source: Tutorials/LeBail/LeBailSucrose.htm @ 5027

Last change on this file since 5027 was 5027, checked in by vondreele, 17 months ago

revise LeBail? tutorial

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412  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
413  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
414  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
415  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
416  <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
417  <w:LsdException Locked="false" Priority="34" QFormat="true"
418   Name="List Paragraph"/>
419  <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
420  <w:LsdException Locked="false" Priority="30" QFormat="true"
421   Name="Intense Quote"/>
422  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
423  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
424  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
425  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
426  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
427  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
428  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
429  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
430  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
431  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
432  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
433  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
434  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
435  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
436  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
437  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
438  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
439  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
440  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
441  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
442  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
443  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
444  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
445  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
446  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
447  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
448  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
449  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
450  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
451  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
452  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
453  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
454  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
455  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
456  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
457  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
458  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
459  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
460  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
461  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
462  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
463  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
464  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
465  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
466  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
467  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
468  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
469  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
470  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
471  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
472  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
473  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
474  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
475  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
476  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
477  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
478  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
479  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
480  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
481  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
482  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
483  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
484  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
485  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
486  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
487  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
488  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
489  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
490  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
491  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
492  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
493  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
494  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
495  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
496  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
497  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
498  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
499  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
500  <w:LsdException Locked="false" Priority="19" QFormat="true"
501   Name="Subtle Emphasis"/>
502  <w:LsdException Locked="false" Priority="21" QFormat="true"
503   Name="Intense Emphasis"/>
504  <w:LsdException Locked="false" Priority="31" QFormat="true"
505   Name="Subtle Reference"/>
506  <w:LsdException Locked="false" Priority="32" QFormat="true"
507   Name="Intense Reference"/>
508  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
509  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
510   UnhideWhenUsed="true" Name="Bibliography"/>
511  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
512   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
513  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
514  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
515  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
516  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
517  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
518  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
519  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
520  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
521  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
522  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
523  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
524  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
525  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
526  <w:LsdException Locked="false" Priority="46"
527   Name="Grid Table 1 Light Accent 1"/>
528  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
529  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
530  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
531  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
532  <w:LsdException Locked="false" Priority="51"
533   Name="Grid Table 6 Colorful Accent 1"/>
534  <w:LsdException Locked="false" Priority="52"
535   Name="Grid Table 7 Colorful Accent 1"/>
536  <w:LsdException Locked="false" Priority="46"
537   Name="Grid Table 1 Light Accent 2"/>
538  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
539  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
540  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
541  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
542  <w:LsdException Locked="false" Priority="51"
543   Name="Grid Table 6 Colorful Accent 2"/>
544  <w:LsdException Locked="false" Priority="52"
