Changeset 1856


Ignore:
Timestamp:
May 14, 2015 12:41:07 PM (8 years ago)
Author:
vondreele
Message:

put spaces around paragraphs

Location:
Tutorials/2DTexture
Files:
25 deleted
3 edited

Legend:

Unmodified
Added
Removed

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

    r1855 r1856  
    2525  <o:Author>Von Dreele</o:Author>
    2626  <o:LastAuthor>Von Dreele</o:LastAuthor>
    27   <o:Revision>8</o:Revision>
    28   <o:TotalTime>2140</o:TotalTime>
     27  <o:Revision>9</o:Revision>
     28  <o:TotalTime>2142</o:TotalTime>
    2929  <o:Created>2015-05-14T17:06:00Z</o:Created>
    30   <o:LastSaved>2015-05-14T17:30:00Z</o:LastSaved>
     30  <o:LastSaved>2015-05-14T17:39:00Z</o:LastSaved>
    3131  <o:Pages>1</o:Pages>
    3232  <o:Words>4340</o:Words>
    … …  
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    12761273@page WordSection1
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    … …  
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    … …  
    14181413<div class=WordSection1>
    14191414
    1420 <h1 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Texture analysis
    1421 of 2D data in GSAS-II</h1>
    1422 
    1423 <h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Introduction</h2>
    1424 
    1425 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    1426 115%'>Texture analysis using GSAS-II employs spherical harmonics modeling, as
    1427 described by Bunge, &quot;Texture Analysis in Materials Science&quot; (1982),
    1428 and implemented by Von Dreele, J. Appl. <span class=SpellE>Cryst</span>., <b
     1415<h1 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     14160in;line-height:115%'>Texture analysis of 2D data in GSAS-II</h1>
     1417
     1418<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     14190in;line-height:115%'>Introduction</h2>
     1420
     1421<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Texture
     1422analysis using GSAS-II employs spherical harmonics modeling, as described by
     1423Bunge, &quot;Texture Analysis in Materials Science&quot; (1982), and
     1424implemented by Von Dreele, J. Appl. <span class=SpellE>Cryst</span>., <b
    14291425style='mso-bidi-font-weight:normal'>30</b>, 517-525 (1997) in GSAS. The even
    14301426part of the orientation distribution function (ODF) via the general axis
    14311427equation</p>
    14321428
    1433 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    1434 115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc m:val="left"/></m:oMathParaPr><m:oMath><i
    1435   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><span
     1429<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1430   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
     1431  style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><span
    14361432    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    14371433    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    … …  
    15131509  o:title="" chromakey="white"/>
    15141510</v:shape><![endif]--><![if !vml]><img width=357 height=56
    1515 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
     1511src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image002.png"
    15161512v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    15171513
    1518 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
    1519 class=GramE>is</span> used to give the intensity corrections due to texture.
    1520 The two harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1514<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     1515margin-left:0in;line-height:115%'><span class=GramE>is</span> used to give the
     1516intensity corrections due to texture. The two harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    15211517   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    15221518   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    … …  
    15341530EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    15351531 type="#_x0000_t75" style='width:32.25pt;height:26.25pt'>
    1536  <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"
     1532 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image003.png"
    15371533  o:title="" chromakey="white"/>
    15381534</v:shape><![endif]--><![if !vml]><img width=43 height=35
    1539 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image105.png"
     1535src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"
    15401536v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    15411537style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    … …  
    15551551  o:title="" chromakey="white"/>
    15561552</v:shape><![endif]--><![if !vml]><img width=40 height=35
    1557 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image107.png"
     1553src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"
    15581554v:shapes="_x0000_i1025"><![endif]></span><![endif]>, take on values according
    15591555to the crystal and sample symmetries, respectively, and thus the two inner
    … …  
    15801576  o:title="" chromakey="white"/>
    15811577</v:shape><![endif]--><![if !vml]><img width=39 height=35
    1582 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image108.png"
     1578src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image008.png"
    15831579v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    15841580style='mso-spacerun:yes'> </span>terms are nonzero so the rest are excluded
    … …  
    15981594  o:title="" chromakey="white"/>
    15991595</v:shape><![endif]--><![if !vml]><img width=28 height=35
    1600 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image109.png"
     1596src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image010.png"
    16011597v:shapes="_x0000_i1025"><![endif]></span><![endif]>coefficients is sufficient
    1602 to describe the effect on the d<span class=SpellE>iffraction</span> patterns
    1603 due to texture. The crystal harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1598to describe the effect on the diffraction patterns due to texture. The crystal
     1599harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    16041600   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    16051601   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    … …  
    16171613  o:title="" chromakey="white"/>
    16181614</v:shape><![endif]--><![if !vml]><img width=43 height=35
    1619 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image110.png"
     1615src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image012.png"
    16201616v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined for each
    16211617reflection, h, <i>via</i> polar and azimuthal coordinates (<span
    … …  
    16431639  o:title="" chromakey="white"/>
    16441640</v:shape><![endif]--><![if !vml]><img width=40 height=35
    1645 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image107.png"
     1641src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"
    16461642v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined according to
    16471643polar and azimuthal coordinates (<span style='font-family:Symbol'>y</span>, <span
    … …  
    16551651the general axis equation becomes</p>
    16561652
    1657 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1653<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     1654margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
    16581655   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
    16591656  style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><span
    … …  
    17171714  o:title="" chromakey="white"/>
    17181715</v:shape><![endif]--><![if !vml]><img width=428 height=72
    1719 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image111.png"
     1716src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image014.png"
    17201717v:shapes="_x0000_i1025"><![endif]></span><![endif]><br style='mso-special-character:
    17211718line-break'>
    … …  
    17231720<![endif]></p>
    17241721
    1725 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    1726 115%'>In a diffraction experiment the crystal reflection coordinates (<span
     1722<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In a
     1723diffraction experiment the crystal reflection coordinates (<span
    17271724style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
    17281725are determined by the choice of reflection index (<span class=SpellE>hkl</span>)
    … …  
    17311728on the diffractometer.</p>
    17321729
    1733 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>To
    1734 define the sample coordinates (<span style='font-family:Symbol'>y</span>, <span
    1735 style='font-family:Symbol'>g</span>), we have defined an instrument coordinate
    1736 system (I, J, K) such that K is normal to the diffraction plane and J is
    1737 coincident with the direction of the incident radiation beam toward the source.
    1738 We further define a standard set of right-handed goniometer <span class=SpellE>eulerian</span>
    1739 angles (<span style='font-family:Symbol'>W</span>, <span style='font-family:
    1740 Symbol'>C</span>, <span style='font-family:Symbol'>F</span>) so that <span
    1741 style='font-family:Symbol'>W</span> and <span style='font-family:Symbol'>F</span>
    1742 are rotations about K and <span style='font-family:Symbol'>C</span> is a
    1743 rotation about J when <span style='font-family:Symbol'>W</span> <span
    1744 style='font-family:Symbol'><span style='mso-spacerun:yes'> </span></span>=
    1745 0.<span style='mso-spacerun:yes'>  </span>Finally, as the sample may be mounted
    1746 so that the sample coordinate system (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>,
    1747 K<sub>s</sub>) does not coincide with the instrument coordinate system (I, J,
    1748 K), we define three <span class=SpellE>eulerian</span> sample rotation offset
    1749 angles (<span style='font-family:Symbol'>W</span><sub>s</sub>, <span
    1750 style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:Symbol'>F</span><sub>s</sub>)
    1751 that describe the rotation from (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>,
    1752 K<sub>s</sub>) to (I, J, K).<span style='mso-spacerun:yes'>  </span>The sample
    1753 rotation angles are defined so that with the goniometer angles at zero <span
    1754 style='font-family:Symbol'>W</span><sub>s</sub> and <span style='font-family:
    1755 Symbol'>F</span><sub>s</sub> are rotations about I and <span style='font-family:
    1756 Symbol'>C</span><sub>s</sub> is a rotation about J.<span
    1757 style='mso-spacerun:yes'>  </span>The zeros of these three sample rotation
    1758 angles can be refined as part of the Rietveld analysis to accommodate any
    1759 angular offset in sample mounting. After including the diffraction angle, <span
    1760 style='font-family:Symbol'>Q</span>, and a detector azimuthal angle, A, the
    1761 full rotation matrix, <b style='mso-bidi-font-weight:normal'>M</b>, is </p>
    1762 
    1763 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><b
    1764 style='mso-bidi-font-weight:normal'>M = -</b><b style='mso-bidi-font-weight:
    1765 normal'><span style='font-family:Symbol'>Q</span>A</b><b style='mso-bidi-font-weight:
    1766 normal'><span style='font-family:Symbol'>W<span class=GramE>C<span
    1767 style='font-family:"Times New Roman",serif'>(</span></span>F</span>+</b><b
     1730<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     1731margin-left:0in;line-height:115%'>To define the sample coordinates (<span
     1732style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>),
     1733we have defined an instrument coordinate system (I, J, K) such that K is normal
     1734to the diffraction plane and J is coincident with the direction of the incident
     1735radiation beam toward the source. We further define a standard set of
     1736right-handed goniometer <span class=SpellE>eulerian</span> angles (<span
     1737style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>,
     1738<span style='font-family:Symbol'>F</span>) so that <span style='font-family:
     1739Symbol'>W</span> and <span style='font-family:Symbol'>F</span> are rotations
     1740about K and <span style='font-family:Symbol'>C</span> is a rotation about J
     1741when <span style='font-family:Symbol'>W</span> <span style='font-family:Symbol'><span
     1742style='mso-spacerun:yes'> </span></span>= 0.<span style='mso-spacerun:yes'> 
     1743</span>Finally, as the sample may be mounted so that the sample coordinate
     1744system (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>)
     1745does not coincide with the instrument coordinate system (I, J, K), we define
     1746three <span class=SpellE>eulerian</span> sample rotation offset angles (<span
     1747style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
     1748<span style='font-family:Symbol'>F</span><sub>s</sub>) that describe the
     1749rotation from (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>)
     1750to (I, J, K).<span style='mso-spacerun:yes'>  </span>The sample rotation angles
     1751are defined so that with the goniometer angles at zero <span style='font-family:
     1752Symbol'>W</span><sub>s</sub> and <span style='font-family:Symbol'>F</span><sub>s</sub>
     1753are rotations about I and <span style='font-family:Symbol'>C</span><sub>s</sub>
     1754is a rotation about J.<span style='mso-spacerun:yes'>  </span>The zeros of
     1755these three sample rotation angles can be refined as part of the Rietveld
     1756analysis to accommodate any angular offset in sample mounting. After including
     1757the diffraction angle, <span style='font-family:Symbol'>Q</span>, and a
     1758detector azimuthal angle, A, the full rotation matrix, <b style='mso-bidi-font-weight:
     1759normal'>M</b>, is </p>
     1760
     1761<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     1762margin-left:0in;line-height:115%'><b style='mso-bidi-font-weight:normal'>M = -</b><b
     1763style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>Q</span>A</b><b
     1764style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>W<span
     1765class=GramE>C<span style='font-family:"Times New Roman",serif'>(</span></span>F</span>+</b><b
    17681766style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span><sub>s</sub>)</b><b
    17691767style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>C</span><span
    17701768class=SpellE><sub>s</sub><span style='font-family:Symbol'>W</span><sub>s</sub></span><o:p></o:p></b></p>
    17711769
    1772 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>By
    1773 transformation of unit Cartesian vectors (100, 010 and 001) with this rotation
    1774 matrix, the sample orientation coordinates (<span style='font-family:Symbol'>y</span>,
    1775 <span style='font-family:Symbol'>g</span>) are given by</p>
    1776 
    1777 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
    1778 class=GramE><i>cos</i>(</span><span style='font-family:Symbol'>y</span>) = <!--[if gte msEquation 12]><m:oMath><i
     1770<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     1771margin-left:0in;line-height:115%'>By transformation of unit Cartesian vectors
     1772(100, 010 and 001) with this rotation matrix, the sample orientation
     1773coordinates (<span style='font-family:Symbol'>y</span>, <span style='font-family:
     1774Symbol'>g</span>) are given by</p>
     1775
     1776<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     1777margin-left:0in;line-height:115%'><span class=GramE><i>cos</i>(</span><span
     1778style='font-family:Symbol'>y</span>) = <!--[if gte msEquation 12]><m:oMath><i
    17791779 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
    17801780   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    … …  
    17961796  o:title="" chromakey="white"/>
    17971797</v:shape><![endif]--><![if !vml]><img width=45 height=67
    1798 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image112.png"
     1798src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.png"
    17991799v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    18001800style='mso-spacerun:yes'> </span>and<span style='mso-spacerun:yes'>   </span><i>tan</i>(<span
    … …  
    18331833  o:title="" chromakey="white"/>
    18341834</v:shape><![endif]--><![if !vml]><img width=107 height=67
    1835 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image113.png"
     1835src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.png"
    18361836v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    18371837
    1838 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>The
    1839 harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1838<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     1839margin-left:0in;line-height:115%'>The harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    18401840   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    18411841   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    … …  
    18531853  o:title="" chromakey="white"/>
    18541854</v:shape><![endif]--><![if !vml]><img width=62 height=35
    1855 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image114.png"
     1855src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"
    18561856v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    18571857style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    … …  
    18711871  o:title="" chromakey="white"/>
    18721872</v:shape><![endif]--><![if !vml]><img width=57 height=35
    1873 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image115.png"
     1873src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.png"
    18741874v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are developed from</p>
    18751875
    1876 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1876<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     1877margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
    18771878   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
    18781879    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    … …  
    19251926  o:title="" chromakey="white"/>
    19261927</v:shape><![endif]--><![if !vml]><img width=220 height=56
    1927 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image116.png"
     1928src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"
    19281929v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    19291930
    1930 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
    1931 class=GramE>where</span> the normalized associated Legendre functions, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     1931<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     1932margin-left:0in;line-height:115%'><span class=GramE>where</span> the normalized
     1933associated Legendre functions, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    19321934   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    19331935   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    … …  
