Changeset 1853


Ignore:
Timestamp:
May 14, 2015 12:08:01 PM (7 years ago)
Author:
vondreele
Message:

replace all equations with new ones

Location:
Tutorials/2DTexture
Files:
30 added
78 edited

Legend:

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

    r1849 r1853  
    1414<link rel=Edit-Time-Data
    1515href="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/editdata.mso">
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    2725  <o:Author>Von Dreele</o:Author>
    2826  <o:LastAuthor>Von Dreele</o:LastAuthor>
    29   <o:Revision>15</o:Revision>
    30   <o:TotalTime>2065</o:TotalTime>
    31   <o:Created>2015-05-11T19:45:00Z</o:Created>
    32   <o:LastSaved>2015-05-13T21:37:00Z</o:LastSaved>
     27  <o:Revision>2</o:Revision>
     28  <o:TotalTime>2121</o:TotalTime>
     29  <o:Created>2015-05-14T17:06:00Z</o:Created>
     30  <o:LastSaved>2015-05-14T17:06:00Z</o:LastSaved>
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    3634  <o:Company>Argonne National Laboratory</o:Company>
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    14171416modeling, as described by Bunge, &quot;Texture Analysis in Materials
    14181417Science&quot; (1982), and implemented by Von Dreele, J. Appl. <span
    1419 class=SpellE>Cryst</span>., <b style='mso-bidi-font-weight:normal'>30</b>,
    1420 517-525 (1997) in GSAS. The even part of the orientation distribution function
    1421 (ODF) via the general axis equation</p>
    1422 
    1423 <p class=gsastext><span style='position:relative;top:14.0pt;mso-text-raise:
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     1418class=SpellE>Cryst</span>., <b style='mso-bidi-font-weight:normal'>30</b>, 517-525
     1419(1997) in GSAS. The even part of the orientation distribution function (ODF)
     1420via the general axis equation</p>
     1421
     1422<p class=MsoNormal><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1423   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
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     1426    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1427    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     1428    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
     1429  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
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     1434    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
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     1440      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
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     1443      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1444      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
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     1446      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
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     1463          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
     1464          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
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     1468      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1469      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     1470      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
     1471      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
     1472      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
     1473  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>h</m:r><m:r>)</m:r></span></i><m:sSubSup><m:sSubSupPr><span
     1474    style='mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif;
     1475    mso-ascii-font-family:"Cambria Math";mso-fareast-font-family:"Times New Roman";
     1476    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
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     1478    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1479    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
     1480    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
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    14551511
    14561512<p class=gsastext><span class=GramE>is</span> used to give the intensity
    1457 corrections due to texture. The two harmonic terms, <span style='position:relative;
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     1513corrections due to texture. The two harmonic terms, <!--[if gte msEquation 12]><m:oMath><i
     1514 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><w:Sdt
     1515  ShowingPlcHdr="t" Temporary="t" Equation="t"
     1516  DocPart="5A1AF1CD80C54DC98EA094C12465F069" ID="1604071880"><span
     1517  class=MsoPlaceholderText><span style='mso-fareast-font-family:Calibri;
     1518  mso-fareast-theme-font:minor-latin'><m:r>Type equation here.</m:r></span></span></w:Sdt></span></i><m:sSubSup><m:sSubSupPr><span
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     1520   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1521   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1522   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1523   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
     1524   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
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     1526   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
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     1528   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
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     1539style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1540   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1541   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1542   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1543   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1544   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
     1545   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
     1546 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
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    1479 </xml><![endif]-->, take on values according to the crystal and sample
    1480 symmetries, respectively, and thus the two inner summations are over only the
    1481 resulting unique, nonzero harmonic terms. These unique terms are automatically
    1482 selected by <span style='mso-bidi-font-weight:bold'>GSAS-II</span> according to
    1483 the space group symmetry and the user chosen sample symmetry. The available
    1484 sample symmetries are cylindrical symmetry, 2/m, mmm and no symmetry. The
    1485 choice of sample symmetry profoundly affects the selection of harmonic
    1486 coefficients. For example, in the case of cylindrical sample symmetry (fiber
    1487 texture) only <span style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
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    1489  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image007.wmz"
    1490   o:title=""/>
    1491 </v:shape><![endif]--><![if !vml]><img width=40 height=24
     1556v:shapes="_x0000_i1025"><![endif]></span><![endif]>, take on values according
     1557to the crystal and sample symmetries, respectively, and thus the two inner
     1558summations are over only the resulting unique, nonzero harmonic terms. These
     1559unique terms are automatically selected by <span style='mso-bidi-font-weight:
     1560bold'>GSAS-II</span> according to the space group symmetry and the user chosen
     1561sample symmetry. The available sample symmetries are cylindrical symmetry, 2/m,
     1562mmm and no symmetry. The choice of sample symmetry profoundly affects the
     1563selection of harmonic coefficients. For example, in the case of cylindrical
     1564sample symmetry (fiber texture) only <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1565   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1566   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1567   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1568   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1569   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
     1570   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
     1571 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
     1572style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1573"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1574top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1575EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1576 type="#_x0000_t75" style='width:29.25pt;height:26.25pt'>
     1577 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image007.png"
     1578  o:title="" chromakey="white"/>
     1579</v:shape><![endif]--><![if !vml]><img width=39 height=35
    14921580src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image008.png"
    1493 v:shapes="_x0000_i1041"><![endif]></span><!--[if gte mso 9]><xml>
    1494  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1041"
    1495   DrawAspect="Content" ObjectID="_1493040242">
    1496  </o:OLEObject>
    1497 </xml><![endif]--><span style='mso-spacerun:yes'> </span>terms are nonzero so
    1498 the rest are excluded from the summations and the set of <span
    1499 style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
    1500  id="_x0000_i1043" type="#_x0000_t75" style='width:21.75pt;height:18pt' o:ole="">
    1501  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image009.wmz"
    1502   o:title=""/>
    1503 </v:shape><![endif]--><![if !vml]><img width=29 height=24
     1581v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     1582style='mso-spacerun:yes'> </span>terms are nonzero so the rest are excluded
     1583from the summations and the set of <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1584   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1585   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1586   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1587   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
     1588   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
     1589   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
     1590style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1591"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1592top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1593EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1594 type="#_x0000_t75" style='width:21pt;height:26.25pt'>
     1595 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image009.png"
     1596  o:title="" chromakey="white"/>
     1597</v:shape><![endif]--><![if !vml]><img width=28 height=35
    15041598src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image010.png"
    1505 v:shapes="_x0000_i1043"><![endif]></span><!--[if gte mso 9]><xml>
    1506  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1043"
    1507   DrawAspect="Content" ObjectID="_1493040243">
    1508  </o:OLEObject>
    1509 </xml><![endif]-->coefficients is sufficient to describe the effect on the
    1510 diffraction patterns due to texture. The crystal harmonic factor, <span
    1511 style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
    1512  id="_x0000_i1042" type="#_x0000_t75" style='width:30.75pt;height:18pt' o:ole="">
    1513  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image011.wmz"
    1514   o:title=""/>
    1515 </v:shape><![endif]--><![if !vml]><img width=41 height=24
    1516 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"
    1517 v:shapes="_x0000_i1042"><![endif]></span><!--[if gte mso 9]><xml>
    1518  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1042"
    1519   DrawAspect="Content" ObjectID="_1493040244">
    1520  </o:OLEObject>
    1521 </xml><![endif]-->, is defined for each reflection, h, <i>via</i> polar and
    1522 azimuthal coordinates (<span style='font-family:Symbol'>f</span>, <span
    1523 style='font-family:Symbol'>b</span>) of a unit vector coincident with h
    1524 relative to the reciprocal lattice. For most crystal symmetries, <span
    1525 style='font-family:Symbol'>f</span> is the angle between h and the n-<span
    1526 class=SpellE>th</span> order major rotation axis of the space group (usually
    1527 the c-axis) and <span style='font-family:Symbol'>b</span> is the angle between
    1528 the projections of h and any secondary axis (usually the a-axis) onto the
    1529 normal plane.<span style='mso-spacerun:yes'>  </span>In a similar way the
    1530 sample harmonic factor, <span style='position:relative;top:5.0pt;mso-text-raise:
    1531 -5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1025" type="#_x0000_t75"
    1532  style='width:32.25pt;height:20.25pt' o:ole="">
    1533  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image012.wmz"
    1534   o:title=""/>
    1535 </v:shape><![endif]--><![if !vml]><img width=43 height=27
    1536 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image013.png"
    1537 v:shapes="_x0000_i1025"><![endif]></span><!--[if gte mso 9]><xml>
    1538  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025"
    1539   DrawAspect="Content" ObjectID="_1493040245">
    1540  </o:OLEObject>
    1541 </xml><![endif]-->, is defined according to polar and azimuthal coordinates (<span
    1542 style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
    1543 of a unit vector coincident with the diffraction vector relative to a
    1544 coordinate system attached to the external form of the sample. For example, in
    1545 the case of a rolled steel plate having mmm symmetry, the polar angle, <span
    1546 style='font-family:Symbol'>y</span>, is frequently measured from the normal
    1547 direction (ND) and <span style='font-family:Symbol'>g</span> is then measured
    1548 from the rolling direction (RD) in the TD (transverse direction) - RD
    1549 plane.<span style='mso-spacerun:yes'>  </span>Thus, the general axis equation
    1550 becomes</p>
    1551 
    1552 <p class=gsastext><span style='position:relative;top:14.0pt;mso-text-raise:
    1553 -14.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1044" type="#_x0000_t75"
    1554  style='width:272.25pt;height:35.25pt' o:ole="">
    1555  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image014.wmz"
    1556   o:title=""/>
    1557 </v:shape><![endif]--><![if !vml]><img width=363 height=47
    1558 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image015.png"
    1559 v:shapes="_x0000_i1044"><![endif]></span><!--[if gte mso 9]><xml>
    1560  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1044"
    1561   DrawAspect="Content" ObjectID="_1493040246">
    1562  </o:OLEObject>
    1563 </xml><![endif]--><br style='mso-special-character:line-break'>
     1599v:shapes="_x0000_i1025"><![endif]></span><![endif]>coefficients is sufficient
     1600to describe the effect on the diffraction patterns due to texture. The crystal
     1601harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1602   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1603   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1604   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1605   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1606   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
     1607   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
     1608 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
     1609style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1610"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1611top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1612EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1613 type="#_x0000_t75" style='width:32.25pt;height:26.25pt'>
     1614 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image011.png"
     1615  o:title="" chromakey="white"/>
     1616</v:shape><![endif]--><![if !vml]><img width=43 height=35
     1617src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image012.png"
     1618v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined for each
     1619reflection, h, <i>via</i> polar and azimuthal coordinates (<span
     1620style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
     1621of a unit vector coincident with h relative to the reciprocal lattice. For most
     1622crystal symmetries, <span style='font-family:Symbol'>f</span> is the angle
     1623between h and the n-<span class=SpellE>th</span> order major rotation axis of
     1624the space group (usually the c-axis) and <span style='font-family:Symbol'>b</span>
     1625is the angle between the projections of h and any secondary axis (usually the
     1626a-axis) onto the normal plane.<span style='mso-spacerun:yes'>  </span>In a
     1627similar way the sample harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1628   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1629   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1630   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1631   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1632   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
     1633   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
     1634 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
     1635style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1636"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1637top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1638EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1639 type="#_x0000_t75" style='width:30pt;height:26.25pt'>
     1640 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png"
     1641  o:title="" chromakey="white"/>
     1642</v:shape><![endif]--><![if !vml]><img width=40 height=35
     1643src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"
     1644v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined according to
     1645polar and azimuthal coordinates (<span style='font-family:Symbol'>y</span>, <span
     1646style='font-family:Symbol'>g</span>) of a unit vector coincident with the
     1647diffraction vector relative to a coordinate system attached to the external
     1648form of the sample. For example, in the case of a rolled steel plate having mmm
     1649symmetry, the polar angle, <span style='font-family:Symbol'>y</span>, is
     1650frequently measured from the normal direction (ND) and <span style='font-family:
     1651Symbol'>g</span> is then measured from the rolling direction (RD) in the TD
     1652(transverse direction) - RD plane.<span style='mso-spacerun:yes'>  </span>Thus,
     1653the general axis equation becomes</p>
     1654
     1655<p class=gsastext><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1656   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
     1657  style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><span
     1658    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1659    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1660    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     1661    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
     1662  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
     1663     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     1664    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     1665    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     1666    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
     1667      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1668      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1669      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
     1670      normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i
     1671      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
     1672      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1673      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1674      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
     1675      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
     1676      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
     1677     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     1678    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     1679    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     1680    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
     1681    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
     1682       m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
     1683      "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
     1684      "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     1685      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
     1686      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
     1687        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1688        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1689        normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     1690        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
     1691        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
     1692        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
     1693      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1694      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1695      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     1696      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
     1697      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
     1698      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
     1699      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1700      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1701      normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     1702      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
     1703    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1704    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1705    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1706    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1707    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
     1708    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
     1709  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
     1710style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1711"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     1712mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     1713 id="_x0000_i1025" type="#_x0000_t75" style='width:321pt;height:54pt'>
     1714 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image013.png"
     1715  o:title="" chromakey="white"/>
     1716</v:shape><![endif]--><![if !vml]><img width=428 height=72
     1717src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image014.png"
     1718v:shapes="_x0000_i1025"><![endif]></span><![endif]><br style='mso-special-character:
     1719line-break'>
    15641720<![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'>
    15651721<![endif]></p>
     
