Changeset 4962


Ignore:
Timestamp:
Jun 18, 2021 8:44:17 AM (3 months ago)
Author:
vondreele
Message:

revise equations to match code

Location:
Tutorials/2DTexture
Files:
33 added
69 edited

Legend:

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

    r4961 r4962  
    2525  <o:Author>Von Dreele</o:Author>
    2626  <o:LastAuthor>Von Dreele, Robert B.</o:LastAuthor>
    27   <o:Revision>8</o:Revision>
    28   <o:TotalTime>2953</o:TotalTime>
     27  <o:Revision>10</o:Revision>
     28  <o:TotalTime>3035</o:TotalTime>
    2929  <o:Created>2021-06-08T17:35:00Z</o:Created>
    30   <o:LastSaved>2021-06-17T16:44:00Z</o:LastSaved>
    31   <o:Pages>1</o:Pages>
    32   <o:Words>4709</o:Words>
    33   <o:Characters>26844</o:Characters>
     30  <o:LastSaved>2021-06-18T13:41:00Z</o:LastSaved>
     31  <o:Pages>40</o:Pages>
     32  <o:Words>4738</o:Words>
     33  <o:Characters>27010</o:Characters>
    3434  <o:Company>Argonne National Laboratory</o:Company>
    35   <o:Lines>223</o:Lines>
    36   <o:Paragraphs>62</o:Paragraphs>
    37   <o:CharactersWithSpaces>31491</o:CharactersWithSpaces>
     35  <o:Lines>225</o:Lines>
     36  <o:Paragraphs>63</o:Paragraphs>
     37  <o:CharactersWithSpaces>31685</o:CharactersWithSpaces>
    3838  <o:Version>16.00</o:Version>
    3939 </o:DocumentProperties>
     
    728728        font-weight:bold;}
    729729h2
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    15131515      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
    15141516      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
    1515   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(h)</m:r></span></i><m:sSubSup><m:sSubSupPr><span
     1517  style='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:sSubSup><m:sSubSupPr><span
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    15201522    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
    15211523    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
    1522   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
     1524  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:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
    15231525style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
    15241526"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
     
    15481550  o:title="" chromakey="white"/>
    15491551</v:shape><![endif]--><![if !vml]><img width=357 height=56
    1550 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image002.png"
     1552src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
    15511553v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    15521554
     
    15631565   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    15641566   normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
    1565    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
     1567   normal'><span style='font-family:"Cambria Math",serif'><m:r>y</m:r></span></i></m:e></m:d></m:oMath><![endif]--><![if !msEquation]><span
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    15711573 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image003.png"
    15721574  o:title="" chromakey="white"/>
    1573 </v:shape><![endif]--><![if !vml]><img width=43 height=35
    1574 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"
     1575</v:shape><![endif]--><![if !vml]><img width=44 height=35
     1576src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
    15751577v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    15761578style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     
    15811583   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
    15821584   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
    1583  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
     1585 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:oMath><![endif]--><![if !msEquation]><span
    15841586style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
    15851587"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     
    15901592  o:title="" chromakey="white"/>
    15911593</v:shape><![endif]--><![if !vml]><img width=40 height=35
    1592 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"
     1594src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
    15931595v:shapes="_x0000_i1025"><![endif]></span><![endif]>, take on values according
    1594 to the crystal and sample symmetries, respectively, and thus the two inner
     1596to the sample and crystal symmetries, respectively, and thus the two inner
    15951597summations are over only the resulting unique, nonzero harmonic terms. These
    15961598unique terms are automatically selected by <span style='mso-bidi-font-weight:
    15971599bold'>GSAS-II</span> according to the space group symmetry and the user chosen
    1598 sample symmetry. The available sample symmetries are cylindrical symmetry, 2/m,
    1599 mmm and no symmetry. The choice of sample symmetry profoundly affects the
    1600 selection of harmonic coefficients. For example, in the case of cylindrical
    1601 sample symmetry (fiber texture) only <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1600sample symmetry. The available sample symmetries are cylindrical, 2/m, mmm and
     1601no symmetry. The choice of sample symmetry profoundly affects the selection of
     1602harmonic coefficients. For example, in the case of cylindrical sample symmetry
     1603(fiber texture) only <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    16021604   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    16031605   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    16151617  o:title="" chromakey="white"/>
    16161618</v:shape><![endif]--><![if !vml]><img width=39 height=35
    1617 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image008.png"
     1619src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
    16181620v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    16191621style='mso-spacerun:yes'> </span>terms are nonzero so the rest are excluded
     
    16241626   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
    16251627   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
    1626    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
     1628   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>on</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
    16271629style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
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    16331635  o:title="" chromakey="white"/>
    1634 </v:shape><![endif]--><![if !vml]><img width=28 height=35
    1635 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image010.png"
     1636</v:shape><![endif]--><![if !vml]><img width=25 height=35
     1637src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
    16361638v:shapes="_x0000_i1025"><![endif]></span><![endif]>coefficients is sufficient
    16371639to describe the effect on the diffraction pattern due to texture. The crystal
     
    16421644   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
    16431645   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
    1644    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i
     1646   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
    16451647 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
    16461648style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     
    16481650top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
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     1655</v:shape><![endif]--><![if !vml]><img width=40 height=35
     1656src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
    16551657v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined for each
    16561658reflection, h, <i>via</i> polar and azimuthal coordinates (<span
     
    16681670   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
    16691671   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
    1670    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
     1672   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i
    16711673 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
    16721674style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     
    16741676top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
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    1679 </v:shape><![endif]--><![if !vml]><img width=40 height=35
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     1681</v:shape><![endif]--><![if !vml]><img width=44 height=35
     1682src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
    16811683v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined according to
    16821684polar and azimuthal coordinates (<span style='font-family:Symbol'>y</span>, <span
     
    17391741      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    17401742      normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
    1741       normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r></span></i></m:e></m:d></m:e></m:nary><m:sSubSup><m:sSubSupPr><span
     1743      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#968;</m:r><m:r>,</m:r><m:r>&#947;</m:r></span></i></m:e></m:d></m:e></m:nary><m:sSubSup><m:sSubSupPr><span
    17421744    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    17431745    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    17461748    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
    17471749    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
    1748   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#968;</m:r><m:r>,</m:r><m:r>&#947;</m:r><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
     1750  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></m:oMathPara><![endif]--><![if !msEquation]><span
    17491751style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
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    18381840</v:shape><![endif]--><![if !vml]><img width=45 height=67
    1839 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.png"
     1841src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
    18401842v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    18411843style='mso-spacerun:yes'> </span>and<span style='mso-spacerun:yes'>   </span><i>tan</i>(<span
     