    19481950  o:title="" chromakey="white"/>
    19491951</v:shape><![endif]--><![if !vml]><img width=44 height=35
    1950 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image117.png"
    1951 v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are defin<span
    1952 class=SpellE>ed</span> via a Fourier expansion as</p>
    1953 
    1954 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     1952src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image026.png"
     1953v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are defined via a Fourier
     1954expansion as</p>
     1955
     1956<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     1957margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
    19551958   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
    19561959    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    … …  
    19992002  o:title="" chromakey="white"/>
    20002003</v:shape><![endif]--><![if !vml]><img width=206 height=70
    2001 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image118.png"
     2004src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image028.png"
    20022005v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    20032006
    2004 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
    2005 class=GramE>for</span> m even and</p>
    2006 
    2007 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2007<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2008margin-left:0in;line-height:115%'><span class=GramE>for</span> m even and</p>
     2009
     2010<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2011margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
    20082012   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
    20092013    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    … …  
    20522056  o:title="" chromakey="white"/>
    20532057</v:shape><![endif]--><![if !vml]><img width=211 height=70
    2054 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image119.png"
     2058src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image030.png"
    20552059v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    20562060
    2057 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
    2058 class=GramE>for</span> m odd.<span style='mso-spacerun:yes'>  </span>Each sum
    2059 is only over either the even or odd values of s, respectively, because of the
    2060 properties of the Fourier coefficients<span class=GramE>, </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2061<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2062margin-left:0in;line-height:115%'><span class=GramE>for</span> m odd.<span
     2063style='mso-spacerun:yes'>  </span>Each sum is only over either the even or odd
     2064values of s, respectively, because of the properties of the Fourier
     2065coefficients<span class=GramE>, </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    20612066   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    20622067   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    … …  
    20742079  o:title="" chromakey="white"/>
    20752080</v:shape><![endif]--><![if !vml]><img width=33 height=35
    2076 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image120.png"
     2081src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image032.png"
    20772082v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
    20782083style='mso-spacerun:yes'>  </span>These Fourier coefficients are determined so
    20792084that the definition</p>
    20802085
    2081 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2086<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2087margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
    20822088   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
    20832089    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    … …  
    22002206  o:title="" chromakey="white"/>
    22012207</v:shape><![endif]--><![if !vml]><img width=565 height=74
    2202 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image121.png"
     2208src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image034.png"
    22032209v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    22042210
    2205 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
    2206 class=GramE>is</span> satisfied.<span style='mso-spacerun:yes'>  </span>Terms
    2207 of the form <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
     2211<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2212margin-left:0in;line-height:115%'><span class=GramE>is</span> satisfied.<span
     2213style='mso-spacerun:yes'>  </span>Terms of the form <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
    22082214   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    22092215   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    … …  
    22382244  o:title="" chromakey="white"/>
    22392245</v:shape><![endif]--><![if !vml]><img width=148 height=35
    2240 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image122.png"
     2246src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image036.png"
    22412247v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    22422248style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
    … …  
    22732279  o:title="" chromakey="white"/>
    22742280</v:shape><![endif]--><![if !vml]><img width=134 height=35
    2275 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image123.png"
     2281src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image038.png"
    22762282v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    22772283style='mso-spacerun:yes'> </span>are combined depending on the symmetry and the
    … …  
    22942300  o:title="" chromakey="white"/>
    22952301</v:shape><![endif]--><![if !vml]><img width=64 height=35
    2296 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image124.png"
     2302src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"
    22972303v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    22982304style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    … …  
    23132319  o:title="" chromakey="white"/>
    23142320</v:shape><![endif]--><![if !vml]><img width=60 height=35
    2315 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image125.png"
     2321src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image042.png"
    23162322v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
    23172323style='mso-spacerun:yes'>  </span>For cubic crystal symmetry, the term <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    … …  
    23322338  o:title="" chromakey="white"/>
    23332339</v:shape><![endif]--><![if !vml]><img width=64 height=35
    2334 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image124.png"
     2340src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"
    23352341v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    2336 style='mso-spacerun:yes'> </span>is obtained direc<span class=SpellE>tly</span>
    2337 from the Fourier expansion</p>
    2338 
    2339 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2342style='mso-spacerun:yes'> </span>is obtained directly from the Fourier
     2343expansion</p>
     2344
     2345<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2346margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
    23402347   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
    23412348    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    … …  
    23922399  o:title="" chromakey="white"/>
    23932400</v:shape><![endif]--><![if !vml]><img width=258 height=70
    2394 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image126.png"
     2401src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image044.png"
    23952402v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    23962403
    2397 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
    2398 class=GramE>using</span> the coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2404<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2405margin-left:0in;line-height:115%'><span class=GramE>using</span> the
     2406coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    23992407   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    24002408   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    … …  
    24112419  o:title="" chromakey="white"/>
    24122420</v:shape><![endif]--><![if !vml]><img width=30 height=35
    2413 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image127.png"
     2421src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image046.png"
    24142422v:shapes="_x0000_i1025"><![endif]></span><![endif]>, as tabulated by Bunge
    24152423(1982). </p>
    24162424
    2417 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>The
    2418 Rietveld refinement of texture then proceeds by constructing derivatives of the
    2419 profile intensities with respect to the allowed harmonic coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
     2425<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2426margin-left:0in;line-height:115%'>The Rietveld refinement of texture then
     2427proceeds by constructing derivatives of the profile intensities with respect to
     2428the allowed harmonic coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
    24202429   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    24212430   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    … …  
    24322441  o:title="" chromakey="white"/>
    24332442</v:shape><![endif]--><![if !vml]><img width=29 height=35
    2434 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image128.png"
     2443src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
    24352444v:shapes="_x0000_i1025"><![endif]></span><![endif]>, and the three sample
    24362445orientation angles, <span style='font-family:Symbol'>W</span><sub>s</sub>, <span
    … …  
    24532462  o:title="" chromakey="white"/>
    24542463</v:shape><![endif]--><![if !vml]><img width=29 height=35
    2455 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image128.png"
     2464src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
    24562465v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    24572466style='mso-spacerun:yes'> </span>and the sample orientation angles <span
    … …  
    24602469</p>
    24612470
    2462 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>The
    2463 magnitude of the texture is evaluated from the texture index by</p>
    2464 
    2465 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
     2471<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2472margin-left:0in;line-height:115%'>The magnitude of the texture is evaluated
     2473from the texture index by</p>
     2474
     2475<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2476margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
    24662477   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
    24672478  style='font-family:"Cambria Math",serif'><m:r>J</m:r><m:r>=1+</m:r></span></i><m:nary><m:naryPr><m:chr
    … …  
    25062517"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
    25072518mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    2508  id="_x0000_i1025" type="#_x0000_t75" style='width:180.7pt;height:54pt'>
     2519 id="_x0000_i1025" type="#_x0000_t75" style='width:180.75pt;height:54pt'>
    25092520 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.png"
    25102521  o:title="" chromakey="white"/>
    25112522</v:shape><![endif]--><![if !vml]><img width=241 height=72
    2512 src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image129.png"
     2523src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
    25132524v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    25142525
    2515 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>If
    2516 the texture is random then J = 1, otherwise J &gt; 1; for a single crystal J = <span
    2517 style='font-family:Symbol'>¥.</span> </p>
    2518 
    2519 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>In
    2520 GSAS-II the texture is defined in two ways to accommodate the two possible uses
    2521 of this correction. In one a suite of spherical harmonics coefficients is
    2522 defined for the texture of a phase in the sample; this can have any of the
    2523 possible sample symmetries and is the usual result desired for texture
    2524 analysis. The other is the suite of spherical harmonics terms for cylindrical
    2525 sample symmetry for each phase in each powder pattern (“histogram”) and is usually
    2526 used to accommodate preferred orientation effects in a Rietveld refinement. The
    2527 former description allows refinement of the sample orientation zeros, <span
    2528 style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
    2529 <span style='font-family:Symbol'>F</span><sub>s</sub>, but the latter
    2530 description does not (they are assumed to be zero and not refinable). The sample
    2531 orientation angles, (<span style='font-family:Symbol'>W</span>, <span
    2532 style='font-family:Symbol'>C</span>, <span style='font-family:Symbol'>F) </span>are
    2533 specified in the Sample Parameters table in the GSAS-II data tree structure and
    2534 are applied for either description.</p>
    2535 
    2536 <p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>In
    2537 this tutorial we will use both of these descriptions to determine the texture
    2538 of the two phases in a <span class=SpellE>NiTi</span> shape memory alloy sample
    2539 with cylindrical symmetry (wire texture) as collected at APS on beam line 1ID-C
    2540 (data kindly provided by Paul Paradise &amp; Aaron <span class=SpellE>Stebner</span>
    2541 of Colo. School of Mines). Thus, there are three ways within GSAS-II that can
    2542 be used for this texture analysis all beginning with the same 2D area detector
    2543 image. Each will be described in turn after the initial setup of the GSAS-II
    2544 project, image input &amp; integration.</p>
    2545 
    2546 <h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 1. Image
    2547 input &amp; integration</h2>
    2548 
    2549 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2550 115%'>If you have not done so already, <u><span style='color:#0070C0'><a
     2526<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2527margin-left:0in;line-height:115%'>If the texture is random then J = 1,
     2528otherwise J &gt; 1; for a single crystal J = <span style='font-family:Symbol'>¥.</span>
     2529</p>
     2530
     2531<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2532margin-left:0in;line-height:115%'>In GSAS-II the texture is defined in two ways
     2533to accommodate the two possible uses of this correction. In one a suite of
     2534spherical harmonics coefficients is defined for the texture of a phase in the
     2535sample; this can have any of the possible sample symmetries and is the usual
     2536result desired for texture analysis. The other is the suite of spherical
     2537harmonics terms for cylindrical sample symmetry for each phase in each powder
     2538pattern (“histogram”) and is usually used to accommodate preferred orientation
     2539effects in a Rietveld refinement. The former description allows refinement of
     2540the sample orientation zeros, <span style='font-family:Symbol'>W</span><sub>s</sub>,
     2541<span style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:
     2542Symbol'>F</span><sub>s</sub>, but the latter description does not (they are
     2543assumed to be zero and not refinable). The sample orientation angles, (<span
     2544style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>,
     2545<span style='font-family:Symbol'>F) </span>are specified in the Sample
     2546Parameters table in the GSAS-II data tree structure and are applied for either
     2547description.</p>
     2548
     2549<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     2550margin-left:0in;line-height:115%'>In this tutorial we will use both of these
     2551descriptions to determine the texture of the two phases in a <span
     2552class=SpellE>NiTi</span> shape memory alloy sample with cylindrical symmetry
     2553(wire texture) as collected at APS on beam line 1ID-C (data kindly provided by
     2554Paul Paradise &amp; Aaron <span class=SpellE>Stebner</span> of Colo. School of
     2555Mines). Thus, there are three ways within GSAS-II that can be used for this
     2556texture analysis all beginning with the same 2D area detector image. Each will
     2557be described in turn after the initial setup of the GSAS-II project, image
     2558input &amp; integration.</p>
     2559
     2560<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     25610in;line-height:115%'>Step 1. Image input &amp; integration</h2>
     2562
     2563<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you have
     2564not done so already, <u><span style='color:#0070C0'><a
    25512565href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none;
    25522566text-underline:none'>start GSAS-II</span></a></span></u>. Note that menu
    … …  
    25662580mso-bidi-theme-font:minor-latin'>About GSAS-II</span></b>). </p>
    25672581
    2568 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2569 115%'>Use the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    2570 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    2571 minor-latin'>Data/Read image data</span></b> menu item to read the data file
    2572 into the current GSAS-II project. A file selection dialog will be shown; its
    2573 appearance will depend on your OS. Change the search directory to <b
    2574 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2575 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
    2576 Calibri;mso-bidi-theme-font:minor-latin'>/exercises/2DTexture </span></b>and
    2577 then select the file <b style='mso-bidi-font-weight:normal'><span
    2578 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2579 mso-hansi-theme-font:minor-latin'>NDC5_01588_1.ge2</span></b>. A (faint) image
    2580 will appear</p>
    2581 
    2582 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2583 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_29"
     2582<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Use the <b
     2583style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2584mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Read
     2585image data</span></b> menu item to read the data file into the current GSAS-II
     2586project. A file selection dialog will be shown; its appearance will depend on
     2587your OS. Change the search directory to <b style='mso-bidi-font-weight:normal'><span
     2588style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2589mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
     2590minor-latin'>/exercises/2DTexture </span></b>and then select the file <b
     2591style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2592mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NDC5_01588_1.ge2</span></b>.
