Changeset 2385 for Tutorials


Ignore:
Timestamp:
Jul 28, 2016 2:16:36 PM (5 years ago)
Author:
vondreele
Message:
 
File:
1 edited

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

    r1870 r2385  
    2525  <o:Author>Von Dreele</o:Author>
    2626  <o:LastAuthor>Von Dreele</o:LastAuthor>
    27   <o:Revision>9</o:Revision>
    28   <o:TotalTime>2142</o:TotalTime>
     27  <o:Revision>10</o:Revision>
     28  <o:TotalTime>2143</o:TotalTime>
    2929  <o:Created>2015-05-14T17:06:00Z</o:Created>
    30   <o:LastSaved>2015-05-14T17:39:00Z</o:LastSaved>
    31   <o:Pages>1</o:Pages>
    32   <o:Words>4340</o:Words>
    33   <o:Characters>24741</o:Characters>
     30  <o:LastSaved>2016-07-28T18:35:00Z</o:LastSaved>
     31  <o:Pages>54</o:Pages>
     32  <o:Words>4339</o:Words>
     33  <o:Characters>24736</o:Characters>
    3434  <o:Company>Argonne National Laboratory</o:Company>
    3535  <o:Lines>206</o:Lines>
    3636  <o:Paragraphs>58</o:Paragraphs>
    37   <o:CharactersWithSpaces>29023</o:CharactersWithSpaces>
    38   <o:Version>15.00</o:Version>
     37  <o:CharactersWithSpaces>29017</o:CharactersWithSpaces>
     38  <o:Version>16.00</o:Version>
    3939 </o:DocumentProperties>
    4040 <o:OfficeDocumentSettings>
     
    4848<!--[if gte mso 9]><xml>
    4949 <w:WordDocument>
    50   <w:Zoom>108</w:Zoom>
     50  <w:View>Print</w:View>
    5151  <w:SpellingState>Clean</w:SpellingState>
    5252  <w:GrammarState>Clean</w:GrammarState>
     
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    15131527
    15141528<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    1515 margin-left:0in;line-height:115%'><span class=GramE>is</span> used to give the
    1516 intensity corrections due to texture. The two harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1529margin-left:0in;line-height:115%'>is used to give the intensity corrections due
     1530to texture. The two harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    15171531   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    15181532   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    15351549src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"
    15361550v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    1537 style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1551style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    15381552   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    15391553   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    15791593v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    15801594style='mso-spacerun:yes'> </span>terms are nonzero so the rest are excluded
    1581 from the <span class=GramE>summations</span> and the set of <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1595from the summations and the set of <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    15821596   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    15831597   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    17101724"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
    17111725mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    1712  id="_x0000_i1025" type="#_x0000_t75" style='width:321pt;height:54pt'>
     1726 id="_x0000_i1025" type="#_x0000_t75" style='width:320.95pt;height:54pt'>
    17131727 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image013.png"
    17141728  o:title="" chromakey="white"/>
     
    17621776margin-left:0in;line-height:115%'><b style='mso-bidi-font-weight:normal'>M = -</b><b
    17631777style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>Q</span>A</b><b
    1764 style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>W<span
    1765 class=GramE>C<span style='font-family:"Times New Roman",serif'>(</span></span>F</span>+</b><b
     1778style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>WC</span>(</b><b
     1779style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span>+</b><b
    17661780style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span><sub>s</sub>)</b><b
    17671781style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>C</span><span
     