    15761732an instrument coordinate system (I, J, K) such that K is normal to the
    15771733diffraction plane and J is coincident with the direction of the incident
    1578 radiation beam toward the source. We further define a standard set of right-handed
    1579 goniometer <span class=SpellE>eulerian</span> angles (<span style='font-family:
    1580 Symbol'>W</span>, <span style='font-family:Symbol'>C</span>, <span
    1581 style='font-family:Symbol'>F</span>) so that <span style='font-family:Symbol'>W</span>
    1582 and <span style='font-family:Symbol'>F</span> are rotations about K and <span
    1583 style='font-family:Symbol'>C</span> is a rotation about J when <span
    1584 style='font-family:Symbol'>W</span> <span style='font-family:Symbol'><span
     1734radiation beam toward the source. We further define a standard set of
     1735right-handed goniometer <span class=SpellE>eulerian</span> angles (<span
     1736style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>,
     1737<span style='font-family:Symbol'>F</span>) so that <span style='font-family:
     1738Symbol'>W</span> and <span style='font-family:Symbol'>F</span> are rotations
     1739about K and <span style='font-family:Symbol'>C</span> is a rotation about J
     1740when <span style='font-family:Symbol'>W</span> <span style='font-family:Symbol'><span
    15851741style='mso-spacerun:yes'> </span></span>= 0.<span style='mso-spacerun:yes'> 
    15861742</span>Finally, as the sample may be mounted so that the sample coordinate
    1587 system (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>) does
    1588 not coincide with the instrument coordinate system (I, J, K), we define three <span
    1589 class=SpellE>eulerian</span> sample rotation offset angles (<span
     1743system (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>)
     1744does not coincide with the instrument coordinate system (I, J, K), we define
     1745three <span class=SpellE>eulerian</span> sample rotation offset angles (<span
    15901746style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
    15911747<span style='font-family:Symbol'>F</span><sub>s</sub>) that describe the
     