     2593A (faint) image will appear</p>
     2594
     2595<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2596style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_29"
    25842597 o:spid="_x0000_i1081" type="#_x0000_t75" style='width:525pt;height:450pt;
    25852598 visibility:visible;mso-wrap-style:square'>
    … …  
    25902603v:shapes="Picture_x0020_29"><![endif]></span></p>
    25912604
    2592 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2593 115%'><span class=GramE>and</span> the <b style='mso-bidi-font-weight:normal'><span
     2605<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2606class=GramE>and</span> the <b style='mso-bidi-font-weight:normal'><span
    25942607style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    25952608mso-hansi-theme-font:minor-latin'>Image Controls</span></b> data page will show</p>
    25962609
    2597 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2598 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_30"
     2610<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2611style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_30"
    25992612 o:spid="_x0000_i1080" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
    26002613 visibility:visible;mso-wrap-style:square'>
    … …  
    26052618v:shapes="Picture_x0020_30"><![endif]></span></p>
    26062619
    2607 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2608 115%'>The detector was previously calibrated and the coefficients are stored in
    2609 a file found by doing <b style='mso-bidi-font-weight:normal'><span
    2610 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2611 mso-hansi-theme-font:minor-latin'>Operations/Load Controls</span></b> from the <b
    2612 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2620<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detector
     2621was previously calibrated and the coefficients are stored in a file found by
     2622doing <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2623mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Load
     2624Controls</span></b> from the <b style='mso-bidi-font-weight:normal'><span
     2625style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2626mso-hansi-theme-font:minor-latin'>Image Controls</span></b> menu. A file
     2627selection popup will appear showing <b style='mso-bidi-font-weight:normal'><span
     2628style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2629mso-hansi-theme-font:minor-latin'>NDC5.imctrl</span></b>; select it and press <b
     2630style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2631mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Open</span></b>.
     2632The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    26132633mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
    2614 Controls</span></b> menu. A file selection popup will appear showing <b
    2615 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2616 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NDC5.imctrl</span></b>;
    2617 select it and press <b style='mso-bidi-font-weight:normal'><span
    2618 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2619 mso-hansi-theme-font:minor-latin'>Open</span></b>. The <b style='mso-bidi-font-weight:
    2620 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2621 minor-latin;mso-hansi-theme-font:minor-latin'>Image Controls</span></b> window
    2622 will be repainted with the new values (do a reselect of the image from the tree
    2623 and then <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2624 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
    2625 Controls</span></b> to make sure the image is up to date.)</p>
    2626 
    2627 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2628 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_31"
     2634Controls</span></b> window will be repainted with the new values (do a reselect
     2635of the image from the tree and then <b style='mso-bidi-font-weight:normal'><span
     2636style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2637mso-hansi-theme-font:minor-latin'>Image Controls</span></b> to make sure the
     2638image is up to date.)</p>
     2639
     2640<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2641style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_31"
    26292642 o:spid="_x0000_i1079" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
    26302643 visibility:visible;mso-wrap-style:square'>
    … …  
    26352648v:shapes="Picture_x0020_31"><![endif]></span></p>
    26362649
    2637 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2638 115%'>The detail in the image can be enhanced by lowering the <b
    2639 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2640 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Max
    2641 intensity</span></b> (<b style='mso-bidi-font-weight:normal'><span
    2642 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2643 mso-hansi-theme-font:minor-latin'>15000</span></b> is suitable) and shows that
    2644 the diffraction rings show the effect of texture and that the image has a
    2645 fairly high background. Placing the cursor in the corners or inside the inner
    2646 ring shows a background &gt;1700. This can be suppressed by adjusting the <b
    2647 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2648 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Flat <span
    2649 class=SpellE>Bkg</span></span></b> (I chose <b style='mso-bidi-font-weight:
    2650 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2651 minor-latin;mso-hansi-theme-font:minor-latin'>1700</span></b> for this). The
    2652 image will now show the rings much more clearly.</p>
    2653 
    2654 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2655 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32"
     2650<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detail in
     2651the image can be enhanced by lowering the <b style='mso-bidi-font-weight:normal'><span
     2652style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2653mso-hansi-theme-font:minor-latin'>Max intensity</span></b> (<b
     2654style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2655mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>15000</span></b>
     2656is suitable) and shows that the diffraction rings show the effect of texture
     2657and that the image has a fairly high background. Placing the cursor in the
     2658corners or inside the inner ring shows a background &gt;1700. This can be suppressed
     2659by adjusting the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     2660"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     2661minor-latin'>Flat <span class=SpellE>Bkg</span></span></b> (I chose <b
     2662style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2663mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>1700</span></b>
     2664for this). The image will now show the rings much more clearly.</p>
     2665
     2666<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2667style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32"
    26562668 o:spid="_x0000_i1078" type="#_x0000_t75" style='width:525pt;height:450pt;
    26572669 visibility:visible;mso-wrap-style:square'>
    … …  
    26622674v:shapes="Picture_x0020_32"><![endif]></span></p>
    26632675
    2664 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2665 115%'>For texture analysis we will need to integrate the image into a number of
    2666 slices sampling the changing ring intensity with azimuthal angle. Also note
    2667 that the image seems to have <b style='mso-bidi-font-weight:normal'><span
    2668 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2669 mso-hansi-theme-font:minor-latin'>mm</span></b> symmetry so that the unique
    2670 part of this intensity variation covers 0-90° of azimuth. In addition the ring
    2671 intensity variation is such that using 10° slices will capture it reasonably
    2672 well. However, we want to include both 0° and 90° as slice centers. Thus there
    2673 will be 10 slices beginning at -5° and ending at 95°. Check the <b
    2674 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2675 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show
    2676 integration limits?</span></b> <span class=GramE>box</span> and uncheck the <b
    2677 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2678 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Do full
    2679 integration? </span></b><span class=GramE>box</span>, enter <b
    2680 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2681 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>
     2676<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For texture
     2677analysis we will need to integrate the image into a number of slices sampling
     2678the changing ring intensity with azimuthal angle. Also note that the image
     2679seems to have <b style='mso-bidi-font-weight:normal'><span style='font-family:
     2680"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     2681minor-latin'>mm</span></b> symmetry so that the unique part of this intensity
     2682variation covers 0-90° of azimuth. In addition the ring intensity variation is
     2683such that using 10° slices will capture it reasonably well. However, we want to
     2684include both 0° and 90° as slice centers. Thus there will be 10 slices
     2685beginning at -5° and ending at 95°. Check the <b style='mso-bidi-font-weight:
     2686normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2687minor-latin;mso-hansi-theme-font:minor-latin'>Show integration limits?</span></b>
     2688<span class=GramE>box</span> and uncheck the <b style='mso-bidi-font-weight:
     2689normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2690minor-latin;mso-hansi-theme-font:minor-latin'>Do full integration? </span></b><span
     2691class=GramE>box</span>, enter <b style='mso-bidi-font-weight:normal'><span
     2692style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2693mso-hansi-theme-font:minor-latin'>10</span></b> in the <b style='mso-bidi-font-weight:
     2694normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2695minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth bins</span></b>,
     2696enter <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2697mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-5</span></b>
    26822698in the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2683 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth
    2684 bins</span></b>, enter <b style='mso-bidi-font-weight:normal'><span
    2685 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2686 mso-hansi-theme-font:minor-latin'>-5</span></b> in the <b style='mso-bidi-font-weight:
     2699mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Start
     2700azimuth</span></b> box (it will change to 355) and enter <b style='mso-bidi-font-weight:
    26872701normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2688 minor-latin;mso-hansi-theme-font:minor-latin'>Start azimuth</span></b> box (it
    2689 will change to 355) and enter <b style='mso-bidi-font-weight:normal'><span
    2690 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2691 mso-hansi-theme-font:minor-latin'>455</span></b> in the <b style='mso-bidi-font-weight:
    2692 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2693 minor-latin;mso-hansi-theme-font:minor-latin'>End azimuth</span></b> box. In
    2694 addition, recall that the sample was mounted vertically and thus is aligned
    2695 with the defined laboratory I axis. Thus, the sample coordinate system needs to
    2696 be rotated by 90° to match the sample axis with the K axis; this can be done by
    2697 making the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    2698 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    2699 minor-latin'>Sample goniometer axis Chi</span></b> = <b style='mso-bidi-font-weight:
    2700 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2701 minor-latin;mso-hansi-theme-font:minor-latin'>90</span></b>. The plot will
    2702 change with each entry and at the end should look like</p>
    2703 
    2704 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2705 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_33"
     2702minor-latin;mso-hansi-theme-font:minor-latin'>455</span></b> in the <b
     2703style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2704mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>End azimuth</span></b>
     2705box. In addition, recall that the sample was mounted vertically and thus is
     2706aligned with the defined laboratory I axis. Thus, the sample coordinate system
     2707needs to be rotated by 90° to match the sample axis with the K axis; this can
     2708be done by making the <b style='mso-bidi-font-weight:normal'><span
     2709style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2710mso-hansi-theme-font:minor-latin'>Sample goniometer axis Chi</span></b> = <b
     2711style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2712mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>90</span></b>.