    17701784<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    17711785margin-left:0in;line-height:115%'>By transformation of unit Cartesian vectors
    1772 (100, 010 and 001) with this rotation matrix, the sample orientation
    1773 coordinates (<span style='font-family:Symbol'>y</span>, <span style='font-family:
    1774 Symbol'>g</span>) are given by</p>
     1786(100, 010 and 001) with this rotation matrix, the sample orientation coordinates
     1787(<span style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
     1788are given by</p>
    17751789
    17761790<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    1777 margin-left:0in;line-height:115%'><span class=GramE><i>cos</i>(</span><span
    1778 style='font-family:Symbol'>y</span>) = <!--[if gte msEquation 12]><m:oMath><i
    1779  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
     1791margin-left:0in;line-height:115%'><i>cos</i>(<span style='font-family:Symbol'>y</span>)
     1792= <!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span
     1793 style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
    17801794   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    17811795   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    18551869src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"
    18561870v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    1857 style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1871style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    18581872   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    18591873   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    19301944
    19311945<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    1932 margin-left:0in;line-height:115%'><span class=GramE>where</span> the normalized
    1933 associated Legendre functions, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1946margin-left:0in;line-height:115%'>where the normalized associated Legendre
     1947functions, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    19341948   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    19351949   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    20062020
    20072021<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    2008 margin-left:0in;line-height:115%'><span class=GramE>for</span> m even and</p>
     2022margin-left:0in;line-height:115%'>for m even and</p>
    20092023
    20102024<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     
    20602074
    20612075<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    2062 margin-left:0in;line-height:115%'><span class=GramE>for</span> m odd.<span
    2063 style='mso-spacerun:yes'>  </span>Each sum is only over either the even or odd
    2064 values of s, respectively, because of the properties of the Fourier
    2065 coefficients<span class=GramE>, </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2076margin-left:0in;line-height:115%'>for m odd.<span style='mso-spacerun:yes'> 
     2077</span>Each sum is only over either the even or odd values of s, respectively,
     2078because of the properties of the Fourier coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    20662079   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    20672080   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    22022215"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
    22032216mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    2204  id="_x0000_i1025" type="#_x0000_t75" style='width:423.75pt;height:55.5pt'>
     2217 id="_x0000_i1025" type="#_x0000_t75" style='width:423.7pt;height:55.5pt'>
    22052218 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.png"
    22062219  o:title="" chromakey="white"/>
     
    22102223
    22112224<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    2212 margin-left:0in;line-height:115%'><span class=GramE>is</span> satisfied.<span
    2213 style='mso-spacerun:yes'>  </span>Terms of the form <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
     2225margin-left:0in;line-height:115%'>is satisfied.<span style='mso-spacerun:yes'> 
     2226</span>Terms of the form <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
    22142227   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    22152228   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    23022315src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"
    23032316v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    2304 style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2317style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    23052318   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    23062319   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    24032416
    24042417<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    2405 margin-left:0in;line-height:115%'><span class=GramE>using</span> the
    2406 coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2418margin-left:0in;line-height:115%'>using the coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    24072419   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    24082420   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    24662478style='mso-spacerun:yes'> </span>and the sample orientation angles <span
    24672479style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
    2468 <span class=GramE><span style='font-family:Symbol'>F</span></span><sub>s</sub>.
    2469 </p>
     2480<span style='font-family:Symbol'>F</span><sub>s</sub>. </p>
    24702481
    24712482<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     
    25252536
    25262537<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    2527 margin-left:0in;line-height:115%'>If the texture is random then J = 1,
    2528 otherwise J &gt; 1; for a single crystal J = <span style='font-family:Symbol'>¥.</span>
    2529 </p>
     2538margin-left:0in;line-height:115%'>If the texture is random then J = 1, otherwise
     2539J &gt; 1; for a single crystal J = <span style='font-family:Symbol'>¥.</span> </p>
    25302540
    25312541<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     
    25822592<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Use the <b
    25832593style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2584 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Read
    2585 image data</span></b> menu item to read the data file into the current GSAS-II
     2594mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Read image
     2595data</span></b> menu item to read the data file into the current GSAS-II
    25862596project. A file selection dialog will be shown; its appearance will depend on
    25872597your OS. Change the search directory to <b style='mso-bidi-font-weight:normal'><span
    25882598style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    25892599mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
    2590 minor-latin'>/exercises/2DTexture </span></b>and then select the file <b
     2600minor-latin'>2DTexture/data </span></b>and then select the file <b
    25912601style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    25922602mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NDC5_01588_1.ge2</span></b>.
     
    26032613v:shapes="Picture_x0020_29"><![endif]></span></p>
    26042614
    2605 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
    2606 class=GramE>and</span> the <b style='mso-bidi-font-weight:normal'><span
    2607 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2608 mso-hansi-theme-font:minor-latin'>Image Controls</span></b> data page will show</p>
     2615<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and the <b
     2616style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2617mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
     2618Controls</span></b> data page will show</p>
    26092619
    26102620<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    26562666is suitable) and shows that the diffraction rings show the effect of texture
    26572667and that the image has a fairly high background. Placing the cursor in the
    2658 corners or inside the inner ring shows a background &gt;1700. This can be suppressed
    2659 by adjusting the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    2660 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    2661 minor-latin'>Flat <span class=SpellE>Bkg</span></span></b> (I chose <b
    2662 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2668corners or inside the inner ring shows a background &gt;1700. This can be
     2669suppressed by adjusting the <b style='mso-bidi-font-weight:normal'><span
     2670style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2671mso-hansi-theme-font:minor-latin'>Flat <span class=SpellE>Bkg</span></span></b>
     2672(I chose <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    26632673mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>1700</span></b>
    26642674for this). The image will now show the rings much more clearly.</p>
     