    16161772
    16171773<p class=gsastext><span class=GramE><i>cos</i>(</span><span style='font-family:
    1618 Symbol'>y</span>) = <b style='mso-bidi-font-weight:normal'><span
    1619 style='position:relative;top:25.0pt;mso-text-raise:-25.0pt'><!--[if gte vml 1]><v:shape
    1620  id="_x0000_i1046" type="#_x0000_t75" style='width:33.75pt;height:56.25pt'
    1621  o:ole="">
    1622  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.wmz"
    1623   o:title=""/>
    1624 </v:shape><![endif]--><![if !vml]><img width=45 height=75
    1625 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image017.png"
    1626 v:shapes="_x0000_i1046"><![endif]></span><!--[if gte mso 9]><xml>
    1627  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1046"
    1628   DrawAspect="Content" ObjectID="_1493040247">
    1629  </o:OLEObject>
    1630 </xml><![endif]--></b><span style='mso-spacerun:yes'>  </span>and<span
    1631 style='mso-spacerun:yes'>   </span><i>tan</i>(<span style='font-family:Symbol'>g</span>)
    1632 = <span style='position:relative;top:25.0pt;mso-text-raise:-25.0pt'><!--[if gte vml 1]><v:shape
    1633  id="_x0000_i1045" type="#_x0000_t75" style='width:81.75pt;height:56.25pt'
    1634  o:ole="">
    1635  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.wmz"
    1636   o:title=""/>
    1637 </v:shape><![endif]--><![if !vml]><img width=109 height=75
    1638 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png"
    1639 v:shapes="_x0000_i1045"><![endif]></span><!--[if gte mso 9]><xml>
    1640  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1045"
    1641   DrawAspect="Content" ObjectID="_1493040249">
    1642  </o:OLEObject>
    1643 </xml><![endif]--></p>
    1644 
    1645 <p class=gsastext>The harmonic terms, <span style='position:relative;
    1646 top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1047"
    1647  type="#_x0000_t75" style='width:44.25pt;height:18pt' o:ole="">
    1648  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.wmz"
    1649   o:title=""/>
    1650 </v:shape><![endif]--><![if !vml]><img width=59 height=24
    1651 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png"
    1652 v:shapes="_x0000_i1047"><![endif]></span><!--[if gte mso 9]><xml>
    1653  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1047"
    1654   DrawAspect="Content" ObjectID="_1493040250">
    1655  </o:OLEObject>
    1656 </xml><![endif]--><span class=GramE>and </span><span style='position:relative;
    1657 top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1048"
    1658  type="#_x0000_t75" style='width:42.75pt;height:18pt' o:ole="">
    1659  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.wmz"
    1660   o:title=""/>
    1661 </v:shape><![endif]--><![if !vml]><img width=57 height=24
    1662 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.png"
    1663 v:shapes="_x0000_i1048"><![endif]></span><!--[if gte mso 9]><xml>
    1664  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1048"
    1665   DrawAspect="Content" ObjectID="_1493040251">
    1666  </o:OLEObject>
    1667 </xml><![endif]-->, are developed from</p>
    1668 
    1669 <p class=gsastext><span style='position:relative;top:8.0pt;mso-text-raise:-8.0pt'><!--[if gte vml 1]><v:shape
    1670  id="_x0000_i1049" type="#_x0000_t75" style='width:138pt;height:21pt' o:ole="">
    1671  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.wmz"
    1672   o:title=""/>
    1673 </v:shape><![endif]--><![if !vml]><img width=184 height=28
    1674 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image025.png"
    1675 v:shapes="_x0000_i1049"><![endif]></span><!--[if gte mso 9]><xml>
    1676  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1049"
    1677   DrawAspect="Content" ObjectID="_1493040252">
    1678  </o:OLEObject>
    1679 </xml><![endif]--></p>
     1774Symbol'>y</span>) = <!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
     1775 normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
     1776   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1777   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1778   normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
     1779         m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
     1780     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1781     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1782     normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
     1783      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
     1784      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
     1785      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
     1786style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1787"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1788top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1789EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1790 type="#_x0000_t75" style='width:33.75pt;height:50.25pt'>
     1791 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image015.png"
     1792  o:title="" chromakey="white"/>
     1793</v:shape><![endif]--><![if !vml]><img width=45 height=67
     1794src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.png"
     1795v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     1796style='mso-spacerun:yes'> </span>and<span style='mso-spacerun:yes'>   </span><i>tan</i>(<span
     1797style='font-family:Symbol'>g</span>) = <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type
     1798    m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     1799   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1800   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
     1801   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
     1802     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1803     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1804     normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
     1805           m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
     1806       style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1807       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1808       normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
     1809        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
     1810        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
     1811        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
     1812   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
     1813     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1814     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1815     normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
     1816           m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
     1817       style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1818       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1819       normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
     1820        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
     1821        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
     1822        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
     1823style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1824"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1825top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1826EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1827 type="#_x0000_t75" style='width:80.25pt;height:50.25pt'>
     1828 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image017.png"
     1829  o:title="" chromakey="white"/>
     1830</v:shape><![endif]--><![if !vml]><img width=107 height=67
     1831src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.png"
     1832v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
     1833
     1834<p class=gsastext>The harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1835   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1836   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1837   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1838   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1839   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
     1840   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
     1841 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
     1842style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1843"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1844top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1845EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1846 type="#_x0000_t75" style='width:46.5pt;height:26.25pt'>
     1847 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png"
     1848  o:title="" chromakey="white"/>
     1849</v:shape><![endif]--><![if !vml]><img width=62 height=35
     1850src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"
     1851v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     1852style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1853   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1854   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1855   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1856   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1857   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
     1858   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
     1859 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
     1860style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1861"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1862top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1863EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1864 type="#_x0000_t75" style='width:42.75pt;height:26.25pt'>
     1865 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png"
     1866  o:title="" chromakey="white"/>
     1867</v:shape><![endif]--><![if !vml]><img width=57 height=35
     1868src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.png"
     1869v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are developed from</p>
     1870
     1871<p class=gsastext><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1872   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
     1873    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1874    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1875    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1876    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1877    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
     1878    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
     1879    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1880    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1881    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     1882    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
     1883  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:f><m:fPr><span
     1884    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1885    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1886    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
     1887    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
     1888       m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     1889      "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1890      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
     1891      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
     1892    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1893    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1894    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     1895    normal'><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:e><m:sup><i
     1896    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
     1897    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1898    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1899    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     1900       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     1901      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     1902      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     1903      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
     1904    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
     1905    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     1906     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     1907  normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
     1908    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1909    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1910    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     1911    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     1912       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     1913    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
     1914  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
     1915style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1916"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     1917mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     1918 id="_x0000_i1025" type="#_x0000_t75" style='width:165pt;height:42pt'>
     1919 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.png"
     1920  o:title="" chromakey="white"/>
     1921</v:shape><![endif]--><![if !vml]><img width=220 height=56
     1922src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"
     1923v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    16801924
    16811925<p class=gsastext><span class=GramE>where</span> the normalized associated
    1682 Legendre functions, <span style='position:relative;top:5.0pt;mso-text-raise:
    1683 -5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1050" type="#_x0000_t75"
    1684  style='width:33.75pt;height:18pt' o:ole="">
    1685  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image026.wmz"
    1686   o:title=""/>
    1687 </v:shape><![endif]--><![if !vml]><img width=45 height=24
    1688 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image027.png"
    1689 v:shapes="_x0000_i1050"><![endif]></span><!--[if gte mso 9]><xml>
    1690  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1050"
    1691   DrawAspect="Content" ObjectID="_1493040253">
    1692  </o:OLEObject>
    1693 </xml><![endif]-->, are defined via a Fourier expansion as</p>
    1694 
    1695 <p class=gsastext><span style='position:relative;top:14.0pt;mso-text-raise:
    1696 -14.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1051" type="#_x0000_t75"
    1697  style='width:132.75pt;height:33.75pt' o:ole="">
    1698  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image028.wmz"
    1699   o:title=""/>
    1700 </v:shape><![endif]--><![if !vml]><img width=177 height=45
    1701 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image029.png"
    1702 v:shapes="_x0000_i1051"><![endif]></span><!--[if gte mso 9]><xml>
    1703  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1051"
    1704   DrawAspect="Content" ObjectID="_1493040254">
    1705  </o:OLEObject>
    1706 </xml><![endif]--></p>
     1926Legendre functions, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1927   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1928   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1929   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     1930      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     1931     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1932     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     1933     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
     1934   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
     1935   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
     1936 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
     1937style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1938"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1939top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1940EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1941 type="#_x0000_t75" style='width:33.25pt;height:26.3pt'>
     1942 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image025.png"
     1943  o:title="" chromakey="white"/>
     1944</v:shape><![endif]--><![if !vml]><img width=44 height=35
     1945src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image026.png"
     1946v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are defined via a Fourier
     1947expansion as</p>
     1948
     1949<p class=gsastext><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1950   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
     1951    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1952    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1953    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     1954       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     1955      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     1956      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     1957      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
     1958    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
     1959    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     1960     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     1961    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1962    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1963    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
     1964      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1965      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1966      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     1967      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     1968         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     1969      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
     1970  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
     1971     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     1972    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     1973    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     1974    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
     1975    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
     1976      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1977      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1978      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     1979      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
     1980      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
     1981      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     1982       </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
     1983    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1984    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1985    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     1986    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     1987       m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     1988    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
     1989style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1990"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     1991mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     1992 id="_x0000_i1025" type="#_x0000_t75" style='width:154.4pt;height:52.6pt'>
     1993 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image027.png"
     1994  o:title="" chromakey="white"/>
     1995</v:shape><![endif]--><![if !vml]><img width=206 height=70
     1996src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image028.png"
     1997v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    17071998
    17081999<p class=gsastext><span class=GramE>for</span> m even and</p>
    17092000
    1710 <p class=gsastext><span style='position:relative;top:14.0pt;mso-text-raise:
    1711 -14.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1052" type="#_x0000_t75"
    1712  style='width:132pt;height:33.75pt' o:ole="">
    1713  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image030.wmz"
    1714   o:title=""/>
    1715 </v:shape><![endif]--><![if !vml]><img width=176 height=45
    1716 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image031.png"
    1717 v:shapes="_x0000_i1052"><![endif]></span><!--[if gte mso 9]><xml>
    1718  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1052"
    1719   DrawAspect="Content" ObjectID="_1493040255">
    1720  </o:OLEObject>
    1721 </xml><![endif]--></p>
     2001<p class=gsastext><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2002   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
     2003    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2004    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2005    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2006       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     2007      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2008      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2009      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
     2010    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
     2011    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2012     </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2013    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2014    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2015    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
     2016      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2017      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2018      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2019      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2020         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2021      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
     2022  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
     2023     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     2024    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2025    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     2026    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
     2027    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
     2028      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2029      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2030      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     2031      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
     2032      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
     2033      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2034       </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
     2035    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2036    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2037    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2038    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2039       m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2040    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
     2041style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2042"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     2043mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     2044 id="_x0000_i1025" type="#_x0000_t75" style='width:158.55pt;height:52.6pt'>
     2045 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image029.png"
     2046  o:title="" chromakey="white"/>
     2047</v:shape><![endif]--><![if !vml]><img width=211 height=70
     2048src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image030.png"
     2049v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    17222050
    17232051<p class=gsastext><span class=GramE>for</span> m odd.<span
    17242052style='mso-spacerun:yes'>  </span>Each sum is only over either the even or odd
    17252053values of s, respectively, because of the properties of the Fourier
    1726 coefficients<span class=GramE>, </span><span style='position:relative;
    1727 top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1026"
    1728  type="#_x0000_t75" style='width:23.25pt;height:20.25pt' o:ole="">
    1729  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image032.wmz"
    1730   o:title=""/>
    1731 </v:shape><![endif]--><![if !vml]><img width=31 height=27
    1732 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.png"
    1733 v:shapes="_x0000_i1026"><![endif]></span><!--[if gte mso 9]><xml>
    1734  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1026"
    1735   DrawAspect="Content" ObjectID="_1493040256">
    1736  </o:OLEObject>
    1737 </xml><![endif]-->.<span style='mso-spacerun:yes'>  </span>These Fourier
    1738 coefficients are determined so that the definition</p>
    1739 
    1740 <p class=gsastext><span style='position:relative;top:16.0pt;mso-text-raise:
    1741 -16.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75"
    1742  style='width:356.25pt;height:38.25pt' o:ole="">
    1743  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image034.wmz"
    1744   o:title=""/>
    1745 </v:shape><![endif]--><![if !vml]><img width=475 height=51
    1746 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image035.png"
    1747 v:shapes="_x0000_i1027"><![endif]></span><!--[if gte mso 9]><xml>
    1748  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1027"
    1749   DrawAspect="Content" ObjectID="_1493040257">
    1750  </o:OLEObject>
    1751 </xml><![endif]--></p>
     2054coefficients<span class=GramE>, </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2055   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2056   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2057   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2058   normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i
     2059   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
     2060   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2061    </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
     2062style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2063"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2064top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2065EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2066 type="#_x0000_t75" style='width:24.9pt;height:26.3pt'>
     2067 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image031.png"
     2068  o:title="" chromakey="white"/>
     2069</v:shape><![endif]--><![if !vml]><img width=33 height=35
     2070src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image032.png"
     2071v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
     2072style='mso-spacerun:yes'>  </span>These Fourier coefficients are determined so
     2073that the definition</p>
     2074
     2075<p class=gsastext><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2076   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
     2077    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2078    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2079    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2080       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     2081      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2082      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2083      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
     2084    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
     2085    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2086     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2087    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2088    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2089    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
     2090      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2091      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2092      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2093      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2094         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2095      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
     2096  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:sSubSup><m:sSubSupPr><span
     2097    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2098    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2099    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2100       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     2101      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2102      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2103      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
     2104    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
     2105    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2106     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2107    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2108    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2109    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     2110    normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e></m:d><i
     2111  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
     2112     m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     2113    "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     2114    mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
     2115      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2116      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2117      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
     2118        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2119        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2120        normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     2121        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
     2122      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
     2123        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2124        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2125        normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     2126        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
     2127      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
     2128     m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     2129    "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     2130    mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
     2131      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2132      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2133      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
     2134      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
     2135      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
     2136    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2137    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2138    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
     2139      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2140      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2141      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2142      normal'><span style='font-family:"Cambria Math",serif'><m:r>(-1)</m:r></span></i></m:e><m:sup><i
     2143      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
     2144      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2145      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2146      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2147      normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:e><m:sup><i
     2148      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
     2149    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
     2150    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2151    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2152    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2153    normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><span
     2154      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2155      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2156      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2157      normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i
     2158      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
     2159    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
     2160       m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     2161      "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     2162      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
     2163      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
     2164      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
     2165    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2166    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2167    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
     2168      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2169      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2170      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2171      normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
     2172      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
     2173      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2174      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2175      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2176      normal'><span style='font-family:"Cambria Math",serif'><m:r>dx</m:r></span></i></m:e><m:sup><i
     2177      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
     2178    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2179    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2180    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
     2181    normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><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:sSupPr><m:e><i style='mso-bidi-font-style:
     2185      normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i
     2186      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
     2187    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:e><m:sup><i
     2188    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
     2189style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2190"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     2191mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     2192 id="_x0000_i1025" type="#_x0000_t75" style='width:423.75pt;height:55.5pt'>
     2193 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.png"
     2194  o:title="" chromakey="white"/>
     2195</v:shape><![endif]--><![if !vml]><img width=565 height=74
     2196src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image034.png"
     2197v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    17522198
    17532199<p class=gsastext><span class=GramE>is</span> satisfied.<span
    1754 style='mso-spacerun:yes'>  </span>Terms of the form <span style='position:relative;
    1755 top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1028"
    1756  type="#_x0000_t75" style='width:92.25pt;height:20.25pt' o:ole="">
    1757  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image036.wmz"
    1758   o:title=""/>
    1759 </v:shape><![endif]--><![if !vml]><img width=123 height=27
    1760 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image037.png"
    1761 v:shapes="_x0000_i1028"><![endif]></span><!--[if gte mso 9]><xml>
    1762  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1028"
    1763   DrawAspect="Content" ObjectID="_1493040258">
    1764  </o:OLEObject>
    1765 </xml><![endif]--><span style='mso-spacerun:yes'> </span>and <span
    1766 style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
    1767  id="_x0000_i1029" type="#_x0000_t75" style='width:90pt;height:20.25pt' o:ole="">
    1768  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image038.wmz"
    1769   o:title=""/>
    1770 </v:shape><![endif]--><![if !vml]><img width=120 height=27
    1771 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
    1772 v:shapes="_x0000_i1029"><![endif]></span><!--[if gte mso 9]><xml>
    1773  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1029"
    1774   DrawAspect="Content" ObjectID="_1493040259">
    1775  </o:OLEObject>
    1776 </xml><![endif]-->are combined depending on the symmetry and the value of m
    1777 along with appropriate normalization coefficients to give the harmonic terms <span
    1778 style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
    1779  id="_x0000_i1030" type="#_x0000_t75" style='width:44.25pt;height:20.25pt'
    1780  o:ole="">
    1781  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.wmz"
    1782   o:title=""/>
    1783 </v:shape><![endif]--><![if !vml]><img width=59 height=27
    1784 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png"
    1785 v:shapes="_x0000_i1030"><![endif]></span><!--[if gte mso 9]><xml>
    1786  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1030"
    1787   DrawAspect="Content" ObjectID="_1493040260">
    1788  </o:OLEObject>
    1789 </xml><![endif]--><span class=GramE>and </span><span style='position:relative;
    1790 top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1031"
    1791  type="#_x0000_t75" style='width:44.25pt;height:20.25pt' o:ole="">
    1792  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image042.wmz"
    1793   o:title=""/>
    1794 </v:shape><![endif]--><![if !vml]><img width=59 height=27
    1795 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image043.png"
    1796 v:shapes="_x0000_i1031"><![endif]></span><!--[if gte mso 9]><xml>
    1797  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1031"
    1798   DrawAspect="Content" ObjectID="_1493040261">
    1799  </o:OLEObject>
    1800 </xml><![endif]-->.<span style='mso-spacerun:yes'>  </span>For cubic crystal
    1801 symmetry, the term <span style='position:relative;top:5.0pt;mso-text-raise:
    1802 -5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75"
    1803  style='width:44.25pt;height:20.25pt' o:ole="">
    1804  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image044.wmz"
    1805   o:title=""/>
    1806 </v:shape><![endif]--><![if !vml]><img width=59 height=27
    1807 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png"
    1808 v:shapes="_x0000_i1032"><![endif]></span><!--[if gte mso 9]><xml>
    1809  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1032"
    1810   DrawAspect="Content" ObjectID="_1493040262">
    1811  </o:OLEObject>
    1812 </xml><![endif]-->is obtained directly from the Fourier expansion</p>
    1813 
    1814 <p class=gsastext><span style='position:relative;top:16.0pt;mso-text-raise:
    1815 -16.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1033" type="#_x0000_t75"
    1816  style='width:167.25pt;height:38.25pt' o:ole="">
    1817  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image045.wmz"
    1818   o:title=""/>
    1819 </v:shape><![endif]--><![if !vml]><img width=223 height=51
     2200style='mso-spacerun:yes'>  </span>Terms of the form <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><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:funcPr><m:fName><span
     2204   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2205      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2206   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
     2207   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2208   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2209   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2210      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     2211     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     2212     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2213     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
     2214   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
     2215   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2216    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2217 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
     2218   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2219   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2220   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2221   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2222      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2223   normal'><span style='font-family:"Cambria Math",serif'><m:r>m&#946;</m:r></span></i></m:e></m:func><i
     2224 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
     2225style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2226"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2227top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2228EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2229 type="#_x0000_t75" style='width:111pt;height:26.25pt'>
     2230 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image035.png"
     2231  o:title="" chromakey="white"/>
     2232</v:shape><![endif]--><![if !vml]><img width=148 height=35
     2233src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image036.png"
     2234v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     2235style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
     2236   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2237   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2238   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2239   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2240      m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2241   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
     2242   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2243   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2244   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2245      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     2246     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     2247     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2248     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
     2249   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
     2250   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2251    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2252 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><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>&#966;</m:r></span></i></m:e></m:func><i
     2259 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
     2260style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2261"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2262top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2263EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2264 type="#_x0000_t75" style='width:100.5pt;height:26.25pt'>
     2265 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image037.png"
     2266  o:title="" chromakey="white"/>
     2267</v:shape><![endif]--><![if !vml]><img width=134 height=35
     2268src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image038.png"
     2269v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     2270style='mso-spacerun:yes'> </span>are combined depending on the symmetry and the
     2271value of m along with appropriate normalization coefficients to give the
     2272harmonic terms <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2273   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2274   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2275   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2276   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     2277   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
     2278   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2279    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2280 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
     2281style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2282"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2283top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2284EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2285 type="#_x0000_t75" style='width:48pt;height:26.25pt'>
     2286 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
     2287  o:title="" chromakey="white"/>
     2288</v:shape><![endif]--><![if !vml]><img width=64 height=35
     2289src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"
     2290v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     2291style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2292   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2293   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2294   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2295   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     2296   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
     2297   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2298    </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2299 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
     2300style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2301"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2302top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2303EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2304 type="#_x0000_t75" style='width:45pt;height:26.25pt'>
     2305 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png"
     2306  o:title="" chromakey="white"/>
     2307</v:shape><![endif]--><![if !vml]><img width=60 height=35
     2308src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image042.png"
     2309v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
     2310style='mso-spacerun:yes'>  </span>For cubic crystal symmetry, the term <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2311   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2312   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2313   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2314   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     2315   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
     2316   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2317    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2318 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
     2319style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2320"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2321top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2322EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2323 type="#_x0000_t75" style='width:48pt;height:26.25pt'>
     2324 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
     2325  o:title="" chromakey="white"/>
     2326</v:shape><![endif]--><![if !vml]><img width=64 height=35
     2327src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"
     2328v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     2329style='mso-spacerun:yes'> </span>is obtained directly from the Fourier
     2330expansion</p>
     2331
     2332<p class=gsastext><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2333   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
     2334    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2335    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2336    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2337    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     2338    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
     2339    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
     2340    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2341    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2342    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
     2343    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
     2344  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
     2345     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     2346    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2347    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     2348    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
     2349    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
     2350      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2351      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2352      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     2353      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
     2354      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
     2355      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
     2356    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2357    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2358    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
     2359       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
     2360      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2361      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
     2362      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
     2363    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
     2364    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
     2365     </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2366  normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
     2367    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2368    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2369    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2370    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2371       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2372    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
     2373  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i><m:func><m:funcPr><span
     2374    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2375    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2376    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
     2377    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
     2378       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
     2379    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
     2380style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2381"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     2382mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     2383 id="_x0000_i1025" type="#_x0000_t75" style='width:193.5pt;height:52.5pt'>
     2384 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image043.png"
     2385  o:title="" chromakey="white"/>
     2386</v:shape><![endif]--><![if !vml]><img width=258 height=70
     2387src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image044.png"
     2388v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
     2389
     2390<p class=gsastext><span class=GramE>using</span> the coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2391   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2392   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2393   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2394   normal'><span style='font-family:"Cambria Math",serif'><m:r>B</m:r></span></i></m:e><m:sub><i
     2395   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
     2396   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
     2397style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2398"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2399top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2400EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2401 type="#_x0000_t75" style='width:22.5pt;height:26.25pt'>
     2402 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image045.png"
     2403  o:title="" chromakey="white"/>
     2404</v:shape><![endif]--><![if !vml]><img width=30 height=35
    18202405src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image046.png"
    1821 v:shapes="_x0000_i1033"><![endif]></span><!--[if gte mso 9]><xml>
    1822  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1033"
    1823   DrawAspect="Content" ObjectID="_1493040263">
    1824  </o:OLEObject>
    1825 </xml><![endif]--></p>
    1826 
    1827 <p class=gsastext><span class=GramE>using</span> the coefficients, <span
    1828 style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
    1829  id="_x0000_i1034" type="#_x0000_t75" style='width:24pt;height:20.25pt' o:ole="">
    1830  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.wmz"
    1831   o:title=""/>
    1832 </v:shape><![endif]--><![if !vml]><img width=32 height=27
    1833 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
    1834 v:shapes="_x0000_i1034"><![endif]></span><!--[if gte mso 9]><xml>
    1835  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1034"
    1836   DrawAspect="Content" ObjectID="_1493040264">
    1837  </o:OLEObject>
    1838 </xml><![endif]-->, as tabulated by Bunge (1982). </p>
     2406v:shapes="_x0000_i1025"><![endif]></span><![endif]>, as tabulated by Bunge
     2407(1982). </p>
    18392408
    18402409<p class=gsastext>The Rietveld refinement of texture then proceeds by
    18412410constructing derivatives of the profile intensities with respect to the allowed
    1842 harmonic coefficients, <span style='position:relative;top:5.0pt;mso-text-raise:
    1843 -5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1035" type="#_x0000_t75"
    1844  style='width:24pt;height:20.25pt' o:ole="">
    1845  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.wmz"
    1846   o:title=""/>
    1847 </v:shape><![endif]--><![if !vml]><img width=32 height=27
    1848 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
    1849 v:shapes="_x0000_i1035"><![endif]></span><!--[if gte mso 9]><xml>
    1850  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1035"
    1851   DrawAspect="Content" ObjectID="_1493040265">
    1852  </o:OLEObject>
    1853 </xml><![endif]-->, and the three sample orientation angles, <span
     2411harmonic coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2412   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2413   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2414   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2415   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></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>mn</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
     2418style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2419"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2420top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2421EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2422 type="#_x0000_t75" style='width:21.75pt;height:26.25pt'>
     2423 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"
     2424  o:title="" chromakey="white"/>
     2425</v:shape><![endif]--><![if !vml]><img width=29 height=35
     2426src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
     2427v:shapes="_x0000_i1025"><![endif]></span><![endif]>, and the three sample
     2428orientation angles, <span style='font-family:Symbol'>W</span><sub>s</sub>, <span
     2429style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:Symbol'>F</span><sub>s</sub>,
     2430all of which can be adjustable parameters of the refinement. Once the
     2431refinement is complete, pole figures for any reflection may be constructed by
     2432use of the general axis equation, the refined values for <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2433   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2434   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2435   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     2436   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
     2437   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
     2438   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
     2439style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2440"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     2441top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2442EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     2443 type="#_x0000_t75" style='width:21.75pt;height:26.25pt'>
     2444 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"
     2445  o:title="" chromakey="white"/>
     2446</v:shape><![endif]--><![if !vml]><img width=29 height=35
     2447src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
     2448v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     2449style='mso-spacerun:yes'> </span>and the sample orientation angles <span
    18542450style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
    1855 <span style='font-family:Symbol'>F</span><sub>s</sub>, all of which can be
    1856 adjustable parameters of the refinement. Once the refinement is complete, pole
    1857 figures for any reflection may be constructed by use of the general axis
    1858 equation, the refined values for <span style='position:relative;top:5.0pt;
    1859 mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1036" type="#_x0000_t75"
    1860  style='width:24pt;height:20.25pt' o:ole="">
    1861  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.wmz"
    1862   o:title=""/>
    1863 </v:shape><![endif]--><![if !vml]><img width=32 height=27
    1864 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
    1865 v:shapes="_x0000_i1036"><![endif]></span><!--[if gte mso 9]><xml>
    1866  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1036"
    1867   DrawAspect="Content" ObjectID="_1493040266">
    1868  </o:OLEObject>
    1869 </xml><![endif]-->and the sample orientation angles <span style='font-family:
    1870 Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
    18712451<span class=GramE><span style='font-family:Symbol'>F</span></span><sub>s</sub>.
    18722452</p>
     