     2713The plot will change with each entry and at the end should look like</p>
     2714
     2715<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2716style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_33"
    27062717 o:spid="_x0000_i1077" type="#_x0000_t75" style='width:525pt;height:450pt;
    27072718 visibility:visible;mso-wrap-style:square'>
    … …  
    27122723v:shapes="Picture_x0020_33"><![endif]></span></p>
    27132724
    2714 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2715 115%'>The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2725<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The <b
     2726style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    27162727mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
    27172728Controls</span></b> should be</p>
    27182729
    2719 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2720 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_34"
     2730<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2731style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_34"
    27212732 o:spid="_x0000_i1076" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
    27222733 visibility:visible;mso-wrap-style:square'>
    … …  
    27272738v:shapes="Picture_x0020_34"><![endif]></span></p>
    27282739
    2729 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2730 115%'>It turns out that the image contains a number of “picked bits” (very high
    2731 count “zingers”); these can be mostly eliminated by setting the upper threshold
    2732 in Masks. Select <b style='mso-bidi-font-weight:normal'><span style='font-family:
    2733 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    2734 minor-latin'>Masks</span></b> and the following should appear</p>
    2735 
    2736 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2737 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35"
     2740<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It turns out
     2741that the image contains a number of “picked bits” (very high count “zingers”);
     2742these can be mostly eliminated by setting the upper threshold in Masks. Select <b
     2743style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2744mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Masks</span></b>
     2745and the following should appear</p>
     2746
     2747<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2748style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35"
    27382749 o:spid="_x0000_i1075" type="#_x0000_t75" style='width:297.75pt;height:99.75pt;
    27392750 visibility:visible;mso-wrap-style:square'>
    … …  
    27442755v:shapes="Picture_x0020_35"><![endif]></span></p>
    27452756
    2746 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2747 115%'>Change the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    2748 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    2749 minor-latin'>Upper threshold</span></b> to <b style='mso-bidi-font-weight:normal'><span
     2757<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the <b
     2758style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2759mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Upper
     2760threshold</span></b> to <b style='mso-bidi-font-weight:normal'><span
    27502761style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    27512762mso-hansi-theme-font:minor-latin'>2500</span></b>; the image will be redrawn
    … …  
    27542765points. For example with the level set to 2200 the plot shows</p>
    27552766
    2756 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2757 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_36"
     2767<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2768style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_36"
    27582769 o:spid="_x0000_i1074" type="#_x0000_t75" style='width:525pt;height:450pt;
    27592770 visibility:visible;mso-wrap-style:square'>
    … …  
    27642775v:shapes="Picture_x0020_36"><![endif]></span></p>
    27652776
    2766 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2767 115%'><span class=GramE>for</span> one ring. This level is too low. Return to
    2768 the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2777<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2778class=GramE>for</span> one ring. This level is too low. Return to the <b
     2779style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    27692780mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
    27702781Controls</span></b> item in the data tree.</p>
    27712782
    2772 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2773 115%'>We are now ready to integrate the image; do <b style='mso-bidi-font-weight:
    2774 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2775 minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Integrate</span></b>
    2776 from the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2783<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
     2784ready to integrate the image; do <b style='mso-bidi-font-weight:normal'><span
     2785style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2786mso-hansi-theme-font:minor-latin'>Operations/Integrate</span></b> from the <b
     2787style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    27772788mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
    27782789Controls</span></b> menu. When done the last powder pattern in the tree will be
    27792790displayed</p>
    27802791
    2781 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2782 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_37"
     2792<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2793style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_37"
    27832794 o:spid="_x0000_i1073" type="#_x0000_t75" style='width:525pt;height:450pt;
    27842795 visibility:visible;mso-wrap-style:square'>
    … …  
    27892800v:shapes="Picture_x0020_37"><![endif]></span></p>
    27902801
    2791 <h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 2. Enter <span
    2792 class=SpellE>NiTi</span> phases</h2>
    2793 
    2794 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2795 115%'>This <span class=SpellE>NiTi</span> alloy consists of two phases, cubic
    2796 B2 and monoclinic B19’. Their parameters are:</p>
    2797 
    2798 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2799 115%'>B2: <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2802<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     28030in;line-height:115%'>Step 2. Enter <span class=SpellE>NiTi</span> phases</h2>
     2804
     2805<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This <span
     2806class=SpellE>NiTi</span> alloy consists of two phases, cubic B2 and monoclinic
     2807B19’. Their parameters are<span class=GramE>:</span><br>
     2808B2: <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    28002809mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P m 3 m</span></b>,
    28012810a=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    28022811mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>3.0240</span></b>,
    28032812Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2804 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0<span
    2805 class=GramE>,0,0</span></span></b>, <span class=SpellE>Ti</span> <b
    2806 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2807 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>œ,œ,œ</span></b>,
    2808 <span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
    2809 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2810 mso-hansi-theme-font:minor-latin'>0.005 </span></b>for both.</p>
    2811 
    2812 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2813 115%'>B19’:<span style='mso-spacerun:yes'>  </span><b style='mso-bidi-font-weight:
     2813mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0,0,0</span></b>,
     2814<span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span
     2815style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2816mso-hansi-theme-font:minor-latin'>œ,œ,œ</span></b>, <span class=SpellE>U<sub>iso</sub></span>=<b
     2817style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2818mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.005 </span></b>for
     2819both.<br>
     2820B19’:<span style='mso-spacerun:yes'>  </span><b style='mso-bidi-font-weight:
    28142821normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    28152822minor-latin;mso-hansi-theme-font:minor-latin'>P 1 1 21/m</span></b>, a=<b
    … …  
    28292836<span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
    28302837style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2831 mso-hansi-theme-font:minor-latin'>0.005</span></b> for both.</p>
    2832 
    2833 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2834 115%'>Use the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    2835 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    2836 minor-latin'>Data/Add phase</span></b> to enter the <b style='mso-bidi-font-weight:
     2838mso-hansi-theme-font:minor-latin'>0.005</span></b> for both.<br>
     2839Use the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2840mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Add
     2841phase</span></b> to enter the <b style='mso-bidi-font-weight:normal'><span
     2842style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2843mso-hansi-theme-font:minor-latin'>B2</span></b> and <b style='mso-bidi-font-weight:
    28372844normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2838 minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> and <b
    2839 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2840 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
    2841 phases; then for each enter the information given above on their respective <b
    2842 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2843 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>General</span></b>
    2844 and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2845minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b> phases; then for
     2846each enter the information given above on their respective <b style='mso-bidi-font-weight:
     2847normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2848minor-latin;mso-hansi-theme-font:minor-latin'>General</span></b> and <b
     2849style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    28452850mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms</span></b>
    28462851tabs. Don’t forget the spaces between the axial fields for the space group
    … …  
    28612866should look like</p>
    28622867
    2863 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2864 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_38"
     2868<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2869style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_38"
    28652870 o:spid="_x0000_i1072" type="#_x0000_t75" style='width:525pt;height:166.5pt;
    28662871 visibility:visible;mso-wrap-style:square'>
    … …  
    28712876v:shapes="Picture_x0020_38"><![endif]></span></p>
    28722877
    2873 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2874 115%'><span class=GramE>and</span> the B19’ Atoms table should be</p>
    2875 
    2876 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2877 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_39"
     2878<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2879class=GramE>and</span> the B19’ Atoms table should be</p>
     2880
     2881<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2882style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_39"
    28782883 o:spid="_x0000_i1071" type="#_x0000_t75" style='width:525pt;height:163.5pt;
    28792884 visibility:visible;mso-wrap-style:square'>
    … …  
    28842889v:shapes="Picture_x0020_39"><![endif]></span></p>
    28852890
    2886 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2887 115%'>Next go to the <b style='mso-bidi-font-weight:normal'><span
    2888 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2889 mso-hansi-theme-font:minor-latin'>Data</span></b> tab for each phase; there
    2890 will be a message indicating the lack of data for each. Do <b style='mso-bidi-font-weight:
    2891 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2892 minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add powder histograms</span></b>,
    2893 do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2894 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b>
    2895 on the popup selection window and press <b style='mso-bidi-font-weight:normal'><span
    2896 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    2897 mso-hansi-theme-font:minor-latin'>OK</span></b>. The window for B2 will change
    2898 to</p>
    2899 
    2900 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2901 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40"
     2891<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
     2892<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2893mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
     2894tab for each phase; there will be a message indicating the lack of data for
     2895each. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     2896mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add
     2897powder histograms</span></b>, do <b style='mso-bidi-font-weight:normal'><span
     2898style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2899mso-hansi-theme-font:minor-latin'>Set All</span></b> on the popup selection
     2900window and press <b style='mso-bidi-font-weight:normal'><span style='font-family:
     2901"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     2902minor-latin'>OK</span></b>. The window for B2 will change to</p>
     2903
     2904<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2905style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40"
    29022906 o:spid="_x0000_i1070" type="#_x0000_t75" style='width:342.75pt;height:375pt;
    29032907 visibility:visible;mso-wrap-style:square'>
    … …  
    29082912v:shapes="Picture_x0020_40"><![endif]></span></p>
    29092913
    2910 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2911 115%'><span class=GramE>and</span> that for B19’ will be</p>
    2912 
    2913 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2914 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_41"
     2914<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2915class=GramE>and</span> that for B19’ will be</p>
     2916
     2917<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2918style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_41"
    29152919 o:spid="_x0000_i1069" type="#_x0000_t75" style='width:370.5pt;height:375pt;
    29162920 visibility:visible;mso-wrap-style:square'>
    … …  
    29212925v:shapes="Picture_x0020_41"><![endif]></span></p>
    29222926
    2923 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2924 115%'>You should now save the project file (I used <span class=SpellE><b
    2925 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2926 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span>
    2927 for a name); we will use this as a starting point for three different texture
     2927<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You should now
     2928save the project file (I used <span class=SpellE><b style='mso-bidi-font-weight:
     2929normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     2930minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span> for a
     2931name); we will use this as a starting point for three different texture
    29282932determinations. Do a <b style='mso-bidi-font-weight:normal'><span
    29292933style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    … …  
    29372941the new project name for the next part of this tutorial.</p>
    29382942
    2939 <h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Method A. Full
    2940 refinement</h2>
    2941 
    2942 <h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Introduction</h3>
    2943 
    2944 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2945 115%'>In this method we will do a full Rietveld refinement of the texture,
    2946 profile parameters, peak position variables and crystal structure parameters.
    2947 This is suitable in this case because of the relatively small number of
    2948 histograms (10 in this case) needed for the texture determination; do recall
    2949 that each phase in each histogram has a set of parameters (e.g. phase fraction,
    2950 size, <span class=SpellE>mustrain</span> &amp; hydrostatic strain) in addition
    2951 to the ones for each histogram (e.g. background &amp; scale factor). Consequently
    2952 the total number of parameters can build up very quickly in this method of
    2953 analysis. The other two methods seek to reduce this problem by splitting the
    2954 fitting into a sequential refinement (histogram by histogram) step followed by
    2955 a texture fitting step.</p>
    2956 
    2957 <h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 1. Initial
    2958 refinement</h3>
    2959 
    2960 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2961 115%'>In the initial refinement we need to vary the phase fraction for each
    2962 phase/histogram and the background in each histogram. To start select any <b
    2963 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    2964 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b>
    2965 entry from the GSAS-II data tree and select <b style='mso-bidi-font-weight:
     2943<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     29440in;line-height:115%'>Method A. Full refinement</h2>
     2945
     2946<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     29470in;line-height:115%'>Introduction</h3>
     2948
     2949<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In this method
     2950we will do a full Rietveld refinement of the texture, profile parameters, peak
     2951position variables and crystal structure parameters. This is suitable in this
     2952case because of the relatively small number of histograms (10 in this case)
     2953needed for the texture determination; do recall that each phase in each
     2954histogram has a set of parameters (e.g. phase fraction, size, <span
     2955class=SpellE>mustrain</span> &amp; hydrostatic strain) in addition to the ones
     2956for each histogram (e.g. background &amp; scale factor). Consequently the total
     2957number of parameters can build up very quickly in this method of analysis. The
     2958other two methods seek to reduce this problem by splitting the fitting into a
     2959sequential refinement (histogram by histogram) step followed by a texture
     2960fitting step.</p>
     2961
     2962<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     29630in;line-height:115%'>Step 1. Initial refinement</h3>
     2964
     2965<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In the initial
     2966refinement we need to vary the phase fraction for each phase/histogram and the
     2967background in each histogram. To start select any <b style='mso-bidi-font-weight:
    29662968normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    2967 minor-latin;mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b> for
    2968 it. Note that Goniometer chi is set to 90; that came from the same entry in the
    2969 Image Controls during integration. Also, if you chose other than the 1<sup>st</sup>
     2969minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b> entry from the
     2970GSAS-II data tree and select <b style='mso-bidi-font-weight:normal'><span
     2971style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     2972mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b> for it. Note
     2973that Goniometer chi is set to 90; that came from the same entry in the Image
     2974Controls during integration. Also, if you chose other than the 1<sup>st</sup>
    29702975PWDR data set the Detector azimuth will be some nonzero value; that is also
    29712976reflected in the name assigned to the histogram (e.g. <b style='mso-bidi-font-weight:
    … …  
    29852990varying the phase fractions instead.</p>
    29862991
    2987 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2988 115%'>Next select the B2 phase and pick the Data tab; you will see</p>
    2989 
    2990 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    2991 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42"
     2992<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select
     2993the B2 phase and pick the Data tab; you will see</p>
     2994
     2995<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     2996style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42"
    29922997 o:spid="_x0000_i1068" type="#_x0000_t75" style='width:342.75pt;height:375pt;
    29932998 visibility:visible;mso-wrap-style:square'>
    … …  
    29983003v:shapes="Picture_x0020_42"><![endif]></span></p>
    29993004
    3000 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3001 115%'>Select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    3002 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3003 minor-latin'>Phase fraction</span></b> box. Then do <b style='mso-bidi-font-weight:
    3004 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3005 minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b>, select
    3006 <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3005<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Select the <b
     3006style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3007mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase
     3008fraction</span></b> box. Then do <b style='mso-bidi-font-weight:normal'><span
     3009style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3010mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b>, select <b
     3011style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    30073012mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set <span
    30083013class=GramE>All</span></span></b> &amp; press <b style='mso-bidi-font-weight:
    30093014normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3010 minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to copy these to the
    3011 other histograms. Next select the <b style='mso-bidi-font-weight:normal'><span
    3012 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3013 mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and repeat this
    3014 process. We are now ready for the first refinement; do <b style='mso-bidi-font-weight:
     3015minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to copy these to
     3016the other histograms. Next select the <b style='mso-bidi-font-weight:normal'><span
     3017style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3018mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and repeat this process.