    18741876  o:title="" chromakey="white"/>
    18751877</v:shape><![endif]--><![if !vml]><img width=107 height=67
    1876 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.png"
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    18771879v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    18781880
     
    18851887   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
    18861888   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
    1887  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
     1889 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
    18881890style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
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    18901892top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    18911893EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    1892  type="#_x0000_t75" style='width:46.5pt;height:26.25pt'>
     1894 type="#_x0000_t75" style='width:45.75pt;height:26.25pt'>
    18931895 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png"
    18941896  o:title="" chromakey="white"/>
    1895 </v:shape><![endif]--><![if !vml]><img width=62 height=35
    1896 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"
     1897</v:shape><![endif]--><![if !vml]><img width=61 height=35
     1898src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
    18971899v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    18981900style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     
    19031905   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
    19041906   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
     1907 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
     1908style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1909"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1910top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1911EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1912 type="#_x0000_t75" style='width:43.5pt;height:26.25pt'>
     1913 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png"
     1914  o:title="" chromakey="white"/>
     1915</v:shape><![endif]--><![if !vml]><img width=58 height=35
     1916src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
     1917v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are developed from (those
     1918for <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1919   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     1920   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     1921   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
     1922   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
     1923   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
     1924   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i
    19051925 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
    19061926style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     
    19081928top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    19091929EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    1910  type="#_x0000_t75" style='width:42.75pt;height:26.25pt'>
    1911  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png"
     1930 type="#_x0000_t75" style='width:45.75pt;height:26.25pt'>
     1931 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png"
    19121932  o:title="" chromakey="white"/>
    1913 </v:shape><![endif]--><![if !vml]><img width=57 height=35
    1914 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.png"
    1915 v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are developed from</p>
     1933</v:shape><![endif]--><![if !vml]><img width=61 height=35
     1934src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
     1935v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     1936style='mso-spacerun:yes'> </span>are similar)</p>
    19161937
    19171938<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     
    19231944    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
    19241945    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
    1925     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
     1946    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
    19261947    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    19271948    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    19411962    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    19421963    normal'><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:e><m:sup><i
    1943     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
     1964    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>i</m:r><m:r>n</m:r><m:r>&#946;</m:r></span></i></m:sup></m:sSup><m:sSubSup><m:sSubSupPr><span
    19441965    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    19451966    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    19511972    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
    19521973    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    1953      </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     1974     </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
    19541975  normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
    19551976    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     
    19631984"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
    19641985mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    1965  id="_x0000_i1025" type="#_x0000_t75" style='width:165pt;height:42pt'>
    1966  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.png"
     1986 id="_x0000_i1025" type="#_x0000_t75" style='width:158.25pt;height:42pt'>
     1987 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
    19671988  o:title="" chromakey="white"/>
    1968 </v:shape><![endif]--><![if !vml]><img width=220 height=56
    1969 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"
     1989</v:shape><![endif]--><![if !vml]><img width=211 height=56
     1990src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
    19701991v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    19711992
     
    19812002     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
    19822003   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
    1983    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
     2004   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
    19842005 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
    19852006style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     
    19872008top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    19882009EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    1989  type="#_x0000_t75" style='width:33pt;height:26.25pt'>
    1990  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image025.png"
     2010 type="#_x0000_t75" style='width:30.75pt;height:26.25pt'>
     2011 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
    19912012  o:title="" chromakey="white"/>
    1992 </v:shape><![endif]--><![if !vml]><img width=44 height=35
    1993 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image026.png"
     2013</v:shape><![endif]--><![if !vml]><img width=41 height=35
     2014src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
    19942015v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are defined via a Fourier
    19952016expansion as</p>
     
    20072028    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
    20082029    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2009      </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2030     </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
    20102031    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    20112032    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    20292050      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
    20302051      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2031        </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
     2052       </m:r><m:r>n</m:r><m:r>s</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
    20322053    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    20332054    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    20392060"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
    20402061mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    2041  id="_x0000_i1025" type="#_x0000_t75" style='width:154.5pt;height:52.5pt'>
    2042  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image027.png"
     2062 id="_x0000_i1025" type="#_x0000_t75" style='width:149.25pt;height:52.5pt'>
     2063 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
    20432064  o:title="" chromakey="white"/>
    2044 </v:shape><![endif]--><![if !vml]><img width=206 height=70
    2045 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image028.png"
     2065</v:shape><![endif]--><![if !vml]><img width=199 height=70
     2066src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
    20462067v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    20472068
    20482069<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    2049 margin-left:0in;line-height:115%'>for m even and</p>
     2070margin-left:0in;line-height:115%'>for n even and</p>
    20502071
    20512072<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     
    20612082    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
    20622083    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2063      </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2084     </m:r><m:r>n</m:r><m:r>s</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
    20642085    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    20652086    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    20832104      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
    20842105      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2085        </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
     2106       </m:r><m:r>n</m:r><m:r>s</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
    20862107    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    20872108    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    20932114"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
    20942115mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    2095  id="_x0000_i1025" type="#_x0000_t75" style='width:158.25pt;height:52.5pt'>
    2096  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image029.png"
     2116 id="_x0000_i1025" type="#_x0000_t75" style='width:153.75pt;height:52.5pt'>
     2117 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
    20972118  o:title="" chromakey="white"/>
    2098 </v:shape><![endif]--><![if !vml]><img width=211 height=70
    2099 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image030.png"
     2119</v:shape><![endif]--><![if !vml]><img width=205 height=70
     2120src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
    21002121v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    21012122
    21022123<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    2103 margin-left:0in;line-height:115%'>for m odd.<span style='mso-spacerun:yes'> 
    2104 </span>Each sum is only over either the even or odd values of s, respectively,
    2105 because of the properties of the Fourier coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2124margin-left:0in;line-height:115%'>for <span class=SpellE>n</span> odd.<span
     2125style='mso-spacerun:yes'>  </span>Each sum is only over either the even or odd
     2126values of s, respectively, because of the properties of the Fourier
     2127coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    21062128   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    21072129   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    21102132   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
    21112133   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2112     </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
     2134    </m:r><m:r>n</m:r><m:r>s</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
    21132135style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
    21142136"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
    21152137top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    21162138EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    2117  type="#_x0000_t75" style='width:24.75pt;height:26.25pt'>
    2118  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image031.png"
     2139 type="#_x0000_t75" style='width:21.75pt;height:26.25pt'>
     2140 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
    21192141  o:title="" chromakey="white"/>
    2120 </v:shape><![endif]--><![if !vml]><img width=33 height=35
    2121 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image032.png"
     2142</v:shape><![endif]--><![if !vml]><img width=29 height=35
     2143src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
    21222144v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
    21232145style='mso-spacerun:yes'>  </span>These Fourier coefficients are determined so
     