    18752455index by</p>
    18762456
    1877 <p class=gsastext><span style='position:relative;top:16.0pt;mso-text-raise:
    1878 -16.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1037" type="#_x0000_t75"
    1879  style='width:167.25pt;height:39pt' o:ole="">
    1880  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.wmz"
    1881   o:title=""/>
    1882 </v:shape><![endif]--><![if !vml]><img width=223 height=52
    1883 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
    1884 v:shapes="_x0000_i1037"><![endif]></span><!--[if gte mso 9]><xml>
    1885  <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1037"
    1886   DrawAspect="Content" ObjectID="_1493040267">
    1887  </o:OLEObject>
    1888 </xml><![endif]--></p>
     2457<p class=gsastext><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2458   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
     2459  style='font-family:"Cambria Math",serif'><m:r>J</m:r><m:r>=1+</m:r></span></i><m:nary><m:naryPr><m:chr
     2460     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     2461    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2462    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     2463    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
     2464      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2465      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2466      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
     2467      normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i
     2468      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
     2469      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2470      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2471      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
     2472      normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:num><m:den><i
     2473      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
     2474     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
     2475    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2476    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     2477    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
     2478    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
     2479       m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
     2480      "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
     2481      "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
     2482      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
     2483      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
     2484        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2485        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2486        normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><m:begChr
     2487           m:val="|"/><m:endChr m:val="|"/><span style='font-family:"Cambria Math",serif;
     2488          mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
     2489          font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:sSubSup><m:sSubSupPr><span
     2490            style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     2491            mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     2492            normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
     2493            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
     2494            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
     2495            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
     2496        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
     2497style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     2498"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     2499mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
     2500 id="_x0000_i1025" type="#_x0000_t75" style='width:180.75pt;height:54pt'>
     2501 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.png"
     2502  o:title="" chromakey="white"/>
     2503</v:shape><![endif]--><![if !vml]><img width=241 height=72
     2504src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
     2505v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    18892506
    18902507<p class=gsastext>If the texture is random then J = 1, otherwise J &gt; 1; for
     