     3019We are now ready for the first refinement; do <b style='mso-bidi-font-weight:
    30153020normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    30163021minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from
    … …  
    30243029the 1<sup>st</sup> powder pattern showing you the fit</p>
    30253030
    3026 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3027 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_43"
     3031<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3032style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_43"
    30283033 o:spid="_x0000_i1067" type="#_x0000_t75" style='width:525pt;height:450pt;
    30293034 visibility:visible;mso-wrap-style:square'>
    … …  
    30343039v:shapes="Picture_x0020_43"><![endif]></span></p>
    30353040
    3036 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3037 115%'>This is quite poor. You can survey the fit successively by 1<sup>st</sup>
    3038 selecting say the 1<sup>st</sup> PWDR entry from the tree and then using the
    3039 up/down arrow keys to step to the next one; the plot will redraw at each step
    3040 (NB: at full scale) and the data window will show statistics of the fit. There
    3041 is a substantial intensity discrepancy; this is due to the texture. It is also
    3042 evident that some of the peaks are out of place relative to the reflection
    3043 markers; this is due to macroscopic strain in the drawn wire. For the <span
    3044 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3045 mso-hansi-theme-font:minor-latin'>B2</span> phase select the <b
    3046 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3047 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
    3048 tab; it should look like</p>
    3049 
    3050 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3051 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44"
     3041<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is quite
     3042poor. You can survey the fit successively by 1<sup>st</sup> selecting say the 1<sup>st</sup>
     3043PWDR entry from the tree and then using the up/down arrow keys to step to the
     3044next one; the plot will redraw at each step (NB: at full scale) and the data
     3045window will show statistics of the fit. There is a substantial intensity
     3046discrepancy; this is due to the texture. It is also evident that some of the
     3047peaks are out of place relative to the reflection markers; this is due to
     3048macroscopic strain in the drawn wire. For the <span style='font-family:"Calibri",sans-serif;
     3049mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span>
     3050phase select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3051"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3052minor-latin'>Texture</span></b> tab; it should look like</p>
     3053
     3054<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3055style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44"
    30523056 o:spid="_x0000_i1066" type="#_x0000_t75" style='width:456pt;height:217.5pt;
    30533057 visibility:visible;mso-wrap-style:square'>
    … …  
    30583062v:shapes="Picture_x0020_44"><![endif]></span></p>
    30593063
    3060 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3061 115%'>The texture model is <b style='mso-bidi-font-weight:normal'><span
    3062 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3063 mso-hansi-theme-font:minor-latin'>cylindrical</span></b> by default; that is
    3064 what we want. Change the <b style='mso-bidi-font-weight:normal'><span
    3065 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3066 mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to <b
     3064<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The texture
     3065model is <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3066mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>cylindrical</span></b>
     3067by default; that is what we want. Change the <b style='mso-bidi-font-weight:
     3068normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3069minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to <b
    30673070style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    30683071mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>8</span></b>
    … …  
    30743077The window should look like</p>
    30753078
    3076 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3077 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45"
     3079<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3080style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45"
    30783081 o:spid="_x0000_i1065" type="#_x0000_t75" style='width:456pt;height:250.5pt;
    30793082 visibility:visible;mso-wrap-style:square'>
    … …  
    30843087v:shapes="Picture_x0020_45"><![endif]></span></p>
    30853088
    3086 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3087 115%'>Then go to the <b style='mso-bidi-font-weight:normal'><span
    3088 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3089 mso-hansi-theme-font:minor-latin'>Data</span></b> tab, select <b
    3090 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3091 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>D11</span></b>;
    3092 the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3089<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the
     3090<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    30933091mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
    3094 window should look like (any PWDR item will do)</p>
    3095 
    3096 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3097 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_46"
     3092tab, select <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3093"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3094minor-latin'>D11</span></b>; the <b style='mso-bidi-font-weight:normal'><span
     3095style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3096mso-hansi-theme-font:minor-latin'>Data</span></b> window should look like (any
     3097PWDR item will do)</p>
     3098
     3099<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3100style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_46"
    30983101 o:spid="_x0000_i1064" type="#_x0000_t75" style='width:342.75pt;height:375pt;
    30993102 visibility:visible;mso-wrap-style:square'>
    … …  
    31043107v:shapes="Picture_x0020_46"><![endif]></span></p>
    31053108
    3106 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3107 115%'>Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3109<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then do <b
     3110style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3111mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
     3112flags</span></b> to have <b style='mso-bidi-font-weight:normal'><span
     3113style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3114mso-hansi-theme-font:minor-latin'>D11</span></b> refined for all PWDR data
     3115sets.</p>
     3116
     3117<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select
     3118the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3119mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
     3120phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3121mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
     3122tab. Then select <b style='mso-bidi-font-weight:normal'><span style='font-family:
    31083123"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3109 minor-latin'>Edit/Copy flags</span></b> to have <b style='mso-bidi-font-weight:
    3110 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3111 minor-latin;mso-hansi-theme-font:minor-latin'>D11</span></b> refined for all
    3112 PWDR data sets.</p>
    3113 
    3114 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3115 115%'>Next select the <b style='mso-bidi-font-weight:normal'><span
    3116 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3117 mso-hansi-theme-font:minor-latin'>B19’</span></b> phase <b style='mso-bidi-font-weight:
    3118 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3119 minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b> tab. Then
    3120 select <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3121 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>6</span></b>
    3122 for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3123 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic
    3124 order</span></b> and check the two boxes as before.</p>
    3125 
    3126 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3127 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_47"
     3124minor-latin'>6</span></b> for the <b style='mso-bidi-font-weight:normal'><span
     3125style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3126mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> and check the two
     3127boxes as before.</p>
     3128
     3129<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3130style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_47"
    31283131 o:spid="_x0000_i1063" type="#_x0000_t75" style='width:478.5pt;height:302.25pt;
    31293132 visibility:visible;mso-wrap-style:square'>
    … …  
    31343137v:shapes="Picture_x0020_47"><![endif]></span></p>
    31353138
    3136 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3137 115%'>Then go to the <b style='mso-bidi-font-weight:normal'><span
    3138 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3139 mso-hansi-theme-font:minor-latin'>Data</span></b> tab for the <b
    3140 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3141 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
    3142 phase and check all 4 of the <span class=SpellE><b style='mso-bidi-font-weight:
    3143 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3144 minor-latin;mso-hansi-theme-font:minor-latin'>Dij</span></b></span> boxes and
    3145 do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3146 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
    3147 flags</span></b> as before. The tab will look like</p>
    3148 
    3149 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3150 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48"
     3139<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the
     3140<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3141mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
     3142tab for the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3143"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3144minor-latin'>B19’</span></b> phase and check all 4 of the <span class=SpellE><b
     3145style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3146mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dij</span></b></span>
     3147boxes and do <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3148"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3149minor-latin'>Edit/Copy flags</span></b> as before. The tab will look like</p>
     3150
     3151<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3152style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48"
    31513153 o:spid="_x0000_i1062" type="#_x0000_t75" style='width:370.5pt;height:375pt;
    31523154 visibility:visible;mso-wrap-style:square'>
    … …  
    31573159v:shapes="Picture_x0020_48"><![endif]></span></p>
    31583160
    3159 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3160 115%'>Now do <b style='mso-bidi-font-weight:normal'><span style='font-family:
    3161 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3162 minor-latin'>Calculate/Refine</span></b> from the main menu. The refinement
    3163 will finish with <span class=SpellE>Rw</span> ~27%; the 1<sup>st</sup> PWDR
    3164 pattern looks like</p>
    3165 
    3166 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3167 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_49"
     3161<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do <b
     3162style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3163mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
     3164from the main menu. The refinement will finish with <span class=SpellE>Rw</span>
     3165~27%; the 1<sup>st</sup> PWDR pattern looks like</p>
     3166
     3167<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3168style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_49"
    31683169 o:spid="_x0000_i1061" type="#_x0000_t75" style='width:525pt;height:413.25pt;
    31693170 visibility:visible;mso-wrap-style:square'>
    … …  
    31743175v:shapes="Picture_x0020_49"><![endif]></span></p>
    31753176
    3176 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3177 115%'>The calculated peaks for both phases are too sharp. It is likely that
    3178 this is a <span class=SpellE>microstrain</span> effect. Select <b
    3179 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3180 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
    3181 for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3177<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The calculated
     3178peaks for both phases are too sharp. It is likely that this is a <span
     3179class=SpellE>microstrain</span> effect. Select <b style='mso-bidi-font-weight:
     3180normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3181minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b> for the <b
     3182style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    31823183mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2 </span></b>phase
    31833184and select the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
    … …  
    31943195substantially improved with <span class=SpellE>Rw</span> ~9.2%.</p>
    31953196
    3196 <h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 2. Finish
    3197 refinement and examine texture</h3>
    3198 
    3199 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3200 115%'>Looking at the individual PWDR data sets (e.g. the one for <span
    3201 class=SpellE>Azm</span>=20.00)</p>
    3202 
    3203 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3204 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_50"
     3197<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     31980in;line-height:115%'>Step 2. Finish refinement and examine texture</h3>
     3199
     3200<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Looking at the
     3201individual PWDR data sets (e.g. the one for <span class=SpellE>Azm</span>=20.00)</p>
     3202
     3203<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3204style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_50"
    32053205 o:spid="_x0000_i1060" type="#_x0000_t75" style='width:525pt;height:413.25pt;
    32063206 visibility:visible;mso-wrap-style:square'>
    … …  
    32113211v:shapes="Picture_x0020_50"><![endif]></span></p>
    32123212
    3213 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3214 115%'>It is evident that there remains intensity differences due to texture. We
    3215 can increase the harmonic order to more closely fit these, however one should
    3216 only do this carefully. Select the Texture tab for the B2 phase; the Texture
    3217 tab will show</p>
    3218 
    3219 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3220 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_18"
     3213<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is evident
     3214that there remains intensity differences due to texture. We can increase the
     3215harmonic order to more closely fit these, however one should only do this
     3216carefully. Select the Texture tab for the B2 phase; the Texture tab will show</p>
     3217
     3218<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3219style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_18"
    32213220 o:spid="_x0000_i1059" type="#_x0000_t75" style='width:456pt;height:250.5pt;
    32223221 visibility:visible;mso-wrap-style:square'>
    … …  
    32273226v:shapes="Picture_x0020_18"><![endif]></span></p>
    32283227
    3229 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3230 115%'>And a drawing of the 001 pole figure will be drawn. This is the very
    3231 typical “bulls eye” for cylindrical texture; of much more use is an inverse
    3232 pole figure. Select that from the Texture plot type; the plot will be redrawn</p>
    3233 
    3234 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3235 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_52"
     3228<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a drawing
     3229of the 001 pole figure will be drawn. This is the very typical “bulls eye” for
     3230cylindrical texture; of much more use is an inverse pole figure. Select that
     3231from the Texture plot type; the plot will be redrawn</p>
     3232
     3233<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3234style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_52"
    32363235 o:spid="_x0000_i1058" type="#_x0000_t75" style='width:525pt;height:413.25pt;
    32373236 visibility:visible;mso-wrap-style:square'>
    … …  
    32423241v:shapes="Picture_x0020_52"><![endif]></span></p>
    32433242
    3244 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3245 115%'>This shows the probability of reflection vectors coinciding with the
    3246 sample wire axis the high spots are the 111 family of reflections. We should
    3247 try the next higher Harmonic order (10). </p>
    3248 
    3249 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3250 115%'>Next go to the Texture tab for the B19’ phase. Again a <span
    3251 class=SpellE>bullseye</span> pole figure is drawn; change that to an Inverse
    3252 pole figure.</p>
    3253 
    3254 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3255 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_53"
     3243<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This shows the
     3244probability of reflection vectors coinciding with the sample wire axis the high
     3245spots are the 111 family of reflections. We should try the next higher Harmonic
     3246order (10). </p>
     3247
     3248<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
     3249Texture tab for the B19’ phase. Again a <span class=SpellE>bullseye</span> pole
     3250figure is drawn; change that to an Inverse pole figure.</p>
     3251
     3252<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3253style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_53"
    32563254 o:spid="_x0000_i1057" type="#_x0000_t75" style='width:525pt;height:413.25pt;
    32573255 visibility:visible;mso-wrap-style:square'>
    … …  
    32623260v:shapes="Picture_x0020_53"><![endif]></span></p>
    32633261
    3264 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3265 115%'>This phase is very strongly textured (the cursor shows 12-13 MRD at the
    3266 peaks) along the -140 direction. Again we want to increment the Harmonic order
    3267 to the next higher level (8). Again do Calculate/Refine from the main menu; the
    3268 <span class=SpellE>Rwp</span> has dropped to ~7.9%. One can add the atom <span
     3262<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This phase is
     3263very strongly textured (the cursor shows 12-13 MRD at the peaks) along the -140
     3264direction. Again we want to increment the Harmonic order to the next higher
     3265level (8). Again do Calculate/Refine from the main menu; the <span
     3266class=SpellE>Rwp</span> has dropped to ~7.9%. One can add the atom <span
    32693267class=SpellE>Uiso</span> for the Ni and <span class=SpellE>Ti</span> atoms in
    32703268the B2 phase and the coordinates and <span class=SpellE>Uiso</span> for the
    … …  
    32763274peaks are ~7MRD.</p>
    32773275
    3278 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3279 115%'>The B19’ coefficients</p>
    3280 
    3281 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3282 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_54"
     3276<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B19’
     3277coefficients</p>
     3278
     3279<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3280style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_54"
    32833281 o:spid="_x0000_i1056" type="#_x0000_t75" style='width:502.5pt;height:375pt;
    32843282 visibility:visible;mso-wrap-style:square'>
    … …  
    32893287v:shapes="Picture_x0020_54"><![endif]></span></p>
    32903288
    3291 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3292 115%'><span class=GramE>and</span> inverse pole figure</p>
    3293 
    3294 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3295 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_55"
     3289<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3290class=GramE>and</span> inverse pole figure</p>
     3291
     3292<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3293style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_55"
    32963294 o:spid="_x0000_i1055" type="#_x0000_t75" style='width:525pt;height:413.25pt;
    32973295 visibility:visible;mso-wrap-style:square'>
    … …  
    33023300v:shapes="Picture_x0020_55"><![endif]></span></p>
    33033301
    3304 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3305 115%'>The B2 coefficients</p>
    3306 
    3307 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3308 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_56"
     3302<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B2
     3303coefficients</p>
     3304
     3305<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3306style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_56"
    33093307 o:spid="_x0000_i1054" type="#_x0000_t75" style='width:480pt;height:267.75pt;
    33103308 visibility:visible;mso-wrap-style:square'>
    … …  
    33153313v:shapes="Picture_x0020_56"><![endif]></span></p>
    33163314
    3317 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3318 115%'><span class=GramE>and</span> inverse pole figure</p>
    3319 
    3320 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3321 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_57"
     3315<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3316class=GramE>and</span> inverse pole figure</p>
     3317
     3318<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3319style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_57"
    33223320 o:spid="_x0000_i1053" type="#_x0000_t75" style='width:525pt;height:413.25pt;
    33233321 visibility:visible;mso-wrap-style:square'>
    … …  
    33283326v:shapes="Picture_x0020_57"><![endif]></span></p>
    33293327
    3330 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3331 115%'>This completes the tutorial on Method A for doing texture analysis. It is
    3332 useful for a case like this one where there are very few data sets required for
    3333 the texture analysis. However, for the case of lower sample symmetry one must
    3334 several dozen or even a few hundred histograms and then the suite of parameters
    3335 can easily be &gt; 1000 of which only a few dozen describe the texture. This
    3336 leads to the next Methods for texture analysis in GSAS-II.</p>
    3337 
    3338 <h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Method B.