    26752685
    26762686<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For texture
    2677 analysis we will need to integrate the image into a number of slices sampling
    2678 the changing ring intensity with azimuthal angle. Also note that the image
    2679 seems to have <b style='mso-bidi-font-weight:normal'><span style='font-family:
     2687analysis we will need to integrate the image into a number of slices sampling the
     2688changing ring intensity with azimuthal angle. Also note that the image seems to
     2689have <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2690mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>mm</span></b>
     2691symmetry so that the unique part of this intensity variation covers 0-90° of
     2692azimuth. In addition the ring intensity variation is such that using 10° slices
     2693will capture it reasonably well. However, we want to include both 0° and 90° as
     2694slice centers. Thus there will be 10 slices beginning at -5° and ending at 95°.
     2695Check the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2696mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show
     2697integration limits?</span></b> box and uncheck the <b style='mso-bidi-font-weight:
     2698normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2699minor-latin;mso-hansi-theme-font:minor-latin'>Do full integration? </span></b>box,
     2700enter <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2701mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>
     2702in the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2703mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth
     2704bins</span></b>, enter <b style='mso-bidi-font-weight:normal'><span
     2705style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2706mso-hansi-theme-font:minor-latin'>-5</span></b> in the <b style='mso-bidi-font-weight:
     2707normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2708minor-latin;mso-hansi-theme-font:minor-latin'>Start azimuth</span></b> box (it
     2709will change to 355) and enter <b style='mso-bidi-font-weight:normal'><span
     2710style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2711mso-hansi-theme-font:minor-latin'>455</span></b> in the <b style='mso-bidi-font-weight:
     2712normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2713minor-latin;mso-hansi-theme-font:minor-latin'>End azimuth</span></b> box. In
     2714addition, recall that the sample was mounted vertically and thus is aligned
     2715with the defined laboratory I axis. Thus, the sample coordinate system needs to
     2716be rotated by 90° to match the sample axis with the K axis; this can be done by
     2717making the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    26802718"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    2681 minor-latin'>mm</span></b> symmetry so that the unique part of this intensity
    2682 variation covers 0-90° of azimuth. In addition the ring intensity variation is
    2683 such that using 10° slices will capture it reasonably well. However, we want to
    2684 include both 0° and 90° as slice centers. Thus there will be 10 slices
    2685 beginning at -5° and ending at 95°. Check the <b style='mso-bidi-font-weight:
     2719minor-latin'>Sample goniometer axis Chi</span></b> = <b style='mso-bidi-font-weight:
    26862720normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2687 minor-latin;mso-hansi-theme-font:minor-latin'>Show integration limits?</span></b>
    2688 <span class=GramE>box</span> and uncheck the <b style='mso-bidi-font-weight:
    2689 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2690 minor-latin;mso-hansi-theme-font:minor-latin'>Do full integration? </span></b><span
    2691 class=GramE>box</span>, enter <b style='mso-bidi-font-weight:normal'><span
    2692 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2693 mso-hansi-theme-font:minor-latin'>10</span></b> in the <b style='mso-bidi-font-weight:
    2694 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2695 minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth bins</span></b>,
    2696 enter <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2697 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-5</span></b>
    2698 in the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2699 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Start
    2700 azimuth</span></b> box (it will change to 355) and enter <b style='mso-bidi-font-weight:
    2701 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2702 minor-latin;mso-hansi-theme-font:minor-latin'>455</span></b> in the <b
    2703 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2704 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>End azimuth</span></b>
    2705 box. In addition, recall that the sample was mounted vertically and thus is
    2706 aligned with the defined laboratory I axis. Thus, the sample coordinate system
    2707 needs to be rotated by 90° to match the sample axis with the K axis; this can
    2708 be done by making the <b style='mso-bidi-font-weight:normal'><span
    2709 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2710 mso-hansi-theme-font:minor-latin'>Sample goniometer axis Chi</span></b> = <b
    2711 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2712 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>90</span></b>.
    2713 The plot will change with each entry and at the end should look like</p>
     2721minor-latin;mso-hansi-theme-font:minor-latin'>90</span></b>. The plot will
     2722change with each entry and at the end should look like</p>
    27142723
    27152724<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    27752784v:shapes="Picture_x0020_36"><![endif]></span></p>
    27762785
    2777 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
    2778 class=GramE>for</span> one ring. This level is too low. Return to the <b
    2779 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2780 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
    2781 Controls</span></b> item in the data tree.</p>
     2786<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>for one ring.
     2787This level is too low. Return to the <b style='mso-bidi-font-weight:normal'><span
     2788style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2789mso-hansi-theme-font:minor-latin'>Image Controls</span></b> item in the data
     2790tree.</p>
    27822791
    27832792<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
     