    19202537<p class=MsoNormal>If you have not done so already, <u><span style='color:#0070C0'><a
    19212538href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none;
    1922 text-underline:none'>start GSAS-II</span></a></span></u>. Note that menu
    1923 entries are listed in <b style='mso-bidi-font-weight:normal'><span
    1924 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1925 mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
    1926 minor-latin'>bold face</span></b> below as <b style='mso-bidi-font-weight:normal'><span
     2539text-underline:none'>start GSAS-II</span></a></span></u>. Note that menu entries
     2540are listed in <b style='mso-bidi-font-weight:normal'><span style='font-family:
     2541"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     2542minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>bold
     2543face</span></b> below as <b style='mso-bidi-font-weight:normal'><span
    19272544style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    19282545mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
     
    19502567
    19512568<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1952  id="Picture_x0020_29" o:spid="_x0000_i1109" type="#_x0000_t75" style='width:525pt;
     2569 id="Picture_x0020_29" o:spid="_x0000_i1081" type="#_x0000_t75" style='width:525pt;
    19532570 height:450pt;visibility:visible;mso-wrap-style:square'>
    1954  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
     2571 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
    19552572  o:title=""/>
    19562573</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    1957 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
     2574src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
    19582575v:shapes="Picture_x0020_29"><![endif]></span></p>
    19592576
     
    19642581
    19652582<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1966  id="Picture_x0020_30" o:spid="_x0000_i1108" type="#_x0000_t75" style='width:472.5pt;
     2583 id="Picture_x0020_30" o:spid="_x0000_i1080" type="#_x0000_t75" style='width:472.5pt;
    19672584 height:388.5pt;visibility:visible;mso-wrap-style:square'>
    1968  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
     2585 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
    19692586  o:title=""/>
    19702587</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
    1971 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
     2588src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
    19722589v:shapes="Picture_x0020_30"><![endif]></span></p>
    19732590
     
    19922609
    19932610<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1994  id="Picture_x0020_31" o:spid="_x0000_i1107" type="#_x0000_t75" style='width:472.5pt;
     2611 id="Picture_x0020_31" o:spid="_x0000_i1079" type="#_x0000_t75" style='width:472.5pt;
    19952612 height:388.5pt;visibility:visible;mso-wrap-style:square'>
    1996  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
     2613 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
    19972614  o:title=""/>
    19982615</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
    1999 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
     2616src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
    20002617v:shapes="Picture_x0020_31"><![endif]></span></p>
    20012618
     
    20172634
    20182635<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2019  id="Picture_x0020_32" o:spid="_x0000_i1106" type="#_x0000_t75" style='width:525pt;
     2636 id="Picture_x0020_32" o:spid="_x0000_i1078" type="#_x0000_t75" style='width:525pt;
    20202637 height:450pt;visibility:visible;mso-wrap-style:square'>
    2021  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
     2638 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
    20222639  o:title=""/>
    20232640</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    2024 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
     2641src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
    20252642v:shapes="Picture_x0020_32"><![endif]></span></p>
    20262643
     
    20652682
    20662683<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2067  id="Picture_x0020_33" o:spid="_x0000_i1105" type="#_x0000_t75" style='width:525pt;
     2684 id="Picture_x0020_33" o:spid="_x0000_i1077" type="#_x0000_t75" style='width:525pt;
    20682685 height:450pt;visibility:visible;mso-wrap-style:square'>
    2069  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
     2686 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
    20702687  o:title=""/>
    20712688</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    2072 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
     2689src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
    20732690v:shapes="Picture_x0020_33"><![endif]></span></p>
    20742691
     
    20782695
    20792696<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2080  id="Picture_x0020_34" o:spid="_x0000_i1104" type="#_x0000_t75" style='width:472.5pt;
     2697 id="Picture_x0020_34" o:spid="_x0000_i1076" type="#_x0000_t75" style='width:472.5pt;
    20812698 height:388.5pt;visibility:visible;mso-wrap-style:square'>
    2082  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
     2699 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
    20832700  o:title=""/>
    20842701</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
    2085 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
     2702src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
    20862703v:shapes="Picture_x0020_34"><![endif]></span></p>
    20872704
     
    20942711
    20952712<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2096  id="Picture_x0020_35" o:spid="_x0000_i1103" type="#_x0000_t75" style='width:297.75pt;
     2713 id="Picture_x0020_35" o:spid="_x0000_i1075" type="#_x0000_t75" style='width:297.75pt;
    20972714 height:99.75pt;visibility:visible;mso-wrap-style:square'>
    2098  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
     2715 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
    20992716  o:title=""/>
    21002717</v:shape><![endif]--><![if !vml]><img border=0 width=397 height=133
    2101 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
     2718src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
    21022719v:shapes="Picture_x0020_35"><![endif]></span></p>
    21032720
     
    21132730
    21142731<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2115  id="Picture_x0020_36" o:spid="_x0000_i1102" type="#_x0000_t75" style='width:525pt;
     2732 id="Picture_x0020_36" o:spid="_x0000_i1074" type="#_x0000_t75" style='width:525pt;
    21162733 height:450pt;visibility:visible;mso-wrap-style:square'>
    2117  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
     2734 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
    21182735  o:title=""/>
    21192736</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    2120 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
     2737src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
    21212738v:shapes="Picture_x0020_36"><![endif]></span></p>
    21222739
     