    3339 Sequential refinement &amp; texture analysis from result</h2>
    3340 
    3341 <h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Introduction</h3>
    3342 
    3343 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3344 115%'>This begins the texture analysis in much the same way as Method A except
    3345 that all the initial refinements are done “sequentially”, that is refinements
    3346 are done for the parameters associated with each powder pattern to convergence
    3347 in a serial fashion. In this case where there are 10 PWDR data sets, there will
    3348 be 10 refinements done in sequence. Parameters that span all the data (e.g.
    3349 lattice parameters, atom parameters &amp; texture) are not varied in this
    3350 sequence refinement. The effect of texture is modeled as a Preferred
    3351 Orientation correction to each histogram. To begin do <b style='mso-bidi-font-weight:
     3328<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This completes
     3329the tutorial on Method A for doing texture analysis. It is useful for a case
     3330like this one where there are very few data sets required for the texture
     3331analysis. However, for the case of lower sample symmetry one must several dozen
     3332or even a few hundred histograms and then the suite of parameters can easily be
     3333&gt; 1000 of which only a few dozen describe the texture. This leads to the
     3334next Methods for texture analysis in GSAS-II.</p>
     3335
     3336<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     33370in;line-height:115%'>Method B. Sequential refinement &amp; texture analysis
     3338from result</h2>
     3339
     3340<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     33410in;line-height:115%'>Introduction</h3>
     3342
     3343<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
     3344the texture analysis in much the same way as Method A except that all the
     3345initial refinements are done “sequentially”, that is refinements are done for
     3346the parameters associated with each powder pattern to convergence in a serial
     3347fashion. In this case where there are 10 PWDR data sets, there will be 10
     3348refinements done in sequence. Parameters that span all the data (e.g. lattice
     3349parameters, atom parameters &amp; texture) are not varied in this sequence
     3350refinement. The effect of texture is modeled as a Preferred Orientation
     3351correction to each histogram. To begin do <b style='mso-bidi-font-weight:normal'><span
     3352style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3353mso-hansi-theme-font:minor-latin'>File/Open project
     3354</span></b> for the <span
     3355class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
     3356"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3357minor-latin'>NiTi.gpx</span></b></span> file created in the first step and then
     3358do a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3359mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Save
     3360project as
     3361</span></b> to save it as <span class=SpellE><b style='mso-bidi-font-weight:
    33523362normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3353 minor-latin;mso-hansi-theme-font:minor-latin'>File/Open project
    3354 </span></b> for
    3355 the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
    3356 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3357 mso-hansi-theme-font:minor-latin'>NiTi.gpx</span></b></span> file created in
    3358 the first step and then do a <b style='mso-bidi-font-weight:normal'><span
    3359 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3360 mso-hansi-theme-font:minor-latin'>File/Save project as
    3361 </span></b> to save it
    3362 as <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
    3363 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3364 mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight:
    3365 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3366 minor-latin;mso-hansi-theme-font:minor-latin'>-B</span></b>. This renames the
    3367 project and it should have one IMG, 10 PWDR entries and two phases of <span
    3368 class=SpellE>NiTi</span> (B2 and B19’).</p>
    3369 
    3370 <h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 1. Initial
    3371 refinement</h3>
    3372 
    3373 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3374 115%'>This begins the same way as Method A so I’ll be brief. Do the following
    3375 steps:</p>
    3376 
    3377 <p class=MsoListParagraphCxSpFirst style='margin-bottom:0in;margin-bottom:.0001pt;
    3378 mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
     3363minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b
     3364style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3365mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-B</span></b>.
     3366This renames the project and it should have one IMG, 10 PWDR entries and two
     3367phases of <span class=SpellE>NiTi</span> (B2 and B19’).</p>
     3368
     3369<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     33700in;line-height:115%'>Step 1. Initial refinement</h3>
     3371
     3372<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
     3373the same way as Method A so I’ll be brief. Do the following steps:</p>
     3374
     3375<p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;mso-add-space:
     3376auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
    33793377style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
    33803378style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
    … …  
    33883386Then copy the flags to the other PWDR entries.</p>
    33893387
    3390 <p class=MsoListParagraphCxSpMiddle style='margin-bottom:0in;margin-bottom:
    3391 .0001pt;mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
     3388<p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;mso-add-space:
     3389auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
    33923390style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
    33933391style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
    … …  
    34113409flag and the model to the other PWDR entries.</p>
    34123410
    3413 <p class=MsoListParagraphCxSpLast style='margin-bottom:0in;margin-bottom:.0001pt;
    3414 mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
     3411<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space:
     3412auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
    34153413style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
    34163414style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
    … …  
    34283426mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b
    34293427style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3430 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical harmonics</span></b>.
    3431 Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3432 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
    3433 data</span></b> to copy both the flag and the model to the other PWDR entries.</p>
    3434 
    3435 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3436 115%'>Now select <b style='mso-bidi-font-weight:normal'><span style='font-family:
    3437 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3438 minor-latin'>Controls</span></b> from the GSAS-II data tree</p>
    3439 
    3440 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3441 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_1"
     3428mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical
     3429harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span
     3430style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3431mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the
     3432flag and the model to the other PWDR entries.</p>
     3433
     3434<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select <b
     3435style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3436mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b>
     3437from the GSAS-II data tree</p>
     3438
     3439<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3440style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_1"
    34423441 o:spid="_x0000_i1052" type="#_x0000_t75" style='width:330.75pt;height:153.75pt;
    34433442 visibility:visible;mso-wrap-style:square'>
    … …  
    34483447v:shapes="Picture_x0020_1"><![endif]></span></p>
    34493448
    3450 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3451 115%'>Press the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3449<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Press the <b
     3450style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3451mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Select Data</span></b>
     3452button for <b style='mso-bidi-font-weight:normal'><span style='font-family:
    34523453"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3453 minor-latin'>Select Data</span></b> button for <b style='mso-bidi-font-weight:
     3454minor-latin'>Sequential Refinement</span></b>; a file selection popup will
     3455appear. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3456"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3457minor-latin'>Set All</span></b> and press <b style='mso-bidi-font-weight:normal'><span
     3458style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3459mso-hansi-theme-font:minor-latin'>OK</span></b>. The <b style='mso-bidi-font-weight:
    34543460normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3455 minor-latin;mso-hansi-theme-font:minor-latin'>Sequential Refinement</span></b>;
    3456 a file selection popup will appear. Do <b style='mso-bidi-font-weight:normal'><span
    3457 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3458 mso-hansi-theme-font:minor-latin'>Set All</span></b> and press <b
    3459 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3460 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
    3461 The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3462 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b>
    3463 page will be repainted indicating that 10 data sets are selected for sequential
    3464 refinement.</p>
    3465 
    3466 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3467 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_2"
     3461minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b> page will be
     3462repainted indicating that 10 data sets are selected for sequential refinement.</p>
     3463
     3464<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3465style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_2"
    34683466 o:spid="_x0000_i1051" type="#_x0000_t75" style='width:330.75pt;height:163.5pt;
    34693467 visibility:visible;mso-wrap-style:square'>
    … …  
    34743472v:shapes="Picture_x0020_2"><![endif]></span></p>
    34753473
    3476 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3477 115%'>You have the choice of starting at the last one and for copying results
    3478 from one to the next. We won’t do either here. Each refinement will use the
    3479 other controls (e.g. <b style='mso-bidi-font-weight:normal'><span
    3480 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3481 mso-hansi-theme-font:minor-latin'>Max cycles</span></b>) as controls. We are
    3482 now ready to do the 1<sup>st</sup> sequential refinement. Do <b
    3483 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3474<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You have the
     3475choice of starting at the last one and for copying results from one to the
     3476next. We won’t do either here. Each refinement will use the other controls
     3477(e.g. <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3478mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Max cycles</span></b>)
     3479as controls. We are now ready to do the 1<sup>st</sup> sequential refinement.
     3480Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    34843481mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Sequential
    34853482refine</span></b> from the main menu. A progress bar popup will appear showing
    … …  
    34953492table.</p>
    34963493
    3497 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3498 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3"
     3494<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3495style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3"
    34993496 o:spid="_x0000_i1050" type="#_x0000_t75" style='width:525pt;height:262.5pt;
    35003497 visibility:visible;mso-wrap-style:square'>
    … …  
    35053502v:shapes="Picture_x0020_3"><![endif]></span></p>
    35063503
    3507 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3508 115%'>There is a row for each data set and columns for all refined parameters
    3509 and some derived ones along with residual and convergence indicators. The
    3510 residuals are not very good (we haven’t really refined much) but the
    3511 &#916;&#967;<sup>2</sup> column shows that convergence was achieved (NB: poor
    3512 convergence will be highlighted in yellow or red depending on how bad it is).</p>
    3513 
    3514 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3515 115%'>If you examine one of the PWDR entries, you’ll see that just in this
    3516 point in Method <span class=GramE>A</span> much of the misfit is texture and
    3517 perhaps peak position.</p>
    3518 
    3519 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3520 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_4"
     3504<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>There is a row
     3505for each data set and columns for all refined parameters and some derived ones
     3506along with residual and convergence indicators. The residuals are not very good
     3507(we haven’t really refined much) but the &#916;&#967;<sup>2</sup> column shows
     3508that convergence was achieved (NB: poor convergence will be highlighted in
     3509yellow or red depending on how bad it is).</p>
     3510
     3511<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you examine
     3512one of the PWDR entries, you’ll see that just in this point in Method <span
     3513class=GramE>A</span> much of the misfit is texture and perhaps peak position.</p>
     3514
     3515<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3516style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_4"
    35213517 o:spid="_x0000_i1049" type="#_x0000_t75" style='width:525pt;height:450pt;
    35223518 visibility:visible;mso-wrap-style:square'>
    … …  
    35273523v:shapes="Picture_x0020_4"><![endif]></span></p>
    35283524
    3529 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3530 115%'>To set these parameters, select the Data tab for the B2 phase</p>
    3531 
    3532 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3533 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5"
     3525<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>To set these
     3526parameters, select the Data tab for the B2 phase</p>
     3527
     3528<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3529style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5"
    35343530 o:spid="_x0000_i1048" type="#_x0000_t75" style='width:381pt;height:375pt;
    35353531 visibility:visible;mso-wrap-style:square'>
    … …  
    35403536v:shapes="Picture_x0020_5"><![endif]></span></p>
    35413537
    3542 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3543 115%'>Check the D11 box under Hydrostatic/elastic strain, set the Harmonic
    3544 order to 6 and check the Refine box for it (Preferred orientation). Then in two
    3545 steps, do Edit/Copy flags and Set All for the file selection. Then do Edit/Copy
    3546 selected data; that will bring up a new popup</p>
    3547 
    3548 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3549 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_6"
     3538<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Check the D11
     3539box under Hydrostatic/elastic strain, set the Harmonic order to 6 and check the
     3540Refine box for it (Preferred orientation). Then in two steps, do Edit/Copy
     3541flags and Set All for the file selection. Then do Edit/Copy selected data; that
     3542will bring up a new popup</p>
     3543
     3544<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3545style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_6"
    35503546 o:spid="_x0000_i1047" type="#_x0000_t75" style='width:240pt;height:232.5pt;
    35513547 visibility:visible;mso-wrap-style:square'>
    … …  
    35563552v:shapes="Picture_x0020_6"><![endif]></span></p>
    35573553
    3558 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3559 115%'>This allows you to select which parameters to copy data and flags. Select
    3560 Pref. <span class=SpellE>Ori</span>. And press OK; the file selection is next.
    3561 Do Set <span class=GramE>All</span> and OK to do this copy. That copies the
    3562 full spherical harmonics model to the other data sets. Select one to check if
    3563 you’d like.</p>
    3564 
    3565 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3566 115%'>Next do the same thing for the B19’ phase; here there are 4 <span
    3567 class=SpellE>Dij</span> parameters to check (do all of them) and use spherical
    3568 harmonics order 4. When done that Data window will look like</p>
    3569 
    3570 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3571 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_7"
     3554<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This allows
     3555you to select which parameters to copy data and flags. Select Pref. <span
     3556class=SpellE>Ori</span>. And press OK; the file selection is next. Do Set <span
     3557class=GramE>All</span> and OK to do this copy. That copies the full spherical
     3558harmonics model to the other data sets. Select one to check if you’d like.</p>
     3559
     3560<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next do the
     3561same thing for the B19’ phase; here there are 4 <span class=SpellE>Dij</span>
     3562parameters to check (do all of them) and use spherical harmonics order 4. When
     3563done that Data window will look like</p>
     3564
     3565<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3566style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_7"
    35723567 o:spid="_x0000_i1046" type="#_x0000_t75" style='width:381pt;height:467.25pt;
    35733568 visibility:visible;mso-wrap-style:square'>
    … …  
    35783573v:shapes="Picture_x0020_7"><![endif]></span></p>
    35793574
    3580 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3581 115%'>We are now ready for the next refinement; do Calculate/Sequential refine.