    21362158    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
    21372159    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2138      </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2160     </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
    21392161    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    21402162    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    21562178    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
    21572179    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2158      </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
     2180     </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
    21592181    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    21602182    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    21712193        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    21722194        normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
    2173         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
     2195        normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>+</m:r><m:r>n</m:r></span></i></m:e></m:d><i
    21742196      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
    21752197        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    21762198        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    21772199        normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
    2178         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
     2200        normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>n</m:r></span></i></m:e></m:d><i
    21792201      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
    21802202     m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     
    21932215      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    21942216      normal'><span style='font-family:"Cambria Math",serif'><m:r>(-1)</m:r></span></i></m:e><m:sup><i
    2195       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
     2217      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>n</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span
    21962218      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    21972219      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    22132235      "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
    22142236      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
    2215       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
     2237      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>n</m:r></span></i></m:num><m:den><i
    22162238      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
    22172239    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     
    22222244      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    22232245      normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
    2224       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
     2246      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>n</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span
    22252247      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    22262248      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    22272249      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    22282250      normal'><span style='font-family:"Cambria Math",serif'><m:r>dx</m:r></span></i></m:e><m:sup><i
    2229       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
     2251      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>n</m:r></span></i></m:sup></m:sSup></m:den></m:f><m:sSup><m:sSupPr><span
    22302252    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    22312253    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    22422264"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
    22432265mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    2244  id="_x0000_i1025" type="#_x0000_t75" style='width:423.75pt;height:55.5pt'>
    2245  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.png"
     2266 id="_x0000_i1025" type="#_x0000_t75" style='width:408.7pt;height:55.5pt'>
     2267 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
    22462268  o:title="" chromakey="white"/>
    2247 </v:shape><![endif]--><![if !vml]><img width=565 height=74
    2248 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image034.png"
     2269</v:shape><![endif]--><![if !vml]><img width=545 height=74
     2270src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
    22492271v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    22502272
     
    22572279   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
    22582280      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
    2259    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
     2281   normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>n</m:r><m:r>&#946;</m:r><m:r>)</m:r></span></i></m:e></m:func><m:sSubSup><m:sSubSupPr><span
    22602282   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    22612283   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    22672289   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
    22682290   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2269     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2291    </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
    22702292 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
    22712293   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     
    22742296   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
    22752297      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
    2276    normal'><span style='font-family:"Cambria Math",serif'><m:r>m&#946;</m:r></span></i></m:e></m:func><i
     2298   normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>&#946;</m:r></span></i></m:e></m:func><i
    22772299 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
    22782300style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     
    22802302top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    22812303EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    2282  type="#_x0000_t75" style='width:111pt;height:26.25pt'>
    2283  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image035.png"
     2304 type="#_x0000_t75" style='width:102pt;height:26.25pt'>
     2305 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
    22842306  o:title="" chromakey="white"/>
    2285 </v:shape><![endif]--><![if !vml]><img width=148 height=35
    2286 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image036.png"
     2307</v:shape><![endif]--><![if !vml]><img width=136 height=35
     2308src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
    22872309v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    22882310style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
     
    22922314   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
    22932315      m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
    2294    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
     2316   normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>n</m:r><m:r>&#946;</m:r><m:r>)</m:r></span></i></m:e></m:func><m:sSubSup><m:sSubSupPr><span
    22952317   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    22962318   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    23022324   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
    23032325   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2304     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2326    </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
    23052327 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
    23062328   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     
    23152337top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    23162338EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    2317  type="#_x0000_t75" style='width:100.5pt;height:26.25pt'>
    2318  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image037.png"
     2339 type="#_x0000_t75" style='width:94.5pt;height:26.25pt'>
     2340 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
    23192341  o:title="" chromakey="white"/>
    2320 </v:shape><![endif]--><![if !vml]><img width=134 height=35
    2321 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image038.png"
     2342</v:shape><![endif]--><![if !vml]><img width=126 height=35
     2343src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
    23222344v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    23232345style='mso-spacerun:yes'> </span>are combined depending on the symmetry and the
    2324 value of m along with appropriate normalization coefficients to give the
     2346value of n along with appropriate normalization coefficients to give the
    23252347harmonic terms <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    23262348   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     
    23302352   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
    23312353   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2332     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2354    </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
    23332355 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
    23342356style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     
    23362358top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    23372359EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    2338  type="#_x0000_t75" style='width:48pt;height:26.25pt'>
     2360 type="#_x0000_t75" style='width:45.75pt;height:26.25pt'>
    23392361 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
    23402362  o:title="" chromakey="white"/>
    2341 </v:shape><![endif]--><![if !vml]><img width=64 height=35
    2342 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"
     2363</v:shape><![endif]--><![if !vml]><img width=61 height=35
     2364src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"
    23432365v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    23442366style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     
    23492371   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
    23502372   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2351     </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2373    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
    23522374 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
    23532375style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     
    23552377top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    23562378EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    2357  type="#_x0000_t75" style='width:45pt;height:26.25pt'>
     2379 type="#_x0000_t75" style='width:47.25pt;height:26.25pt'>
    23582380 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png"
    23592381  o:title="" chromakey="white"/>
    2360 </v:shape><![endif]--><![if !vml]><img width=60 height=35
    2361 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image042.png"
     2382</v:shape><![endif]--><![if !vml]><img width=63 height=35
     2383src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image108.png"
    23622384v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
    23632385style='mso-spacerun:yes'>  </span>For cubic crystal symmetry, the term <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     
    23682390   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
    23692391   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
    2370     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
     2392    </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
    23712393 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
    23722394style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     
    23742396top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    23752397EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    2376  type="#_x0000_t75" style='width:48pt;height:26.25pt'>
     2398 type="#_x0000_t75" style='width:45.75pt;height:26.25pt'>
    23772399 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
    23782400  o:title="" chromakey="white"/>
    2379 </v:shape><![endif]--><![if !vml]><img width=64 height=35
    2380 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"
     2401</v:shape><![endif]--><![if !vml]><img width=61 height=35
     2402src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"
    23812403v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    23822404style='mso-spacerun:yes'> </span>is obtained directly from the Fourier
     