    21362753
    21372754<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2138  id="Picture_x0020_37" o:spid="_x0000_i1101" type="#_x0000_t75" style='width:525pt;
     2755 id="Picture_x0020_37" o:spid="_x0000_i1073" type="#_x0000_t75" style='width:525pt;
    21392756 height:450pt;visibility:visible;mso-wrap-style:square'>
    2140  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
     2757 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
    21412758  o:title=""/>
    21422759</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    2143 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
     2760src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
    21442761v:shapes="Picture_x0020_37"><![endif]></span></p>
    21452762
     
    22132830
    22142831<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2215  id="Picture_x0020_38" o:spid="_x0000_i1100" type="#_x0000_t75" style='width:525pt;
     2832 id="Picture_x0020_38" o:spid="_x0000_i1072" type="#_x0000_t75" style='width:525pt;
    22162833 height:166.5pt;visibility:visible;mso-wrap-style:square'>
    2217  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
     2834 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
    22182835  o:title=""/>
    22192836</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=222
    2220 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
     2837src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
    22212838v:shapes="Picture_x0020_38"><![endif]></span></p>
    22222839
     
    22242841
    22252842<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2226  id="Picture_x0020_39" o:spid="_x0000_i1099" type="#_x0000_t75" style='width:525pt;
     2843 id="Picture_x0020_39" o:spid="_x0000_i1071" type="#_x0000_t75" style='width:525pt;
    22272844 height:163.5pt;visibility:visible;mso-wrap-style:square'>
    2228  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
     2845 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
    22292846  o:title=""/>
    22302847</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=218
    2231 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
     2848src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
    22322849v:shapes="Picture_x0020_39"><![endif]></span></p>
    22332850
    22342851<p class=MsoNormal>Next go to the <b style='mso-bidi-font-weight:normal'><span
    22352852style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2236 mso-hansi-theme-font:minor-latin'>Data</span></b> tab for each phase; there
    2237 will be a message indicating the lack of data for each. Do <b style='mso-bidi-font-weight:
     2853mso-hansi-theme-font:minor-latin'>Data</span></b> tab for each phase; there will
     2854be a message indicating the lack of data for each. Do <b style='mso-bidi-font-weight:
    22382855normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    22392856minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add powder histograms</span></b>,
     
    22462863
    22472864<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2248  id="Picture_x0020_40" o:spid="_x0000_i1098" type="#_x0000_t75" style='width:342.75pt;
     2865 id="Picture_x0020_40" o:spid="_x0000_i1070" type="#_x0000_t75" style='width:342.75pt;
    22492866 height:375pt;visibility:visible;mso-wrap-style:square'>
    2250  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
     2867 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
    22512868  o:title=""/>
    22522869</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
    2253 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
     2870src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
    22542871v:shapes="Picture_x0020_40"><![endif]></span></p>
    22552872
     
    22572874
    22582875<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2259  id="Picture_x0020_41" o:spid="_x0000_i1097" type="#_x0000_t75" style='width:370.5pt;
     2876 id="Picture_x0020_41" o:spid="_x0000_i1069" type="#_x0000_t75" style='width:370.5pt;
    22602877 height:375pt;visibility:visible;mso-wrap-style:square'>
    2261  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
     2878 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
    22622879  o:title=""/>
    22632880</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
    2264 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
     2881src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
    22652882v:shapes="Picture_x0020_41"><![endif]></span></p>
    22662883
     
    22842901<h3>Introduction</h3>
    22852902
    2286 <p class=MsoNormal>In this method we will do a full Rietveld refinement of the texture,
    2287 profile parameters, peak position variables and crystal structure parameters.
    2288 This is suitable in this case because of the relatively small number of
    2289 histograms (10 in this case) needed for the texture determination; do recall
    2290 that each phase in each histogram has a set of parameters (e.g. phase fraction,
    2291 size, <span class=SpellE>mustrain</span> &amp; hydrostatic strain) in addition
    2292 to the ones for each histogram (e.g. background &amp; scale factor).
     2903<p class=MsoNormal>In this method we will do a full Rietveld refinement of the
     2904texture, profile parameters, peak position variables and crystal structure
     2905parameters. This is suitable in this case because of the relatively small
     2906number of histograms (10 in this case) needed for the texture determination; do
     2907recall that each phase in each histogram has a set of parameters (e.g. phase
     2908fraction, size, <span class=SpellE>mustrain</span> &amp; hydrostatic strain) in
     2909addition to the ones for each histogram (e.g. background &amp; scale factor).
    22932910Consequently the total number of parameters can build up very quickly in this
    22942911method of analysis. The other two methods seek to reduce this problem by
     
    23272944
    23282945<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2329  id="Picture_x0020_42" o:spid="_x0000_i1096" type="#_x0000_t75" style='width:342.75pt;
     2946 id="Picture_x0020_42" o:spid="_x0000_i1068" type="#_x0000_t75" style='width:342.75pt;
    23302947 height:375pt;visibility:visible;mso-wrap-style:square'>
    2331  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
     2948 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
    23322949  o:title=""/>
    23332950</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
    2334 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
     2951src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
    23352952v:shapes="Picture_x0020_42"><![endif]></span></p>
    23362953
     
    23612978
    23622979<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2363  id="Picture_x0020_43" o:spid="_x0000_i1095" type="#_x0000_t75" style='width:525pt;
     2980 id="Picture_x0020_43" o:spid="_x0000_i1067" type="#_x0000_t75" style='width:525pt;
    23642981 height:450pt;visibility:visible;mso-wrap-style:square'>
    2365  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
     2982 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
    23662983  o:title=""/>
    23672984</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    2368 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
     2985src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
    23692986v:shapes="Picture_x0020_43"><![endif]></span></p>
    23702987
     
    23833000
    23843001<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2385  id="Picture_x0020_44" o:spid="_x0000_i1094" type="#_x0000_t75" style='width:456pt;
     3002 id="Picture_x0020_44" o:spid="_x0000_i1066" type="#_x0000_t75" style='width:456pt;
    23863003 height:217.5pt;visibility:visible;mso-wrap-style:square'>
    2387  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
     3004 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
    23883005  o:title=""/>
    23893006</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290
    2390 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
     3007src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
    23913008v:shapes="Picture_x0020_44"><![endif]></span></p>
    23923009
     
    24073024
    24083025<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2409  id="Picture_x0020_45" o:spid="_x0000_i1093" type="#_x0000_t75" style='width:456pt;
     3026 id="Picture_x0020_45" o:spid="_x0000_i1065" type="#_x0000_t75" style='width:456pt;
    24103027 height:250.5pt;visibility:visible;mso-wrap-style:square'>
    2411  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
     3028 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
    24123029  o:title=""/>
    24133030</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
    2414 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
     3031src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
    24153032v:shapes="Picture_x0020_45"><![endif]></span></p>
    24163033
     
    24253042
    24263043<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2427  id="Picture_x0020_46" o:spid="_x0000_i1092" type="#_x0000_t75" style='width:342.75pt;
     3044 id="Picture_x0020_46" o:spid="_x0000_i1064" type="#_x0000_t75" style='width:342.75pt;
    24283045 height:375pt;visibility:visible;mso-wrap-style:square'>
    2429  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
     3046 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
    24303047  o:title=""/>
    24313048</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
    2432 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
     3049src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
    24333050v:shapes="Picture_x0020_46"><![endif]></span></p>
    24343051
     
    24523069
    24533070<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2454  id="Picture_x0020_47" o:spid="_x0000_i1091" type="#_x0000_t75" style='width:478.5pt;
     3071 id="Picture_x0020_47" o:spid="_x0000_i1063" type="#_x0000_t75" style='width:478.5pt;
    24553072 height:302.25pt;visibility:visible;mso-wrap-style:square'>
    2456  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
     3073 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
    24573074  o:title=""/>
    24583075</v:shape><![endif]--><![if !vml]><img border=0 width=638 height=403
    2459 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
     3076src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
    24603077v:shapes="Picture_x0020_47"><![endif]></span></p>
    24613078
     
    24733090
    24743091<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2475  id="Picture_x0020_48" o:spid="_x0000_i1090" type="#_x0000_t75" style='width:370.5pt;
     3092 id="Picture_x0020_48" o:spid="_x0000_i1062" type="#_x0000_t75" style='width:370.5pt;
    24763093 height:375pt;visibility:visible;mso-wrap-style:square'>
    2477  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
     3094 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
    24783095  o:title=""/>
    24793096</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
    2480 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
     3097src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
    24813098v:shapes="Picture_x0020_48"><![endif]></span></p>
    24823099
     
    24883105
    24893106<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2490  id="Picture_x0020_49" o:spid="_x0000_i1089" type="#_x0000_t75" style='width:525pt;
     3107 id="Picture_x0020_49" o:spid="_x0000_i1061" type="#_x0000_t75" style='width:525pt;
    24913108 height:413.25pt;visibility:visible;mso-wrap-style:square'>
    2492  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
     3109 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
    24933110  o:title=""/>
    24943111</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
    2495 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
     3112src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
    24963113v:shapes="Picture_x0020_49"><![endif]></span></p>
    24973114
     
    25213138
    25223139<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2523  id="Picture_x0020_50" o:spid="_x0000_i1088" type="#_x0000_t75" style='width:525pt;
     3140 id="Picture_x0020_50" o:spid="_x0000_i1060" type="#_x0000_t75" style='width:525pt;
    25243141 height:413.25pt;visibility:visible;mso-wrap-style:square'>
    2525  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
     3142 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
    25263143  o:title=""/>
    25273144</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
    2528 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
     3145src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
    25293146v:shapes="Picture_x0020_50"><![endif]></span></p>
    25303147
     
    25353152
    25363153<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2537  id="Picture_x0020_18" o:spid="_x0000_i1087" type="#_x0000_t75" style='width:456pt;
     3154 id="Picture_x0020_18" o:spid="_x0000_i1059" type="#_x0000_t75" style='width:456pt;
    25383155 height:250.5pt;visibility:visible;mso-wrap-style:square'>
    2539  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
     3156 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
    25403157  o:title=""/>
    25413158</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
    2542 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
     3159src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
    25433160v:shapes="Picture_x0020_18"><![endif]></span></p>
    25443161
     
