    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i
     1720    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:nary><m:naryPr><m:chr
     1721       m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
     1722      "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
     1723      "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     1724      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i
     1725      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span
     1726        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1727        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1728        normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     1729        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
     1730        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1731        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:sSubSup><m:sSubSupPr><span
     1732      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1733      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1734      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     1735      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1736      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1737      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     1738      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1739      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1740      normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     1741      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r></span></i></m:e></m:d></m:e></m:nary><m:sSubSup><m:sSubSupPr><span
     1742    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1743    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1744    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1745    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1746    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1747    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
     1748  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#968;</m:r><m:r>,</m:r><m:r>&#947;</m:r><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
     1749style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1750"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     1751mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     1752 id="_x0000_i1025" type="#_x0000_t75" style='width:320.95pt;height:54pt'>
     1753 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
     1754  o:title="" chromakey="white"/>
     1755</v:shape><![endif]--><![if !vml]><img width=428 height=72
     1756src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
     1757v:shapes="_x0000_i1025"><![endif]></span><![endif]><br style='mso-special-character:
     1758line-break'>
     1759<![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'>
     1760<![endif]></p>
    3571761
    3581762<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In a
    3591763diffraction experiment the crystal reflection coordinates (<span
    3601764style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
    361 are determined by the choice of reflection index (hkl) while the sample coordinates
    362 (<span style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
    363 are determined by the sample orientation on the diffractometer.</p>
     1765are determined by the choice of reflection index (<span class=SpellE>hkl</span>)
     1766while the sample coordinates (<span style='font-family:Symbol'>y</span>, <span
     1767style='font-family:Symbol'>g</span>) are determined by the sample orientation
     1768on the diffractometer.</p>
    3641769
    3651770<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    3661771margin-left:0in;line-height:115%'>To define the sample coordinates (<span
    3671772style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>),
    368 we have defined an instrument coordinate system (I, J, K) such that K is
    369 parallel to the diffraction vector and J is coincident with the direction of
    370 the incident radiation beam toward the source. We further define a standard set
    371 of right-handed goniometer eulerian angles (<span style='font-family:Symbol'>W</span>,
    372 <span style='font-family:Symbol'>C</span>, <span style='font-family:Symbol'>F</span>)
    373 so that <span style='font-family:Symbol'>W</span> and <span style='font-family:
    374 Symbol'>F</span> are rotations about K and <span style='font-family:Symbol'>C</span>
    375 is a rotation about J when <span style='font-family:Symbol'>W</span> <span
    376 style='font-family:Symbol'> </span>= 0.  Finally, as the sample may be mounted
     1773we have defined an instrument coordinate system (I, J, K) such that K is normal
     1774to the diffraction plane and J is coincident with the direction of the incident
     1775radiation beam toward the source. We further define a standard set of
     1776right-handed <span class=GramE>goniometer</span> <span class=SpellE>eulerian</span>
     1777angles (<span style='font-family:Symbol'>W</span>, <span style='font-family:
     1778Symbol'>C</span>, <span style='font-family:Symbol'>F</span>) so that <span
     1779style='font-family:Symbol'>W</span> and <span style='font-family:Symbol'>F</span>
     1780are rotations about K and <span style='font-family:Symbol'>C</span> is a
     1781rotation about J when <span style='font-family:Symbol'>W</span> <span
     1782style='font-family:Symbol'><span style='mso-spacerun:yes'> </span></span>=
     17830.<span style='mso-spacerun:yes'>  </span>Finally, as the sample may be mounted
    3771784so that the sample coordinate system (I<sub>s</sub>, J<sub>s</sub>, K<sub>s</sub>)
    3781785does not coincide with the instrument coordinate system (I, J, K), we define
    379 three eulerian sample rotation offset angles (<span style='font-family:Symbol'>W</span><sub>s</sub>,
    380 <span style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:
    381 Symbol'>F</span><sub>s</sub>) that describe the rotation from (I<sub>s</sub>, J<sub>s</sub>,
    382 K<sub>s</sub>) to (I, J, K).  The sample rotation angles are defined so that
    383 with the goniometer angles at zero <span style='font-family:Symbol'>W</span><sub>s</sub>
     1786three <span class=SpellE>eulerian</span> sample rotation offset angles (<span
     1787style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
     1788<span style='font-family:Symbol'>F</span><sub>s</sub>) that describe the
     1789rotation from (I<sub>s</sub>, J<sub>s</sub>, K<sub>s</sub>) to (I, J, K).<span
     1790style='mso-spacerun:yes'>  </span>The sample rotation angles are defined so
     1791that with the goniometer angles at zero <span style='font-family:Symbol'>W</span><sub>s</sub>
    3841792and <span style='font-family:Symbol'>F</span><sub>s</sub> are rotations about K
    3851793and <span style='font-family:Symbol'>C</span><sub>s</sub> is a rotation about
    386 J.  The zeros of these three sample rotation angles can be refined as part of
    387 the Rietveld analysis to accommodate any angular offset in sample mounting.
    388 After including the diffraction angle, <span style='font-family:Symbol'>Q</span>,
    389 and a detector azimuthal angle, A, the full rotation matrix, <b>M</b>, is </p>
     1794J.<span style='mso-spacerun:yes'>  </span>The zeros of these three sample
     1795rotation angles can be refined as part of the Rietveld analysis to accommodate
     1796any angular offset in sample mounting. After including the diffraction angle, <span
     1797style='font-family:Symbol'>Q</span>, and a detector azimuthal angle, A, the
     1798full rotation matrix, <b style='mso-bidi-font-weight:normal'>M</b>, is <span
     1799style='mso-spacerun:yes'> </span></p>
    3901800
    3911801<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    392 margin-left:0in;line-height:115%'><b>M = -</b><b><span style='font-family:Symbol'>Q</span>A</b><b><span
    393 style='font-family:Symbol'>WC</span>(</b><b><span style='font-family:Symbol'>F</span>+</b><b><span
    394 style='font-family:Symbol'>F</span><sub>s</sub>)</b><b><span style='font-family:
    395 Symbol'>C</span><sub>s</sub></b><b><span style='font-family:Symbol'>W</span><sub>s</sub></b></p>
     1802margin-left:0in;line-height:115%'><b style='mso-bidi-font-weight:normal'>M = -</b><b
     1803style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>Q</span>A</b><b
     1804style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>WC</span>(</b><b
     1805style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span>+</b><b
     1806style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span><sub>s</sub>)</b><b
     1807style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>C</span><span
     1808class=SpellE><sub>s</sub><span style='font-family:Symbol'>W</span><sub>s</sub></span><o:p></o:p></b></p>
    3961809
    3971810<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     
    4021815
    4031816<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    404 margin-left:0in;line-height:115%'><i>cos</i>(<span style='font-family:Symbol'>y</span>)
    405 = <span
    406 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    407 top:15.0pt'><img width=45 height=67
    408 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image008.png"></span> and  
    409 <i>tan</i>(<span style='font-family:Symbol'>g</span>) = <span
    410 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    411 top:15.0pt'><img width=107 height=67
    412 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image009.png"></span></p>
     1817margin-left:0in;line-height:115%'><span class=GramE><i>cos</i>(</span><span
     1818style='font-family:Symbol'>y</span>) = <!--[if gte msEquation 12]><m:oMath><i
     1819 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
     1820   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1821   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1822   normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
     1823         m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
     1824     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1825     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1826     normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
     1827      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
     1828      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
     1829      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:oMath><![endif]--><![if !msEquation]><span
     1830style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1831"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1832top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1833EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1834 type="#_x0000_t75" style='width:33.75pt;height:50.25pt'>
     1835 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
     1836  o:title="" chromakey="white"/>
     1837</v:shape><![endif]--><![if !vml]><img width=45 height=67
     1838src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
     1839v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     1840style='mso-spacerun:yes'> </span>and<span style='mso-spacerun:yes'>   </span><i>tan</i>(<span
     1841style='font-family:Symbol'>g</span>) = <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type
     1842    m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     1843   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1844   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
     1845   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
     1846     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1847     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1848     normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
     1849           m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
     1850       style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1851       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1852       normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
     1853        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
     1854        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr><m:mr><m:e><i
     1855        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:num><m:den><i
     1856   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
     1857     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1858     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1859     normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
     1860           m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
     1861       style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1862       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1863       normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
     1864        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr><m:mr><m:e><i
     1865        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
     1866        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
     1867style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1868"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1869top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1870EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1871 type="#_x0000_t75" style='width:80.25pt;height:50.25pt'>
     1872 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
     1873  o:title="" chromakey="white"/>
     1874</v:shape><![endif]--><![if !vml]><img width=107 height=67
     1875src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
     1876v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    4131877
    4141878<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    415 margin-left:0in;line-height:115%'>The harmonic terms, <span
    416 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    417 top:3.0pt'><img width=62 height=35
    418 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image010.png"></span> and
    419 <span
    420 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    421 top:3.0pt'><img width=57 height=35
    422 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image011.png"></span>,
    423 are developed from</p>
     1879margin-left:0in;line-height:115%'>The harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1880   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1881   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1882   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1883   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1884   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1885   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i
     1886 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     1887style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1888"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1889top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1890EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1891 type="#_x0000_t75" style='width:46.5pt;height:26.25pt'>
     1892 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
     1893  o:title="" chromakey="white"/>
     1894</v:shape><![endif]--><![if !vml]><img width=62 height=35
     1895src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
     1896v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     1897style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1898   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1899   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1900   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1901   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1902   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1903   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
     1904 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#968;</m:r><m:r>,</m:r><m:r>&#947;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     1905style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1906"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1907top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1908EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1909 type="#_x0000_t75" style='width:42.75pt;height:26.25pt'>
     1910 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
     1911  o:title="" chromakey="white"/>
     1912</v:shape><![endif]--><![if !vml]><img width=57 height=35
     1913src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
     1914v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are developed from</p>
    4241915
    4251916<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    426 margin-left:0in;line-height:115%'><span
    427 style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=220
    428 height=56
    429 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image012.png"></span></p>
     1917margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1918   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
     1919    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1920    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1921    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1922    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1923    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1924    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     1925    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1926    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1927    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     1928    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r></span></i></m:e></m:d><i
     1929  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:f><m:fPr><span
     1930    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1931    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1932    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
     1933    normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:num><m:den><m:rad><m:radPr><m:degHide
     1934       m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     1935      "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1936      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
     1937      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>&#960;</m:r></span></i></m:e></m:rad></m:den></m:f><m:sSup><m:sSupPr><span
     1938    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1939    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1940    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     1941    normal'><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:e><m:sup><i
     1942    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>im&#946;</m:r></span></i></m:sup></m:sSup><m:sSubSup><m:sSubSupPr><span
     1943    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1944    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1945    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     1946       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     1947      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     1948      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     1949      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
     1950    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1951    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     1952     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     1953  normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
     1954    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1955    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1956    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     1957    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     1958       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     1959    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
     1960  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
     1961style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1962"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     1963mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     1964 id="_x0000_i1025" type="#_x0000_t75" style='width:165pt;height:42pt'>
     1965 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
     1966  o:title="" chromakey="white"/>
     1967</v:shape><![endif]--><![if !vml]><img width=220 height=56
     1968src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
     1969v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    4301970
    4311971<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    4321972margin-left:0in;line-height:115%'>where the normalized associated Legendre
    433 functions, <span
    434 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    435 top:3.0pt'><img width=44 height=35
    436 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image013.png"></span>,
    437 are defined via a Fourier expansion as</p>
     1973functions, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1974   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1975   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1976   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     1977      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     1978     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1979     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     1980     style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
     1981   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1982   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i
     1983 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     1984style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1985"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1986top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1987EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1988 type="#_x0000_t75" style='width:33pt;height:26.25pt'>
     1989 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
     1990  o:title="" chromakey="white"/>
     1991</v:shape><![endif]--><![if !vml]><img width=44 height=35
     1992src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
     1993v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are defined via a Fourier
     1994expansion as</p>
    4381995
    4391996<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    440 margin-left:0in;line-height:115%'><span
    441 style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=206
    442 height=70
    443 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image014.png"></span></p>
     1997margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1998   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
     1999    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2000    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2001    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2002       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     2003      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2004      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2005      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
     2006    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2007    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2008     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2009    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2010    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2011    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
     2012      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2013      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2014      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2015      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2016         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2017      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
     2018  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:nary><m:naryPr><m:chr
     2019     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     2020    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2021    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     2022    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>s</m:r><m:r>=0</m:r></span></i></m:sub><m:sup><i
     2023    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span
     2024      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2025      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2026      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     2027      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i
     2028      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2029      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2030       </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
     2031    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2032    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2033    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2034    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2035       m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2036    normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>s&#966;</m:r><m:r>)</m:r></span></i></m:e></m:func></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
     2037style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2038"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     2039mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     2040 id="_x0000_i1025" type="#_x0000_t75" style='width:154.5pt;height:52.5pt'>
     2041 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
     2042  o:title="" chromakey="white"/>
     2043</v:shape><![endif]--><![if !vml]><img width=206 height=70
     2044src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
     2045v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    4442046
    4452047<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     
    4472049
    4482050<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    449 margin-left:0in;line-height:115%'><span
    450 style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=211
    451 height=70
    452 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image015.png"></span></p>
     2051margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2052   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
     2053    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2054    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2055    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2056       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     2057      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2058      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2059      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
     2060    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2061    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2062     </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2063    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2064    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2065    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
     2066      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2067      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2068      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2069      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2070         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2071      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
     2072  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:nary><m:naryPr><m:chr
     2073     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     2074    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2075    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     2076    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>s</m:r><m:r>=1</m:r></span></i></m:sub><m:sup><i
     2077    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span
     2078      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2079      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2080      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     2081      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i
     2082      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2083      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2084       </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
     2085    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2086    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2087    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2088    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2089       m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2090    normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>s&#966;</m:r><m:r>)</m:r></span></i></m:e></m:func></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
     2091style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2092"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     2093mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     2094 id="_x0000_i1025" type="#_x0000_t75" style='width:158.25pt;height:52.5pt'>
     2095 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
     2096  o:title="" chromakey="white"/>
     2097</v:shape><![endif]--><![if !vml]><img width=211 height=70
     2098src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
     2099v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    4532100
    4542101<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    455 margin-left:0in;line-height:115%'>for m odd.  Each sum is only over either the
    456 even or odd values of s, respectively, because of the properties of the Fourier
    457 coefficients, <span
    458 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    459 top:3.0pt'><img width=33 height=35
    460 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.png"></span>. 