545   Name="Grid Table 7 Colorful Accent 2"/>
546  <w:LsdException Locked="false" Priority="46"
547   Name="Grid Table 1 Light Accent 3"/>
548  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
549  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
550  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
551  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
552  <w:LsdException Locked="false" Priority="51"
553   Name="Grid Table 6 Colorful Accent 3"/>
554  <w:LsdException Locked="false" Priority="52"
555   Name="Grid Table 7 Colorful Accent 3"/>
556  <w:LsdException Locked="false" Priority="46"
557   Name="Grid Table 1 Light Accent 4"/>
558  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
559  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
560  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
561  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
562  <w:LsdException Locked="false" Priority="51"
563   Name="Grid Table 6 Colorful Accent 4"/>
564  <w:LsdException Locked="false" Priority="52"
565   Name="Grid Table 7 Colorful Accent 4"/>
566  <w:LsdException Locked="false" Priority="46"
567   Name="Grid Table 1 Light Accent 5"/>
568  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
569  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
570  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
571  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
572  <w:LsdException Locked="false" Priority="51"
573   Name="Grid Table 6 Colorful Accent 5"/>
574  <w:LsdException Locked="false" Priority="52"
575   Name="Grid Table 7 Colorful Accent 5"/>
576  <w:LsdException Locked="false" Priority="46"
577   Name="Grid Table 1 Light Accent 6"/>
578  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
579  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
580  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
581  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
582  <w:LsdException Locked="false" Priority="51"
583   Name="Grid Table 6 Colorful Accent 6"/>
584  <w:LsdException Locked="false" Priority="52"
585   Name="Grid Table 7 Colorful Accent 6"/>
586  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
587  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
588  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
589  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
590  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
591  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
592  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
593  <w:LsdException Locked="false" Priority="46"
594   Name="List Table 1 Light Accent 1"/>
595  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
596  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
597  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
598  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
599  <w:LsdException Locked="false" Priority="51"
600   Name="List Table 6 Colorful Accent 1"/>
601  <w:LsdException Locked="false" Priority="52"
602   Name="List Table 7 Colorful Accent 1"/>
603  <w:LsdException Locked="false" Priority="46"
604   Name="List Table 1 Light Accent 2"/>
605  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
606  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
607  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
608  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
609  <w:LsdException Locked="false" Priority="51"
610   Name="List Table 6 Colorful Accent 2"/>
611  <w:LsdException Locked="false" Priority="52"
612   Name="List Table 7 Colorful Accent 2"/>
613  <w:LsdException Locked="false" Priority="46"
614   Name="List Table 1 Light Accent 3"/>
615  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
616  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
617  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
618  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
619  <w:LsdException Locked="false" Priority="51"
620   Name="List Table 6 Colorful Accent 3"/>
621  <w:LsdException Locked="false" Priority="52"
622   Name="List Table 7 Colorful Accent 3"/>
623  <w:LsdException Locked="false" Priority="46"
624   Name="List Table 1 Light Accent 4"/>
625  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
626  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
627  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
628  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
629  <w:LsdException Locked="false" Priority="51"
630   Name="List Table 6 Colorful Accent 4"/>
631  <w:LsdException Locked="false" Priority="52"
632   Name="List Table 7 Colorful Accent 4"/>
633  <w:LsdException Locked="false" Priority="46"
634   Name="List Table 1 Light Accent 5"/>
635  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
636  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
637  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
638  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
639  <w:LsdException Locked="false" Priority="51"
640   Name="List Table 6 Colorful Accent 5"/>
641  <w:LsdException Locked="false" Priority="52"
642   Name="List Table 7 Colorful Accent 5"/>
643  <w:LsdException Locked="false" Priority="46"
644   Name="List Table 1 Light Accent 6"/>
645  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
646  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
647  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
648  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
649  <w:LsdException Locked="false" Priority="51"
650   Name="List Table 6 Colorful Accent 6"/>
651  <w:LsdException Locked="false" Priority="52"
652   Name="List Table 7 Colorful Accent 6"/>
653  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
654   Name="Mention"/>
655  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
656   Name="Smart Hyperlink"/>
657  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
658   Name="Hashtag"/>
659  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
660   Name="Unresolved Mention"/>
661  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
662   Name="Smart Link"/>
663 </w:LatentStyles>
664</xml><![endif]-->
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669        {font-family:Courier;
670        panose-1:2 7 4 9 2 2 5 2 4 4;
671        mso-font-alt:"Courier New";
672        mso-font-charset:0;
673        mso-generic-font-family:modern;
674        mso-font-format:other;
675        mso-font-pitch:fixed;
676        mso-font-signature:3 0 0 0 1 0;}
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681        mso-generic-font-family:auto;
682        mso-font-pitch:variable;
683        mso-font-signature:0 268435456 0 0 -2147483648 0;}
684@font-face
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688        mso-generic-font-family:roman;
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696        mso-font-pitch:variable;
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703        mso-font-pitch:variable;
704        mso-font-signature:-520081665 -1073717157 41 0 66047 0;}
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708        mso-style-qformat:yes;
709        mso-style-parent:"";
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716h1
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720        mso-style-link:"Heading 1 Char";
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723        mso-margin-bottom-alt:auto;
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729        mso-fareast-font-family:"Times New Roman";
730        mso-fareast-theme-font:minor-fareast;
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732h2
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734        mso-style-qformat:yes;
735        mso-style-link:"Heading 2 Char";
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738        mso-margin-bottom-alt:auto;