    25493166
    25503167<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2551  id="Picture_x0020_52" o:spid="_x0000_i1086" type="#_x0000_t75" style='width:525pt;
     3168 id="Picture_x0020_52" o:spid="_x0000_i1058" type="#_x0000_t75" style='width:525pt;
    25523169 height:413.25pt;visibility:visible;mso-wrap-style:square'>
    2553  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
     3170 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
    25543171  o:title=""/>
    25553172</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
    2556 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
     3173src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
    25573174v:shapes="Picture_x0020_52"><![endif]></span></p>
    25583175
     
    25663183
    25673184<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2568  id="Picture_x0020_53" o:spid="_x0000_i1085" type="#_x0000_t75" style='width:525pt;
     3185 id="Picture_x0020_53" o:spid="_x0000_i1057" type="#_x0000_t75" style='width:525pt;
    25693186 height:413.25pt;visibility:visible;mso-wrap-style:square'>
    2570  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
     3187 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
    25713188  o:title=""/>
    25723189</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
    2573 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
     3190src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
    25743191v:shapes="Picture_x0020_53"><![endif]></span></p>
    25753192
     
    25903207
    25913208<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2592  id="Picture_x0020_54" o:spid="_x0000_i1084" type="#_x0000_t75" style='width:502.5pt;
     3209 id="Picture_x0020_54" o:spid="_x0000_i1056" type="#_x0000_t75" style='width:502.5pt;
    25933210 height:375pt;visibility:visible;mso-wrap-style:square'>
     3211 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
     3212  o:title=""/>
     3213</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
     3214src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
     3215v:shapes="Picture_x0020_54"><![endif]></span></p>
     3216
     3217<p class=MsoNormal><span class=GramE>and</span> inverse pole figure</p>
     3218
     3219<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     3220 id="Picture_x0020_55" o:spid="_x0000_i1055" type="#_x0000_t75" style='width:525pt;
     3221 height:413.25pt;visibility:visible;mso-wrap-style:square'>
     3222 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
     3223  o:title=""/>
     3224</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
     3225src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
     3226v:shapes="Picture_x0020_55"><![endif]></span></p>
     3227
     3228<p class=MsoNormal>The B2 coefficients</p>
     3229
     3230<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     3231 id="Picture_x0020_56" o:spid="_x0000_i1054" type="#_x0000_t75" style='width:480pt;
     3232 height:267.75pt;visibility:visible;mso-wrap-style:square'>
    25943233 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
    25953234  o:title=""/>
    2596 </v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
     3235</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
    25973236src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
    2598 v:shapes="Picture_x0020_54"><![endif]></span></p>
     3237v:shapes="Picture_x0020_56"><![endif]></span></p>
    25993238
    26003239<p class=MsoNormal><span class=GramE>and</span> inverse pole figure</p>
    26013240
    26023241<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2603  id="Picture_x0020_55" o:spid="_x0000_i1083" type="#_x0000_t75" style='width:525pt;
     3242 id="Picture_x0020_57" o:spid="_x0000_i1053" type="#_x0000_t75" style='width:525pt;
    26043243 height:413.25pt;visibility:visible;mso-wrap-style:square'>
    26053244 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
     
    26073246</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
    26083247src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
    2609 v:shapes="Picture_x0020_55"><![endif]></span></p>
    2610 
    2611 <p class=MsoNormal>The B2 coefficients</p>
    2612 
    2613 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2614  id="Picture_x0020_56" o:spid="_x0000_i1082" type="#_x0000_t75" style='width:480pt;
    2615  height:267.75pt;visibility:visible;mso-wrap-style:square'>
    2616  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
    2617   o:title=""/>
    2618 </v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
    2619 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
    2620 v:shapes="Picture_x0020_56"><![endif]></span></p>
    2621 
    2622 <p class=MsoNormal><span class=GramE>and</span> inverse pole figure</p>
    2623 
    2624 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2625  id="Picture_x0020_57" o:spid="_x0000_i1081" type="#_x0000_t75" style='width:525pt;
    2626  height:413.25pt;visibility:visible;mso-wrap-style:square'>
    2627  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
    2628   o:title=""/>
    2629 </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
    2630 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
    26313248v:shapes="Picture_x0020_57"><![endif]></span></p>
    26323249
     
    27353352
    27363353<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2737  id="Picture_x0020_1" o:spid="_x0000_i1080" type="#_x0000_t75" style='width:330.75pt;
     3354 id="Picture_x0020_1" o:spid="_x0000_i1052" type="#_x0000_t75" style='width:330.75pt;
    27383355 height:153.75pt;visibility:visible;mso-wrap-style:square'>
    2739  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
     3356 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
    27403357  o:title=""/>
    27413358</v:shape><![endif]--><![if !vml]><img border=0 width=441 height=205
    2742 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
     3359src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
    27433360v:shapes="Picture_x0020_1"><![endif]></span></p>
    27443361
     
    27593376
    27603377<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2761  id="Picture_x0020_2" o:spid="_x0000_i1079" type="#_x0000_t75" style='width:330.75pt;
     3378 id="Picture_x0020_2" o:spid="_x0000_i1051" type="#_x0000_t75" style='width:330.75pt;
    27623379 height:163.5pt;visibility:visible;mso-wrap-style:square'>
    2763  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
     3380 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
    27643381  o:title=""/>
    27653382</v:shape><![endif]--><![if !vml]><img border=0 width=441 height=218
    2766 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
     3383src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
    27673384v:shapes="Picture_x0020_2"><![endif]></span></p>
    27683385
    27693386<p class=MsoNormal>You have the choice of starting at the last one and for
    2770 copying results from one to the next. We won’t do either here. Each refinement will
    2771 use the other controls (e.g. <b style='mso-bidi-font-weight:normal'><span
     3387copying results from one to the next. We won’t do either here. Each refinement
     3388will use the other controls (e.g. <b style='mso-bidi-font-weight:normal'><span
    27723389style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    27733390mso-hansi-theme-font:minor-latin'>Max cycles</span></b>) as controls. We are
     
    27883405
    27893406<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2790  id="Picture_x0020_3" o:spid="_x0000_i1078" type="#_x0000_t75" style='width:525pt;
     3407 id="Picture_x0020_3" o:spid="_x0000_i1050" type="#_x0000_t75" style='width:525pt;
    27913408 height:262.5pt;visibility:visible;mso-wrap-style:square'>
    2792  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
     3409 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
    27933410  o:title=""/>
    27943411</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
    2795 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
     3412src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
    27963413v:shapes="Picture_x0020_3"><![endif]></span></p>
    27973414
     
    28083425
    28093426<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    2810  id="Picture_x0020_4" o:spid="_x0000_i1077" type="#_x0000_t75" style='width:525pt;
     3427 id="Picture_x0020_4" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:525pt;
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    28143431</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    2815 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
     3432src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
    28163433v:shapes="Picture_x0020_4"><![endif]></span></p>
    28173434
     
    28203437
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    28233440 height:375pt;visibility:visible;mso-wrap-style:square'>
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    28253442  o:title=""/>
    28263443</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=500
    2827 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
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    28343451
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    28373454 height:232.5pt;visibility:visible;mso-wrap-style:square'>
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    28403457</v:shape><![endif]--><![if !vml]><img border=0 width=320 height=310
    2841 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
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    28433460
     
    28533470
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    28563473 height:467.25pt;visibility:visible;mso-wrap-style:square'>
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    28593476</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=623
    2860 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png"
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    28623479
     
    28673484
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    28703487 height:262.5pt;visibility:visible;mso-wrap-style:square'>
    2871  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
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    28723489  o:title=""/>
    28733490</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
    2874 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
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    28793496
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    28823499 height:450pt;visibility:visible;mso-wrap-style:square'>
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    28853502</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    2886 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png"
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    28953512
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    2899  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
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    29013518</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
    2902 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
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    29043521
     
    29073524
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    2911  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
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    29133530</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
    2914 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
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    29153532v:shapes="Picture_x0020_11"><![endif]></span></p>
    29163533
     
    29193536
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    29223539 height:450pt;visibility:visible;mso-wrap-style:square'>
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    29253542</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    2926 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
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    29283545
     
    29343551
    29353552<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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    29373554 height:262.5pt;visibility:visible;mso-wrap-style:square'>
    2938  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png"
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    29393556  o:title=""/>
    29403557</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
    2941 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png"
     3558src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
    29423559v:shapes="Picture_x0020_13"><![endif]></span></p>
    29433560
     
    29493566<p class=MsoNormal>During the sequential refinements done in Step 1, we fitted
    29503567the profiles allowing strain parameters (<span class=SpellE>Dij</span>) for
    2951 peak position shifts and <span class=SpellE>microstrain</span> for peak shape. We
    2952 modeled the intensity variation with a spherical harmonics preferred
     3568peak position shifts and <span class=SpellE>microstrain</span> for peak shape.
     3569We modeled the intensity variation with a spherical harmonics preferred
    29533570orientation correction. If you select any PWDR entry from the GSAS-II data tree
    29543571and pick the Reflection List subentry (at the bottom) you can see the magnitude
     
    29583575
    29593576<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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    29613578 height:262.5pt;visibility:visible;mso-wrap-style:square'>
    2962  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
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    29633580  o:title=""/>
    29643581</v:shape><![endif]--><![if !vml]><img border=0 width=879 height=350
    2965 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
     3582src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
    29663583v:shapes="Picture_x0020_14"><![endif]></span></p>
    29673584
     
    29693586
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    29723589 height:273pt;visibility:visible;mso-wrap-style:square'>
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    29743591  o:title=""/>
    29753592</v:shape><![endif]--><![if !vml]><img border=0 width=879 height=364
    2976 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png"
     3593src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png"
    29773594v:shapes="Picture_x0020_15"><![endif]></span></p>
    29783595
     
    29843601
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    29873604 height:217.5pt;visibility:visible;mso-wrap-style:square'>
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    29893606  o:title=""/>
    29903607</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290
    2991 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
     3608src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
    29923609v:shapes="Picture_x0020_16"><![endif]></span></p>
    29933610
     
    29983615
    29993616<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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    30013618 height:250.5pt;visibility:visible;mso-wrap-style:square'>
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    30033620  o:title=""/>
    30043621</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
    3005 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
     3622src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
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    30073624
     