    461 These Fourier coefficients are determined so that the definition</p>
     2102margin-left:0in;line-height:115%'>for m odd.<span style='mso-spacerun:yes'> 
     2103</span>Each sum is only over either the even or odd values of s, respectively,
     2104because of the properties of the Fourier coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2105   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2106   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2107   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2108   normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i
     2109   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2110   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2111    </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
     2112style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2113"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2114top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2115EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2116 type="#_x0000_t75" style='width:24.75pt;height:26.25pt'>
     2117 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
     2118  o:title="" chromakey="white"/>
     2119</v:shape><![endif]--><![if !vml]><img width=33 height=35
     2120src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
     2121v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
     2122style='mso-spacerun:yes'>  </span>These Fourier coefficients are determined so
     2123that the definition</p>
    4622124
    4632125<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    464 margin-left:0in;line-height:115%'><span
    465 style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=565
    466 height=74
    467 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image017.png"></span></p>
     2126margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2127   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
     2128    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2129    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2130    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2131       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     2132      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2133      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2134      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
     2135    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2136    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2137     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2138    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2139    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2140    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
     2141      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2142      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2143      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2144      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2145         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2146      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
     2147  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:sSubSup><m:sSubSupPr><span
     2148    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2149    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2150    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2151       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     2152      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2153      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2154      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
     2155    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2156    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2157     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2158    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2159    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2160    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     2161    normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e></m:d><i
     2162  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:rad><m:radPr><m:degHide
     2163     m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     2164    "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     2165    mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
     2166      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2167      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2168      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
     2169        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2170        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2171        normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     2172        normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>+</m:r><m:r>m</m:r></span></i></m:e></m:d><i
     2173      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>!</m:r></span></i></m:num><m:den><m:d><m:dPr><span
     2174        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2175        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2176        normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     2177        normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:e></m:d><i
     2178      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>!</m:r></span></i></m:den></m:f></m:e></m:rad><m:rad><m:radPr><m:degHide
     2179     m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     2180    "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     2181    mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
     2182      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2183      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2184      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
     2185      normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>L</m:r><m:r>+1</m:r></span></i></m:num><m:den><i
     2186      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:den></m:f></m:e></m:rad><m:f><m:fPr><span
     2187    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2188    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2189    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
     2190      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2191      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2192      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2193      normal'><span style='font-family:"Cambria Math",serif'><m:r>(-1)</m:r></span></i></m:e><m:sup><i
     2194      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span
     2195      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2196      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2197      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2198      normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:e><m:sup><i
     2199      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup></m:sSup><i
     2200    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>!</m:r></span></i></m:den></m:f><m:sSup><m:sSupPr><span
     2201    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2202    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2203    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2204    normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><span
     2205      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2206      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2207      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2208      normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i
     2209      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i
     2210    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:e><m:sup><m:f><m:fPr><m:type
     2211       m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     2212      "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     2213      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
     2214      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>m</m:r></span></i></m:num><m:den><i
     2215      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:den></m:f></m:sup></m:sSup><m:f><m:fPr><span
     2216    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2217    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2218    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
     2219      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2220      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2221      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2222      normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
     2223      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span
     2224      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2225      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2226      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2227      normal'><span style='font-family:"Cambria Math",serif'><m:r>dx</m:r></span></i></m:e><m:sup><i
     2228      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:sup></m:sSup></m:den></m:f><m:sSup><m:sSupPr><span
     2229    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2230    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2231    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2232    normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><span
     2233      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2234      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2235      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2236      normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i
     2237      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i
     2238    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:e><m:sup><i
     2239    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup></m:sSup></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
     2240style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2241"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     2242mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     2243 id="_x0000_i1025" type="#_x0000_t75" style='width:423.75pt;height:55.5pt'>
     2244 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
     2245  o:title="" chromakey="white"/>
     2246</v:shape><![endif]--><![if !vml]><img width=565 height=74
     2247src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
     2248v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    4682249
    4692250<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    470 margin-left:0in;line-height:115%'>is satisfied.  Terms of the form <span
    471 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    472 top:3.0pt'><img width=148 height=35
    473 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.png"></span> and
    474 <span
    475 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    476 top:3.0pt'><img width=134 height=35
    477 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png"></span> are
    478 combined depending on the symmetry and the value of m along with appropriate
    479 normalization coefficients to give the harmonic terms <span
    480 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    481 top:3.0pt'><img width=64 height=35
    482 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"></span> and
    483 <span
    484 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    485 top:3.0pt'><img width=60 height=35
    486 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png"></span>. 
    487 For cubic crystal symmetry, the term <span
    488 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    489 top:3.0pt'><img width=64 height=35
    490 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"></span> is
    491 obtained directly from the Fourier expansion</p>
     2251margin-left:0in;line-height:115%'>is satisfied.<span style='mso-spacerun:yes'> 
     2252</span>Terms of the form <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
     2253   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2254   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2255   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2256   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2257      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2258   normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>m&#946;</m:r><m:r>)</m:r></span></i></m:e></m:func><m:sSubSup><m:sSubSupPr><span
     2259   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2260   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2261   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2262      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     2263     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     2264     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2265     style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
     2266   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2267   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2268    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2269 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
     2270   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2271   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2272   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2273   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2274      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2275   normal'><span style='font-family:"Cambria Math",serif'><m:r>m&#946;</m:r></span></i></m:e></m:func><i
     2276 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     2277style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2278"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2279top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2280EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2281 type="#_x0000_t75" style='width:111pt;height:26.25pt'>
     2282 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
     2283  o:title="" chromakey="white"/>
     2284</v:shape><![endif]--><![if !vml]><img width=148 height=35
     2285src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
     2286v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     2287style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
     2288   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2289   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2290   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2291   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2292      m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2293   normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>m&#946;</m:r><m:r>)</m:r></span></i></m:e></m:func><m:sSubSup><m:sSubSupPr><span
     2294   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2295   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2296   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2297      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     2298     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     2299     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2300     style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
     2301   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2302   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2303    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2304 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
     2305   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2306   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2307   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2308   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2309      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2310   normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
     2311 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     2312style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2313"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2314top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2315EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2316 type="#_x0000_t75" style='width:100.5pt;height:26.25pt'>
     2317 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
     2318  o:title="" chromakey="white"/>
     2319</v:shape><![endif]--><![if !vml]><img width=134 height=35
     2320src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
     2321v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     2322style='mso-spacerun:yes'> </span>are combined depending on the symmetry and the
     2323value of m along with appropriate no<span class=SpellE>rmalization</span>
     2324coefficients to give the harmonic terms <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2325   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2326   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2327   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2328   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     2329   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2330   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2331    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2332 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     2333style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2334"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2335top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2336EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2337 type="#_x0000_t75" style='width:48pt;height:26.25pt'>
     2338 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
     2339  o:title="" chromakey="white"/>
     2340</v:shape><![endif]--><![if !vml]><img width=64 height=35
     2341src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
     2342v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     2343style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2344   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2345   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2346   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2347   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     2348   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2349   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2350    </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2351 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#968;</m:r><m:r>,</m:r><m:r>&#947;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     2352style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2353"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2354top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2355EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2356 type="#_x0000_t75" style='width:45pt;height:26.25pt'>
     2357 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
     2358  o:title="" chromakey="white"/>
     2359</v:shape><![endif]--><![if !vml]><img width=60 height=35
     2360src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
     2361v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
     2362style='mso-spacerun:yes'>  </span>For cubic crystal symmetry, the term <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2363   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2364   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2365   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2366   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     2367   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2368   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2369    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2370 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
     2371style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2372"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2373top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2374EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2375 type="#_x0000_t75" style='width:48pt;height:26.25pt'>
     2376 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
     2377  o:title="" chromakey="white"/>
     2378</v:shape><![endif]--><![if !vml]><img width=64 height=35
     2379src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
     2380v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     2381style='mso-spacerun:yes'> </span>is obtained directly from the Fourier
     2382expansion</p>
    4922383
    4932384<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    494 margin-left:0in;line-height:115%'><span
    495 style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=258
    496 height=70
    497 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.png"></span></p>
     2385margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2386   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
     2387    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2388    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2389    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2390    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     2391    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2392    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2393    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2394    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2395    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     2396    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r></span></i></m:e></m:d><i
     2397  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:nary><m:naryPr><m:chr
     2398     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     2399    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2400    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     2401    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>=0</m:r></span></i></m:sub><m:sup><i
     2402    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span
     2403      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2404      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2405      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     2406      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>B</m:r></span></i></m:e><m:sub><i
     2407      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2408      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>nm</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:sSubSup><m:sSubSupPr><span
     2409    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2410    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2411    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2412       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     2413      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2414      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2415      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
     2416    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2417    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2418     </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2419  normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
     2420    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2421    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2422    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2423    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2424       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2425    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
     2426  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i><m:func><m:funcPr><span
     2427    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2428    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2429    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2430    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2431       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2432    normal'><span style='font-family:"Cambria Math",serif'><m:r>n&#946;</m:r></span></i></m:e></m:func></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
     2433style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2434"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     2435mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     2436 id="_x0000_i1025" type="#_x0000_t75" style='width:193.5pt;height:52.5pt'>
     2437 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
     2438  o:title="" chromakey="white"/>
     2439</v:shape><![endif]--><![if !vml]><img width=258 height=70
     2440src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image105.png"
     2441v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    4982442
    4992443<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    500 margin-left:0in;line-height:115%'>using the coefficients, <span
    501 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    502 top:3.0pt'><img width=30 height=35
    503 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.png"></span>,
    504 as tabulated by Bunge (1982). </p>
     2444margin-left:0in;line-height:115%'>using the coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2445   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2446   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2447   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2448   normal'><span style='font-family:"Cambria Math",serif'><m:r>B</m:r></span></i></m:e><m:sub><i
     2449   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2450   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>nm</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
     2451style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2452"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2453top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2454EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2455 type="#_x0000_t75" style='width:22.5pt;height:26.25pt'>
     2456 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"
     2457  o:title="" chromakey="white"/>
     2458</v:shape><![endif]--><![if !vml]><img width=30 height=35
     2459src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image108.png"
     2460v:shapes="_x0000_i1025"><![endif]></span><![endif]>, as tabulated by Bunge
     2461(1982). </p>
    5052462
    5062463<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    507 margin-left:0in;line-height:115%'>The Rietveld refinement of texture then proceeds
    508 by constructing derivatives of the profile intensities with respect to the
    509 allowed harmonic coefficients, <span
    510 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    511 top:3.0pt'><img width=29 height=35
    512 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"></span>,
    513 and the three sample orientation angles, <span style='font-family:Symbol'>W</span><sub>s</sub>,
    514 <span style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:
    515 Symbol'>F</span><sub>s</sub>, all of which can be adjustable parameters of the
    516 refinement. Once the refinement is complete, pole figures for any reflection
    517 may be constructed by use of the general axis equation, the refined values for <span
    518 style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
    519 top:3.0pt'><img width=29 height=35
    520 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"></span> and
    521 the sample orientation angles <span style='font-family:Symbol'>W</span><sub>s</sub>,
    522 <span style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:
    523 Symbol'>F</span><sub>s</sub>. </p>
     2464margin-left:0in;line-height:115%'>The Rietveld refinement of texture then
     2465proceeds by constructing derivatives of the profile intensities with respect to
     2466the allowed harmonic coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2467   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2468   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2469   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2470   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
     2471   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2472   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
     2473style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2474"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2475top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2476EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2477 type="#_x0000_t75" style='width:21.75pt;height:26.25pt'>
     2478 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image110.png"
     2479  o:title="" chromakey="white"/>
     2480</v:shape><![endif]--><![if !vml]><img width=29 height=35
     2481src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image112.png"
     2482v:shapes="_x0000_i1025"><![endif]></span><![endif]>, and the three sample
     2483orientation angles, <span style='font-family:Symbol'>W</span><sub>s</sub>, <span
     2484style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:Symbol'>F</span><sub>s</sub>,
     2485all of which can be adjustable parameters of the refinement. Once the
     2486refinement is complete, pole figures for any reflection may be constructed by
     2487use of the general axis equation, the refined values for <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2488   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2489   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2490   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2491   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
     2492   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2493   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
     2494style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2495"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2496top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2497EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2498 type="#_x0000_t75" style='width:21.75pt;height:26.25pt'>
     2499 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image110.png"
     2500  o:title="" chromakey="white"/>
     2501</v:shape><![endif]--><![if !vml]><img width=29 height=35
     2502src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image112.png"
     2503v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     2504style='mso-spacerun:yes'> </span>and the sample orientation angles <span
     2505style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
     2506<span style='font-family:Symbol'>F</span><sub>s</sub>. </p>
    5242507
    5252508<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     
    5282511
    5292512<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    530 margin-left:0in;line-height:115%'><span
    531 style='font-size:12.0pt;font-family:"Times New Roman",serif'><img width=241
    532 height=72
    533 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image025.png"></span></p>
     2513margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2514   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
     2515  style='font-family:"Cambria Math",serif'><m:r>J</m:r><m:r>=1+</m:r></span></i><m:nary><m:naryPr><m:chr
     2516     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     2517    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2518    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     2519    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>=2</m:r></span></i></m:sub><m:sup><m:sSub><m:sSubPr><span
     2520      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2521      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2522      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
     2523      normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i
     2524      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub></m:sSub></m:sup><m:e><m:f><m:fPr><span
     2525      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2526      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2527      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
     2528      normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:num><m:den><i
     2529      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>L</m:r><m:r>+1</m:r></span></i></m:den></m:f></m:e></m:nary><m:nary><m:naryPr><m:chr
     2530     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     2531    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2532    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     2533    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i
     2534    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:nary><m:naryPr><m:chr
     2535       m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
     2536      "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
     2537      "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     2538      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i
     2539      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSup><m:sSupPr><span
     2540        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2541        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2542        normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><m:begChr
     2543           m:val="|"/><m:endChr m:val="|"/><span style='font-family:"Cambria Math",serif;
     2544          mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2545          font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:sSubSup><m:sSubSupPr><span
     2546            style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2547            mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2548            normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     2549            style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
     2550            style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     2551            style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:e></m:d></m:e><m:sup><i
     2552        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:e></m:nary></m:e></m:nary></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
     2553style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2554"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     2555mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     2556 id="_x0000_i1025" type="#_x0000_t75" style='width:180.75pt;height:54pt'>
     2557 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image114.png"
     2558  o:title="" chromakey="white"/>
     2559</v:shape><![endif]--><![if !vml]><img width=241 height=72
     2560src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image116.png"
     2561v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    5342562
    5352563<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     
    5442572sample; this can have any of the possible sample symmetries and is the usual
    5452573result desired for texture analysis. The other is the suite of spherical
    546 harmonics terms for cylindrical sample symmetry with the cylinder axis parallel
    547 to K for each phase in each powder pattern (“histogram”) and is usually used to
    548 accommodate preferred orientation effects in a Rietveld refinement. The former
    549 description allows refinement of the sample orientation zeros, <span
    550 style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
    551 <span style='font-family:Symbol'>F</span><sub>s</sub>, but the latter
    552 description does not (they are assumed to be zero and not refinable). The
    553 sample orientation angles, (<span style='font-family:Symbol'>W</span>, <span
    554 style='font-family:Symbol'>C</span>, <span style='font-family:Symbol'>F) </span>are
    555 specified in the Sample Parameters table in the GSAS-II data tree structure and
    556 are applied for either description.</p>
     2574harmonics terms for cylindrical sample symmetry for each phase in each powder
     2575pattern (“histogram”) and is usually used to accommodate preferred orientation
     2576effects in a Rietveld refinement. The former description allows refinement of
     2577the sample orientation zeros, <span style='font-family:Symbol'>W</span><sub>s</sub>,
     2578<span style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:
     2579Symbol'>F</span><sub>s</sub>, but the latter description does not (they are
     2580assumed to be zero and not refinable). The sample orientation angles, (<span
     2581style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>,
     2582<span style='font-family:Symbol'>F) </span>are specified in the Sample
     2583Parameters table in the GSAS-II data tree structure and are applied for either
     2584description.</p>
    5572585
    5582586<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    5592587margin-left:0in;line-height:115%'>In this tutorial we will use both of these
    560 descriptions to determine the texture of the two phases in a NiTi shape memory
    561 alloy sample with cylindrical symmetry (wire texture) as collected at APS on
    562 beam line 1ID-C (data kindly provided by Paul Paradise &amp; Aaron Stebner of
    563 Colo. School of Mines). Thus, there are three ways within GSAS-II that can be
    564 used for this texture analysis all beginning with the same 2D area detector
    565 image. Each will be described in turn after the initial setup of the GSAS-II
    566 project, image input &amp; integration.</p>
     2588descriptions to determine the texture of the two phases in a <span
     2589class=SpellE>NiTi</span> shape memory alloy sample with cylindrical symmetry
     2590(wire texture) as collected at APS on beam line 1ID-C (data kindly provided by
     2591Paul Paradise &amp; Aaron <span class=SpellE>Stebner</span> of Colo. School of
     2592Mines). Thus, there are three ways within GSAS-II that can be used for this
     2593texture analysis all beginning with the same 2D area detector image. Each will
     2594be described in turn after the initial setup of the GSAS-II project, image
     2595input &amp; integration.</p>
    5672596
    5682597<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     
    5712600<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you have
    5722601not done so already, <u><span style='color:#0070C0'><a
    573 href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none'>start
    574 GSAS-II</span></a></span></u>. Note that menu entries are listed in <b><span
    575 style='font-family:"Calibri",sans-serif'>bold face</span></b> below as <b><span
    576 style='font-family:"Calibri",sans-serif'>Help/About GSAS-II</span></b>, which
    577 lists first the name of the menu (here <b><span style='font-family:"Calibri",sans-serif'>Help</span></b>)
    578 and second the name of the entry in the menu (here <b><span style='font-family:
    579 "Calibri",sans-serif'>About GSAS-II</span></b>). </p>
    580 
    581 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Use the <b><span
    582 style='font-family:"Calibri",sans-serif'>Import/Image/from GE image file</span></b>
    583 menu item to read the data file into the current GSAS-II project. A file
    584 selection dialog will be shown; its appearance will depend on your OS. Change
    585 the search directory to <b><span style='font-family:"Calibri",sans-serif'>2DTexture/data
    586 </span></b>and then select the file <b><span style='font-family:"Calibri",sans-serif'>NDC5_01588_1.ge2</span></b>.