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744        mso-fareast-font-family:"Times New Roman";
745        mso-fareast-theme-font:minor-fareast;
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749        mso-style-priority:99;
750        color:blue;
751        text-decoration:underline;
752        text-underline:single;}
753a:visited, span.MsoHyperlinkFollowed
754        {mso-style-noshow:yes;
755        mso-style-priority:99;
756        color:#954F72;
757        mso-themecolor:followedhyperlink;
758        text-decoration:underline;
759        text-underline:single;}
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762        mso-style-priority:99;
763        mso-margin-top-alt:auto;
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765        mso-margin-bottom-alt:auto;
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767        mso-pagination:widow-orphan;
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770        mso-fareast-font-family:"Times New Roman";
771        mso-fareast-theme-font:minor-fareast;}
772p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
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774        mso-style-priority:99;
775        mso-style-link:"Balloon Text Char";
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1113
1114<body lang=EN-US link=blue vlink="#954F72" style='tab-interval:.5in;word-wrap:
1115break-word'>
1116
1117<div class=WordSection1>
1118
1119<h1><span style='mso-fareast-font-family:"Times New Roman"'>Le Bail Intensity
1120Extraction in GSAS-II - Sucrose<o:p></o:p></span></h1>
1121
1122<p class=MsoNormal><BL><span style='font-family:Symbol;mso-ascii-font-family:
1123"Times New Roman";mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>·</span><span
1124style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'><span
1125style='mso-spacerun:yes'>  </span>Exercise files are found <a href="data/"
1126target="_blank">here</a>. The data files are also used in the 3rd section of
1127the <a href="../FitPeaks/Fit%20Peaks.htm#sucrose_peak_fit" target="_blank">Fit
1128Peaks/Autoindexing tutorial</a>. <o:p></o:p></span></p>
1129
1130</BL>
1131
1132<h1><span style='mso-fareast-font-family:"Times New Roman"'>Background <o:p></o:p></span></h1>
1133
1134<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1135minor-latin'>In a Rietveld fit, a number of different items are fit,
1136potentially at the same time. These include the lattice parameters, atomic positions
1137and displacement (aka “temperature”, <span class=SpellE>U<sub>iso</sub></span>
1138and <span class=SpellE>U<sub>ij</sub></span>) parameters for one or more
1139phases, as well as peak shapes parameters either for broadening from either the
1140sample or the instrument (avoid doing both together), background fitting terms
1141and one or two correction terms needed to describe peak shifts due to apparent
1142sample placement. In addition, there could be other terms needed to describe
1143additional experimental conditions such as for absorption, preferred
1144orientation or extinction. These parameters can be divided into four
1145categories: experimental (peak shapes, peak shifts and background), lattice
1146parameters, structural parameters (atom positions and U values) and intensity
1147correction terms (absorption, preferred orientation and extinction).<o:p></o:p></span></p>
1148
1149<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1150minor-latin'><o:p>&nbsp;</o:p></span></p>
1151
1152<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1153minor-latin'>In Rietveld, the reflection intensities are generated from the
1154structural and intensity correction parameters, but there are two approaches to
1155full-pattern fitting that treat reflection intensities as arbitrary: (1) Pawley
1156fitting, developed by Stuart Pawley [Pawley, G. S. (1981). &quot;Unit-Cell
1157Refinement from Powder Diffraction Scans.&quot; Journal of Applied
1158Crystallography 14: 357-361.], where peak intensities are treated as
1159least-squares variables. (2) Le Bail fitting, from Armel Le Bail [Le Bail, A.
1160(2005). &quot;Whole powder pattern decomposition methods and applications: A
1161retrospection.&quot; Powder Diffraction 20(4): 316-326.] The Le Bail approach,
1162demonstrated by this tutorial, takes advantage of the fact that Hugo Rietveld
1163developed a rather ingenious approach to estimating reflection intensities: the
1164idea behind this is that for every point in a pattern where one or more
1165reflections contribute, one can estimate the relative contribution from each
1166reflection from the structure factor magnitude, F<sup>2</sup><sub>calc</sub>,
1167from the approximate crystal structure model, adjusted for reflection
1168multiplicity (<i>m</i>), preferred orientation and various other geometric
1169corrections. Simply apportioning the observed powder pattern intensities point
1170by point to each reflection provides an estimate for the observed structure
1171factors, F<sup>2</sup><sub>obs</sub>. The quality of this estimate improves as
1172the crystal structure model approaches reality. Le Bail’s method cleverly
1173appropriates Rietveld’s intensity extraction, but assuming the crystal
1174structure model is unknown, sets all F<sup>2</sup><sub>calc</sub> values to an
1175initial value (e.g. 1.0). After the intensity extraction is performed, a set of
1176F<sup>2</sup><sub>obs</sub> values is obtained. These initially treat every F<sup>2</sup><sub>obs</sub>/<i>m</i>
1177ratio as equivalent and will not be very accurate, but they are much better
1178reflection estimates than the initial F<sup>2</sup><sub>calc</sub> values (all
1179unity). The F<sup>2</sup><sub>calc</sub> values are set to the extracted F<sup>2</sup><sub>obs</sub>
1180and the Le Bail fit can be repeated, giving even better intensity estimates.
1181This process is equivalent to a steepest descents minimization and it will converge
1182to a self-consistent set of intensities that will give best possible agreement
1183to the observed pattern. Note that the apportionment of intensity for
1184reflections that are very closely overlapped will tend to make their F<sup>2</sup><sub>calc</sub>
1185values approximately equal. (Note that the Pawley approach will tend make <i>m</i>*F<sup>2</sup><sub>obs</sub>
1186values equal for complete reflection overlap; neither is likely to be
1187accurate.) <o:p></o:p></span></p>
1188
1189<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1190minor-latin'><o:p>&nbsp;</o:p></span></p>
1191
1192<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1193minor-latin'>Note that when either Pawley or Le Bail intensity extraction are
1194used, the structural and intensity correction parameters no longer affect the
1195intensity computations. Such parameters should not be included in the fit as
1196they will produce singularities in the refinement. If included inadvertently,
1197GSAS-II will usually remove them from the fit along with providing annoying warning
1198messages, but it is possible that this parameter removal process could fail and
1199the refinement may not run properly.</span></p>
1200
1201<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1202minor-latin'><o:p>&nbsp;</o:p></span></p>
1203
1204<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1205minor-latin'>After the LeBail option has been invoked, the Calculate/Refine
1206menu command will execute a preliminary LeBail only “zero cycles” refinement in
1207which only F<sup>2</sup><sub>obs</sub> is adjusted via the LeBail method. It is
1208cycled 10 times or until a minimum is reached. After that completes, the
1209Rietveld/LeBail refinement proceeds allowing least-squares minimization of
1210non-intensity dependent parameters toward a more global fit to the data.