    23912413    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
    23922414    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
    2393     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
     2415    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
    23942416    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    23952417    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    24002422    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
    24012423    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
    2402     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
     2424    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>j</m:r><m:r>=0</m:r></span></i></m:sub><m:sup><i
    24032425    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
    24042426      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
     
    24072429      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
    24082430      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
    2409       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
     2431      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>j</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:sSubSup><m:sSubSupPr><span
    24102432    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    24112433    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    24352457"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
    24362458mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    2437  id="_x0000_i1025" type="#_x0000_t75" style='width:193.5pt;height:52.5pt'>
     2459 id="_x0000_i1025" type="#_x0000_t75" style='width:186pt;height:54pt'>
    24382460 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image043.png"
    24392461  o:title="" chromakey="white"/>
    2440 </v:shape><![endif]--><![if !vml]><img width=258 height=70
    2441 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image044.png"
     2462</v:shape><![endif]--><![if !vml]><img width=248 height=72
     2463src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image110.png"
    24422464v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    24432465
     
    24492471   normal'><span style='font-family:"Cambria Math",serif'><m:r>B</m:r></span></i></m:e><m:sub><i
    24502472   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
    2451    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
     2473   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>j</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
    24522474style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
    24532475"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
    2454 top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     2476top:4.0pt;mso-text-raise:-4.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    24552477EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    2456  type="#_x0000_t75" style='width:22.5pt;height:26.25pt'>
     2478 type="#_x0000_t75" style='width:18.75pt;height:29.25pt'>
    24572479 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image045.png"
    24582480  o:title="" chromakey="white"/>
    2459 </v:shape><![endif]--><![if !vml]><img width=30 height=35
    2460 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image046.png"
     2481</v:shape><![endif]--><![if !vml]><img width=25 height=39
     2482src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image112.png"
    24612483v:shapes="_x0000_i1025"><![endif]></span><![endif]>, as tabulated by Bunge
    24622484(1982). </p>
    24632485
     2486<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Note that this
     2487version of the general axis equation differs from that shown in Von Dreele (1997)
     2488in that the assignment of m and n are reversed.<o:p></o:p></p>
     2489
    24642490<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    2465 margin-left:0in;line-height:115%'>The Rietveld refinement of texture then
    2466 proceeds by constructing derivatives of the profile intensities with respect to
    2467 the allowed harmonic coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2491margin-left:0in;line-height:115%'>The Rietveld refinement of texture then proceeds
     2492by constructing derivatives of the profile intensities with respect to the
     2493allowed harmonic coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    24682494   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    24692495   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    24802506  o:title="" chromakey="white"/>
    24812507</v:shape><![endif]--><![if !vml]><img width=29 height=35
    2482 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
     2508src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image114.png"
    24832509v:shapes="_x0000_i1025"><![endif]></span><![endif]>, and the three sample
    24842510orientation angles, <span style='font-family:Symbol'>W</span><sub>s</sub>, <span
    24852511style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:Symbol'>F</span><sub>s</sub>,
    2486 all of which can be adjustable parameters of the refinement. Once the
    2487 refinement is complete, pole figures for any reflection may be constructed by
    2488 use of the general axis equation, the refined values for <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2512all of which can be adjustable parameters of the refinement. Once the refinement
     2513is complete, pole figures for any reflection may be constructed by use of the
     2514general axis equation, the refined values for <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    24892515   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    24902516   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
     
    24972523top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    24982524EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    2499  type="#_x0000_t75" style='width:21.75pt;height:26.25pt'>
     2525 type="#_x0000_t75" style='width:21.6pt;height:26.4pt'>
    25002526 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"
    25012527  o:title="" chromakey="white"/>
    25022528</v:shape><![endif]--><![if !vml]><img width=29 height=35
    2503 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
     2529src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image114.png"
    25042530v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    25052531style='mso-spacerun:yes'> </span>and the sample orientation angles <span
     
    25552581"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
    25562582mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    2557  id="_x0000_i1025" type="#_x0000_t75" style='width:180.75pt;height:54pt'>
     2583 id="_x0000_i1025" type="#_x0000_t75" style='width:180.8pt;height:54pt'>
    25582584 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.png"
    25592585  o:title="" chromakey="white"/>
    25602586</v:shape><![endif]--><![if !vml]><img width=241 height=72
    2561 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
     2587src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image116.png"
    25622588v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    25632589
     