    587 An image will appear</p>
    588 
    589 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    590 width=624 height=535 id="Picture 58"
    591 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image026.png"></p>
    592 
    593 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and the <b><span
    594 style='font-family:"Calibri",sans-serif'>Image Controls</span></b> data page
    595 will show</p>
    596 
    597 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    598 width=624 height=389 id="Picture 59"
    599 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image027.png"></p>
     2602href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none;
     2603text-underline:none'>start GSAS-II</span></a></span></u>. Note that menu
     2604entries are listed in <b style='mso-bidi-font-weight:normal'><span
     2605style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2606mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>bold face</span></b>
     2607below as <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2608mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     2609minor-latin'>Help/About GSAS-II</span></b>, which lists first the name of the
     2610menu (here <b style='mso-bidi-font-weight:normal'><span style='font-family:
     2611"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     2612minor-latin;mso-bidi-theme-font:minor-latin'>Help</span></b>) and second the
     2613name of the entry in the menu (here <b style='mso-bidi-font-weight:normal'><span
     2614style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2615mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>About GSAS-II</span></b>).
     2616</p>
     2617
     2618<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Use the <b
     2619style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2620mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Import/Image/from
     2621GE image file</span></b> menu item to read the data file into the current
     2622GSAS-II project. A file selection dialog will be shown; its appearance will
     2623depend on your OS. Change the search directory to <b style='mso-bidi-font-weight:
     2624normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2625minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>2DTexture/data
     2626</span></b>and then select the file <b style='mso-bidi-font-weight:normal'><span
     2627style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2628mso-hansi-theme-font:minor-latin'>NDC5_01588_1.ge2</span></b>. An image will
     2629appear</p>
     2630
     2631<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2632style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_58"
     2633 o:spid="_x0000_i1081" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     2634 visibility:visible;mso-wrap-style:square'>
     2635 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image118.png"
     2636  o:title=""/>
     2637</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     2638src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image118.png"
     2639v:shapes="Picture_x0020_58"><![endif]></span></p>
     2640
     2641<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and the <b
     2642style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2643mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
     2644Controls</span></b> data page will show</p>
     2645
     2646<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2647style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_59"
     2648 o:spid="_x0000_i1080" type="#_x0000_t75" style='width:468pt;height:291.75pt;
     2649 visibility:visible;mso-wrap-style:square'>
     2650 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image120.png"
     2651  o:title=""/>
     2652</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=389
     2653src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image122.png"
     2654v:shapes="Picture_x0020_59"><![endif]></span></p>
    6002655
    6012656<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detector
    602 was previously calibrated and the coefficients are stored in a file found by
    603 doing <b><span style='font-family:"Calibri",sans-serif'>Parms/Load Controls</span></b>
    604 from the <b><span style='font-family:"Calibri",sans-serif'>Image Controls</span></b>
    605 menu. A file selection popup will appear showing <b><span style='font-family:
    606 "Calibri",sans-serif'>NDC5.imctrl</span></b>; select it and press <b><span
    607 style='font-family:"Calibri",sans-serif'>Open</span></b>. The <b><span
    608 style='font-family:"Calibri",sans-serif'>Image Controls</span></b> window will
    609 be repainted with the new values and the image will be redrawn.</p>
    610 
    611 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    612 width=624 height=389 id="Picture 60"
    613 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image028.png"></p>
     2657was previously <span class=GramE>calibrated</span> and the coefficients are
     2658stored in a file found by doing <span class=SpellE><b style='mso-bidi-font-weight:
     2659normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2660minor-latin;mso-hansi-theme-font:minor-latin'>Parms</span></b></span><b
     2661style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2662mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>/Load
     2663Controls</span></b> from the <b style='mso-bidi-font-weight:normal'><span
     2664style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2665mso-hansi-theme-font:minor-latin'>Image Controls</span></b> menu. A file
     2666selection popup will appear showing <b style='mso-bidi-font-weight:normal'><span
     2667style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2668mso-hansi-theme-font:minor-latin'>NDC5.imctrl</span></b>; select it and press <b
     2669style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2670mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Open</span></b>.
     2671The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2672mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
     2673Controls</span></b> window will be repainted with the new values and the image
     2674will be redrawn.</p>
     2675
     2676<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2677style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_60"
     2678 o:spid="_x0000_i1079" type="#_x0000_t75" style='width:468pt;height:291.75pt;
     2679 visibility:visible;mso-wrap-style:square'>
     2680 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image124.png"
     2681  o:title=""/>
     2682</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=389
     2683src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image126.png"
     2684v:shapes="Picture_x0020_60"><![endif]></span></p>
    6142685
    6152686<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detail in
    616 the image can be enhanced by lowering the <b><span style='font-family:"Calibri",sans-serif'>Max
    617 intensity</span></b> (<b><span style='font-family:"Calibri",sans-serif'>15000</span></b>
     2687the image can be enhanced by lowering the <b style='mso-bidi-font-weight:normal'><span
     2688style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2689mso-hansi-theme-font:minor-latin'>Max intensity</span></b> (<b
     2690style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2691mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>15000</span></b>
    6182692is suitable) and shows that the diffraction rings show the effect of texture
    6192693and that the image has a fairly high background. Placing the cursor in the
    6202694corners or inside the inner ring shows a background &gt;1700. This can be
    621 suppressed by adjusting the <b><span style='font-family:"Calibri",sans-serif'>Flat
    622 Bkg</span></b> (I chose <b><span style='font-family:"Calibri",sans-serif'>1700</span></b>
     2695suppressed by adjusting the <b style='mso-bidi-font-weight:normal'><span
     2696style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2697mso-hansi-theme-font:minor-latin'>Flat <span class=SpellE>Bkg</span></span></b>
     2698(I chose <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2699mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>1700</span></b>
    6232700for this). The image will now show the rings much more clearly.</p>
    6242701
    625 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    626 width=624 height=522 id="Picture 61"
    627 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image029.png"></p>
     2702<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2703style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_61"
     2704 o:spid="_x0000_i1078" type="#_x0000_t75" style='width:468pt;height:391.5pt;
     2705 visibility:visible;mso-wrap-style:square'>
     2706 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image128.png"
     2707  o:title=""/>
     2708</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=522
     2709src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image130.png"
     2710v:shapes="Picture_x0020_61"><![endif]></span></p>
    6282711
    6292712<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For texture
    6302713analysis we will need to integrate the image into a number of slices sampling
    6312714the changing ring intensity with azimuthal angle. Also note that the image
    632 seems to have <b><span style='font-family:"Calibri",sans-serif'>mm</span></b>
    633 symmetry so that the unique part of this intensity variation covers 0-90° of
    634 azimuth. In addition the ring intensity variation is such that using 10° slices
    635 will capture it reasonably well. However, we want to include both 0° and 90° as
    636 slice centers. Thus there will be 10 slices beginning at -5° and ending at 95°.
    637 Check the <b><span style='font-family:"Calibri",sans-serif'>Show integration
    638 limits?</span></b> box and uncheck the <b><span style='font-family:"Calibri",sans-serif'>Do
    639 full integration? </span></b>box, enter <b><span style='font-family:"Calibri",sans-serif'>10</span></b>
    640 in the <b><span style='font-family:"Calibri",sans-serif'>No. azimuth bins</span></b>,
    641 enter <b><span style='font-family:"Calibri",sans-serif'>-5</span></b> in the <b><span
    642 style='font-family:"Calibri",sans-serif'>Start azimuth</span></b> box (it will
    643 change to 355) and enter <b><span style='font-family:"Calibri",sans-serif'>455</span></b>
    644 in the <b><span style='font-family:"Calibri",sans-serif'>End azimuth</span></b>
     2715seems to have <b style='mso-bidi-font-weight:normal'><span style='font-family:
     2716"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     2717minor-latin'>mm</span></b> symmetry so that the unique part of this intensity
     2718variation covers 0-90° of azimuth. In <span class=GramE>addition</span> the
     2719ring intensity variation is such that using 10° slices will capture it reasonably
     2720well. However, we want to include both 0° and 90° as slice centers. <span
     2721class=GramE>Thus</span> there will be 10 slices beginning at -5° and ending at
     272295°. Check the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     2723"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     2724minor-latin'>Show integration limits?</span></b> box and uncheck the <b
     2725style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2726mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Do full
     2727integration? </span></b>box, enter <b style='mso-bidi-font-weight:normal'><span
     2728style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2729mso-hansi-theme-font:minor-latin'>10</span></b> in the <b style='mso-bidi-font-weight:
     2730normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2731minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth bins</span></b>,
     2732enter <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2733mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-5</span></b>
     2734in the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2735mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Start
     2736azimuth</span></b> box (it will change to 355) and enter <b style='mso-bidi-font-weight:
     2737normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2738minor-latin;mso-hansi-theme-font:minor-latin'>455</span></b> in the <b
     2739style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2740mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>End azimuth</span></b>
    6452741box. In addition, recall that the sample was mounted vertically and thus is
    6462742aligned with the defined laboratory I axis. Thus, the sample coordinate system
    6472743needs to be rotated by 90° to match the sample axis with the K axis; this can
    648 be done by making the <b><span style='font-family:"Calibri",sans-serif'>Sample
    649 goniometer axis Chi</span></b> = <b><span style='font-family:"Calibri",sans-serif'>90</span></b>.
     2744be done by making the <b style='mso-bidi-font-weight:normal'><span
     2745style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2746mso-hansi-theme-font:minor-latin'>Sample goniometer axis Chi</span></b> = <b
     2747style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2748mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>90</span></b>.
    6502749The plot will change with each entry and at the end should look like</p>
    6512750
    652 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    653 width=624 height=522 id="Picture 62"
    654 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image030.png"></p>
    655 
    656 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The <b><span
    657 style='font-family:"Calibri",sans-serif'>Image Controls</span></b> should be</p>
    658 
    659 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    660 width=624 height=389 id="Picture 63"
    661 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image031.png"></p>
     2751<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2752style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_62"
     2753 o:spid="_x0000_i1077" type="#_x0000_t75" style='width:468pt;height:391.5pt;
     2754 visibility:visible;mso-wrap-style:square'>
     2755 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image131.png"
     2756  o:title=""/>
     2757</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=522
     2758src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image132.png"
     2759v:shapes="Picture_x0020_62"><![endif]></span></p>
     2760
     2761<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The <b
     2762style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2763mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
     2764Controls</span></b> should be</p>
     2765
     2766<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2767style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_63"
     2768 o:spid="_x0000_i1076" type="#_x0000_t75" style='width:468pt;height:291.75pt;
     2769 visibility:visible;mso-wrap-style:square'>
     2770 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image133.png"
     2771  o:title=""/>
     2772</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=389
     2773src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image134.png"
     2774v:shapes="Picture_x0020_63"><![endif]></span></p>
    6622775
    6632776<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It turns out
    6642777that the image contains a number of “picked bits” (very high count “zingers”);
    665 these can be mostly eliminated by setting the upper threshold in Masks. Select <b><span
    666 style='font-family:"Calibri",sans-serif'>Masks</span></b> and the following
    667 should appear</p>
    668 
    669 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    670 width=624 height=191 id="Picture 64"
    671 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image032.png"></p>
    672 
    673 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the <b><span
    674 style='font-family:"Calibri",sans-serif'>Upper threshold</span></b> to <b><span
    675 style='font-family:"Calibri",sans-serif'>2500</span></b>; the image will be
    676 redrawn reflecting this mask. By zooming in you may see isolated red pixels;
    677 these are excluded points. Make sure the diffraction rings do not have any
    678 excluded points. For example with the level set to 2200 the plot shows</p>
    679 
    680 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    681 width=624 height=522 id="Picture 65"
    682 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.png"></p>
     2778these can be mostly eliminated by setting the upper threshold in Masks. Select <b
     2779style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2780mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Masks</span></b>
     2781and the following should appear</p>
     2782
     2783<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2784style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_64"
     2785 o:spid="_x0000_i1075" type="#_x0000_t75" style='width:467.25pt;height:143.25pt;
     2786 visibility:visible;mso-wrap-style:square'>
     2787 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image136.png"
     2788  o:title=""/>
     2789</v:shape><![endif]--><![if !vml]><img border=0 width=623 height=191
     2790src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image139.png"
     2791v:shapes="Picture_x0020_64"><![endif]></span></p>
     2792
     2793<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the <b
     2794style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2795mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Upper
     2796threshold</span></b> to <b style='mso-bidi-font-weight:normal'><span
     2797style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2798mso-hansi-theme-font:minor-latin'>2500</span></b>; the image will be redrawn
     2799reflecting this mask. By zooming in you may see isolated red pixels; these are
     2800excluded points. Make sure the diffraction rings do not have any excluded
     2801points. For <span class=GramE>example</span> with the level set to 2200 the
     2802plot shows</p>
     2803
     2804<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2805style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_65"
     2806 o:spid="_x0000_i1074" type="#_x0000_t75" style='width:468pt;height:391.5pt;
     2807 visibility:visible;mso-wrap-style:square'>
     2808 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image141.png"
     2809  o:title=""/>
     2810</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=522
     2811src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image143.png"
     2812v:shapes="Picture_x0020_65"><![endif]></span></p>
    6832813
    6842814<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>for one ring.