1211Successive runs allowing other parameters to be varied can then be used to
1212progressively improve the fit and produce a best estimate of the F<sup>2</sup><sub>obs</sub>.<o:p></o:p></span></p>
1213
1214<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1215minor-latin'><o:p>&nbsp;</o:p></span></p>
1216
1217<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1218minor-latin'>There are many reasons to use Le Bail fitting. The technique was
1219developed to obtain a set of reflection intensities for structure solution. It
1220can also be used to treat an impurity, where lattice parameters are known but
1221the structural details are not or for fitting lattice parameters where likewise
1222the structure is not known. Le Bail fitting is also useful prior to a
1223structural fit. It can allow determination of reasonable starting values for
1224the background, peak shapes and unit cell parameters so they can be fixed until
1225the late stages of the refinement, although the freedom in peak intensities may
1226bias some parameters (e.g. background and profile coefficients) if there is a
1227large number of overlapping reflections. Another use is to see when artifacts
1228in the background or peak shapes limit how well the pattern can be fit. A Le Bail
1229or Pawley fit provides an estimate for the best possible <span class=SpellE>R<sub>wp</sub></span>
1230and reduced </span><span lang=EL style='mso-fareast-font-family:Calibri;
1231mso-fareast-theme-font:minor-latin;mso-ansi-language:EL'>&#967;</span><sup><span
1232style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>2</span></sup><span
1233style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>
1234values that can be expected for a dataset. For complex patterns, where it is
1235difficult to discern where allowed reflections are present, comparison of Le
1236Bail or Pawley fits can provide insight on extinction conditions. A lower
1237symmetry space group with fewer extinctions should provide a better fit to
1238warrant its consideration.</span></p>
1239
1240<p class=MsoNormal><span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1241minor-latin'><o:p>&nbsp;</o:p></span></p>
1242
1243<h1><span style='mso-fareast-font-family:"Times New Roman"'>Prerequisite <o:p></o:p></span></h1>
1244
1245<p class=MsoNormal>In this exercise you we will use Le Bail fitting to extract
1246approximate reflection intensities. This is similar to what is done in the
1247beginning of the “Charge Flipping in GSAS-II - sucrose” tutorial, which instead
1248uses Pawley fitting. It follows logically from the third example in the “Fit
1249Peaks/Autoindexing in GSAS-II” tutorial, from where the sucrose unit cell was
1250determined. Alternately, a project (<span class=SpellE><span style='font-family:
1251Courier'>start.gpx</span></span>) file is provided in the <a href="data/"
1252target="_blank">exercise files</a> to start without the previous tutorial.</p>
1253
1254<h2>Step 1: Setup for fit</h2>
1255
1256<p class=MsoNormal>From the final project file, after completing the indexing
1257and creating the phase, make the the following changes:</p>
1258
1259<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1260style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1261Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1262</span></span></span><![endif]><b>Controls</b>: Set the “<b><span
1263style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1264mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Max cycles</span></b>”
1265value to 5 </p>
1266
1267<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1268style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1269Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1270</span></span></span><![endif]><b>Limits</b>: Raise the upper data limit from 8
1271to <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1272mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>24</span></b>
1273degrees</p>
1274
1275<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1276style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1277Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1278</span></span></span><![endif]><b>Background</b>: Add a background peak at <b><span
1279style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1280mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>5.5</span></b>
1281deg with sigma=<b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1282minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>10,000</span></b>,
1283set the flag to refine the peak intensity. This is to accommodate a broad peak
1284in the background from the Kapton capillary used to hold the sucrose sample.</p>
1285
1286<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1287style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1288Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1289</span></span></span><![endif]><b>Instrument parameters</b>: Use the <b><span
1290style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1291mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Operations/Reset
1292profile</span></b> menu command to return to the beamline-supplied terms; turn
1293off refinement of all terms</p>
1294
1295<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1296style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1297Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1298</span></span></span><![endif]><b>Sample parameters</b>: turn off refinement of
1299the <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1300mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>histogram
1301scale factor</span></b> and make sure the goniometer radius is <b><span
1302style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1303mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>1000</span></b>
1304mm.</p>
1305