    3582 Be careful not (by habit say) pick Refine; a warning popup will appear. After
    3583 it completes the Sequential refinement results shows that the fit is better but
    3584 convergence wasn’t quite complete.</p>
    3585 
    3586 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3587 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8"
     3575<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
     3576ready for the next refinement; do Calculate/Sequential refine. Be careful not
     3577(by habit say) pick Refine; a warning popup will appear. After it completes the
     3578Sequential refinement results shows that the fit is better but convergence
     3579wasn’t quite complete.</p>
     3580
     3581<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3582style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8"
    35883583 o:spid="_x0000_i1045" type="#_x0000_t75" style='width:525pt;height:262.5pt;
    35893584 visibility:visible;mso-wrap-style:square'>
    … …  
    35943589v:shapes="Picture_x0020_8"><![endif]></span></p>
    35953590
    3596 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3597 115%'>It is probably best to do another round of sequential refinement (I had
    3598 to do two) to get convergence. A plot of one PWDR entry gives</p>
    3599 
    3600 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3601 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9"
     3591<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is probably
     3592best to do another round of sequential refinement (I had to do two) to get
     3593convergence. A plot of one PWDR entry gives</p>
     3594
     3595<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3596style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9"
    36023597 o:spid="_x0000_i1044" type="#_x0000_t75" style='width:525pt;height:450pt;
    36033598 visibility:visible;mso-wrap-style:square'>
    … …  
    36083603v:shapes="Picture_x0020_9"><![endif]></span></p>
    36093604
    3610 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3611 115%'>As our experience in Method A, the calculated peaks are too sharp. We
    3612 need to vary the <span class=SpellE>mustrain</span> parameters for both phases.
    3613 Go to the Data tab for each phase, check the <span class=SpellE>microstrain</span>
    3614 box and do Edit/Copy flags for all the data sets. Then do another
    3615 Calculate/Sequential refine. My Sequential refinement results showed great
    3616 improvement but incomplete refinement</p>
    3617 
    3618 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3619 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10"
     3605<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>As our
     3606experience in Method A, the calculated peaks are too sharp. We need to vary the
     3607<span class=SpellE>mustrain</span> parameters for both phases. Go to the Data
     3608tab for each phase, check the <span class=SpellE>microstrain</span> box and do
     3609Edit/Copy flags for all the data sets. Then do another Calculate/Sequential
     3610refine. My Sequential refinement results showed great improvement but
     3611incomplete refinement</p>
     3612
     3613<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3614style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10"
    36203615 o:spid="_x0000_i1043" type="#_x0000_t75" style='width:525pt;height:262.5pt;
    36213616 visibility:visible;mso-wrap-style:square'>
    … …  
    36263621v:shapes="Picture_x0020_10"><![endif]></span></p>
    36273622
    3628 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3629 115%'>Repeating the sequential refinement (twice) gave convergence.</p>
    3630 
    3631 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3632 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_11"
     3623<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Repeating the
     3624sequential refinement (twice) gave convergence.</p>
     3625
     3626<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3627style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_11"
    36333628 o:spid="_x0000_i1042" type="#_x0000_t75" style='width:525pt;height:262.5pt;
    36343629 visibility:visible;mso-wrap-style:square'>
    … …  
    36393634v:shapes="Picture_x0020_11"><![endif]></span></p>
    36403635
    3641 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3642 115%'>Examination of the PWDR data sets showed a fairly good fit but some
    3643 discrepancies (especially for <span class=SpellE>Azm</span>=20.00)</p>
    3644 
    3645 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3646 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12"
     3636<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Examination of
     3637the PWDR data sets showed a fairly good fit but some discrepancies (especially
     3638for <span class=SpellE>Azm</span>=20.00)</p>
     3639
     3640<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3641style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12"
    36473642 o:spid="_x0000_i1041" type="#_x0000_t75" style='width:525pt;height:450pt;
    36483643 visibility:visible;mso-wrap-style:square'>
    … …  
    36533648v:shapes="Picture_x0020_12"><![endif]></span></p>
    36543649
    3655 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3656 115%'>Showing that perhaps the B19’ phase needs high order spherical harmonics.
    3657 Select the Data tab for the B19’ phase and change the Harmonic order to 6. Then
    3658 do Edit/Copy selected data for <span class=SpellE>Pref.Ori</span>. <span
    3659 class=GramE>to</span> the other data sets. This (after few repeats) gives a
    3660 further improvement in the fit</p>
    3661 
    3662 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3663 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13"
     3650<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Showing that
     3651perhaps the B19’ phase needs high order spherical harmonics. Select the Data
     3652tab for the B19’ phase and change the Harmonic order to 6. Then do Edit/Copy
     3653selected data for <span class=SpellE>Pref.Ori</span>. <span class=GramE>to</span>
     3654the other data sets. This (after few repeats) gives a further improvement in
     3655the fit</p>
     3656
     3657<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3658style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13"
    36643659 o:spid="_x0000_i1040" type="#_x0000_t75" style='width:525pt;height:262.5pt;
    36653660 visibility:visible;mso-wrap-style:square'>
    … …  
    36703665v:shapes="Picture_x0020_13"><![endif]></span></p>
    36713666
    3672 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3673 115%'>This fit is now sufficient for us to proceed to the next step and
    3674 determine the texture of the two phases.</p>
    3675 
    3676 <h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 2. Texture
    3677 analysis</h3>
    3678 
    3679 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3680 115%'>During the sequential refinements done in Step 1, we fitted the profiles
    3681 allowing strain parameters (<span class=SpellE>Dij</span>) for peak position
    3682 shifts and <span class=SpellE>microstrain</span> for peak shape. We modeled the
    3683 intensity variation with a spherical harmonics preferred orientation
    3684 correction. If you select any PWDR entry from the GSAS-II data tree and pick
    3685 the Reflection List subentry (at the bottom) you can see the magnitude of this
    3686 correction for each reflection in each phase.</p>
    3687 
    3688 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3689 115%'>For the B2 phase we see</p>
    3690 
    3691 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3692 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14"
     3667<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This fit is
     3668now sufficient for us to proceed to the next step and determine the texture of
     3669the two phases.</p>
     3670
     3671<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     36720in;line-height:115%'>Step 2. Texture analysis</h3>
     3673
     3674<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>During the
     3675sequential refinements done in Step 1, we fitted the profiles allowing strain
     3676parameters (<span class=SpellE>Dij</span>) for peak position shifts and <span
     3677class=SpellE>microstrain</span> for peak shape. We modeled the intensity
     3678variation with a spherical harmonics preferred orientation correction. If you
     3679select any PWDR entry from the GSAS-II data tree and pick the Reflection List
     3680subentry (at the bottom) you can see the magnitude of this correction for each
     3681reflection in each phase.</p>
     3682
     3683<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For the B2
     3684phase we see</p>
     3685
     3686<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3687style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14"
    36933688 o:spid="_x0000_i1039" type="#_x0000_t75" style='width:659.25pt;height:262.5pt;
    36943689 visibility:visible;mso-wrap-style:square'>
    … …  
    36993694v:shapes="Picture_x0020_14"><![endif]></span></p>
    37003695
    3701 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3702 115%'><span class=GramE>and</span> for the B19’ phase we see</p>
    3703 
    3704 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3705 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15"
     3696<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3697class=GramE>and</span> for the B19’ phase we see</p>
     3698
     3699<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3700style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15"
    37063701 o:spid="_x0000_i1038" type="#_x0000_t75" style='width:659.25pt;height:273pt;
    37073702 visibility:visible;mso-wrap-style:square'>
    … …  
    37123707v:shapes="Picture_x0020_15"><![endif]></span></p>
    37133708
    3714 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3715 115%'>The preferred orientation correction is <span class=SpellE>Prfo</span>;
    3716 notice a few entries in red. These are nonphysical correction values (the
    3717 correction can’t be negative) but by in large these are small. This next step
    3718 uses these corrections as input data for a texture refinement. To start select
    3719 the Texture tab for the B2 phase; you’ll see</p>
    3720 
    3721 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3722 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_16"
     3709<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The preferred
     3710orientation correction is <span class=SpellE>Prfo</span>; notice a few entries
     3711in red. These are nonphysical correction values (the correction can’t be
     3712negative) but by in large these are small. This next step uses these
     3713corrections as input data for a texture refinement. To start select the Texture
     3714tab for the B2 phase; you’ll see</p>
     3715
     3716<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3717style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_16"
    37233718 o:spid="_x0000_i1037" type="#_x0000_t75" style='width:456pt;height:217.5pt;
    37243719 visibility:visible;mso-wrap-style:square'>
    … …  
    37293724v:shapes="Picture_x0020_16"><![endif]></span></p>
    37303725
    3731 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3732 115%'>Since this sample has wire texture, we’ll use the default Texture model
    3733 (cylindrical). Then set the Harmonic order to 12 (what we used earlier) and
    3734 check the Refine and Show <span class=SpellE>coeff</span> boxes. The data
    3735 window will be redrawn (and a blank plot will appear).</p>
    3736 
    3737 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3738 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_17"
     3726<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Since this
     3727sample has wire texture, we’ll use the default Texture model (cylindrical).
     3728Then set the Harmonic order to 12 (what we used earlier) and check the Refine
     3729and Show <span class=SpellE>coeff</span> boxes. The data window will be redrawn
     3730(and a blank plot will appear).</p>
     3731
     3732<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3733style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_17"
    37393734 o:spid="_x0000_i1036" type="#_x0000_t75" style='width:456pt;height:250.5pt;
    37403735 visibility:visible;mso-wrap-style:square'>
    … …  
    37453740v:shapes="Picture_x0020_17"><![endif]></span></p>
    37463741
    3747 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3748 115%'>Do Texture/Refine texture from the menu; the window will be repainted and
    3749 a <span class=SpellE>bullseye</span> pole figure will appear. </p>
    3750 
    3751 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3752 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20"
     3742<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do
     3743Texture/Refine texture from the menu; the window will be repainted and a <span
     3744class=SpellE>bullseye</span> pole figure will appear. </p>
     3745
     3746<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3747style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20"
    37533748 o:spid="_x0000_i1035" type="#_x0000_t75" style='width:480pt;height:267.75pt;
    37543749 visibility:visible;mso-wrap-style:square'>
    … …  
    37593754v:shapes="Picture_x0020_20"><![endif]></span></p>
    37603755
    3761 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3762 115%'>Change the Texture plot type to Inverse pole figure to get a more useful
    3763 plot</p>
    3764 
    3765 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3766 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_19"
     3756<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the
     3757Texture plot type to Inverse pole figure to get a more useful plot</p>
     3758
     3759<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3760style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_19"
    37673761 o:spid="_x0000_i1034" type="#_x0000_t75" style='width:525pt;height:450pt;
    37683762 visibility:visible;mso-wrap-style:square'>
    … …  
    37733767v:shapes="Picture_x0020_19"><![endif]></span></p>
    37743768
    3775 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3776 115%'>This is essentially the same as we obtained earlier in Method <span
    3777 class=GramE>A</span> (maybe not quite as strong here).</p>
    3778 
    3779 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3780 115%'>Now select the Texture tab for the B19’ phase and do the same; use
    3781 Harmonic order 10 as we did earlier in Method A. After setting the two flags
    3782 and doing Texture/Refine texture we get</p>
    3783 
    3784 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3785 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21"
     3769<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is
     3770essentially the same as we obtained earlier in Method <span class=GramE>A</span>
     3771(maybe not quite as strong here).</p>
     3772
     3773<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the
     3774Texture tab for the B19’ phase and do the same; use Harmonic order 10 as we did
     3775earlier in Method A. After setting the two flags and doing Texture/Refine
     3776texture we get</p>
     3777
     3778<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3779style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21"
    37863780 o:spid="_x0000_i1033" type="#_x0000_t75" style='width:502.5pt;height:375pt;
    37873781 visibility:visible;mso-wrap-style:square'>
    … …  
    37923786v:shapes="Picture_x0020_21"><![endif]></span></p>
    37933787
    3794 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3795 115%'>And a <span class=SpellE>bullseye</span> pole figure; change that to
    3796 Inverse pole figure to see the texture</p>
    3797 
    3798 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3799 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_22"
     3788<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a <span
     3789class=SpellE>bullseye</span> pole figure; change that to Inverse pole figure to
     3790see the texture</p>
     3791
     3792<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     3793style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_22"
    38003794 o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt;height:450pt;
    38013795 visibility:visible;mso-wrap-style:square'>
    … …  
    38063800v:shapes="Picture_x0020_22"><![endif]></span></p>
    38073801
    3808 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3809 115%'>Again this is very similar to what we found in Method A but again not
    3810 quite as strong (max MRD ~13 instead of ~18).</p>
    3811 
    3812 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3813 115%'>Now do a File/Save project from the main menu; this saves the final texture
    3814 results done in Step 2 (you also will need it for Method C).</p>
    3815 
    3816 <h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Method C.