    685 This level is too low. Return to the <b><span style='font-family:"Calibri",sans-serif'>Image
    686 Controls</span></b> item in the data tree.</p>
     2815This level is too low. Return to the <b style='mso-bidi-font-weight:normal'><span
     2816style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2817mso-hansi-theme-font:minor-latin'>Image Controls</span></b> item in the data
     2818tree.</p>
    6872819
    6882820<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
    689 ready to integrate the image; do <b><span style='font-family:"Calibri",sans-serif'>Integration/Integrate</span></b>
    690 from the <b><span style='font-family:"Calibri",sans-serif'>Image Controls</span></b>
    691 menu. When done the last powder pattern in the tree will be displayed</p>
    692 
    693 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    694 width=624 height=522 id="Picture 66"
    695 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image034.png"></p>
     2821ready to integrate the image; do <b style='mso-bidi-font-weight:normal'><span
     2822style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2823mso-hansi-theme-font:minor-latin'>Integration/Integrate</span></b> from the <b
     2824style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2825mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
     2826Controls</span></b> menu. When done the last powder pattern in the tree will be
     2827displayed</p>
     2828
     2829<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2830style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_66"
     2831 o:spid="_x0000_i1073" type="#_x0000_t75" style='width:468pt;height:391.5pt;
     2832 visibility:visible;mso-wrap-style:square'>
     2833 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image145.png"
     2834  o:title=""/>
     2835</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=522
     2836src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image147.png"
     2837v:shapes="Picture_x0020_66"><![endif]></span></p>
    6962838
    6972839<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
    698 0in;line-height:115%'>Step 2. Enter NiTi phases</h2>
    699 
    700 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This NiTi
    701 alloy consists of two phases, cubic B2 and monoclinic B19’. Their parameters
    702 are:<br>
    703 B2: <b><span style='font-family:"Calibri",sans-serif'>P m 3 m</span></b>, a=<b><span
    704 style='font-family:"Calibri",sans-serif'>3.0240</span></b>, Ni <b><span
    705 style='font-family:"Calibri",sans-serif'>0,0,0</span></b>, Ti <b><span
    706 style='font-family:"Calibri",sans-serif'>œ,œ,œ</span></b>, U<sub>iso</sub>=<b><span
    707 style='font-family:"Calibri",sans-serif'>0.005 </span></b>for both.<br>
    708 B19’:  <b><span style='font-family:"Calibri",sans-serif'>P 1 1 21/m</span></b>,
    709 a=<b><span style='font-family:"Calibri",sans-serif'>2.8853</span></b>, b=<b><span
    710 style='font-family:"Calibri",sans-serif'>4.6353</span></b>, c=<b><span
    711 style='font-family:"Calibri",sans-serif'>4.1368</span></b>, &#947;=<b><span
    712 style='font-family:"Calibri",sans-serif'>96.821</span></b>, Ti <b><span
    713 style='font-family:"Calibri",sans-serif'>0.5787,0.2841,Œ</span></b>, Ni <b><span
    714 style='font-family:"Calibri",sans-serif'>0.9700,0.8209,Œ</span></b>, U<sub>iso</sub>=<b><span
    715 style='font-family:"Calibri",sans-serif'>0.005</span></b> for both.<br>
    716 Use the <b><span style='font-family:"Calibri",sans-serif'>Data/Add new phase</span></b>
    717 to enter the <b><span style='font-family:"Calibri",sans-serif'>B2</span></b>
    718 and <b><span style='font-family:"Calibri",sans-serif'>B19’</span></b> phases;
    719 then for each enter the information given above on their respective <b><span
    720 style='font-family:"Calibri",sans-serif'>General</span></b> and <b><span
    721 style='font-family:"Calibri",sans-serif'>Atoms</span></b> tabs. Don’t forget
    722 the spaces between the axial fields for the space group symbols. On the <b><span
    723 style='font-family:"Calibri",sans-serif'>Atoms</span></b> tab begin by doing <b><span
    724 style='font-family:"Calibri",sans-serif'>Edit Atoms/Append atom</span></b>
    725 twice then fill in the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
    726 and coordinates boxes. A double click of the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
    727 entry will show a popup of the Periodic Table; select the element as
    728 appropriate. NB: GSAS-II happily takes “1/2” &amp; “1/4” for coordinate values;
    729 these get converted to their decimal equivalent upon entry. Note the use of a
    730 nonstandard space group designation for B19’. When done the B2 Atoms table
    731 should look like</p>
    732 
    733 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    734 width=624 height=176 id="Picture 68"
    735 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image035.png"></p>
     28400in;line-height:115%'>Step 2. Enter <span class=SpellE>NiTi</span> phases</h2>
     2841
     2842<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This <span
     2843class=SpellE>NiTi</span> alloy consists of two phases, cubic B2 and monoclinic
     2844B19’. Their parameters are:<br>
     2845B2: <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2846mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P m 3 m</span></b>,
     2847a=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2848mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>3.0240</span></b>,
     2849Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2850mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0,0,0</span></b>,
     2851<span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span
     2852style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2853mso-hansi-theme-font:minor-latin'>œ,œ,œ</span></b>, <span class=SpellE>U<sub>iso</sub></span>=<b
     2854style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2855mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.005 </span></b>for
     2856both.<br>
     2857B19’:<span style='mso-spacerun:yes'>  </span><b style='mso-bidi-font-weight:
     2858normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2859minor-latin;mso-hansi-theme-font:minor-latin'>P 1 1 21/m</span></b>, a=<b
     2860style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2861mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.8853</span></b>,
     2862b=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2863mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.6353</span></b>,
     2864c=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2865mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.1368</span></b>,
     2866&#947;=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2867mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>96.821</span></b>,
     2868<span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span
     2869style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2870mso-hansi-theme-font:minor-latin'>0.5787,0.2841,Œ</span></b>, Ni <b
     2871style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2872mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.9700,0.8209,Œ</span></b>,
     2873<span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
     2874style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2875mso-hansi-theme-font:minor-latin'>0.005</span></b> for both.<br>
     2876Use the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2877mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Add new
     2878phase</span></b> to enter the <b style='mso-bidi-font-weight:normal'><span
     2879style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2880mso-hansi-theme-font:minor-latin'>B2</span></b> and <b style='mso-bidi-font-weight:
     2881normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2882minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b> phases; then for
     2883each enter the information given above on their respective <b style='mso-bidi-font-weight:
     2884normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2885minor-latin;mso-hansi-theme-font:minor-latin'>General</span></b> and <b
     2886style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2887mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms</span></b>
     2888tabs. Don’t forget the spaces between the axial fields for the space group
     2889symbols. On the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     2890"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     2891minor-latin'>Atoms</span></b> tab begin by doing <b style='mso-bidi-font-weight:
     2892normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2893minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/Append atom</span></b>
     2894twice then fill in the <b style='mso-bidi-font-weight:normal'><span
     2895style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2896mso-hansi-theme-font:minor-latin'>Type</span></b> and coordinates boxes. A
     2897double click of the <b style='mso-bidi-font-weight:normal'><span
     2898style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2899mso-hansi-theme-font:minor-latin'>Type</span></b> entry will show a popup of
     2900the Periodic Table; select the element as appropriate. NB: GSAS-II happily
     2901takes “1/2” &amp; “1/4” for coordinate values; these get converted to their
     2902decimal equivalent upon entry. Note the use of a nonstandard space group
     2903designation for B19’. When done the B2 Atoms table should look like</p>
     2904
     2905<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2906style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_68"
     2907 o:spid="_x0000_i1072" type="#_x0000_t75" style='width:468pt;height:132pt;
     2908 visibility:visible;mso-wrap-style:square'>
     2909 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image149.png"
     2910  o:title=""/>
     2911</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=176
     2912src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image151.png"
     2913v:shapes="Picture_x0020_68"><![endif]></span></p>
    7362914
    7372915<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and the B19’
    7382916Atoms table should be</p>
    7392917
    740 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    741 width=624 height=176 id="Picture 69"
    742 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image036.png"></p>
     2918<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2919style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_69"
     2920 o:spid="_x0000_i1071" type="#_x0000_t75" style='width:468pt;height:132pt;
     2921 visibility:visible;mso-wrap-style:square'>
     2922 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image152.png"
     2923  o:title=""/>
     2924</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=176
     2925src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image154.png"
     2926v:shapes="Picture_x0020_69"><![endif]></span></p>
    7432927
    7442928<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
    745 <b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab for each
    746 phase; there will be a message indicating the lack of data for each. Do <b><span
    747 style='font-family:"Calibri",sans-serif'>Edit Phase/Add powder histograms</span></b>,
    748 do <b><span style='font-family:"Calibri",sans-serif'>Set All</span></b> on the
    749 popup selection window and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>.
    750 The window for B2 will change to</p>
    751 
    752 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    753 width=624 height=434 id="Picture 70"
    754 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image037.png"></p>
     2929<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2930mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
     2931tab for each phase; there will be a message indicating the lack of data for
     2932each. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2933mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
     2934Phase/Add powder histograms</span></b>, do <b style='mso-bidi-font-weight:normal'><span
     2935style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2936mso-hansi-theme-font:minor-latin'>Set All</span></b> on the popup selection
     2937window and press <b style='mso-bidi-font-weight:normal'><span style='font-family:
     2938"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     2939minor-latin'>OK</span></b>. The window for B2 will change to</p>
     2940
     2941<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2942style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_70"
     2943 o:spid="_x0000_i1070" type="#_x0000_t75" style='width:468pt;height:324.75pt;
     2944 visibility:visible;mso-wrap-style:square'>
     2945 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image156.png"
     2946  o:title=""/>
     2947</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=433
     2948src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image158.png"
     2949v:shapes="Picture_x0020_70"><![endif]></span></p>
    7552950
    7562951<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and that for
    7572952B19’ will be</p>
    7582953
    759 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    760 width=624 height=455 id="Picture 71"
    761 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image038.png"></p>
     2954<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2955style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_71"
     2956 o:spid="_x0000_i1069" type="#_x0000_t75" style='width:468pt;height:341.25pt;
     2957 visibility:visible;mso-wrap-style:square'>
     2958 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image159.png"
     2959  o:title=""/>
     2960</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=455
     2961src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image160.png"
     2962v:shapes="Picture_x0020_71"><![endif]></span></p>
    7622963
    7632964<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You should now
    764 save the project file (I used <b><span style='font-family:"Calibri",sans-serif'>NiTi</span></b>
    765 for a name); we will use this as a starting point for three different texture
    766 determinations. Do a <b><span style='font-family:"Calibri",sans-serif'>File/Save
    767 project as
    768 </span></b> and give it a new name (I used <b><span
    769 style='font-family:"Calibri",sans-serif'>NiTi-A</span></b>); this will become
     2965save the project file (I used <span class=SpellE><b style='mso-bidi-font-weight:
     2966normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2967minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span> for a
     2968name); we will use this as a starting point for three different texture
     2969determinations. Do a <b style='mso-bidi-font-weight:normal'><span
     2970style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2971mso-hansi-theme-font:minor-latin'>File/Save project as
     2972</span></b> and give it
     2973a new name (I used <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
     2974style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2975mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight:
     2976normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2977minor-latin;mso-hansi-theme-font:minor-latin'>-A</span></b>); this will become
    7702978the new project name for the next part of this tutorial.</p>
    7712979
     
    7832991histogram has a set of parameters (e.g. phase fraction, size, mustrain &amp;
    7842992hydrostatic strain) in addition to the ones for each histogram (e.g. background
    785 &amp; scale factor). Consequently the total number of parameters can build up
    786 very quickly in this method of analysis. The other two methods seek to reduce
    787 this problem by splitting the fitting into a sequential refinement (histogram
    788 by histogram) step followed by a texture fitting step.</p>
     2993&amp; scale factor). <span class=GramE>Consequently</span> the total number of
     2994parameters can build up very quickly in this method of analysis. The other two
     2995methods seek to reduce this problem by splitting the fitting into a sequential
     2996refinement (histogram by histogram) step followed by a texture fitting step.</p>
    7892997
    7902998<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     
    7933001<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In the initial
    7943002refinement we need to vary the phase fraction for each phase/histogram and the
    795 background in each histogram. To start select any <b><span style='font-family:
    796 "Calibri",sans-serif'>PWDR</span></b> entry from the GSAS-II data tree and
    797 select <b><span style='font-family:"Calibri",sans-serif'>Sample Parameters</span></b>
    798 for it. Note that Goniometer chi is set to 90; that came from the same entry in
    799 the Image Controls during integration. Also, if you chose other than the 1<sup>st</sup>
     3003background in each histogram. To start select any <b style='mso-bidi-font-weight:
     3004normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3005minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b> entry from the
     3006GSAS-II data tree and select <b style='mso-bidi-font-weight:normal'><span
     3007style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3008mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b> for it. Note
     3009that Goniometer chi is set to 90; that came from the same entry in the Image
     3010Controls during integration. Also, if you chose other than the 1<sup>st</sup>
    8003011PWDR data set the Detector azimuth will be some nonzero value; that is also
    801 reflected in the name assigned to the histogram (e.g. <b><span
    802 style='font-family:"Calibri",sans-serif'>PWDR NDC5_01588_1.ge2 Azm= 40.00</span></b>).
    803 Uncheck the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale
    804 factor</span></b> box and then do <b><span style='font-family:"Calibri",sans-serif'>Command/Copy
    805 flags</span></b>; select <b><span style='font-family:"Calibri",sans-serif'>Set
    806 All</span></b> and then press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>.
     3012reflected in the name assigned to the histogram (e.g. <b style='mso-bidi-font-weight:
     3013normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3014minor-latin;mso-hansi-theme-font:minor-latin'>PWDR NDC5_01588_1.ge2 <span
     3015class=SpellE>Azm</span>= 40.00</span></b>). Uncheck the <b style='mso-bidi-font-weight:
     3016normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3017minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>
     3018box and then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3019"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3020minor-latin'>Command/Copy flags</span></b>; select <b style='mso-bidi-font-weight:
     3021normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3022minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b> and then press
     3023<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3024mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
    8073025That will clear the scale factor refinement flag for all histograms; we will be
    8083026varying the phase fractions instead.</p>
     
    8113029the B2 phase and pick the Data tab; you will see</p>
    8123030
    813 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    814 width=624 height=471 id="Picture 72"
    815 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"></p>
    816 
    817 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Select the <b><span
    818 style='font-family:"Calibri",sans-serif'>Phase fraction</span></b> box. Then do
    819 <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy data</span></b>,
    820 select <b><span style='font-family:"Calibri",sans-serif'>Set All</span></b>
    821 &amp; press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b> to
    822 copy these to the other histograms. Next select the <b><span style='font-family:
    823 "Calibri",sans-serif'>B19’</span></b> phase and repeat this process. We are now
    824 ready for the first refinement; do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>
     3031<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3032style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_72"
     3033 o:spid="_x0000_i1068" type="#_x0000_t75" style='width:468pt;height:270pt;
     3034 visibility:visible;mso-wrap-style:square'>
     3035 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image230.png"
     3036  o:title=""/>
     3037</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=360
     3038src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image231.png"
     3039v:shapes="Picture_x0020_72"><![endif]></span></p>
     3040
     3041<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Select the <b
     3042style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3043mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase
     3044fraction</span></b> box. Then do <b style='mso-bidi-font-weight:normal'><span
     3045style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3046mso-hansi-theme-font:minor-latin'>Edit Phase/Copy data</span></b>, select <b
     3047style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3048mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b>
     3049&amp; press <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3050"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3051minor-latin'>OK</span></b> to copy these to the other histograms. Next select
     3052the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3053mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
     3054phase and repeat this process. We are now ready for the first refinement; do <b
     3055style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3056mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
    8253057from the main GSAS-II data tree window. A progress bar popup will appear and
    826 when done a <b><span style='font-family:"Calibri",sans-serif'>Refinement results</span></b>
    827 popup will show with Rw~32%. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
     3058when done a <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3059"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3060minor-latin'>Refinement results</span></b> popup will show with Rw~32%. Press <b
     3061style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3062mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>
    8283063to load this result; GSAS-II will return you to the last window you were using
    8293064and display (NB: pick the 1<sup>st</sup> PWDR entry) the 1<sup>st</sup> powder
    8303065pattern showing you the fit</p>
    8313066
    832 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    833 width=624 height=535 id="Picture 73"
    834 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"></p>
     3067<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3068style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_73"
     3069 o:spid="_x0000_i1067" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3070 visibility:visible;mso-wrap-style:square'>
     3071 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image232.png"
     3072  o:title=""/>
     3073</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3074src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image233.png"
     3075v:shapes="Picture_x0020_73"><![endif]></span></p>
    8353076
    8363077<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is quite
     
    8423083evident that some of the peaks are out of place relative to the reflection
    8433084markers; this is due to macroscopic strain in the drawn wire. For the <span
    844 style='font-family:"Calibri",sans-serif'>B2</span> phase select the <b><span
    845 style='font-family:"Calibri",sans-serif'>Texture</span></b> tab; it should look
    846 like</p>
    847 
    848 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    849 width=624 height=219 id="Picture 74"
    850 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png"></p>
     3085style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3086mso-hansi-theme-font:minor-latin'>B2</span> phase select the <b
     3087style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3088mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
     3089tab; it should look like</p>
     3090
     3091<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3092style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_74"
     3093 o:spid="_x0000_i1066" type="#_x0000_t75" style='width:468pt;height:164.25pt;
     3094 visibility:visible;mso-wrap-style:square'>
     3095 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image234.png"
     3096  o:title=""/>
     3097</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=219
     3098src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image235.png"
     3099v:shapes="Picture_x0020_74"><![endif]></span></p>
    8513100
    8523101<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The texture
    853 model is <b><span style='font-family:"Calibri",sans-serif'>cylindrical</span></b>
    854 by default; that is what we want. Change the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
    855 order</span></b> to <b><span style='font-family:"Calibri",sans-serif'>8</span></b>
    856 and check both <b><span style='font-family:"Calibri",sans-serif'>Refine texture</span></b>
    857 and <b><span style='font-family:"Calibri",sans-serif'>Show coeff</span></b>.