1306<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1307style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1308Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1309</span></span></span><![endif]><b>Phase Sucrose/Data tab</b>: Use <b><span
1310style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1311mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Edit phase/Add
1312powder histograms</span></b> to link this phase to the powder dataset; set the
1313refine flag on for the <b><span style='font-family:"Calibri",sans-serif;
1314mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1315minor-latin'>size</span></b> term and the <span class=SpellE><b><span
1316style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1317mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>microstrain</span></b></span>
1318term. </p>
1319
1320<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1321style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1322Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1323</span></span></span><![endif]><b>Phase Sucrose/General tab</b>: Set the <b><span
1324style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1325mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Refine unit
1326cell</span></b> flag.</p>
1327
1328<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1329
1330<p class=MsoNormal>These changes have been applied to a GSAS-II project file
1331from the conclusion of the 3rd Example within “<b><span style='font-family:
1332"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1333minor-latin;mso-bidi-theme-font:minor-latin'>Fit Peaks/Autoindexing in GSAS-II</span></b>”
1334tutorial and is provided as for this tutorial as file <span class=SpellE><span
1335style='font-family:Courier'>start.gpx</span></span>.</p>
1336
1337<h2>Step 2: Select Le Bail fitting</h2>
1338
1339<p class=MsoNormal>On the phase Data tab, press the <b><span style='font-family:
1340"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1341minor-latin;mso-bidi-theme-font:minor-latin'>Start Le Bail extraction?</span></b>
1342button to put the refinement into Le Bail mode. </p>
1343
1344<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
1345 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
1346 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1347 <v:stroke joinstyle="miter"/>
1348 <v:formulas>
1349  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
1350  <v:f eqn="sum @0 1 0"/>
1351  <v:f eqn="sum 0 0 @1"/>
1352  <v:f eqn="prod @2 1 2"/>
1353  <v:f eqn="prod @3 21600 pixelWidth"/>
1354  <v:f eqn="prod @3 21600 pixelHeight"/>
1355  <v:f eqn="sum @0 0 1"/>
1356  <v:f eqn="prod @6 1 2"/>
1357  <v:f eqn="prod @7 21600 pixelWidth"/>
1358  <v:f eqn="sum @8 21600 0"/>
1359  <v:f eqn="prod @7 21600 pixelHeight"/>
1360  <v:f eqn="sum @10 21600 0"/>
1361 </v:formulas>
1362 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1363 <o:lock v:ext="edit" aspectratio="t"/>
1364</v:shapetype><v:shape id="Picture_x0020_11" o:spid="_x0000_i1039" type="#_x0000_t75"
1365 alt="GSAS-II project: start.gpx" style='width:432.75pt;height:421.5pt;
1366 visibility:visible;mso-wrap-style:square'>
1367 <v:imagedata src="LeBailSucrose.fld/image001.png" o:title=" start"/>
1368</v:shape><![endif]--><![if !vml]><img border=0 width=577 height=562
1369src="LeBailSucrose.fld/image003.png" alt="GSAS-II project: start.gpx" v:shapes="Picture_x0020_11"><![endif]></span></p>
1370
1371<p class=MsoNormal>The window will be redrawn with all intensity dependent
1372variables removed from view</p>
1373
1374<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1375 id="Picture_x0020_12" o:spid="_x0000_i1038" type="#_x0000_t75" alt="GSAS-II project: start.gpx"
1376 style='width:435pt;height:325.5pt;visibility:visible;mso-wrap-style:square'>
1377 <v:imagedata src="LeBailSucrose.fld/image004.png" o:title=" start"/>
1378</v:shape><![endif]--><![if !vml]><img border=0 width=580 height=434
1379src="LeBailSucrose.fld/image006.png" alt="GSAS-II project: start.gpx" v:shapes="Picture_x0020_12"><![endif]></span></p>
1380
1381<p class=MsoNormal>and the LeBail button has changed to “Stop LeBail
1382extraction?”.</p>
1383
1384<h2>Step 3: Do the initial Le Bail fit</h2>
1385
1386<p class=MsoNormal>Do the <b><span style='font-family:"Calibri",sans-serif;
1387mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1388minor-latin'>Calculate/Refine</span></b> menu command. A popup message will
1389appear informing you that it will do the initial zero cycle LeBail fit of the
1390intensities. </p>
1391
1392<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1393 id="Picture_x0020_13" o:spid="_x0000_i1037" type="#_x0000_t75" alt="Le Bail Refinement"
1394 style='width:274.5pt;height:99pt;visibility:visible;mso-wrap-style:square'>
1395 <v:imagedata src="LeBailSucrose.fld/image016.png" o:title="Le Bail Refinement"/>
1396</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=132
1397src="LeBailSucrose.fld/image016.png" alt="Le Bail Refinement" v:shapes="Picture_x0020_13"><![endif]></span></p>
1398
1399<p class=MsoNormal>press <b><span style='font-family:"Calibri",sans-serif;
1400mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1401minor-latin'>Ok</span></b>. The refinement will proceed and yield <span
1402class=SpellE>Rwp</span> ~34%. The popup has an Ok and Cancel buttons. The plot
1403has been updated with this fit. </p>
1404
1405<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1406 id="Picture_x0020_14" o:spid="_x0000_i1036" type="#_x0000_t75" alt="GSAS-II plots: start.gpx"
1407 style='width:501.75pt;height:322.5pt;visibility:visible;mso-wrap-style:square'>
1408 <v:imagedata src="LeBailSucrose.fld/image013.png" o:title=" start"/>
1409</v:shape><![endif]--><![if !vml]><img border=0 width=669 height=430
1410src="LeBailSucrose.fld/image007.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_14"><![endif]></span></p>
1411
1412<p class=MsoNormal>You should have a look to be sure that the peaks are in the
1413right places and that some calculated intensity is present under them.