    28052814<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This <span
    28062815class=SpellE>NiTi</span> alloy consists of two phases, cubic B2 and monoclinic
    2807 B19’. Their parameters are<span class=GramE>:</span><br>
     2816B19’. Their parameters are:<br>
    28082817B2: <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    28092818mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P m 3 m</span></b>,
     
    28312840<span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span
    28322841style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2833 mso-hansi-theme-font:minor-latin'>0.5787<span class=GramE>,0.2841,Œ</span></span></b>,
    2834 Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2842mso-hansi-theme-font:minor-latin'>0.5787,0.2841,Œ</span></b>, Ni <b
     2843style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    28352844mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.9700,0.8209,Œ</span></b>,
    28362845<span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
     
    28762885v:shapes="Picture_x0020_38"><![endif]></span></p>
    28772886
    2878 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
    2879 class=GramE>and</span> the B19’ Atoms table should be</p>
     2887<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and the B19’
     2888Atoms table should be</p>
    28802889
    28812890<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    29122921v:shapes="Picture_x0020_40"><![endif]></span></p>
    29132922
    2914 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
    2915 class=GramE>and</span> that for B19’ will be</p>
     2923<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and that for
     2924B19’ will be</p>
    29162925
    29172926<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    30103019mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b>, select <b
    30113020style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3012 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set <span
    3013 class=GramE>All</span></span></b> &amp; press <b style='mso-bidi-font-weight:
    3014 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3015 minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to copy these to
    3016 the other histograms. Next select the <b style='mso-bidi-font-weight:normal'><span
    3017 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3018 mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and repeat this process.
    3019 We are now ready for the first refinement; do <b style='mso-bidi-font-weight:
    3020 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3021 minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from
    3022 the main GSAS-II data tree window. A progress bar popup will appear and when
    3023 done a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3024 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refinement
    3025 results</span></b> popup will show with Rw~32%. Press <b style='mso-bidi-font-weight:
    3026 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3027 minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to load this
    3028 result; GSAS-II will return you to the last window you were using and display
    3029 the 1<sup>st</sup> powder pattern showing you the fit</p>
     3021mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b>
     3022&amp; press <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3023"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3024minor-latin'>OK</span></b> to copy these to the other histograms. Next select
     3025the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3026mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
     3027phase and repeat this process. We are now ready for the first refinement; do <b
     3028style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3029mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
     3030from the main GSAS-II data tree window. A progress bar popup will appear and
     3031when done a <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3032"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3033minor-latin'>Refinement results</span></b> popup will show with Rw~32%. Press <b
     3034style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3035mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>
     3036to load this result; GSAS-II will return you to the last window you were using
     3037and display the 1<sup>st</sup> powder pattern showing you the fit</p>
    30303038
    30313039<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    32473255
    32483256<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
    3249 Texture tab for the B19’ phase. Again a <span class=SpellE>bullseye</span> pole
    3250 figure is drawn; change that to an Inverse pole figure.</p>
     3257Texture tab for the B19’ phase. Again a bullseye pole figure is drawn; change
     3258that to an Inverse pole figure.</p>
    32513259
    32523260<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    32873295v:shapes="Picture_x0020_54"><![endif]></span></p>
    32883296
    3289 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
    3290 class=GramE>and</span> inverse pole figure</p>
     3297<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and inverse
     3298pole figure</p>
    32913299
    32923300<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    33133321v:shapes="Picture_x0020_56"><![endif]></span></p>
    33143322
    3315 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
    3316 class=GramE>and</span> inverse pole figure</p>
     3323<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and inverse
     3324pole figure</p>
    33173325
    33183326<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    33283336<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This completes
    33293337the tutorial on Method A for doing texture analysis. It is useful for a case
    3330 like this one where there are very few data sets required for the texture
    3331 analysis. However, for the case of lower sample symmetry one must several dozen
    3332 or even a few hundred histograms and then the suite of parameters can easily be
    3333 &gt; 1000 of which only a few dozen describe the texture. This leads to the
    3334 next Methods for texture analysis in GSAS-II.</p>
     3338like this one where there are very few data sets required for the texture analysis.
     3339However, for the case of lower sample symmetry one must several dozen or even a
     3340few hundred histograms and then the suite of parameters can easily be &gt; 1000
     3341of which only a few dozen describe the texture. This leads to the next Methods
     3342for texture analysis in GSAS-II.</p>
    33353343
    33363344<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     
    33423350
    33433351<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
    3344 the texture analysis in much the same way as Method A except that all the
    3345 initial refinements are done “sequentially”, that is refinements are done for
    3346 the parameters associated with each powder pattern to convergence in a serial
     3352the texture analysis in much the same way as Method A except that all the initial
     3353refinements are done “sequentially”, that is refinements are done for the
     3354parameters associated with each powder pattern to convergence in a serial
    33473355fashion. In this case where there are 10 PWDR data sets, there will be 10
    33483356refinements done in sequence. Parameters that span all the data (e.g. lattice
     