     3102model is <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3103mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>cylindrical</span></b>
     3104by default; that is what we want. Change the <b style='mso-bidi-font-weight:
     3105normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3106minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to <b
     3107style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3108mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>8</span></b>
     3109and check both <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3110"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3111minor-latin'>Refine texture</span></b> and <b style='mso-bidi-font-weight:normal'><span
     3112style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3113mso-hansi-theme-font:minor-latin'>Show <span class=SpellE>coeff</span></span></b>.
    8583114The window should look like</p>
    8593115
    860 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    861 width=624 height=232 id="Picture 75"
    862 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image042.png"></p>
     3116<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3117style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_75"
     3118 o:spid="_x0000_i1065" type="#_x0000_t75" style='width:468pt;height:174pt;
     3119 visibility:visible;mso-wrap-style:square'>
     3120 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image236.png"
     3121  o:title=""/>
     3122</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=232
     3123src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image237.png"
     3124v:shapes="Picture_x0020_75"><![endif]></span></p>
    8633125
    8643126<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the
    865 <b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab, select <b><span
    866 style='font-family:"Calibri",sans-serif'>D11</span></b>; the <b><span
    867 style='font-family:"Calibri",sans-serif'>Data</span></b> window should look
    868 like (any PWDR item will do)</p>
    869 
    870 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    871 width=624 height=321 id="Picture 76"
    872 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image043.png"></p>
    873 
    874 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then do <b><span
    875 style='font-family:"Calibri",sans-serif'>Edit Phase/Copy flags</span></b> to
    876 have <b><span style='font-family:"Calibri",sans-serif'>D11</span></b> refined
    877 for all PWDR data sets.</p>
     3127<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3128mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
     3129tab, select <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3130"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3131minor-latin'>D11</span></b>; the <b style='mso-bidi-font-weight:normal'><span
     3132style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3133mso-hansi-theme-font:minor-latin'>Data</span></b> window should look like (any
     3134PWDR item will do)</p>
     3135
     3136<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3137style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_76"
     3138 o:spid="_x0000_i1064" type="#_x0000_t75" style='width:467.25pt;height:240.75pt;
     3139 visibility:visible;mso-wrap-style:square'>
     3140 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image238.png"
     3141  o:title=""/>
     3142</v:shape><![endif]--><![if !vml]><img border=0 width=623 height=321
     3143src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image239.png"
     3144v:shapes="Picture_x0020_76"><![endif]></span></p>
     3145
     3146<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then do <b
     3147style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3148mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
     3149Phase/Copy flags</span></b> to have <b style='mso-bidi-font-weight:normal'><span
     3150style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3151mso-hansi-theme-font:minor-latin'>D11</span></b> refined for all PWDR data
     3152sets.</p>
    8783153
    8793154<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select
    880 the <b><span style='font-family:"Calibri",sans-serif'>B19’</span></b> phase <b><span
    881 style='font-family:"Calibri",sans-serif'>Texture</span></b> tab. Then select <b><span
    882 style='font-family:"Calibri",sans-serif'>6</span></b> for the <b><span
    883 style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> and check
    884 the two boxes as before.</p>
    885 
    886 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    887 width=624 height=303 id="Picture 77"
    888 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image044.png"></p>
     3155the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3156mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
     3157phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3158mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
     3159tab. Then select <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3160"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3161minor-latin'>6</span></b> for the <b style='mso-bidi-font-weight:normal'><span
     3162style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3163mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> and check the two
     3164boxes as before.</p>
     3165
     3166<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3167style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_77"
     3168 o:spid="_x0000_i1063" type="#_x0000_t75" style='width:468pt;height:227.25pt;
     3169 visibility:visible;mso-wrap-style:square'>
     3170 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image240.png"
     3171  o:title=""/>
     3172</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=303
     3173src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image241.png"
     3174v:shapes="Picture_x0020_77"><![endif]></span></p>
    8893175
    8903176<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the
    891 <b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab for the <b><span
    892 style='font-family:"Calibri",sans-serif'>B19’</span></b> phase and check all 4
    893 of the <b><span style='font-family:"Calibri",sans-serif'>Dij</span></b> boxes
    894 and do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy flags</span></b>
    895 as before. The tab will look like</p>
    896 
    897 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    898 width=624 height=360 id="Picture 78"
    899 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image045.png"></p>
    900 
    901 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do <b><span
    902 style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
    903 main menu. The refinement will finish with Rw ~27%; the 1<sup>st</sup> PWDR
    904 pattern looks like</p>
    905 
    906 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    907 width=624 height=535 id="Picture 79"
    908 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image046.png"></p>
     3177<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3178mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
     3179tab for the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3180"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3181minor-latin'>B19’</span></b> phase and check all 4 of the <span class=SpellE><b
     3182style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3183mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dij</span></b></span>
     3184boxes and do <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3185"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3186minor-latin'>Edit Phase/Copy flags</span></b> as before. The tab will look like</p>
     3187
     3188<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3189style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_78"
     3190 o:spid="_x0000_i1062" type="#_x0000_t75" style='width:468pt;height:270pt;
     3191 visibility:visible;mso-wrap-style:square'>
     3192 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image230.png"
     3193  o:title=""/>
     3194</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=360
     3195src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image242.png"
     3196v:shapes="Picture_x0020_78"><![endif]></span></p>
     3197
     3198<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do <b
     3199style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3200mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
     3201from the main menu. The refinement will finish with <span class=SpellE>Rw</span>
     3202~27%; the 1<sup>st</sup> PWDR pattern looks like</p>
     3203
     3204<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3205style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_79"
     3206 o:spid="_x0000_i1061" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3207 visibility:visible;mso-wrap-style:square'>
     3208 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image243.png"
     3209  o:title=""/>
     3210</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3211src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image243.png"
     3212v:shapes="Picture_x0020_79"><![endif]></span></p>
    9093213
    9103214<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The calculated
    911 peaks for both phases are too sharp. It is likely that this is a microstrain
    912 effect. Select <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
    913 for the <b><span style='font-family:"Calibri",sans-serif'>B2 </span></b>phase
    914 and select the <b><span style='font-family:"Calibri",sans-serif'>microstrain</span></b>
    915 box. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy
    916 flags</span></b> to set it for the other PWDR data sets. Do the same for the <b><span
    917 style='font-family:"Calibri",sans-serif'>B19’</span></b> phase. Then do <b><span
    918 style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
    919 main menu. The fit will be substantially improved with Rw ~10%.</p>
     3215peaks for both phases are too sharp. It is likely that this is a <span
     3216class=SpellE>microstrain</span> effect. Select <b style='mso-bidi-font-weight:
     3217normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3218minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b> for the <b
     3219style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3220mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2 </span></b>phase
     3221and select the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
     3222style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3223mso-hansi-theme-font:minor-latin'>microstrain</span></b></span> box. Then do <b
     3224style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3225mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
     3226Phase/Copy flags</span></b> to set it for the other PWDR data sets. Do the same
     3227for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3228mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
     3229phase. Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3230"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3231minor-latin'>Calculate/Refine</span></b> from the main menu. The fit will be
     3232substantially improved with <span class=SpellE>Rw</span> ~10%.</p>
    9203233
    9213234<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     
    9233236
    9243237<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Looking at the
    925 individual PWDR data sets (e.g. the one for Azm=20.00)</p>
    926 
    927 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    928 width=624 height=535 id="Picture 80"
    929 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"></p>
     3238individual PWDR data sets (e.g. the one for <span class=SpellE>Azm</span>=20.00)</p>
     3239
     3240<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3241style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_80"
     3242 o:spid="_x0000_i1060" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3243 visibility:visible;mso-wrap-style:square'>
     3244 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image244.png"
     3245  o:title=""/>
     3246</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3247src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image245.png"
     3248v:shapes="Picture_x0020_80"><![endif]></span></p>
    9303249
    9313250<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is evident
    932 that there remains intensity differences due to texture. We can increase the
    933 harmonic order to more closely fit these, however one should only do this
    934 carefully. Select the Texture tab for the B2 phase; the Texture tab will show</p>
    935 
    936 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    937 width=624 height=257 id="Picture 81"
    938 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"></p>
     3251that there <span class=GramE>remains</span> intensity differences due to
     3252texture. We can increase the harmonic order to more closely fit these, however
     3253one should only do this carefully. Select the Texture tab for the B2 phase; the
     3254Texture tab will show</p>
     3255
     3256<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3257style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_81"
     3258 o:spid="_x0000_i1059" type="#_x0000_t75" style='width:468pt;height:192.75pt;
     3259 visibility:visible;mso-wrap-style:square'>
     3260 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image246.png"
     3261  o:title=""/>
     3262</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=257
     3263src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image247.png"
     3264v:shapes="Picture_x0020_81"><![endif]></span></p>
    9393265
    9403266<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a drawing
    941 of the 001 pole figure will be drawn. This is the very typical “bulls eye” for
    942 cylindrical texture; of much more use is an inverse pole figure. Select that
    943 from the Texture plot type; the plot will be redrawn</p>
    944 
    945 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    946 width=624 height=535 id="Picture 82"
    947 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.png"></p>
     3267of the <span class=GramE>001 pole</span> figure will be drawn. This is the very
     3268typical “<span class=GramE>bulls</span> eye” for cylindrical texture; of much
     3269more use is an inverse pole figure. Select that from the Texture plot type; the
     3270plot will be redrawn</p>
     3271
     3272<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3273style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_82"
     3274 o:spid="_x0000_i1058" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3275 visibility:visible;mso-wrap-style:square'>
     3276 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image248.png"
     3277  o:title=""/>
     3278</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3279src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image249.png"
     3280v:shapes="Picture_x0020_82"><![endif]></span></p>
    9483281
    9493282<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This shows the
     
    9533286
    9543287<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
    955 Texture tab for the B19’ phase. Again a bullseye pole figure is drawn; change
    956 that to an Inverse pole figure.</p>
    957 
    958 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    959 width=624 height=535 id="Picture 83"
    960 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"></p>
     3288Texture tab for the B19’ phase. <span class=GramE>Again</span> a bullseye pole
     3289figure is drawn; change that to an Inverse pole figure.</p>
     3290
     3291<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3292style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_83"
     3293 o:spid="_x0000_i1057" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3294 visibility:visible;mso-wrap-style:square'>
     3295 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image250.png"
     3296  o:title=""/>
     3297</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3298src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image251.png"
     3299v:shapes="Picture_x0020_83"><![endif]></span></p>
    9613300
    9623301<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This phase is very
    9633302strongly textured (the cursor shows 12-13 MRD at the peaks) along the -140
    964 direction. Again we want to increment the Harmonic order to the next higher
    965 level (8). Again do Calculate/Refine from the main menu; the Rwp has dropped to
    966 ~8.9%. One can add the atom Uiso for the Ni and Ti atoms in the B2 phase and
    967 the coordinates and Uiso for the B19’ phase. The Rw drops a bit further to
    968 ~8.4%. Finally, we can increase the harmonic order again for the B19’ phase (it
    969 is very strongly textured!) to 10 and the B2 phase to 12; the final refinement
    970 converged to Rw ~7.8% and the B19’ inverse pole figure has peaks at ~18 MRD
    971 (Multiple of Random Distribution) and the B2 phase peaks are ~7MRD.</p>
     3303direction. <span class=GramE>Again</span> we want to increment the Harmonic
     3304order to the next higher level (8). <span class=GramE>Again</span> do
     3305Calculate/Refine from the main menu; the <span class=SpellE>Rwp</span> has
     3306dropped to ~8.9%. One can add the atom <span class=SpellE>Uiso</span> for the
     3307Ni and <span class=SpellE>Ti</span> atoms in the B2 phase and the coordinates
     3308and <span class=SpellE>Uiso</span> for the B19’ phase. The <span class=SpellE>Rw</span>
     3309drops a bit further to ~8.4%. Finally, we can increase the harmonic order again
     3310for the B19’ phase (it is very strongly textured!) to 10 and the B2 phase to
     331112; the final refinement converged to <span class=SpellE>Rw</span> ~7.8% and
     3312the B19’ inverse pole figure has peaks at ~18 MRD (Multiple of Random
     3313Distribution) and the B2 phase peaks are ~7MRD.</p>
    9723314
    9733315<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B19’
    9743316coefficients</p>
    9753317
    976 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    977 width=624 height=317 id="Picture 84"
    978 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"></p>
     3318<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3319style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_84"
     3320 o:spid="_x0000_i1056" type="#_x0000_t75" style='width:468pt;height:237.75pt;
     3321 visibility:visible;mso-wrap-style:square'>
     3322 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image252.png"
     3323  o:title=""/>
     3324</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=317
     3325src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image253.png"
     3326v:shapes="Picture_x0020_84"><![endif]></span></p>
    9793327
    9803328<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and inverse
    9813329pole figure</p>
    9823330
    983 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    984 width=624 height=535 id="Picture 85"
    985 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"></p>
     3331<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3332style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_85"
     3333 o:spid="_x0000_i1055" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3334 visibility:visible;mso-wrap-style:square'>
     3335 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image254.png"
     3336  o:title=""/>
     3337</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3338src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image255.png"
     3339v:shapes="Picture_x0020_85"><![endif]></span></p>
    9863340
    9873341<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B2
    9883342coefficients</p>
    9893343
    990 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    991 width=624 height=224 id="Picture 86"
    992 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"></p>
     3344<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3345style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_86"
     3346 o:spid="_x0000_i1054" type="#_x0000_t75" style='width:468pt;height:168pt;
     3347 visibility:visible;mso-wrap-style:square'>
     3348 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image256.png"
     3349  o:title=""/>
     3350</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=224
     3351src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image256.png"
     3352v:shapes="Picture_x0020_86"><![endif]></span></p>
    9933353
    9943354<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and inverse
    9953355pole figure</p>
    9963356
    997 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    998 width=624 height=535 id="Picture 87"
    999 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"></p>
     3357<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3358style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_87"
     3359 o:spid="_x0000_i1053" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3360 visibility:visible;mso-wrap-style:square'>
     3361 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image257.png"
     3362  o:title=""/>
     3363</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3364src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image258.png"
     3365v:shapes="Picture_x0020_87"><![endif]></span></p>
    10003366
    10013367<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This completes
    1002 the tutorial on Method A for doing texture analysis. It is useful for a case like
    1003 this one where there are very few data sets required for the texture analysis.
    1004 However, for the case of lower sample symmetry one must several dozen or even a
    1005 few hundred histograms and then the suite of parameters can easily be &gt; 1000
    1006 of which only a few dozen describe the texture. This leads to the next Methods
    1007 for texture analysis in GSAS-II.</p>
     3368the tutorial on Method A for doing texture analysis. It is useful for a case
     3369like this one where there are very few data sets required for the texture
     3370analysis. However, for the case of lower sample symmetry one must several dozen
     3371or even a few hundred histograms and then the suite of parameters can easily be
     3372&gt; 1000 of which only a few dozen describe the texture. This leads to the
     3373next Methods for texture analysis in GSAS-II.</p>
    10083374
    10093375<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     
    10153381
    10163382<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
    1017 the texture analysis in much the same way as Method A except that all the
    1018 initial refinements are done “sequentially”, that is refinements are done for
    1019 the parameters associated with each powder pattern to convergence in a serial
     3383the texture analysis in much the same way as Method A except that all the initial
     3384refinements are done “sequentially”, that is refinements are done for the
     3385parameters associated with each powder pattern to convergence in a serial
    10203386fashion. In this case where there are 10 PWDR data sets, there will be 10
    10213387refinements done in sequence. Parameters that span all the data (e.g. lattice
    10223388parameters, atom parameters &amp; texture) are not varied in this sequence
    10233389refinement. The effect of texture is modeled as a Preferred Orientation
    1024 correction to each histogram. To begin do <b><span style='font-family:"Calibri",sans-serif'>File/Open
    1025 project
    1026 </span></b> for the <b><span style='font-family:"Calibri",sans-serif'>NiTi.gpx</span></b>
    1027 file created in the first step and then do a <b><span style='font-family:"Calibri",sans-serif'>File/Save
     3390correction to each histogram. To begin do <b style='mso-bidi-font-weight:normal'><span
     3391style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3392mso-hansi-theme-font:minor-latin'>File/Open project
     3393</span></b> for the <span
     3394class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
     3395"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3396minor-latin'>NiTi.gpx</span></b></span> file created in the first step and then
     3397do a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3398mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Save
    10283399project as
    1029 </span></b> to save it as <b><span style='font-family:"Calibri",sans-serif'>NiTi-B</span></b>.