    26182644if looking from the x-ray source. The sample is assumed to be a capillary
    26192645(which may be spun to impose cylindrical symmetry), although other sample
    2620 shapes may be used, and is aligned with the cylinder axis horizontal. Integration
    2621 of the image from a series of “caked” slices gives a set of powder patterns,
    2622 each assigned an azimuthal angle where zero is along the X-axis. Thus, this
    2623 diffraction plane is horizontal and contains the cylinder axis so <span
    2624 style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>,
    2625 <span style='font-family:Symbol'>F = 0.</span></p>
    2626 
    2627 <p class=MsoNormal><o:p>&nbsp;</o:p></p>
     2646shapes may be used, and is aligned with the cylinder axis horizontal.
     2647Integration of the image from a series of “caked” slices gives a set of powder
     2648patterns, each assigned an azimuthal angle where zero is along the X-axis.
     2649Thus, at azimuth=0 the diffraction plane is horizontal and contains the
     2650cylinder axis so <span style='font-family:Symbol'>W</span>, <span
     2651style='font-family:Symbol'>C</span>, <span style='font-family:Symbol'>F = 0.</span></p>
    26282652
    26292653<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
    2630 margin-left:0in;line-height:115%'>In this tutorial we will use both of these
    2631 descriptions to determine the texture of the two phases in a <span
    2632 class=SpellE>NiTi</span> shape memory alloy sample with cylindrical symmetry
    2633 (wire texture) as collected at APS on beam line 1ID-C (data kindly provided by
    2634 Paul Paradise &amp; Aaron <span class=SpellE>Stebner</span> of Colo. School of
    2635 Mines) with the sample mounted so the cylinder axis was vertical. Thus, there
    2636 are three ways within GSAS-II that can be used for this texture analysis all
    2637 beginning with the same 2D area detector image. Each will be described in turn
    2638 after the initial setup of the GSAS-II project, image input &amp; integration. </p>
     2654margin-left:0in;line-height:115%'>In this tutorial we will use both of these descriptions
     2655to determine the texture of the two phases in a <span class=SpellE>NiTi</span>
     2656shape memory alloy sample with cylindrical symmetry (wire texture) as collected
     2657at APS on beam line 1ID-C (data kindly provided by Paul Paradise &amp; Aaron <span
     2658class=SpellE>Stebner</span> of Colo. School of Mines) with the sample mounted
     2659so the cylinder axis was vertical. Thus, there are three ways within GSAS-II
     2660that can be used for this texture analysis all beginning with the same 2D area
     2661detector image. Each will be described in turn after the initial setup of the GSAS-II
     2662project, image input &amp; integration. </p>
    26392663
    26402664<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     
    26732697
    26742698<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
    2675 style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="_x0000_i1081" type="#_x0000_t75"
    2676  alt="GSAS-II plots: &lt;unnamed project&gt;" style='width:359.25pt;height:338.25pt;
    2677  visibility:visible;mso-wrap-style:square'>
     2699style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_1"
     2700 o:spid="_x0000_i1081" type="#_x0000_t75" alt="GSAS-II plots: &lt;unnamed project&gt;"
     2701 style='width:359.25pt;height:338.25pt;visibility:visible;mso-wrap-style:square'>
    26782702 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
    26792703  o:title=" &lt;unnamed project&gt;"/>
    26802704</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=451
    2681 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
    2682 alt="GSAS-II plots: &lt;unnamed project&gt;" v:shapes="_x0000_i1081"><![endif]></span></p>
     2705src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image118.png"
     2706alt="GSAS-II plots: &lt;unnamed project&gt;" v:shapes="Picture_x0020_1"><![endif]></span></p>
    26832707
    26842708<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and the <b
     
    26942718  o:title=" &lt;unnamed project&gt;"/>
    26952719</v:shape><![endif]--><![if !vml]><img border=0 width=478 height=332
    2696 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
     2720src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image121.png"
    26972721alt="GSAS-II project: &lt;unnamed project&gt;" v:shapes="Picture_x0020_60"><![endif]></span></p>
    26982722
     
    27232747  o:title=" &lt;unnamed project&gt;"/>
    27242748</v:shape><![endif]--><![if !vml]><img border=0 width=474 height=330
    2725 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
     2749src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image123.png"
    27262750alt="GSAS-II project: &lt;unnamed project&gt;" v:shapes="Picture_x0020_61"><![endif]></span></p>
    27272751
     
    27492773  o:title=" &lt;unnamed project&gt;"/>
    27502774</v:shape><![endif]--><![if !vml]><img border=0 width=474 height=446
    2751 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
     2775src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image125.png"
    27522776alt="GSAS-II plots: &lt;unnamed project&gt;" v:shapes="Picture_x0020_62"><![endif]></span></p>
    27532777
     
    27982822  o:title=" &lt;unnamed project&gt;"/>
    27992823</v:shape><![endif]--><![if !vml]><img border=0 width=477 height=449
    2800 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
     2824src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image127.png"
    28012825alt="GSAS-II plots: &lt;unnamed project&gt;" v:shapes="Picture_x0020_63"><![endif]></span></p>
    28022826
     
    28132837  o:title=" &lt;unnamed project&gt;"/>
    28142838</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=333
    2815 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
     2839src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image129.png"
    28162840alt="GSAS-II project: &lt;unnamed project&gt;" v:shapes="Picture_x0020_64"><![endif]></span></p>
    28172841
     
    28302854  o:title=" &lt;unnamed project&gt;"/>
    28312855</v:shape><![endif]--><![if !vml]><img border=0 width=481 height=181
    2832 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
     2856src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image131.png"
    28332857alt="GSAS-II project: &lt;unnamed project&gt;" v:shapes="Picture_x0020_66"><![endif]></span></p>
    28342858
     
    28502874  o:title=" NiTi"/>
    28512875</v:shape><![endif]--><![if !vml]><img border=0 width=478 height=439
    2852 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
     2876src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image133.png"
    28532877alt="GSAS-II plots: NiTi.gpx" v:shapes="Picture_x0020_59"><![endif]></span></p>
    28542878
     
    28752899  o:title=" &lt;unnamed project&gt;"/>
    28762900</v:shape><![endif]--><![if !vml]><img border=0 width=478 height=450
    2877 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
     2901src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image135.png"
    28782902alt="GSAS-II plots: &lt;unnamed project&gt;" v:shapes="Picture_x0020_68"><![endif]></span></p>
    28792903
     
    29512975  o:title=" NiTi"/>
    29522976</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=123
    2953 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
     2977src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image137.png"
    29542978alt="GSAS-II project: NiTi.gpx" v:shapes="Picture_x0020_82"><![endif]></span></p>
    29552979
     
    29642988  o:title=" &lt;unnamed project&gt;"/>
    29652989</v:shape><![endif]--><![if !vml]><img border=0 width=481 height=136
    2966 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
     2990src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image139.png"
    29672991alt="GSAS-II project: &lt;unnamed project&gt;" v:shapes="Picture_x0020_70"><![endif]></span></p>
    29682992
     
    29873011  o:title=" &lt;unnamed project&gt;"/>
    29883012</v:shape><![endif]--><![if !vml]><img border=0 width=476 height=418
    2989 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
     3013src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image141.png"
    29903014alt="GSAS-II project: &lt;unnamed project&gt;" v:shapes="Picture_x0020_71"><![endif]></span></p>
    29913015
     
    30003024  o:title=" &lt;unnamed project&gt;"/>
    30013025</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=456
    3002 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
     3026src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image143.png"
    30033027alt="GSAS-II project: &lt;unnamed project&gt;" v:shapes="Picture_x0020_72"><![endif]></span></p>
    30043028
     
    30773101  o:title=" NiTi-A"/>
    30783102</v:shape><![endif]--><![if !vml]><img border=0 width=480 height=457
    3079 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
     3103src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image145.png"
    30803104alt="GSAS-II project: NiTi-A.gpx" v:shapes="Picture_x0020_73"><![endif]></span></p>
    30813105
     
    31133137  o:title=" NiTi-A"/>
    31143138</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=588
    3115 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
     3139src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image147.png"
    31163140alt="GSAS-II plots: NiTi-A.gpx" v:shapes="Picture_x0020_84"><![endif]></span></p>
    31173141
     