    33963404tab and check the <b style='mso-bidi-font-weight:normal'><span
    33973405style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3398 mso-hansi-theme-font:minor-latin'>Phase fraction</span></b> box and change the <span
    3399 class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
    3400 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3401 minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span
    3402 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3403 mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b
    3404 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3405 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical
    3406 harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span
    3407 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3408 mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the
    3409 flag and the model to the other PWDR entries.</p>
     3406mso-hansi-theme-font:minor-latin'>Phase fraction</span></b> box and change the <b
     3407style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3408mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
     3409orientation model</span></b> to <b style='mso-bidi-font-weight:normal'><span
     3410style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3411mso-hansi-theme-font:minor-latin'>Spherical harmonics</span></b>. Then do <b
     3412style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3413mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
     3414data</span></b> to copy both the flag and the model to the other PWDR entries.</p>
    34103415
    34113416<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space:
     
    34193424tab and check the <b style='mso-bidi-font-weight:normal'><span
    34203425style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3421 mso-hansi-theme-font:minor-latin'>Phase fraction box</span></b> and change the <span
    3422 class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
    3423 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3424 minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span
    3425 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3426 mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b
    3427 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3428 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical
    3429 harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span
    3430 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3431 mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the
    3432 flag and the model to the other PWDR entries.</p>
     3426mso-hansi-theme-font:minor-latin'>Phase fraction box</span></b> and change the <b
     3427style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3428mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
     3429orientation model</span></b> to <b style='mso-bidi-font-weight:normal'><span
     3430style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3431mso-hansi-theme-font:minor-latin'>Spherical harmonics</span></b>. Then do <b
     3432style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3433mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
     3434data</span></b> to copy both the flag and the model to the other PWDR entries.</p>
    34333435
    34343436<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select <b
     
    35103512
    35113513<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you examine
    3512 one of the PWDR entries, you’ll see that just in this point in Method <span
    3513 class=GramE>A</span> much of the misfit is texture and perhaps peak position.</p>
     3514one of the PWDR entries, you’ll see that just in this point in Method A much of
     3515the misfit is texture and perhaps peak position.</p>
    35143516
    35153517<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    35533555
    35543556<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This allows
    3555 you to select which parameters to copy data and flags. Select Pref. <span
    3556 class=SpellE>Ori</span>. And press OK; the file selection is next. Do Set <span
    3557 class=GramE>All</span> and OK to do this copy. That copies the full spherical
    3558 harmonics model to the other data sets. Select one to check if you’d like.</p>
     3557you to select which parameters to copy data and flags. Select Pref. Ori. And
     3558press OK; the file selection is next. Do Set All and OK to do this copy. That
     3559copies the full spherical harmonics model to the other data sets. Select one to
     3560check if you’d like.</p>
    35593561
    35603562<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next do the
     