     3400</span></b> to save it as <span class=SpellE><b style='mso-bidi-font-weight:
     3401normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3402minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b
     3403style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3404mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-B</span></b>.
    10303405This renames the project and it should have one IMG, 10 PWDR entries and two
    1031 phases of NiTi (B2 and B19’).</p>
     3406phases of <span class=SpellE>NiTi</span> (B2 and B19’).</p>
    10323407
    10333408<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     
    10353410
    10363411<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
    1037 the same way as Method A so I’ll be brief. Do the following steps:</p>
    1038 
    1039 <p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;text-indent:
    1040 -.25in;line-height:115%'>1)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    1041 </span>Select any <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b>
    1042 entry, go to <b><span style='font-family:"Calibri",sans-serif'>Sample Parameters</span></b>
    1043 and uncheck <b><span style='font-family:"Calibri",sans-serif'>Histogram scale
    1044 factor</span></b>. Then copy the flags to the other PWDR entries.</p>
    1045 
    1046 <p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;text-indent:
    1047 -.25in;line-height:115%'>2)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    1048 </span>Select the <b><span style='font-family:"Calibri",sans-serif'>B2</span></b>
    1049 phase <b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab and
    1050 check the <b><span style='font-family:"Calibri",sans-serif'>Phase fraction</span></b>
    1051 box and change the <b><span style='font-family:"Calibri",sans-serif'>Preferred
    1052 orientation model</span></b> to <b><span style='font-family:"Calibri",sans-serif'>Spherical
    1053 harmonics</span></b>. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit
     3412the same way as Method <span class=GramE>A</span> so I’ll be brief. Do the
     3413following steps:</p>
     3414
     3415<p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;mso-add-space:
     3416auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
     3417style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
     3418style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
     3419any <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3420mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b>
     3421entry, go to <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3422"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3423minor-latin'>Sample Parameters</span></b> and uncheck <b style='mso-bidi-font-weight:
     3424normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3425minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>.
     3426Then copy the flags to the other PWDR entries.</p>
     3427
     3428<p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;mso-add-space:
     3429auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
     3430style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
     3431style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
     3432the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3433mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
     3434phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3435mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
     3436tab and check the <b style='mso-bidi-font-weight:normal'><span
     3437style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3438mso-hansi-theme-font:minor-latin'>Phase fraction</span></b> box and change the <b
     3439style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3440mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
     3441orientation model</span></b> to <b style='mso-bidi-font-weight:normal'><span
     3442style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3443mso-hansi-theme-font:minor-latin'>Spherical harmonics</span></b>. Then do <b
     3444style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3445mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
    10543446Phase/Copy data</span></b> to copy both the flag and the model to the other
    10553447PWDR entries.</p>
    10563448
    1057 <p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;text-indent:-.25in;
    1058 line-height:115%'>3)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    1059 </span>Select the <b><span style='font-family:"Calibri",sans-serif'>B19’</span></b>
    1060 phase <b><span style='font-family:"Calibri",sans-serif'>Data</span></b> tab and
    1061 check the <b><span style='font-family:"Calibri",sans-serif'>Phase fraction box</span></b>
    1062 and change the <b><span style='font-family:"Calibri",sans-serif'>Preferred
    1063 orientation model</span></b> to <b><span style='font-family:"Calibri",sans-serif'>Spherical
    1064 harmonics</span></b>. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit
     3449<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space:
     3450auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
     3451style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
     3452style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
     3453the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3454mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
     3455phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3456mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
     3457tab and check the <b style='mso-bidi-font-weight:normal'><span
     3458style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3459mso-hansi-theme-font:minor-latin'>Phase fraction box</span></b> and change the <b
     3460style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3461mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
     3462orientation model</span></b> to <b style='mso-bidi-font-weight:normal'><span
     3463style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3464mso-hansi-theme-font:minor-latin'>Spherical harmonics</span></b>. Then do <b
     3465style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3466mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
    10653467Phase/Copy data</span></b> to copy both the flag and the model to the other
    10663468PWDR entries.</p>
    10673469
    1068 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select <b><span
    1069 style='font-family:"Calibri",sans-serif'>Controls</span></b> from the GSAS-II
    1070 data tree</p>
    1071 
    1072 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1073 width=624 height=191 id="Picture 88"
    1074 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"></p>
    1075 
    1076 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Press the <b><span
    1077 style='font-family:"Calibri",sans-serif'>Select Data</span></b> button for <b><span
    1078 style='font-family:"Calibri",sans-serif'>Sequential Refinement</span></b>; a
    1079 file selection popup will appear. Do <b><span style='font-family:"Calibri",sans-serif'>Set
    1080 All</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>.
    1081 The <b><span style='font-family:"Calibri",sans-serif'>Controls</span></b> page
    1082 will be repainted indicating that 10 data sets are selected for sequential
    1083 refinement.</p>
    1084 
    1085 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1086 width=624 height=199 id="Picture 89"
    1087 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"></p>
     3470<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select <b
     3471style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3472mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b>
     3473from the GSAS-II data tree</p>
     3474
     3475<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3476style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_88"
     3477 o:spid="_x0000_i1052" type="#_x0000_t75" style='width:466.5pt;height:143.25pt;
     3478 visibility:visible;mso-wrap-style:square'>
     3479 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image259.png"
     3480  o:title=""/>
     3481</v:shape><![endif]--><![if !vml]><img border=0 width=622 height=191
     3482src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image260.png"
     3483v:shapes="Picture_x0020_88"><![endif]></span></p>
     3484
     3485<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Press the <b
     3486style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3487mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Select Data</span></b>
     3488button for <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3489"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3490minor-latin'>Sequential Refinement</span></b>; a file selection popup will
     3491appear. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3492"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3493minor-latin'>Set All</span></b> and press <b style='mso-bidi-font-weight:normal'><span
     3494style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3495mso-hansi-theme-font:minor-latin'>OK</span></b>. The <b style='mso-bidi-font-weight:
     3496normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3497minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b> page will be
     3498repainted indicating that 10 data sets are selected for sequential refinement.</p>
     3499
     3500<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3501style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_89"
     3502 o:spid="_x0000_i1051" type="#_x0000_t75" style='width:468pt;height:149.25pt;
     3503 visibility:visible;mso-wrap-style:square'>
     3504 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image261.png"
     3505  o:title=""/>
     3506</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=199
     3507src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image262.png"
     3508v:shapes="Picture_x0020_89"><![endif]></span></p>
    10883509
    10893510<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You have the
    10903511choice of starting at the last one and for copying results from one to the
    10913512next. We won’t do either here. Each refinement will use the other controls
    1092 (e.g. <b><span style='font-family:"Calibri",sans-serif'>Max cycles</span></b>)
     3513(e.g. <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3514mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Max cycles</span></b>)
    10933515as controls. We are now ready to do the 1<sup>st</sup> sequential refinement.
    1094 Do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Sequential
     3516Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3517mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Sequential
    10953518refine</span></b> from the main menu. A progress bar popup will appear showing
    1096 residuals as it processes each of 10 data sets. After a few seconds the <b><span
    1097 style='font-family:"Calibri",sans-serif'>Refinement results</span></b> popup
    1098 will appear; press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
    1099 to accept them. The data window displays the <b><span style='font-family:"Calibri",sans-serif'>Sequential
    1100 refinement results</span></b> as a table.</p>
    1101 
    1102 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1103 width=624 height=176 id="Picture 90"
    1104 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"></p>
     3519residuals as it processes each of 10 data sets. After a few seconds the <b
     3520style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3521mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refinement
     3522results</span></b> popup will appear; press <b style='mso-bidi-font-weight:
     3523normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3524minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to accept them. The
     3525data window displays the <b style='mso-bidi-font-weight:normal'><span
     3526style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3527mso-hansi-theme-font:minor-latin'>Sequential refinement results</span></b> as a
     3528table.</p>
     3529
     3530<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3531style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_90"
     3532 o:spid="_x0000_i1050" type="#_x0000_t75" style='width:468pt;height:132pt;
     3533 visibility:visible;mso-wrap-style:square'>
     3534 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image263.png"
     3535  o:title=""/>
     3536</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=176
     3537src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image264.png"
     3538v:shapes="Picture_x0020_90"><![endif]></span></p>
    11053539
    11063540<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>There is a row
    1107 for each data set and columns for all refined parameters and some derived ones along
    1108 with residual and convergence indicators. The residuals are not very good (we
    1109 haven’t really refined much) but the &#916;&#967;<sup>2</sup> column shows that
    1110 convergence was achieved (NB: poor convergence will be highlighted in yellow or
    1111 red depending on how bad it is).</p>
     3541for each data set and columns for all refined parameters and some derived ones
     3542along with residual and convergence indicators. The residuals are not very good
     3543(we haven’t really refined much) but the &#916;&#967;<sup>2</sup> column shows
     3544that convergence was achieved (NB: poor convergence will be highlighted in
     3545yellow or red depending on how bad it is).</p>
    11123546
    11133547<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you examine
     
    11153549the misfit is texture and perhaps peak position.</p>
    11163550
    1117 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1118 width=624 height=535 id="Picture 91"
    1119 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"></p>
     3551<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3552style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_91"
     3553 o:spid="_x0000_i1049" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3554 visibility:visible;mso-wrap-style:square'>
     3555 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image265.png"
     3556  o:title=""/>
     3557</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3558src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image266.png"
     3559v:shapes="Picture_x0020_91"><![endif]></span></p>
    11203560
    11213561<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>To set these
    11223562parameters, select the Data tab for the B2 phase</p>
    11233563
    1124 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1125 width=508 height=500 id="Picture 5"
    1126 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image117.png"></p>
    1127 
    1128 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Check the <b><span
    1129 style='font-family:"Calibri",sans-serif'>D11</span></b> box under
    1130 Hydrostatic/elastic strain, set the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
    1131 order</span></b> to <b><span style='font-family:"Calibri",sans-serif'>6</span></b>
    1132 and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
    1133 box for it (Preferred orientation). Then in two steps, do <b><span
    1134 style='font-family:"Calibri",sans-serif'>Edit Phase/Copy flags</span></b> and <b><span
    1135 style='font-family:"Calibri",sans-serif'>Set All</span></b> for the file
    1136 selection. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit
     3564<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3565style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5"
     3566 o:spid="_x0000_i1048" type="#_x0000_t75" style='width:381pt;height:256.5pt;
     3567 visibility:visible;mso-wrap-style:square'>
     3568 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image267.png"
     3569  o:title=""/>
     3570</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=342
     3571src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image268.png"
     3572v:shapes="Picture_x0020_5"><![endif]></span></p>
     3573
     3574<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Check the <b
     3575style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3576mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3577minor-latin'>D11</span></b> box under Hydrostatic/elastic strain, set the <b
     3578style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3579mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3580minor-latin'>Harmonic order</span></b> to <b style='mso-bidi-font-weight:normal'><span
     3581style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3582mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>6</span></b>
     3583and check the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3584"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3585minor-latin;mso-bidi-theme-font:minor-latin'>Refine</span></b> box for it
     3586(Preferred orientation). Then in two steps, do <b style='mso-bidi-font-weight:
     3587normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3588minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Edit
     3589Phase/Copy flags</span></b> and <b style='mso-bidi-font-weight:normal'><span
     3590style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3591mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Set All</span></b>
     3592for the file selection. Then do <b style='mso-bidi-font-weight:normal'><span
     3593style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3594mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Edit
    11373595Phase/Copy selected data</span></b>; that will bring up a new popup</p>
    11383596
    1139 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1140 width=322 height=390 id="Picture 92"
    1141 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image118.png"></p>
     3597<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3598style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_92"
     3599 o:spid="_x0000_i1047" type="#_x0000_t75" style='width:241.5pt;height:292.5pt;
     3600 visibility:visible;mso-wrap-style:square'>
     3601 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image269.png"
     3602  o:title=""/>
     3603</v:shape><![endif]--><![if !vml]><img border=0 width=322 height=390
     3604src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image269.png"
     3605v:shapes="Picture_x0020_92"><![endif]></span></p>
    11423606
    11433607<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This allows
    1144 you to select which parameters to copy data and flags. Select <b><span
    1145 style='font-family:"Calibri",sans-serif'>Pref. Ori.</span></b> And press <b><span
    1146 style='font-family:"Calibri",sans-serif'>OK</span></b>; the file selection is
    1147 next. Do <b><span style='font-family:"Calibri",sans-serif'>Set All</span></b>
    1148 and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b> to do this
    1149 copy. That copies the full spherical harmonics model to the other data sets.
    1150 Select one to check if you’d like.</p>
     3608you to select which parameters to copy data and flags. Select <b
     3609style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3610mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3611minor-latin'>Pref. Ori.</span></b> And press <b style='mso-bidi-font-weight:
     3612normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3613minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>OK</span></b>;
     3614the file selection is next. Do <b style='mso-bidi-font-weight:normal'><span
     3615style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3616mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Set All</span></b>
     3617and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3618mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3619minor-latin'>OK</span></b> to do this copy. That copies the full spherical
     3620harmonics model to the other data sets. Select one to check if you’d like.</p>
    11513621
    11523622<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next do the
    1153 same thing for the B19’ phase; here there are 4 <b><span style='font-family:
    1154 "Calibri",sans-serif'>Dij </span></b>parameters to check (do all of them) and
    1155 use spherical harmonics order <b><span style='font-family:"Calibri",sans-serif'>4</span></b>.