1414Otherwise you should press Cancel &amp; adjust things as appropriate (e.g.
1415lattice parameters). </p>
1416
1417<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1418
1419<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1420 id="Picture_x0020_15" o:spid="_x0000_i1035" type="#_x0000_t75" alt="Le Bail fit: Rwp=34.149"
1421 style='width:274.5pt;height:117pt;visibility:visible;mso-wrap-style:square'>
1422 <v:imagedata src="LeBailSucrose.fld/image027.png" o:title=" Rwp=34"/>
1423</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=156
1424src="LeBailSucrose.fld/image027.png" alt="Le Bail fit: Rwp=34.149" v:shapes="Picture_x0020_15"><![endif]></span></p>
1425
1426<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif;
1427mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1428minor-latin'>Ok</span></b> to save this &amp; proceed to the 1<sup>st</sup>
1429full Rietveld/LeBail refinement. The next refinement will include those
1430parameters you selected for a full Rietveld/LeBail refinement. The initial
1431residual should be where the initial LeBail fit finished<span style='mso-no-proof:
1432yes'>. </span>This will run through five cycles of Rietveld/Le Bail fitting and
1433the residual will drop to <span class=SpellE>Rwp</span> ~12.6%</p>
1434
1435<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1436 id="Picture_x0020_17" o:spid="_x0000_i1034" type="#_x0000_t75" alt="Refinement results, Rw =12.560"
1437 style='width:274.5pt;height:177.75pt;visibility:visible;mso-wrap-style:square'>
1438 <v:imagedata src="LeBailSucrose.fld/image028.png" o:title="Refinement results, Rw =12"/>
1439</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=237
1440src="LeBailSucrose.fld/image028.png" alt="Refinement results, Rw =12.560"
1441v:shapes="Picture_x0020_17"><![endif]></span></p>
1442
1443<p class=MsoNormal>and the fit will be much improved</p>
1444
1445<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1446 id="Picture_x0020_18" o:spid="_x0000_i1033" type="#_x0000_t75" alt="GSAS-II plots: start.gpx"
1447 style='width:7in;height:324pt;visibility:visible;mso-wrap-style:square'>
1448 <v:imagedata src="LeBailSucrose.fld/image029.png" o:title=" start"/>
1449</v:shape><![endif]--><![if !vml]><img border=0 width=672 height=432
1450src="LeBailSucrose.fld/image008.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_18"><![endif]></span></p>
1451
1452<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif;
1453mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1454minor-latin'>OK</span></b> to accept these results. </p>
1455
1456<h2>Step 4: Add more parameters</h2>
1457
1458<p class=MsoNormal>Clearly, further improvement in the fit is desirable. Closely
1459examining the fit shows issues with background, profile shape and peak
1460positions.</p>
1461
1462<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1463 id="Picture_x0020_19" o:spid="_x0000_i1032" type="#_x0000_t75" alt="GSAS-II plots: start.gpx"
1464 style='width:501.75pt;height:322.5pt;visibility:visible;mso-wrap-style:square'>
1465 <v:imagedata src="LeBailSucrose.fld/image031.png" o:title=" start"/>
1466</v:shape><![endif]--><![if !vml]><img border=0 width=669 height=430
1467src="LeBailSucrose.fld/image009.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_19"><![endif]></span><span
1468style='mso-spacerun:yes'> </span></p>
1469
1470<p class=MsoNormal>Plotting the (<span class=SpellE>obs-cal</span>)/sigma curve
1471(press the <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1472minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>w</span></b>
1473key) and enlarging it (use the crossed-arrows button and drag the right mouse
1474button upwards inside the lower box), as shown above, shows that further
1475background improvement might be expected with more background terms. </p>
1476
1477<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l1 level1 lfo4'><![if !supportLists]><span
1478style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1479Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1480</span></span></span><![endif]>Change to use <b><span style='font-family:"Calibri",sans-serif;