    30103627
    30113628<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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    30133630 height:267.75pt;visibility:visible;mso-wrap-style:square'>
    3014  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
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    3017 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
     3634src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
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    30193636
     
    30223639
    30233640<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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    30253642 height:450pt;visibility:visible;mso-wrap-style:square'>
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    30283645</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    3029 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
     3646src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png"
    30303647v:shapes="Picture_x0020_19"><![endif]></span></p>
    30313648
     
    30383655
    30393656<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    3040  id="Picture_x0020_21" o:spid="_x0000_i1061" type="#_x0000_t75" style='width:502.5pt;
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    30413658 height:375pt;visibility:visible;mso-wrap-style:square'>
    3042  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
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    30443661</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
    3045 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
     3662src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
    30463663v:shapes="Picture_x0020_21"><![endif]></span></p>
    30473664
     
    30503667
    30513668<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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    30533670 height:450pt;visibility:visible;mso-wrap-style:square'>
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    30563673</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    3057 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
     3674src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
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    30593676
     
    31963813
    31973814<p class=MsoNormal style='margin-left:.25in'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    3198  id="Picture_x0020_23" o:spid="_x0000_i1059" type="#_x0000_t75" style='width:480pt;
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    31993816 height:267.75pt;visibility:visible;mso-wrap-style:square'>
    3200  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
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    32013818  o:title=""/>
    32023819</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
    3203 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
     3820src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
    32043821v:shapes="Picture_x0020_23"><![endif]></span></p>
    32053822
     
    32173834
    32183835<p class=MsoNormal style='margin-left:.25in'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    3219  id="Picture_x0020_24" o:spid="_x0000_i1058" type="#_x0000_t75" style='width:480pt;
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    32203837 height:267.75pt;visibility:visible;mso-wrap-style:square'>
    3221  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
     3838 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
    32223839  o:title=""/>
    32233840</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
    3224 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
     3841src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
    32253842v:shapes="Picture_x0020_24"><![endif]></span></p>
    32263843
     
    32523869
    32533870<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    3254  id="Picture_x0020_25" o:spid="_x0000_i1057" type="#_x0000_t75" style='width:363pt;
     3871 id="Picture_x0020_25" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:363pt;
    32553872 height:120.75pt;visibility:visible;mso-wrap-style:square'>
    3256  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
     3873 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
    32573874  o:title=""/>
    32583875</v:shape><![endif]--><![if !vml]><img border=0 width=484 height=161
    3259 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
     3876src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
    32603877v:shapes="Picture_x0020_25"><![endif]></span></p>
    32613878
     
    32783895
    32793896<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    3280  id="Picture_x0020_26" o:spid="_x0000_i1056" type="#_x0000_t75" style='width:525pt;
     3897 id="Picture_x0020_26" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:525pt;
     3898 height:450pt;visibility:visible;mso-wrap-style:square'>
     3899 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
     3900  o:title=""/>
     3901</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
     3902src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
     3903v:shapes="Picture_x0020_26"><![endif]></span></p>
     3904
     3905<p class=MsoNormal><span class=GramE>which</span> is almost identical to that
     3906from Method A. The coefficients are seen in</p>
     3907
     3908<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     3909 id="Picture_x0020_27" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:480pt;
     3910 height:267.75pt;visibility:visible;mso-wrap-style:square'>
     3911 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
     3912  o:title=""/>
     3913</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
     3914src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
     3915v:shapes="Picture_x0020_27"><![endif]></span></p>
     3916
     3917<p class=MsoNormal>Now select the <b style='mso-bidi-font-weight:normal'><span
     3918style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3919mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and its <b
     3920style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3921mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
     3922tab; the inverse pole figure is</p>
     3923
     3924<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     3925 id="Picture_x0020_28" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:525pt;
    32813926 height:450pt;visibility:visible;mso-wrap-style:square'>
    32823927 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png"
     
    32843929</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    32853930src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png"
    3286 v:shapes="Picture_x0020_26"><![endif]></span></p>
    3287 
    3288 <p class=MsoNormal><span class=GramE>which</span> is almost identical to that
    3289 from Method A. The coefficients are seen in</p>
    3290 
    3291 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    3292  id="Picture_x0020_27" o:spid="_x0000_i1055" type="#_x0000_t75" style='width:480pt;
    3293  height:267.75pt;visibility:visible;mso-wrap-style:square'>
    3294  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
    3295   o:title=""/>
    3296 </v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
    3297 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
    3298 v:shapes="Picture_x0020_27"><![endif]></span></p>
    3299 
    3300 <p class=MsoNormal>Now select the <b style='mso-bidi-font-weight:normal'><span
    3301 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3302 mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and its <b
    3303 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3304 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
    3305 tab; the inverse pole figure is</p>
    3306 
    3307 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    3308  id="Picture_x0020_28" o:spid="_x0000_i1054" type="#_x0000_t75" style='width:525pt;
    3309  height:450pt;visibility:visible;mso-wrap-style:square'>
    3310  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image105.png"
    3311   o:title=""/>
    3312 </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
    3313 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image105.png"
    33143931v:shapes="Picture_x0020_28"><![endif]></span></p>
    33153932
     
    33183935
    33193936<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    3320  id="Picture_x0020_58" o:spid="_x0000_i1053" type="#_x0000_t75" style='width:502.5pt;
     3937 id="Picture_x0020_58" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:502.5pt;
    33213938 height:375pt;visibility:visible;mso-wrap-style:square'>
    3322  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"
     3939 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
    33233940  o:title=""/>
    33243941</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
    3325 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"
     3942src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
    33263943v:shapes="Picture_x0020_58"><![endif]></span></p>
    33273944
  • Tutorials/2DTexture/Texture analysis of 2D data in GSAS-II_files/filelist.xml

    r1848 r1853  
    33 <o:File HRef="themedata.thmx"/>
    44 <o:File HRef="colorschememapping.xml"/>
    5  <o:File HRef="image001.wmz"/>
     5 <o:File HRef="plchdr.htm"/>
     6 <o:File HRef="image001.png"/>
    67 <o:File HRef="image002.png"/>
    7  <o:File HRef="oledata.mso"/>
    8  <o:File HRef="image003.wmz"/>
     8 <o:File HRef="image003.png"/>
    99 <o:File HRef="image004.png"/>
    10  <o:File HRef="image005.wmz"/>
     10 <o:File HRef="image005.png"/>
    1111 <o:File HRef="image006.png"/>
    12  <o:File HRef="image007.wmz"/>
     12 <o:File HRef="image007.png"/>
    1313 <o:File HRef="image008.png"/>
    14  <o:File HRef="image009.wmz"/>
     14 <o:File HRef="image009.png"/>
    1515 <o:File HRef="image010.png"/>
    16  <o:File HRef="image011.wmz"/>
    17  <o:File HRef="image012.wmz"/>
     16 <o:File HRef="image011.png"/>
     17 <o:File HRef="image012.png"/>
    1818 <o:File HRef="image013.png"/>
    19  <o:File HRef="image014.wmz"/>
     19 <o:File HRef="image014.png"/>
    2020 <o:File HRef="image015.png"/>
    21  <o:File HRef="image016.wmz"/>
     21 <o:File HRef="image016.png"/>
    2222 <o:File HRef="image017.png"/>
    23  <o:File HRef="image018.wmz"/>
     23 <o:File HRef="image018.png"/>
    2424 <o:File HRef="image019.png"/>
    25  <o:File HRef="image020.wmz"/>
     25 <o:File HRef="image020.png"/>
    2626 <o:File HRef="image021.png"/>
    27  <o:File HRef="image022.wmz"/>
     27 <o:File HRef="image022.png"/>
    2828 <o:File HRef="image023.png"/>
    29  <o:File HRef="image024.wmz"/>
     29 <o:File HRef="image024.png"/>
    3030 <o:File HRef="image025.png"/>
    31  <o:File HRef="image026.wmz"/>
     31 <o:File HRef="image026.png"/>
    3232 <o:File HRef="image027.png"/>
    33  <o:File HRef="image028.wmz"/>
     33 <o:File HRef="image028.png"/>
    3434 <o:File HRef="image029.png"/>
    35  <o:File HRef="image030.wmz"/>
     35 <o:File HRef="image030.png"/>
    3636 <o:File HRef="image031.png"/>
    37  <o:File HRef="image032.wmz"/>
     37 <o:File HRef="image032.png"/>
    3838 <o:File HRef="image033.png"/>
    39  <o:File HRef="image034.wmz"/>
     39 <o:File HRef="image034.png"/>
    4040 <o:File HRef="image035.png"/>
    41  <o:File HRef="image036.wmz"/>
     41 <o:File HRef="image036.png"/>
    4242 <o:File HRef="image037.png"/>
    43  <o:File HRef="image038.wmz"/>
     43 <o:File HRef="image038.png"/>
    4444 <o:File HRef="image039.png"/>
    45  <o:File HRef="image040.wmz"/>
     45 <o:File HRef="image040.png"/>
    4646 <o:File HRef="image041.png"/>
    47  <o:File HRef="image042.wmz"/>
     47 <o:File HRef="image042.png"/>
    4848 <o:File HRef="image043.png"/>
    49  <o:File HRef="image044.wmz"/>
    50  <o:File HRef="image045.wmz"/>
     49 <o:File HRef="image044.png"/>
     50 <o:File HRef="image045.png"/>
    5151 <o:File HRef="image046.png"/>
    52  <o:File HRef="image047.wmz"/>
     52 <o:File HRef="image047.png"/>
    5353 <o:File HRef="image048.png"/>
    54  <o:File HRef="image049.wmz"/>
     54 <o:File HRef="image049.png"/>
    5555 <o:File HRef="image050.png"/>
    56  <o:File HRef="image051.wmz"/>
     56 <o:File HRef="image051.png"/>
    5757 <o:File HRef="image052.png"/>
    5858 <o:File HRef="image053.png"/>
     
    108108 <o:File HRef="image103.png"/>
    109109 <o:File HRef="image104.png"/>
    110  <o:File HRef="image105.png"/>
    111  <o:File HRef="image106.png"/>
    112110 <o:File HRef="filelist.xml"/>
    113111</xml>
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