    31373161  o:title=" NiTi-A"/>
    31383162</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=164
    3139 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
     3163src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image149.png"
    31403164alt="GSAS-II project: NiTi-A.gpx" v:shapes="Picture_x0020_75"><![endif]></span></p>
    31413165
     
    31623186  o:title=" NiTi-A"/>
    31633187</v:shape><![endif]--><![if !vml]><img border=0 width=477 height=184
    3164 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
     3188src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image151.png"
    31653189alt="GSAS-II project: NiTi-A.gpx" v:shapes="Picture_x0020_76"><![endif]></span></p>
    31663190
     
    31783202style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_77"
    31793203 o:spid="_x0000_i1064" type="#_x0000_t75" alt="GSAS-II project: NiTi-A.gpx"
    3180  style='width:363.75pt;height:237pt;visibility:visible;mso-wrap-style:square'>
     3204 style='width:363pt;height:237pt;visibility:visible;mso-wrap-style:square'>
    31813205 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
    31823206  o:title=" NiTi-A"/>
    3183 </v:shape><![endif]--><![if !vml]><img border=0 width=485 height=316
    3184 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
     3207</v:shape><![endif]--><![if !vml]><img border=0 width=484 height=316
     3208src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image154.png"
    31853209alt="GSAS-II project: NiTi-A.gpx" v:shapes="Picture_x0020_77"><![endif]></span></p>
    31863210
     
    32123236  o:title=" NiTi-A"/>
    32133237</v:shape><![endif]--><![if !vml]><img border=0 width=480 height=228
    3214 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
     3238src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image156.png"
    32153239alt="GSAS-II project: NiTi-A.gpx" v:shapes="Picture_x0020_78"><![endif]></span></p>
    32163240
     
    32343258  o:title=" NiTi-A"/>
    32353259</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=344
    3236 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
     3260src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image158.png"
    32373261alt="GSAS-II project: NiTi-A.gpx" v:shapes="Picture_x0020_79"><![endif]></span></p>
    32383262
     
    32503274  o:title=" NiTi-A"/>
    32513275</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=451
    3252 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
     3276src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image160.png"
    32533277alt="GSAS-II plots: NiTi-A.gpx" v:shapes="Picture_x0020_85"><![endif]></span></p>
    32543278
     
    32863310  o:title=" NiTi-A"/>
    32873311</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=451
    3288 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
     3312src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image162.png"
    32893313alt="GSAS-II plots: NiTi-A.gpx" v:shapes="Picture_x0020_86"><![endif]></span></p>
    32903314
     
    33033327  o:title=" NiTi-A"/>
    33043328</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=182
    3305 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
     3329src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image218.png"
    33063330alt="GSAS-II project: NiTi-A.gpx" v:shapes="Picture_x0020_87"><![endif]></span></p>
    33073331
     
    33213345  o:title=" NiTi-A"/>
    33223346</v:shape><![endif]--><![if !vml]><img border=0 width=478 height=450
    3323 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
     3347src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image219.png"
    33243348alt="GSAS-II plots: NiTi-A.gpx" v:shapes="Picture_x0020_88"><![endif]></span></p>
    33253349
    33263350<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This shows the
    33273351probability of reflection vectors coinciding with the sample wire axis; the
    3328 high spots are the 111 family of reflections. We should try the next higher harmonic
    3329 order (10). </p>
     3352high spots are the 111 family of reflections. We should try the next higher
     3353harmonic order (10). </p>
    33303354
    33313355<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
     
    33423366  o:title=" NiTi-A"/>
    33433367</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=451
    3344 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
     3368src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image220.png"
    33453369alt="GSAS-II plots: NiTi-A.gpx" v:shapes="Picture_x0020_89"><![endif]></span></p>
    33463370
     
    33713395  o:title=" NiTi-A"/>
    33723396</v:shape><![endif]--><![if !vml]><img border=0 width=480 height=266
    3373 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
     3397src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image221.png"
    33743398alt="GSAS-II project: NiTi-A.gpx" v:shapes="Picture_x0020_90"><![endif]></span></p>
    33753399
     
    33843408  o:title=" NiTi-A"/>
    33853409</v:shape><![endif]--><![if !vml]><img border=0 width=480 height=452
    3386 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
     3410src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image222.png"
    33873411alt="GSAS-II plots: NiTi-A.gpx" v:shapes="Picture_x0020_91"><![endif]></span></p>
    33883412
     
    33973421  o:title=" NiTi-A"/>
    33983422</v:shape><![endif]--><![if !vml]><img border=0 width=480 height=190
    3399 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"
     3423src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image223.png"
    34003424alt="GSAS-II project: NiTi-A.gpx" v:shapes="Picture_x0020_92"><![endif]></span></p>
    34013425
     
    34103434  o:title=" NiTi-A"/>
    34113435</v:shape><![endif]--><![if !vml]><img border=0 width=478 height=450
    3412 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image108.png"
     3436src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image224.png"
    34133437alt="GSAS-II plots: NiTi-A.gpx" v:shapes="Picture_x0020_93"><![endif]></span></p>
    34143438
     
    34163440the tutorial on Method A for doing texture analysis. It is useful for a case
    34173441like this one where there are very few data sets required for the texture
    3418 analysis. However, for the case of lower sample symmetry one must several dozen
    3419 or even a few hundred histograms and then the suite of parameters can easily be
    3420 &gt; 1000 of which only a few dozen describe the texture. This leads to the
    3421 next Methods for texture analysis in GSAS-II.</p>
     3442analysis. However, for the case of lower sample symmetry one must have several
     3443dozen or even a few hundred histograms and then the suite of parameters can
     3444easily be &gt; 1000 of which only a few dozen describe the texture. This leads
     3445to the next Methods for texture analysis in GSAS-II.</p>
    34223446
    34233447<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     
    34293453
    34303454<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
    3431 the texture analysis in much the same way as Method A except that all the initial
    3432 refinements are done “sequentially”, that is refinements are done for the
    3433 parameters associated with each powder pattern to convergence in a serial
     3455the texture analysis in much the same way as Method A except that all the
     3456initial refinements are done “sequentially”, that is refinements are done for
     3457the parameters associated with each powder pattern to convergence in a serial
    34343458fashion. In this case where there are 10 PWDR data sets, there will be 10
    34353459refinements done in sequence. Parameters that span all the data (e.g. lattice
     