    35763578ready for the next refinement; do Calculate/Sequential refine. Be careful not
    35773579(by habit say) pick Refine; a warning popup will appear. After it completes the
    3578 Sequential refinement results shows that the fit is better but convergence
    3579 wasn’t quite complete.</p>
     3580Sequential refinement results shows that the fit is better but convergence wasn’t
     3581quite complete.</p>
    35803582
    35813583<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    36513653perhaps the B19’ phase needs high order spherical harmonics. Select the Data
    36523654tab for the B19’ phase and change the Harmonic order to 6. Then do Edit/Copy
    3653 selected data for <span class=SpellE>Pref.Ori</span>. <span class=GramE>to</span>
    3654 the other data sets. This (after few repeats) gives a further improvement in
    3655 the fit</p>
     3655selected data for <span class=SpellE>Pref.Ori</span>. to the other data sets.
     3656This (after few repeats) gives a further improvement in the fit</p>
    36563657
    36573658<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    367236730in;line-height:115%'>Step 2. Texture analysis</h3>
    36733674
    3674 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>During the
    3675 sequential refinements done in Step 1, we fitted the profiles allowing strain
    3676 parameters (<span class=SpellE>Dij</span>) for peak position shifts and <span
    3677 class=SpellE>microstrain</span> for peak shape. We modeled the intensity
    3678 variation with a spherical harmonics preferred orientation correction. If you
    3679 select any PWDR entry from the GSAS-II data tree and pick the Reflection List
    3680 subentry (at the bottom) you can see the magnitude of this correction for each
    3681 reflection in each phase.</p>
     3675<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>During the sequential
     3676refinements done in Step 1, we fitted the profiles allowing strain parameters (<span
     3677class=SpellE>Dij</span>) for peak position shifts and <span class=SpellE>microstrain</span>
     3678for peak shape. We modeled the intensity variation with a spherical harmonics
     3679preferred orientation correction. If you select any PWDR entry from the GSAS-II
     3680data tree and pick the Reflection List subentry (at the bottom) you can see the
     3681magnitude of this correction for each reflection in each phase.</p>
    36823682
    36833683<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For the B2
     
    36943694v:shapes="Picture_x0020_14"><![endif]></span></p>
    36953695
    3696 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
    3697 class=GramE>and</span> for the B19’ phase we see</p>
     3696<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and for the
     3697B19’ phase we see</p>
    36983698
    36993699<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    37413741
    37423742<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do
    3743 Texture/Refine texture from the menu; the window will be repainted and a <span
    3744 class=SpellE>bullseye</span> pole figure will appear. </p>
     3743Texture/Refine texture from the menu; the window will be repainted and a
     3744bullseye pole figure will appear. </p>
    37453745
    37463746<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    37683768
    37693769<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is
    3770 essentially the same as we obtained earlier in Method <span class=GramE>A</span>
    3771 (maybe not quite as strong here).</p>
     3770essentially the same as we obtained earlier in Method A (maybe not quite as
     3771strong here).</p>
    37723772
    37733773<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the
     
    37863786v:shapes="Picture_x0020_21"><![endif]></span></p>
    37873787
    3788 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a <span
    3789 class=SpellE>bullseye</span> pole figure; change that to Inverse pole figure to
    3790 see the texture</p>
     3788<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a bullseye
     3789pole figure; change that to Inverse pole figure to see the texture</p>
    37913790
    37923791<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    38003799v:shapes="Picture_x0020_22"><![endif]></span></p>
    38013800
    3802 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Again this is
    3803 very similar to what we found in Method A but again not quite as strong (max
    3804 MRD ~13 instead of ~18).</p>
     3801<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Again this is very
     3802similar to what we found in Method A but again not quite as strong (max MRD ~13
     3803instead of ~18).</p>
    38053804
    38063805<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do a
     
    38433842<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Here we want
    38443843to clear refinement flags for all parameters that need not be varied in a
    3845 texture analysis refinement. The general rule is to not refine any parameter
    3846 unless we expect it to affect the peak intensities. These are listed below:</p>
     3844texture analysis refinement. The general rule is to not refine any parameter unless
     3845we expect it to affect the peak intensities. These are listed below:</p>
    38473846
    38483847<p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;mso-add-space:
     