1481mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1482minor-latin'>6</span></b> chebyschev-1 parameters. </p>
1483
1484<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l1 level1 lfo4'><![if !supportLists]><span
1485style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1486Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1487</span></span></span><![endif]>Also refine <b><span style='font-family:"Calibri",sans-serif;
1488mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1489minor-latin'>sig</span></b> and <b><span style='font-family:"Calibri",sans-serif;
1490mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1491minor-latin'>pos</span></b> for the single background peak. </p>
1492
1493<p class=MsoNormal>The peak positions are probably offset from a sample
1494position error (it is almost always present)</p>
1495
1496<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l2 level1 lfo5'><![if !supportLists]><span
1497style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1498Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1499</span></span></span><![endif]>Select <b><span style='font-family:"Calibri",sans-serif;
1500mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1501minor-latin'>Sample X <span class=SpellE>displ</span></span></b> in Sample
1502Parameters </p>
1503
1504<p class=MsoNormal>The peak shape shows perhaps (in this case) inadequately
1505determined instrumental U, V &amp; W parameters</p>
1506
1507<p class=MsoListParagraph style='text-indent:-.25in;mso-list:l2 level1 lfo5'><![if !supportLists]><span
1508style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1509Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1510</span></span></span><![endif]>In Instrument Parameters select <b><span
1511style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1512mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>U, V &amp; W</span></b>
1513for refinement. </p>
1514
1515<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1516
1517<p class=MsoNormal>Do <b><span style='font-family:"Calibri",sans-serif;
1518mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1519minor-latin'>Calculate/Refine</span></b>; there will be a high residual for the
1520initial steps but will quickly settle down to <span class=SpellE>Rwp</span> ~
15216.0%</p>
1522
1523<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1524 id="Picture_x0020_21" o:spid="_x0000_i1031" type="#_x0000_t75" alt="GSAS-II plots: start.gpx"
1525 style='width:7in;height:324pt;visibility:visible;mso-wrap-style:square'>
1526 <v:imagedata src="LeBailSucrose.fld/image033.png" o:title=" start"/>
1527</v:shape><![endif]--><![if !vml]><img border=0 width=672 height=432
1528src="LeBailSucrose.fld/image010.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_21"><![endif]></span></p>
1529
1530<p class=MsoNormal>Pretty clearly, this sucrose sample gave an instrumental
1531profile that was better than what the provided instrument parameter file
1532indicated</p>
1533
1534<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1535 id="Picture_x0020_22" o:spid="_x0000_i1030" type="#_x0000_t75" alt="GSAS-II plots: start.gpx"
1536 style='width:503.25pt;height:324pt;visibility:visible;mso-wrap-style:square'>
1537 <v:imagedata src="LeBailSucrose.fld/image035.png" o:title=" start"/>
1538</v:shape><![endif]--><![if !vml]><img border=0 width=671 height=432
1539src="LeBailSucrose.fld/image011.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_22"><![endif]></span></p>
1540
1541<p class=MsoNormal>The solid line is from the default set of instrument
1542parameters, the crosses are from the single peak fits done in the peak fitting
1543tutorial and the dashed curve is from the results of this fit.</p>
1544
1545<h2>Step 5: Explore peak shape terms</h2>
1546
1547<p class=MsoNormal>At this point the fit is still poorer than what would be
1548expected based on counting statistics (which would yield a reduced <span
1549lang=EL style='mso-ansi-language:EL'>&#967;</span><sup>2</sup> value close to 1.)