    1156 When done that Data window will look like</p>
    1157 
    1158 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1159 width=624 height=421 id="Picture 93"
    1160 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"></p>
     3623same thing for the B19’ phase; here there are 4 <span class=SpellE><b
     3624style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3625mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3626minor-latin'>Dij</span></b></span><b style='mso-bidi-font-weight:normal'><span
     3627style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3628mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'> </span></b>parameters
     3629to check (do all of them) and use spherical harmonics order <b
     3630style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3631mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3632minor-latin'>4</span></b>. When done that Data window will look <span
     3633class=GramE>like</span></p>
     3634
     3635<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3636style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_93"
     3637 o:spid="_x0000_i1046" type="#_x0000_t75" style='width:468pt;height:315.75pt;
     3638 visibility:visible;mso-wrap-style:square'>
     3639 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image267.png"
     3640  o:title=""/>
     3641</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=421
     3642src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image270.png"
     3643v:shapes="Picture_x0020_93"><![endif]></span></p>
    11613644
    11623645<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
    1163 ready for the next refinement; do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Sequential
     3646ready for the next refinement; do <b style='mso-bidi-font-weight:normal'><span
     3647style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3648mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Sequential
    11643649refine</span></b>. Be careful not (by habit say) pick Refine; a warning popup
    11653650will appear. After it completes the Sequential refinement results shows that
    1166 the fit is better but convergence wasn’t quite complete.</p>
    1167 
    1168 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1169 width=624 height=204 id="Picture 95"
    1170 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"></p>
     3651the fit is <span class=GramE>better</span> but convergence wasn’t quite
     3652complete.</p>
     3653
     3654<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3655style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_95"
     3656 o:spid="_x0000_i1045" type="#_x0000_t75" style='width:467.25pt;height:153pt;
     3657 visibility:visible;mso-wrap-style:square'>
     3658 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image271.png"
     3659  o:title=""/>
     3660</v:shape><![endif]--><![if !vml]><img border=0 width=623 height=204
     3661src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image272.png"
     3662v:shapes="Picture_x0020_95"><![endif]></span></p>
    11713663
    11723664<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is probably
     
    11743666convergence. A plot of one PWDR entry gives</p>
    11753667
    1176 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1177 width=624 height=535 id="Picture 96"
    1178 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"></p>
     3668<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3669style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_96"
     3670 o:spid="_x0000_i1044" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3671 visibility:visible;mso-wrap-style:square'>
     3672 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image273.png"
     3673  o:title=""/>
     3674</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3675src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image274.png"
     3676v:shapes="Picture_x0020_96"><![endif]></span></p>
    11793677
    11803678<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>As our
    11813679experience in Method A, the calculated peaks are too sharp. We need to vary the
    11823680mustrain parameters for both phases. Go to the Data tab for each phase, check
    1183 the <b><span style='font-family:"Calibri",sans-serif'>microstrain</span></b>
    1184 box and do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy
    1185 flags</span></b> for all the data sets. Then do another <b><span
    1186 style='font-family:"Calibri",sans-serif'>Calculate/Sequential refine</span></b>.
    1187 My Sequential refinement results showed great improvement but incomplete
    1188 refinement</p>
    1189 
    1190 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1191 width=624 height=204 id="Picture 97"
    1192 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"></p>
     3681the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
     3682style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3683mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>microstrain</span></b></span>
     3684box and do <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3685"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3686minor-latin;mso-bidi-theme-font:minor-latin'>Edit Phase/Copy flags</span></b>
     3687for all the data sets. Then do another <b style='mso-bidi-font-weight:normal'><span
     3688style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3689mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Sequential
     3690refine</span></b>. My Sequential refinement results showed great improvement
     3691but incomplete refinement</p>
     3692
     3693<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3694style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_97"
     3695 o:spid="_x0000_i1043" type="#_x0000_t75" style='width:467.25pt;height:153pt;
     3696 visibility:visible;mso-wrap-style:square'>
     3697 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image275.png"
     3698  o:title=""/>
     3699</v:shape><![endif]--><![if !vml]><img border=0 width=623 height=204
     3700src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image276.png"
     3701v:shapes="Picture_x0020_97"><![endif]></span></p>
    11933702
    11943703<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Repeating the
    11953704sequential refinement (twice) gave convergence.</p>
    11963705
    1197 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1198 width=624 height=204 id="Picture 98"
    1199 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"></p>
     3706<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3707style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_98"
     3708 o:spid="_x0000_i1042" type="#_x0000_t75" style='width:467.25pt;height:153pt;
     3709 visibility:visible;mso-wrap-style:square'>
     3710 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image277.png"
     3711  o:title=""/>
     3712</v:shape><![endif]--><![if !vml]><img border=0 width=623 height=204
     3713src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image278.png"
     3714v:shapes="Picture_x0020_98"><![endif]></span></p>
    12003715
    12013716<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Examination of
    12023717the PWDR data sets showed a fairly good fit but some discrepancies (especially
    1203 for Azm=20.00)</p>
    1204 
    1205 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1206 width=624 height=535 id="Picture 99"
    1207 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"></p>
     3718for <span class=SpellE>Azm</span>=20.00)</p>
     3719
     3720<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3721style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_99"
     3722 o:spid="_x0000_i1041" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3723 visibility:visible;mso-wrap-style:square'>
     3724 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image279.png"
     3725  o:title=""/>
     3726</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3727src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image280.png"
     3728v:shapes="Picture_x0020_99"><![endif]></span></p>
    12083729
    12093730<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Showing that
    12103731perhaps the B19’ phase needs high order spherical harmonics. Select the Data
    1211 tab for the B19’ phase and change the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
    1212 order</span></b> to <b><span style='font-family:"Calibri",sans-serif'>6</span></b>.
    1213 Then do <b><span style='font-family:"Calibri",sans-serif'>Edit Phase/Copy
    1214 selected data</span></b> for <b><span style='font-family:"Calibri",sans-serif'>Pref.Ori.</span></b>
     3732tab for the B19’ phase and change the <b style='mso-bidi-font-weight:normal'><span
     3733style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3734mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Harmonic
     3735order</span></b> to <b style='mso-bidi-font-weight:normal'><span
     3736style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3737mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>6</span></b>.
     3738Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3739mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3740minor-latin'>Edit Phase/Copy selected data</span></b> for <span class=SpellE><b
     3741style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3742mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3743minor-latin'>Pref.Ori</span></b></span><b style='mso-bidi-font-weight:normal'><span
     3744style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3745mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>.</span></b>
    12153746to the other data sets. This (after few repeats) gives a further improvement in
    12163747the fit</p>
    12173748
    1218 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1219 width=624 height=204 id="Picture 100"
    1220 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"></p>
     3749<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3750style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_100"
     3751 o:spid="_x0000_i1040" type="#_x0000_t75" style='width:467.25pt;height:153pt;
     3752 visibility:visible;mso-wrap-style:square'>
     3753 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image281.png"
     3754  o:title=""/>
     3755</v:shape><![endif]--><![if !vml]><img border=0 width=623 height=204
     3756src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image282.png"
     3757v:shapes="Picture_x0020_100"><![endif]></span></p>
    12213758
    12223759<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This fit is
     
    12293766<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>During the
    12303767sequential refinements done in Step 1, we fitted the profiles allowing strain
    1231 parameters (Dij) for peak position shifts and microstrain for peak shape. We
    1232 modeled the intensity variation with a spherical harmonics preferred
     3768parameters (<span class=SpellE>Dij</span>) for peak position shifts and <span
     3769class=SpellE>microstrain</span> for peak shape. We modeled the intensity
     3770variation with a <span class=GramE>spherical harmonics</span> preferred
    12333771orientation correction. If you select any PWDR entry from the GSAS-II data tree
    12343772and pick the Reflection List subentry (at the bottom) you can see the magnitude
     
    12383776phase we see</p>
    12393777
    1240 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1241 width=624 height=204 id="Picture 101"
    1242 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"></p>
     3778<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3779style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_101"
     3780 o:spid="_x0000_i1039" type="#_x0000_t75" style='width:467.25pt;height:153pt;
     3781 visibility:visible;mso-wrap-style:square'>
     3782 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image283.png"
     3783  o:title=""/>
     3784</v:shape><![endif]--><![if !vml]><img border=0 width=623 height=204
     3785src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image284.png"
     3786v:shapes="Picture_x0020_101"><![endif]></span></p>
    12433787
    12443788<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and for the
    12453789B19’ phase we see</p>
    12463790
    1247 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1248 width=624 height=204 id="Picture 102"
    1249 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"></p>
     3791<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3792style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_102"
     3793 o:spid="_x0000_i1038" type="#_x0000_t75" style='width:467.25pt;height:153pt;
     3794 visibility:visible;mso-wrap-style:square'>
     3795 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image285.png"
     3796  o:title=""/>
     3797</v:shape><![endif]--><![if !vml]><img border=0 width=623 height=204
     3798src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image286.png"
     3799v:shapes="Picture_x0020_102"><![endif]></span></p>
    12503800
    12513801<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The preferred
    1252 orientation correction is Prfo; notice a few entries in red. These are
    1253 nonphysical correction values (the correction can’t be negative) but by in
    1254 large these are small. This next step uses these corrections as input data for
    1255 a texture refinement. To start select the Texture tab for the B2 phase; you’ll
    1256 see</p>
    1257 
    1258 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1259 width=608 height=290 id="Picture 16"
    1260 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image137.png"></p>
     3802orientation correction is <span class=SpellE>Prfo</span>; notice a few entries
     3803in red. These are nonphysical correction values (the correction can’t be
     3804negative) but by in large these are small. This next step uses these
     3805corrections as input data for a texture refinement. To start select the Texture
     3806tab for the B2 phase; you’ll see</p>
     3807
     3808<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3809style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_16"
     3810 o:spid="_x0000_i1037" type="#_x0000_t75" style='width:456pt;height:164.25pt;
     3811 visibility:visible;mso-wrap-style:square'>
     3812 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image287.png"
     3813  o:title=""/>
     3814</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=219
     3815src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image288.png"
     3816v:shapes="Picture_x0020_16"><![endif]></span></p>
    12613817
    12623818<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Since this
    1263 sample has wire texture, we’ll use the default Texture model (<b><span
    1264 style='font-family:"Calibri",sans-serif'>cylindrical</span></b>). Then set the <b><span
    1265 style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> to <b><span
    1266 style='font-family:"Calibri",sans-serif'>12</span></b> (what we used earlier)
    1267 and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
    1268 and <b><span style='font-family:"Calibri",sans-serif'>Show coeff</span></b>
    1269 boxes. The data window will be redrawn (and an orange blank plot will appear).</p>
    1270 
    1271 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1272 width=624 height=225 id="Picture 103"
    1273 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"></p>
    1274 
    1275 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do <b><span
    1276 style='font-family:"Calibri",sans-serif'>Texture/Refine texture</span></b> from
    1277 the menu; the window will be repainted and a bullseye pole figure will appear. </p>
    1278 
    1279 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1280 width=624 height=225 id="Picture 104"
    1281 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"></p>
    1282 
    1283 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the <b><span
    1284 style='font-family:"Calibri",sans-serif'>Texture plot type</span></b> to <b><span
    1285 style='font-family:"Calibri",sans-serif'>Inverse pole figure</span></b> to get
    1286 a more useful plot</p>
    1287 
    1288 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1289 width=624 height=535 id="Picture 105"
    1290 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"></p>
     3819sample has wire texture, we’ll use the default Texture model (<b
     3820style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3821mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3822minor-latin'>cylindrical</span></b>). Then set the <b style='mso-bidi-font-weight:
     3823normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3824minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Harmonic
     3825order</span></b> to <b style='mso-bidi-font-weight:normal'><span
     3826style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3827mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>12</span></b>
     3828(what we used earlier) and check the <b style='mso-bidi-font-weight:normal'><span
     3829style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3830mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Refine</span></b>
     3831and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3832mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3833minor-latin'>Show <span class=SpellE>coeff</span></span></b> boxes. The data
     3834window will be redrawn (and an orange blank plot will appear).</p>
     3835
     3836<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3837style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_103"
     3838 o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt;height:168.75pt;
     3839 visibility:visible;mso-wrap-style:square'>
     3840 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image289.png"
     3841  o:title=""/>
     3842</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=225
     3843src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image289.png"
     3844v:shapes="Picture_x0020_103"><![endif]></span></p>
     3845
     3846<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do <b
     3847style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3848mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3849minor-latin'>Texture/Refine texture</span></b> from the menu; the window will
     3850be <span class=GramE>repainted</span> and a bullseye pole figure will appear. </p>
     3851
     3852<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><!--[if gte vml 1]><v:shape
     3853 id="Picture_x0020_104" o:spid="_x0000_s1026" type="#_x0000_t75" style='width:468pt;
     3854 height:168.75pt;visibility:visible;mso-wrap-style:square;mso-left-percent:-10001;
     3855 mso-top-percent:-10001;mso-position-horizontal:absolute;
     3856 mso-position-horizontal-relative:char;mso-position-vertical:absolute;
     3857 mso-position-vertical-relative:line;mso-left-percent:-10001;mso-top-percent:-10001'>
     3858 <w:wrap type="none"/>
     3859 <w:anchorlock/>
     3860</v:shape><![endif]--><![if !vml]><img width=624 height=225
     3861src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image290.png"
     3862v:shapes="Picture_x0020_104"><![endif]></p>
     3863
     3864<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the <b
     3865style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3866mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3867minor-latin'>Texture plot type</span></b> to <b style='mso-bidi-font-weight:
     3868normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3869minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Inverse
     3870pole figure</span></b> to get a more useful plot</p>
     3871
     3872<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3873style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_105"
     3874 o:spid="_x0000_i1034" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3875 visibility:visible;mso-wrap-style:square'>
     3876 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image291.png"
     3877  o:title=""/>
     3878</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3879src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image292.png"
     3880v:shapes="Picture_x0020_105"><![endif]></span></p>
    12913881
    12923882<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is
     
    12953885
    12963886<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the
    1297 Texture tab for the B19’ phase and do the same; use <b><span style='font-family:
    1298 "Calibri",sans-serif'>Harmonic order 10</span></b> as we did earlier in Method
    1299 A. After setting the two flags and doing <b><span style='font-family:"Calibri",sans-serif'>Texture/Refine
    1300 texture</span></b> we get</p>
    1301 
    1302 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1303 width=624 height=324 id="Picture 106"
    1304 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"></p>
     3887Texture tab for the B19’ phase and do the same; use <b style='mso-bidi-font-weight:
     3888normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3889minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Harmonic
     3890order 10</span></b> as we did earlier in Method A. After setting the two flags
     3891and doing <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3892mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3893minor-latin'>Texture/Refine texture</span></b> we get</p>
     3894
     3895<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3896style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_106"
     3897 o:spid="_x0000_i1033" type="#_x0000_t75" style='width:467.25pt;height:243pt;
     3898 visibility:visible;mso-wrap-style:square'>
     3899 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image293.png"
     3900  o:title=""/>
     3901</v:shape><![endif]--><![if !vml]><img border=0 width=623 height=324
     3902src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image294.png"
     3903v:shapes="Picture_x0020_106"><![endif]></span></p>
    13053904
    13063905<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a bullseye
    13073906pole figure; change that to Inverse pole figure to see the texture</p>
    13083907
    1309 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1310 width=624 height=535 id="Picture 107"
    1311 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"></p>
    1312 
    1313 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Again this is
    1314 very similar to what we found in Method A but again not quite as strong (max
    1315 MRD ~10 instead of ~18) and a bit choppier.</p>
    1316 
    1317 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do a <b><span
    1318 style='font-family:"Calibri",sans-serif'>File/Save project</span></b> from the
    1319 main menu; this saves the final texture results done in Step 2 (you also will
    1320 need it for Method C).</p>
     3908<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3909style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_107"
     3910 o:spid="_x0000_i1032" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     3911 visibility:visible;mso-wrap-style:square'>
     3912 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image295.png"
     3913  o:title=""/>
     3914</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     3915src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image296.png"
     3916v:shapes="Picture_x0020_107"><![endif]></span></p>
     3917
     3918<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3919class=GramE>Again</span> this is very similar to what we found in Method A but
     3920again not quite as strong (max MRD ~10 instead of ~18) and a bit choppier.</p>
     3921
     3922<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do a <b
     3923style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3924mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     3925minor-latin'>File/Save project</span></b> from the main menu; this saves the
     3926final texture results done in Step 2 (you also will need it for Method C).</p>
    13213927
    13223928<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     
    13283934
    13293935<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This uses the
    1330 same approach as Method B except that after the sequential refinements are
    1331 finished we then fix almost all the parameters and then do a final texture
    1332 refinement with all the data. Thus, this is a replacement for Step 2 in Method
    1333 B. To begin do <b><span style='font-family:"Calibri",sans-serif'>File/Open
    1334 project
    1335 </span></b> for the <b><span style='font-family:"Calibri",sans-serif'>NiTi-B.gpx</span></b>
    1336 file created in Method B and then do a <b><span style='font-family:"Calibri",sans-serif'>File/Save
     3936same approach as Method B except that after the sequential refinements are <span
     3937class=GramE>finished</span> we then fix almost all the parameters and then do a
     3938final texture refinement with all the data. Thus, this is a replacement for
     3939Step 2 in Method B. To begin do <b style='mso-bidi-font-weight:normal'><span
     3940style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3941mso-hansi-theme-font:minor-latin'>File/Open project
     3942</span></b> for the <span
     3943class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
     3944"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3945minor-latin'>NiTi-B.gpx</span></b></span> file created in Method B and then do
     3946a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3947mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Save
    13373948project as
    1338 </span></b> to save it as <b><span style='font-family:"Calibri",sans-serif'>NiTi-C</span></b>.