    3817 Sequential refinement &amp; full texture refinement</h2>
    3818 
    3819 <h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Introduction</h3>
    3820 
    3821 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3822 115%'>This uses the same approach as Method B except that after the sequential
    3823 refinements are finished we then fix almost all the parameters and then do a
    3824 final texture refinement with all the data. Thus, this is a replacement for
    3825 Step 2 in Method B. To begin do <b style='mso-bidi-font-weight:normal'><span
    3826 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3827 mso-hansi-theme-font:minor-latin'>File/Open project
    3828 </span></b> for the <span
    3829 class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
     3802<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Again this is
     3803very similar to what we found in Method A but again not quite as strong (max
     3804MRD ~13 instead of ~18).</p>
     3805
     3806<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do a
     3807File/Save project from the main menu; this saves the final texture results done
     3808in Step 2 (you also will need it for Method C).</p>
     3809
     3810<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     38110in;line-height:115%'>Method C. Sequential refinement &amp; full texture
     3812refinement</h2>
     3813
     3814<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     38150in;line-height:115%'>Introduction</h3>
     3816
     3817<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This uses the
     3818same approach as Method B except that after the sequential refinements are
     3819finished we then fix almost all the parameters and then do a final texture
     3820refinement with all the data. Thus, this is a replacement for Step 2 in Method
     3821B. To begin do <b style='mso-bidi-font-weight:normal'><span style='font-family:
    38303822"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3831 minor-latin'>NiTi-B.gpx</span></b></span> file created in Method B and then do
    3832 a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3833 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Save
    3834 project as
    3835 </span></b> to save it as <span class=SpellE><b style='mso-bidi-font-weight:
     3823minor-latin'>File/Open project
     3824</span></b> for the <span class=SpellE><b
     3825style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3826mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NiTi-B.gpx</span></b></span>
     3827file created in Method B and then do a <b style='mso-bidi-font-weight:normal'><span
     3828style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3829mso-hansi-theme-font:minor-latin'>File/Save project as
     3830</span></b> to save it
     3831as <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
     3832style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3833mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight:
    38363834normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    3837 minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b
    3838 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3839 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-C</span></b>.
    3840 This renames the project and it should have one IMG, 10 PWDR entries and two
    3841 phases of <span class=SpellE>NiTi</span> (B2 and B19’).</p>
    3842 
    3843 <h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 1. Clearing
    3844 unwanted variables from sequential refinement</h3>
    3845 
    3846 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    3847 115%'>Here we want to clear refinement flags for all parameters that need not
    3848 be varied in a texture analysis refinement. The general rule is to not refine
    3849 any parameter unless we expect it to affect the peak intensities. These are
    3850 listed below:</p>
    3851 
    3852 <p class=MsoListParagraphCxSpFirst style='margin-bottom:0in;margin-bottom:.0001pt;
    3853 mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
     3835minor-latin;mso-hansi-theme-font:minor-latin'>-C</span></b>. This renames the
     3836project and it should have one IMG, 10 PWDR entries and two phases of <span
     3837class=SpellE>NiTi</span> (B2 and B19’).</p>
     3838
     3839<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     38400in;line-height:115%'>Step 1. Clearing unwanted variables from sequential
     3841refinement</h3>
     3842
     3843<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Here we want
     3844to clear refinement flags for all parameters that need not be varied in a
     3845texture analysis refinement. The general rule is to not refine any parameter
     3846unless we expect it to affect the peak intensities. These are listed below:</p>
     3847
     3848<p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;mso-add-space:
     3849auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
    38543850style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
    38553851style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
    … …  
    38703866refinement flags.</p>
    38713867
    3872 <p class=MsoListParagraphCxSpMiddle style='margin-bottom:0in;margin-bottom:
    3873 .0001pt;mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
     3868<p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;mso-add-space:
     3869auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
    38743870style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
    38753871style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
    … …  
    39043900copy the zeroed out harmonic coefficients.</p>
    39053901
    3906 <p class=MsoListParagraphCxSpLast style='margin-bottom:0in;margin-bottom:.0001pt;
    3907 mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
     3902<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space:
     3903auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
    39083904style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
    39093905style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
    … …  
    39383934copy the zeroed out harmonic coefficients.</p>
    39393935
    3940 <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
    3941 margin-left:.25in;margin-bottom:.0001pt;line-height:115%'><o:p>&nbsp;</o:p></p>
    3942 
    3943 <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
    3944 margin-left:.25in;margin-bottom:.0001pt;line-height:115%'>Notice that we have
    3945 allowed refinement of the <b style='mso-bidi-font-weight:normal'><span
    3946 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3947 mso-hansi-theme-font:minor-latin'>Phase fractions</span></b>; these may change during
    3948 the texture refinement. Now select the <b style='mso-bidi-font-weight:normal'><span
    3949 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    3950 mso-hansi-theme-font:minor-latin'>Texture</span></b> tab for the <b
    3951 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3952 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
    3953 phase (it may still have values from the Method B).</p>
    3954 
    3955 <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
    3956 margin-left:.25in;margin-bottom:.0001pt;line-height:115%'><span
    3957 style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_23"
    3958  o:spid="_x0000_i1031" type="#_x0000_t75" style='width:480pt;height:267.75pt;
    3959  visibility:visible;mso-wrap-style:square'>
     3936<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     3937margin-left:.25in;line-height:115%'><o:p>&nbsp;</o:p></p>
     3938
     3939<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     3940margin-left:.25in;line-height:115%'>Notice that we have allowed refinement of
     3941the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3942mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase fractions</span></b>;
     3943these may change during the texture refinement. Now select the <b
     3944style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3945mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
     3946tab for the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     3947"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     3948minor-latin'>B2</span></b> phase (it may still have values from the Method B).</p>
     3949
     3950<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     3951margin-left:.25in;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     3952 id="Picture_x0020_23" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:480pt;
     3953 height:267.75pt;visibility:visible;mso-wrap-style:square'>
    39603954 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
    39613955  o:title=""/>
    … …  
    39643958v:shapes="Picture_x0020_23"><![endif]></span></p>
    39653959
    3966 <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
    3967 margin-left:.25in;margin-bottom:.0001pt;line-height:115%'>You can clear these
    3968 by setting the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    3969 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    3970 minor-latin'>Harmonic order</span></b> to zero and then back to <b
    3971 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3972 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>12</span></b>.
    3973 Leave the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    3974 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b>
    3975 &amp; <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3960<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     3961margin-left:.25in;line-height:115%'>You can clear these by setting the <b
     3962style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3963mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic
     3964order</span></b> to zero and then back to <b style='mso-bidi-font-weight:normal'><span
     3965style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     3966mso-hansi-theme-font:minor-latin'>12</span></b>. Leave the <b style='mso-bidi-font-weight:
     3967normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
     3968minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b> &amp; <b
     3969style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    39763970mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b>
    39773971boxes checked.</p>
    39783972
    3979 <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
    3980 margin-left:.25in;margin-bottom:.0001pt;line-height:115%'><span
    3981 style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_24"
    3982  o:spid="_x0000_i1030" type="#_x0000_t75" style='width:480pt;height:267.75pt;
    3983  visibility:visible;mso-wrap-style:square'>
     3973<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     3974margin-left:.25in;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     3975 id="Picture_x0020_24" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:480pt;
     3976 height:267.75pt;visibility:visible;mso-wrap-style:square'>
    39843977 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
    39853978  o:title=""/>
    … …  
    39883981v:shapes="Picture_x0020_24"><![endif]></span></p>
    39893982
    3990 <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
    3991 margin-left:.25in;margin-bottom:.0001pt;line-height:115%'>Then do the same for
    3992 the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     3983<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
     3984margin-left:.25in;line-height:115%'>Then do the same for the <b
     3985style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    39933986mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
    39943987phase. Select the <b style='mso-bidi-font-weight:normal'><span
    … …  
    40084001boxes checked. This completes the setup for the full texture refinement.</p>
    40094002
    4010 <h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 2. Texture
    4011 refinement</h3>
    4012 
    4013 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    4014 115%'>Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4003<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
     40040in;line-height:115%'>Step 2. Texture refinement</h3>
     4005
     4006<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do <b
     4007style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    40154008mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
    40164009from the main menu; you will see the warning message</p>
    40174010
    4018 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    4019 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_25"
     4011<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4012style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_25"
    40204013 o:spid="_x0000_i1029" type="#_x0000_t75" style='width:363pt;height:120.75pt;
    40214014 visibility:visible;mso-wrap-style:square'>
    … …  
    40264019v:shapes="Picture_x0020_25"><![endif]></span></p>
    40274020
    4028 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    4029 115%'>In this case you do want to do a <span class=SpellE>nonsequential</span>
    4030 full refinement, so press the OK button. A quick look at the console will show
    4031 that there are 61 variables in this refinement. If yours shows more then you
    4032 didn’t clear all the flags in Step 1. The <b style='mso-bidi-font-weight:normal'><span
     4021<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In this case
     4022you do want to do a <span class=SpellE>nonsequential</span> full refinement, so
     4023press the OK button. A quick look at the console will show that there are 61
     4024variables in this refinement. If yours shows more then you didn’t clear all the
     4025flags in Step 1. The <b style='mso-bidi-font-weight:normal'><span
    40334026style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    40344027mso-hansi-theme-font:minor-latin'>Sequential results</span></b> entry is
    … …  
    40444037B) you should see</p>
    40454038
    4046 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    4047 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26"
     4039<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4040style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26"
    40484041 o:spid="_x0000_i1028" type="#_x0000_t75" style='width:525pt;height:450pt;
    40494042 visibility:visible;mso-wrap-style:square'>
    … …  
    40544047v:shapes="Picture_x0020_26"><![endif]></span></p>
    40554048
    4056 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    4057 115%'><span class=GramE>which</span> is almost identical to that from Method A.
    4058 The coefficients are seen in</p>
    4059 
    4060 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    4061 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27"
     4049<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4050class=GramE>which</span> is almost identical to that from Method A. The
     4051coefficients are seen in</p>
     4052
     4053<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4054style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27"
    40624055 o:spid="_x0000_i1027" type="#_x0000_t75" style='width:480pt;height:267.75pt;
    40634056 visibility:visible;mso-wrap-style:square'>
    … …  
    40684061v:shapes="Picture_x0020_27"><![endif]></span></p>
    40694062
    4070 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    4071 115%'>Now select the <b style='mso-bidi-font-weight:normal'><span
    4072 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    4073 mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and its <b
    4074 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    4075 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
    4076 tab; the inverse pole figure is</p>
    4077 
    4078 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    4079 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28"
     4063<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the
     4064<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     4065mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
     4066phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
     4067"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     4068minor-latin'>Texture</span></b> tab; the inverse pole figure is</p>
     4069
     4070<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4071style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28"
    40804072 o:spid="_x0000_i1026" type="#_x0000_t75" style='width:525pt;height:450pt;
    40814073 visibility:visible;mso-wrap-style:square'>
    … …  
    40864078v:shapes="Picture_x0020_28"><![endif]></span></p>
    40874079
    4088 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    4089 115%'><span class=GramE>and</span> also almost identical to what was obtained
    4090 in Method A; the coefficients are seen in</p>
    4091 
    4092 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    4093 115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_58"
     4080<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4081class=GramE>and</span> also almost identical to what was obtained in Method A;
     4082the coefficients are seen in</p>
     4083
     4084<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
     4085style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_58"
    40944086 o:spid="_x0000_i1025" type="#_x0000_t75" style='width:502.5pt;height:375pt;
    40954087 visibility:visible;mso-wrap-style:square'>
    … …  
    41004092v:shapes="Picture_x0020_58"><![endif]></span></p>
    41014093
    4102 <p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
    4103 115%'>With this Method you can add parameters (atom coordinates &amp; thermal
    4104 motion parameters) that could not be refined in method B. It should be clear
    4105 from this tutorial that in more complex textures where the data set may consist
    4106 of slices obtained from a suite of 2D images collected as the sample is
    4107 rotated, Method C will give a relatively fast determination of the texture
    4108 without resorting to large matrix least-squares refinements.</p>
     4094<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>With this
     4095Method you can add parameters (atom coordinates &amp; thermal motion
     4096parameters) that could not be refined in method B. It should be clear from this
     4097tutorial that in more complex textures where the data set may consist of slices
     4098obtained from a suite of 2D images collected as the sample is rotated, Method C
     4099will give a relatively fast determination of the texture without resorting to large
     4100matrix least-squares refinements.</p>
    41094101
    41104102</div>

  • Tutorials/2DTexture/Texture analysis of 2D data in GSAS-II_files/filelist.xml

    r1855 r1856  
    44 <o:File HRef="colorschememapping.xml"/>
    55 <o:File HRef="image001.png"/>
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