    38783877phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
    38793878"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3880 minor-latin'>Data</span></b> tab. <span class=GramE>Clear</span> the <span
     3879minor-latin'>Data</span></b> <span class=GramE>tab.</span> Clear the <span
    38813880class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
    38823881"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     
    38943893flags</span></b> selecting all data to clear all the flags and an <b
    38953894style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3895mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy selected
     3896data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
     3897style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3898mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to copy the zeroed
     3899out harmonic coefficients.</p>
     3900
     3901<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space:
     3902auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
     3903style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
     3904style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
     3905style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3906mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>:
     3907we do not want to refine either the <span class=SpellE>microstrain</span>, <span
     3908class=SpellE>Dij</span>, or preferred orientation coefficients. Select the <b
     3909style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3910mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
     3911phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3912"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3913minor-latin'>Data</span></b> tab. Clear the <span class=SpellE><b
     3914style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3915mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>microstrain</span></b></span>,
     3916four <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
     3917style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3918mso-hansi-theme-font:minor-latin'>Dij</span></b></span> and <b
     3919style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3920mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
     3921orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
     3922style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3923mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
     3924avoid a lot of nasty (but harmless) messages at the start of the refinement).
     3925Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3926mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
     3927flags</span></b> selecting all data to clear all the flags and an <b
     3928style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    38963929mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
    38973930selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
     
    39003933copy the zeroed out harmonic coefficients.</p>
    39013934
    3902 <p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space:
    3903 auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
    3904 style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
    3905 style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
    3906 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3907 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>:
    3908 we do not want to refine either the <span class=SpellE>microstrain</span>, <span
    3909 class=SpellE>Dij</span>, or preferred orientation coefficients. Select the <b
    3910 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3911 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
    3912 phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
    3913 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3914 minor-latin'>Data</span></b> tab. Clear the <span class=SpellE><b
    3915 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3916 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>microstrain</span></b></span>,
    3917 four <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
    3918 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3919 mso-hansi-theme-font:minor-latin'>Dij</span></b></span> and <b
    3920 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3921 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
    3922 orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
    3923 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3924 mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
    3925 avoid a lot of nasty (but harmless) messages at the start of the refinement).
    3926 Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3927 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
    3928 flags</span></b> selecting all data to clear all the flags and an <b
    3929 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3930 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
    3931 selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
    3932 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3933 minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
    3934 copy the zeroed out harmonic coefficients.</p>
    3935 
    39363935<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    39373936margin-left:.25in;line-height:115%'><o:p>&nbsp;</o:p></p>
     
    39403939margin-left:.25in;line-height:115%'>Notice that we have allowed refinement of
    39413940the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3942 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase fractions</span></b>;
    3943 these may change during the texture refinement. Now select the <b
    3944 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3945 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
    3946 tab for the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3941mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase
     3942fractions</span></b>; these may change during the texture refinement. Now
     3943select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    39473944"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3948 minor-latin'>B2</span></b> phase (it may still have values from the Method B).</p>
     3945minor-latin'>Texture</span></b> tab for the <b style='mso-bidi-font-weight:
     3946normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3947minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> phase (it may still
     3948have values from the Method B).</p>
    39493949
    39503950<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     
    39903990style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    39913991mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
    3992 tab. <span class=GramE>Set</span> the <b style='mso-bidi-font-weight:normal'><span
     3992<span class=GramE>tab.</span> Set the <b style='mso-bidi-font-weight:normal'><span
    39933993style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    39943994mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero and then
     
    40474047v:shapes="Picture_x0020_26"><![endif]></span></p>
    40484048
    4049 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
    4050 class=GramE>which</span> is almost identical to that from Method A. The
     4049<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>which is
     4050almost identical to that from Method <span class=GramE>A.</span> The
    40514051coefficients are seen in</p>
    40524052
     
    40784078v:shapes="Picture_x0020_28"><![endif]></span></p>
    40794079
    4080 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
    4081 class=GramE>and</span> also almost identical to what was obtained in Method A;
    4082 the coefficients are seen in</p>
     4080<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and also
     4081almost identical to what was obtained in Method A; the coefficients are seen in</p>
    40834082
    40844083<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    40974096tutorial that in more complex textures where the data set may consist of slices
    40984097obtained from a suite of 2D images collected as the sample is rotated, Method C
    4099 will give a relatively fast determination of the texture without resorting to large
    4100 matrix least-squares refinements.</p>
     4098will give a relatively fast determination of the texture without resorting to
     4099large matrix least-squares refinements.</p>
    41014100
    41024101</div>
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