     3949</span></b> to save it as <span class=SpellE><b style='mso-bidi-font-weight:
     3950normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3951minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b
     3952style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3953mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-C</span></b>.
    13393954This renames the project and it should have one IMG, 10 PWDR entries and two
    1340 phases of NiTi (B2 and B19’).</p>
     3955phases of <span class=SpellE>NiTi</span> (B2 and B19’).</p>
    13413956
    13423957<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     
    13493964unless we expect it to affect the peak intensities. These are listed below:</p>
    13503965
    1351 <p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;text-indent:
    1352 -.25in;line-height:115%'>1)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    1353 </span><b><span style='font-family:"Calibri",sans-serif'>Background</span></b>:
    1354 as the background was fit during the sequential refinement we should fix it
    1355 here. Select any <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b>
    1356 entry and choose the <b><span style='font-family:"Calibri",sans-serif'>Background</span></b>
    1357 subentry for it. Clear the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
    1358 flags and the do <b><span style='font-family:"Calibri",sans-serif'>File/Copy
     3966<p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;mso-add-space:
     3967auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
     3968style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
     3969style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
     3970style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3971mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>:
     3972as the background was fit during the sequential <span class=GramE>refinement</span>
     3973we should fix it here. Select any <b style='mso-bidi-font-weight:normal'><span
     3974style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3975mso-hansi-theme-font:minor-latin'>PWDR</span></b> entry and choose the <b
     3976style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3977mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>
     3978subentry for it. Clear the <b style='mso-bidi-font-weight:normal'><span
     3979style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3980mso-hansi-theme-font:minor-latin'>Refine</span></b> flags and the do <b
     3981style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3982mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Copy
    13593983flags</span></b> selecting all data sets. This will clear all background
    13603984refinement flags.</p>
    13613985
    1362 <p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;text-indent:
    1363 -.25in;line-height:115%'>2)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    1364 </span><b><span style='font-family:"Calibri",sans-serif'>B2</span></b> phase:
    1365 we do not want to refine either the microstrain, D<sub>11</sub>, or preferred
    1366 orientation coefficients. Select the <b><span style='font-family:"Calibri",sans-serif'>B2</span></b>
    1367 phase and its <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
    1368 tab. Clear the <b><span style='font-family:"Calibri",sans-serif'>microstrain</span></b>,
    1369 <b><span style='font-family:"Calibri",sans-serif'>D<sub>11</sub></span></b> and
    1370 <b><span style='font-family:"Calibri",sans-serif'>Preferred orientation</span></b>
    1371 boxes. Also set the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
    1372 order</span></b> to zero (this will avoid a lot of nasty (but harmless)
    1373 messages at the start of the refinement). Then do <b><span style='font-family:
    1374 "Calibri",sans-serif'>Edit Phase/Copy flags</span></b> selecting all data to
    1375 clear all the flags and an <b><span style='font-family:"Calibri",sans-serif'>Edit
    1376 Phase/Copy selected data</span></b> for <b><span style='font-family:"Calibri",sans-serif'>Pref.Ori</span></b>
    1377 to copy the zeroed out harmonic coefficients.</p>
    1378 
    1379 <p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;text-indent:-.25in;
    1380 line-height:115%'>3)<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    1381 </span><b><span style='font-family:"Calibri",sans-serif'>B19’</span></b>: we do
    1382 not want to refine either the microstrain, Dij, or preferred orientation
    1383 coefficients. Select the <b><span style='font-family:"Calibri",sans-serif'>B19’</span></b>
    1384 phase and its <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
    1385 tab. Clear the <b><span style='font-family:"Calibri",sans-serif'>microstrain</span></b>,
    1386 four <b><span style='font-family:"Calibri",sans-serif'>Dij</span></b> and <b><span
    1387 style='font-family:"Calibri",sans-serif'>Preferred orientation</span></b>
    1388 boxes. Also set the <b><span style='font-family:"Calibri",sans-serif'>Harmonic
    1389 order</span></b> to zero (this will avoid a lot of nasty (but harmless)
    1390 messages at the start of the refinement). Then do <b><span style='font-family:
    1391 "Calibri",sans-serif'>Edit Phase/Copy flags</span></b> selecting all data to
    1392 clear all the flags and an <b><span style='font-family:"Calibri",sans-serif'>Edit
    1393 Phase/Copy selected data</span></b> for <b><span style='font-family:"Calibri",sans-serif'>Pref.Ori</span></b>
    1394 to copy the zeroed out harmonic coefficients.</p>
     3986<p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;mso-add-space:
     3987auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
     3988style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
     3989style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
     3990style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3991mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
     3992phase: we do not want to refine either the <span class=SpellE>microstrain</span>,
     3993D<sub>11</sub>, or preferred orientation coefficients. Select the <b
     3994style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3995mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
     3996phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3997"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3998minor-latin'>Data</span></b> tab. Clear the <span class=SpellE><b
     3999style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4000mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>microstrain</span></b></span>,
     4001<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4002mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>D<sub>11</sub></span></b>
     4003and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4004mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
     4005orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
     4006style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     4007mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
     4008avoid a lot of nasty (but harmless) messages at the start of the refinement).
     4009Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4010mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
     4011Phase/Copy flags</span></b> selecting all data to clear all the flags and an <b
     4012style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4013mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
     4014Phase/Copy selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
     4015normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     4016minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
     4017copy the zeroed out harmonic coefficients.</p>
     4018
     4019<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space:
     4020auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
     4021style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
     4022style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
     4023style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4024mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>:
     4025we do not want to refine either the <span class=SpellE>microstrain</span>, <span
     4026class=SpellE>Dij</span>, or preferred orientation coefficients. Select the <b
     4027style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4028mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
     4029phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
     4030"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     4031minor-latin'>Data</span></b> tab. Clear the <span class=SpellE><b
     4032style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4033mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>microstrain</span></b></span>,
     4034four <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
     4035style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     4036mso-hansi-theme-font:minor-latin'>Dij</span></b></span> and <b
     4037style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4038mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
     4039orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
     4040style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     4041mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
     4042avoid a lot of nasty (but harmless) messages at the start of the refinement).
     4043Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4044mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
     4045Phase/Copy flags</span></b> selecting all data to clear all the flags and an <b
     4046style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4047mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit Phase/Copy
     4048selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
     4049normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     4050minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
     4051copy the zeroed out harmonic coefficients.</p>
    13954052
    13964053<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    1397 margin-left:.25in;line-height:115%'>&nbsp;</p>
     4054margin-left:.25in;line-height:115%'><o:p>&nbsp;</o:p></p>
    13984055
    13994056<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    14004057margin-left:.25in;line-height:115%'>Notice that we have allowed refinement of
    1401 the <b><span style='font-family:"Calibri",sans-serif'>Phase fractions</span></b>;
    1402 these may change during the texture refinement. Now select the <b><span
    1403 style='font-family:"Calibri",sans-serif'>Texture</span></b> tab for the <b><span
    1404 style='font-family:"Calibri",sans-serif'>B2</span></b> phase (it may still have
    1405 values from the Method B).</p>
     4058the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4059mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase
     4060fractions</span></b>; these may change during the texture refinement. Now
     4061select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     4062"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     4063minor-latin'>Texture</span></b> tab for the <b style='mso-bidi-font-weight:
     4064normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     4065minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> phase (it may still
     4066have values from the Method B).</p>
    14064067
    14074068<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    1408 margin-left:.25in;line-height:115%'><img border=0 width=624 height=236
    1409 id="Picture 108"
    1410 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"></p>
     4069margin-left:.25in;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     4070 id="Picture_x0020_108" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
     4071 height:177pt;visibility:visible;mso-wrap-style:square'>
     4072 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image297.png"
     4073  o:title=""/>
     4074</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=236
     4075src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image298.png"
     4076v:shapes="Picture_x0020_108"><![endif]></span></p>
    14114077
    14124078<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    1413 margin-left:.25in;line-height:115%'>You can clear these by setting the <b><span
    1414 style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> to zero and
    1415 then back to <b><span style='font-family:"Calibri",sans-serif'>12</span></b>.
    1416 Leave the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
    1417 &amp; <b><span style='font-family:"Calibri",sans-serif'>Show</span></b> boxes
    1418 checked.</p>
     4079margin-left:.25in;line-height:115%'>You can clear these by setting the <b
     4080style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4081mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic
     4082order</span></b> to zero and then back to <b style='mso-bidi-font-weight:normal'><span
     4083style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     4084mso-hansi-theme-font:minor-latin'>12</span></b>. Leave the <b style='mso-bidi-font-weight:
     4085normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     4086minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b> &amp; <b
     4087style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4088mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b>
     4089boxes checked.</p>
    14194090
    14204091<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    1421 margin-left:.25in;line-height:115%'><img border=0 width=624 height=236
    1422 id="Picture 109"
    1423 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"></p>
     4092margin-left:.25in;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     4093 id="Picture_x0020_109" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;
     4094 height:177pt;visibility:visible;mso-wrap-style:square'>
     4095 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image299.png"
     4096  o:title=""/>
     4097</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=236
     4098src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image300.png"
     4099v:shapes="Picture_x0020_109"><![endif]></span></p>
    14244100
    14254101<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    1426 margin-left:.25in;line-height:115%'>Then do the same for the <b><span
    1427 style='font-family:"Calibri",sans-serif'>B19’</span></b> phase. Select the <b><span
    1428 style='font-family:"Calibri",sans-serif'>B19’</span></b> phase and its <b><span
    1429 style='font-family:"Calibri",sans-serif'>Texture</span></b> tab. Set the <b><span
    1430 style='font-family:"Calibri",sans-serif'>Harmonic order</span></b> to zero and
    1431 then back to <b><span style='font-family:"Calibri",sans-serif'>10</span></b>.
    1432 Leave the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
    1433 and <b><span style='font-family:"Calibri",sans-serif'>Show</span></b> boxes
    1434 checked. This completes the setup for the full texture refinement.</p>
     4102margin-left:.25in;line-height:115%'>Then do the same for the <b
     4103style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4104mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
     4105phase. Select the <b style='mso-bidi-font-weight:normal'><span
     4106style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     4107mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and its <b
     4108style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4109mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
     4110tab. Set the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     4111"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     4112minor-latin'>Harmonic order</span></b> to zero and then back to <b
     4113style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4114mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>.
     4115Leave the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4116mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b>
     4117and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4118mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b>
     4119boxes checked. This completes the setup for the full texture refinement.</p>
    14354120
    14364121<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
    143741220in;line-height:115%'>Step 2. Texture refinement</h3>
    14384123
    1439 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do <b><span
    1440 style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
    1441 main menu; you will see the warning message</p>
    1442 
    1443 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1444 width=562 height=130 id="Picture 110"
    1445 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image152.png"></p>
     4124<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do <b
     4125style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4126mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
     4127from the main menu; you will see the warning message</p>
     4128
     4129<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4130style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_110"
     4131 o:spid="_x0000_i1029" type="#_x0000_t75" style='width:421.5pt;height:97.5pt;
     4132 visibility:visible;mso-wrap-style:square'>
     4133 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image301.png"
     4134  o:title=""/>
     4135</v:shape><![endif]--><![if !vml]><img border=0 width=562 height=130
     4136src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image301.png"
     4137v:shapes="Picture_x0020_110"><![endif]></span></p>
    14464138
    14474139<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In this case
    1448 you do want to do a nonsequential full refinement, so press the <b><span
    1449 style='font-family:"Calibri",sans-serif'>OK</span></b> button. A quick look at
    1450 the console will show that there are 61 variables in this refinement. If yours
    1451 shows more then you didn’t clear all the flags in Step 1. The <b><span
    1452 style='font-family:"Calibri",sans-serif'>Sequential results</span></b> entry is
     4140you do want to do a nonsequential full refinement, so press the <b
     4141style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4142mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     4143minor-latin'>OK</span></b> button. A quick look at the console will show that
     4144there are 61 variables in this refinement. If yours shows more then you didn’t
     4145clear all the flags in Step 1. The <b style='mso-bidi-font-weight:normal'><span
     4146style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     4147mso-hansi-theme-font:minor-latin'>Sequential results</span></b> entry is
    14534148deleted from the GSAS-II data tree. A progress bar will show giving the
    1454 residuals during the refinement. When finished, select the <b><span
    1455 style='font-family:"Calibri",sans-serif'>B2</span></b> phase and its <b><span
    1456 style='font-family:"Calibri",sans-serif'>Texture</span></b> tab; if the Texture
    1457 plot type is still <b><span style='font-family:"Calibri",sans-serif'>Inverse
    1458 pole figure</span></b> (from Method B) you should see</p>
    1459 
    1460 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1461 width=624 height=535 id="Picture 111"
    1462 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"></p>
    1463 
    1464 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>which is
    1465 almost identical to that from Method A. The coefficients are seen in</p>
    1466 
    1467 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1468 width=624 height=236 id="Picture 112"
    1469 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"></p>
     4149residuals during the refinement. When finished, select the <b style='mso-bidi-font-weight:
     4150normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     4151minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> phase and its <b
     4152style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4153mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
     4154tab; if the Texture plot type is still <b style='mso-bidi-font-weight:normal'><span
     4155style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     4156mso-hansi-theme-font:minor-latin'>Inverse pole figure</span></b> (from Method
     4157B) you should see</p>
     4158
     4159<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4160style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_111"
     4161 o:spid="_x0000_i1028" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     4162 visibility:visible;mso-wrap-style:square'>
     4163 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image302.png"
     4164  o:title=""/>
     4165</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     4166src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image303.png"
     4167v:shapes="Picture_x0020_111"><![endif]></span></p>
     4168
     4169<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>which is almost
     4170identical to that from Method <span class=GramE>A.</span> The coefficients are
     4171seen in</p>
     4172
     4173<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4174style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_112"
     4175 o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;height:177pt;
     4176 visibility:visible;mso-wrap-style:square'>
     4177 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image304.png"
     4178  o:title=""/>
     4179</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=236
     4180src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image305.png"
     4181v:shapes="Picture_x0020_112"><![endif]></span></p>
    14704182
    14714183<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the
    1472 <b><span style='font-family:"Calibri",sans-serif'>B19’</span></b> phase and its
    1473 <b><span style='font-family:"Calibri",sans-serif'>Texture</span></b> tab; the
    1474 inverse pole figure is</p>
    1475 
    1476 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1477 width=624 height=535 id="Picture 113"
    1478 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"></p>
    1479 
    1480 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and also
    1481 almost identical to what was obtained in Method A; the coefficients are seen in</p>
    1482 
    1483 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><img border=0
    1484 width=624 height=323 id="Picture 114"
    1485 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"></p>
     4184<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4185mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
     4186phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
     4187"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     4188minor-latin'>Texture</span></b> tab; the inverse pole figure is</p>
     4189
     4190<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4191style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_113"
     4192 o:spid="_x0000_i1026" type="#_x0000_t75" style='width:468pt;height:401.25pt;
     4193 visibility:visible;mso-wrap-style:square'>
     4194 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image306.png"
     4195  o:title=""/>
     4196</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
     4197src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image307.png"
     4198v:shapes="Picture_x0020_113"><![endif]></span></p>
     4199
     4200<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and <span
     4201class=GramE>also</span> almost identical to what was obtained in Method A; the
     4202coefficients are seen in</p>
     4203
     4204<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4205style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_114"
     4206 o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt;height:242.25pt;
     4207 visibility:visible;mso-wrap-style:square'>
     4208 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image308.png"
     4209  o:title=""/>
     4210</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=323
     4211src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image309.png"
     4212v:shapes="Picture_x0020_114"><![endif]></span></p>
    14864213
    14874214<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>With this
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