    35073531mso-hansi-theme-font:minor-latin'>Phase fraction box</span></b> and change the <b
    35083532style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3509 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
    3510 orientation model</span></b> to <b style='mso-bidi-font-weight:normal'><span
     3533mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred orientation
     3534model</span></b> to <b style='mso-bidi-font-weight:normal'><span
    35113535style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    35123536mso-hansi-theme-font:minor-latin'>Spherical harmonics</span></b>. Then do <b
     
    35283552  o:title=" NiTi-B"/>
    35293553</v:shape><![endif]--><![if !vml]><img border=0 width=481 height=244
    3530 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image110.png"
     3554src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image225.png"
    35313555alt="GSAS-II project: NiTi-B.gpx" v:shapes="Picture_x0020_94"><![endif]></span></p>
    35323556
     
    35543578  o:title=" NiTi-B"/>
    35553579</v:shape><![endif]--><![if !vml]><img border=0 width=481 height=244
    3556 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image112.png"
     3580src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image226.png"
    35573581alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_95"><![endif]></span></p>
    35583582
    35593583<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You have the
    3560 choice of starting at the last one and for copying results from one to the
    3561 next. We won’t do either here. Each refinement will use the other controls
    3562 (e.g. <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3584choice of starting at the last one and for copying results from one to the next.
     3585We won’t do either here. Each refinement will use the other controls (e.g. <b
     3586style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    35633587mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Max cycles</span></b>)
    35643588as controls. We are now ready to do the 1<sup>st</sup> sequential refinement.
     
    35843608  o:title=" NiTi-B"/>
    35853609</v:shape><![endif]--><![if !vml]><img border=0 width=477 height=145
    3586 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image114.png"
     3610src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image227.png"
    35873611alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_96"><![endif]></span></p>
    35883612
     
    36053629  o:title=" NiTi-B"/>
    36063630</v:shape><![endif]--><![if !vml]><img border=0 width=477 height=449
    3607 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image116.png"
     3631src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image228.png"
    36083632alt="GSAS-II plots: NiTi-B.gpx" v:shapes="Picture_x0020_97"><![endif]></span></p>
    36093633
     
    36183642  o:title=" NiTi-B"/>
    36193643</v:shape><![endif]--><![if !vml]><img border=0 width=477 height=400
    3620 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image118.png"
     3644src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image229.png"
    36213645alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_98"><![endif]></span></p>
    36223646
     
    36293653minor-latin'>Harmonic order</span></b> to <b style='mso-bidi-font-weight:normal'><span
    36303654style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3631 mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>6</span></b> and
    3632 check the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3633 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
    3634 minor-latin'>Refine</span></b> box for it (Preferred orientation). Then in two
    3635 steps, first do <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3655mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>6</span></b>
     3656and check the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    36363657"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3637 minor-latin;mso-bidi-theme-font:minor-latin'>Edit Phase/Copy flags</span></b>
    3638 and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3639 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
    3640 minor-latin'>Set All</span></b> for the file selection. Then do <b
    3641 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3642 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
    3643 minor-latin'>Edit Phase/Copy selected data</span></b>; that will bring up a new
    3644 popup</p>
     3658minor-latin;mso-bidi-theme-font:minor-latin'>Refine</span></b> box for it
     3659(Preferred orientation). Then in two steps, first do <b style='mso-bidi-font-weight:
     3660normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3661minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Edit
     3662Phase/Copy flags</span></b> and <b style='mso-bidi-font-weight:normal'><span
     3663style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3664mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Set All</span></b>
     3665for the file selection. Then do <b style='mso-bidi-font-weight:normal'><span
     3666style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3667mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Edit
     3668Phase/Copy selected data</span></b>; that will bring up a new popup</p>
    36453669
    36463670<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     
    36543678alt="Select phase data parameters" v:shapes="Picture_x0020_99"><![endif]></span></p>
    36553679
    3656 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This allows
    3657 you to select which parameters to copy data and flags. Select <b
    3658 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3659 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
    3660 minor-latin'>Pref. Ori.</span></b> and press <b style='mso-bidi-font-weight:
     3680<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This allows you
     3681to select which parameters to copy data and flags. Select <b style='mso-bidi-font-weight:
    36613682normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3662 minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>OK</span></b>;
     3683minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Pref.
     3684Ori.</span></b> and press <b style='mso-bidi-font-weight:normal'><span
     3685style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3686mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>OK</span></b>;
    36633687the file selection is next. Do <b style='mso-bidi-font-weight:normal'><span
    36643688style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     
    36893713  o:title=" NiTi-B"/>
    36903714</v:shape><![endif]--><![if !vml]><img border=0 width=477 height=428
    3691 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image121.png"
     3715src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image230.png"
    36923716alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_100"><![endif]></span></p>
    36933717
     
    37063730  o:title=" NiTi-B"/>
    37073731</v:shape><![endif]--><![if !vml]><img border=0 width=477 height=117
    3708 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image123.png"
     3732src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image231.png"
    37093733alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_101"><![endif]></span></p>
    37103734
     
    37203744  o:title=" NiTi-B"/>
    37213745</v:shape><![endif]--><![if !vml]><img border=0 width=478 height=450
    3722 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image125.png"
     3746src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image232.png"
    37233747alt="GSAS-II plots: NiTi-B.gpx" v:shapes="Picture_x0020_102"><![endif]></span></p>
    37243748
     
    37503774  o:title=" NiTi-B"/>
    37513775</v:shape><![endif]--><![if !vml]><img border=0 width=480 height=118
    3752 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image127.png"
     3776src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image233.png"
    37533777alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_103"><![endif]></span></p>
    37543778
     
    37643788  o:title=" NiTi-B"/>
    37653789</v:shape><![endif]--><![if !vml]><img border=0 width=478 height=450
    3766 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image129.png"
     3790src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image234.png"
    37673791alt="GSAS-II plots: NiTi-B.gpx" v:shapes="Picture_x0020_104"><![endif]></span></p>
    37683792
    3769 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Showing that
    3770 perhaps the B19’ phase needs high order spherical harmonics. Select the <b><span
     3793<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Showing that perhaps
     3794the B19’ phase needs high order spherical harmonics. Select the <b><span
    37713795style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    37723796mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Data</span></b>
     
    37953819  o:title=" NiTi-B"/>
    37963820</v:shape><![endif]--><![if !vml]><img border=0 width=480 height=118
    3797 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image131.png"
     3821src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image235.png"
    37983822alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_105"><![endif]></span></p>
    37993823
     
    38263850  o:title=" NiTi-B"/>
    38273851</v:shape><![endif]--><![if !vml]><img border=0 width=477 height=128
    3828 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image133.png"
     3852src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image236.png"
    38293853alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_106"><![endif]></span></p>
    38303854
     
    38393863  o:title=" NiTi-B"/>
    38403864</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=214
    3841 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image135.png"
     3865src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image237.png"
    38423866alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_107"><![endif]></span></p>
    38433867
    3844 <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The preferred orientation
    3845 correction is <span class=SpellE>Prfo</span>; notice a few entries in red.
    3846 These are nonphysical correction values (physically, the correction can’t be
    3847 negative) but by in large these are small. This next step uses these
     3868<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The preferred
     3869orientation correction is <span class=SpellE>Prfo</span>; notice a few entries
     3870in red. These are nonphysical correction values (physically, the correction
     3871can’t be negative) but by in large these are small. This next step uses these
    38483872corrections as input data for a texture refinement. To start select the <b><span
    38493873style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     
    38583882  o:title=" NiTi-B"/>
    38593883</v:shape><![endif]--><![if !vml]><img border=0 width=481 height=166
    3860 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image137.png"
     3884src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image238.png"
    38613885alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_108"><![endif]></span></p>
    38623886
     
    38863910  o:title=" NiTi-B"/>
    38873911</v:shape><![endif]--><![if !vml]><img border=0 width=478 height=202
    3888 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image139.png"
     3912src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image239.png"
    38893913alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_109"><![endif]></span></p>
    38903914
     
    38923916style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    38933917mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
    3894 minor-latin'>Texture/Refine texture</span></b> from the menu; the window will
    3895 be repainted, and a bullseye pole figure will appear. Change the <b
     3918minor-latin'>Texture/Refine texture</span></b> from the menu; the window will be
     3919repainted, and a bullseye pole figure will appear. Change the <b
    38963920style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    38973921mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     
    39083932  o:title=" NiTi-B"/>
    39093933</v:shape><![endif]--><![if !vml]><img border=0 width=478 height=450
    3910 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image141.png"
     3934src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image240.png"
    39113935alt="GSAS-II plots: NiTi-B.gpx" v:shapes="Picture_x0020_110"><![endif]></span></p>
    39123936
     
    39333957  o:title=" NiTi-B"/>
    39343958</v:shape><![endif]--><![if !vml]><img border=0 width=480 height=257
    3935 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image143.png"
     3959src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image241.png"
    39363960alt="GSAS-II project: NiTi-B.gpx (sequential refinement)" v:shapes="Picture_x0020_111"><![endif]></span></p>
    39373961
     
    39463970  o:title=" NiTi-B"/>
    39473971</v:shape><![endif]--><![if !vml]><img border=0 width=478 height=450
    3948 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image145.png"
     3972src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image242.png"
    39493973alt="GSAS-II plots: NiTi-B.gpx" v:shapes="Picture_x0020_112"><![endif]></span></p>
    39503974
     
    41024126margin-left:.25in;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    41034127 id="Picture_x0020_113" o:spid="_x0000_i1033" type="#_x0000_t75" alt="GSAS-II project: NiTi-C.gpx (sequential refinement)"
    4104  style='width:345pt;height:142.5pt;visibility:visible;mso-wrap-style:square'>
     4128 style='width:345.75pt;height:142.5pt;visibility:visible;mso-wrap-style:square'>
    41054129 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image146.png"
    41064130  o:title=" NiTi-C"/>
    4107 </v:shape><![endif]--><![if !vml]><img border=0 width=460 height=190
    4108 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image147.png"
     4131</v:shape><![endif]--><![if !vml]><img border=0 width=461 height=190
     4132src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image243.png"
    41094133alt="GSAS-II project: NiTi-C.gpx (sequential refinement)" v:shapes="Picture_x0020_113"><![endif]></span></p>
    41104134
     
    41294153  o:title=" NiTi-C"/>
    41304154</v:shape><![endif]--><![if !vml]><img border=0 width=461 height=191
    4131 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image149.png"
     4155src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image244.png"
    41324156alt="GSAS-II project: NiTi-C.gpx (sequential refinement)" v:shapes="Picture_x0020_114"><![endif]></span></p>
    41334157
     
    41674191  o:title=" NiTi-C"/>
    41684192</v:shape><![endif]--><![if !vml]><img border=0 width=476 height=254
    4169 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image151.png"
     4193src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image245.png"
    41704194alt="GSAS-II project: NiTi-C.gpx (sequential refinement)" v:shapes="Picture_x0020_115"><![endif]></span></p>
    41714195
     
    42004224  o:title=" NiTi-C"/>
    42014225</v:shape><![endif]--><![if !vml]><img border=0 width=480 height=248
    4202 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image154.png"
     4226src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image246.png"
    42034227alt="GSAS-II project: NiTi-C.gpx" v:shapes="Picture_x0020_117"><![endif]></span></p>
    42044228
     
    42314255  o:title=" NiTi-C"/>
    42324256</v:shape><![endif]--><![if !vml]><img border=0 width=476 height=448
    4233 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image156.png"
     4257src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image247.png"
    42344258alt="GSAS-II plots: NiTi-C.gpx" v:shapes="Picture_x0020_118"><![endif]></span></p>
    42354259
     
    42454269  o:title=" NiTi-C"/>
    42464270</v:shape><![endif]--><![if !vml]><img border=0 width=476 height=205
    4247 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image158.png"
     4271src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image248.png"
    42484272alt="GSAS-II project: NiTi-C.gpx" v:shapes="Picture_x0020_119"><![endif]></span></p>
    42494273
     
    42624286  o:title=" NiTi-C"/>
    42634287</v:shape><![endif]--><![if !vml]><img border=0 width=480 height=452
    4264 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image160.png"
     4288src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image249.png"
    42654289alt="GSAS-II plots: NiTi-C.gpx" v:shapes="Picture_x0020_120"><![endif]></span></p>
    42664290
     
    42754299  o:title=" NiTi-C"/>
    42764300</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=264
    4277 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image162.png"
     4301src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image250.png"
    42784302alt="GSAS-II project: NiTi-C.gpx" v:shapes="Picture_x0020_121"><![endif]></span></p>
    42794303
  • Tutorials/2DTexture/Texture analysis of 2D data in GSAS-II_files/filelist.xml

    r4961 r4962  
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