1550Looking closely at the data and computed pattern, as shown below for example,
1551leads one to believe that the profile is still not being well-fit.</p>
1552
1553<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1554 id="Picture_x0020_23" o:spid="_x0000_i1029" type="#_x0000_t75" alt="GSAS-II plots: start.gpx"
1555 style='width:503.25pt;height:324pt;visibility:visible;mso-wrap-style:square'>
1556 <v:imagedata src="LeBailSucrose.fld/image037.png" o:title=" start"/>
1557</v:shape><![endif]--><![if !vml]><img border=0 width=671 height=432
1558src="LeBailSucrose.fld/image012.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_23"><![endif]></span></p>
1559
1560<p class=MsoNormal>A Le Bail fit provides a good way to explore different peak
1561shape broadening options. Moreover, if the intended use of the extracted
1562structure factors is structure solution, then one wants the best LeBail fit
1563possible. Investigation of a number of models for anisotropic peak broadening
1564finds that the <span class=SpellE>R<sub>wp</sub></span> can be reduced to 5.23%,
1565through use of the Popa/Stephens model for <span class=SpellE>microstrain</span>
1566(refining 9 terms in the generalized mustrain model), with a plausible <span
1567class=SpellE>microstrain</span> directional plot, as below. A fit that uses
1568fewer terms that is almost as good uses uniaxial crystallite domain size
1569broadening along the 010 axis and uniaxial <span class=SpellE>microstrain</span>
1570broadening along the 010 axis, my residual was <span class=SpellE>R<sub>wp</sub></span>
1571= 5.38%. This adds 2 only parameters. We will continue with the isotropic size
1572and generalized mustrain models; my final <span class=SpellE>R<sub>wp</sub></span>
1573after several sets of LeBail/Rietveld refinement was <span class=SpellE>R<sub>wp</sub></span>
1574= 5.197%.</p>
1575
1576<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1577
1578<p class=MsoNormal><b><i>The important result here is that this sample exhibit
1579non-ideal broadening artifacts. This could be due to milling of the sucrose
1580during manufacture creating defects that cannot be well-fit with a conventional
1581peak shape. From this fit, it is now clear that best possible fit to be
1582expected from any structural model will have a <span class=SpellE>R<sub>wp</sub></span>
1583on the order of 5% and a reduced </i></b><b><i><span lang=EL style='mso-ansi-language:
1584EL'>&#967;</span><sup>2</sup> value on the order of 1.5, since no crystal
1585structure model could give a better intensity fit than a Le Bail or Pawley fit.
1586<o:p></o:p></i></b></p>
1587
1588<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1589 id="Picture_x0020_24" o:spid="_x0000_i1028" type="#_x0000_t75" alt="GSAS-II plots: start.gpx"
1590 style='width:505.5pt;height:510.75pt;visibility:visible;mso-wrap-style:square'>
1591 <v:imagedata src="LeBailSucrose.fld/image015.png" o:title=" start"/>
1592</v:shape><![endif]--><![if !vml]><img border=0 width=674 height=681
1593src="LeBailSucrose.fld/image017.png" alt="GSAS-II plots: start.gpx" v:shapes="Picture_x0020_24"><![endif]></span></p>
1594
1595<h2>Step 6. Resetting the LeBail extracted intensities</h2>
1596
1597<p class=MsoNormal>A perhaps further improvement in the extracted structure factors
1598with the aim of using then in structure solution can be obtained by
1599reinitializing the LeBail extraction using the now better parameter set. Go to
1600the Data tab.</p>
1601
1602<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1603 id="Picture_x0020_25" o:spid="_x0000_i1027" type="#_x0000_t75" alt="GSAS-II project: start.gpx"
1604 style='width:508.5pt;height:430.5pt;visibility:visible;mso-wrap-style:square'>
1605 <v:imagedata src="LeBailSucrose.fld/image018.png" o:title=" start"/>
1606</v:shape><![endif]--><![if !vml]><img border=0 width=678 height=574
1607src="LeBailSucrose.fld/image019.png" alt="GSAS-II project: start.gpx" v:shapes="Picture_x0020_25"><![endif]></span></p>
1608
1609<p class=MsoNormal>Notice the message on the righthand status line; to reset
1610the LeBail intensities, “cycle” the Le Bail button. Press <b><span
1611style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1612mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Stop Le Bail
1613extraction</span></b> (NB: this will set the refinement into normal Rietveld mode
1614– impossible because the model contains no atoms!). The window will be redrawn
1615to include the intensity dependent parameters. Now press it again (<b><span
1616style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1617mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Start Le bail
1618extraction?</span></b>). The window will be redrawn again. The next refinement
1619will start with new initial structure factor values (=1.0) and will do the
1620preliminary “zero cycle” Le Bail refinement. You may leave the refinement
1621parameters alone. The refinement will start out high (Rwp~67%) but will quickly
1622drop to ~5.7% because all the other parameters are near their optimal values.</p>
1623
1624<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1625 id="Picture_x0020_26" o:spid="_x0000_i1026" type="#_x0000_t75" alt="Le Bail fit: Rwp=5.756"
1626 style='width:274.5pt;height:117pt;visibility:visible;mso-wrap-style:square'>
1627 <v:imagedata src="LeBailSucrose.fld/image020.png" o:title=" Rwp=5"/>
1628</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=156
1629src="LeBailSucrose.fld/image020.png" alt="Le Bail fit: Rwp=5.756" v:shapes="Picture_x0020_26"><![endif]></span></p>
1630
1631<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif;
1632mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1633minor-latin'>OK</span></b> to continue with the Rietveld/LeBail part of the
1634refinement; a popup will show the status of this part.</p>
1635
1636<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1637 id="Picture_x0020_27" o:spid="_x0000_i1025" type="#_x0000_t75" alt="Refinement results, Rw =5.469"
1638 style='width:274.5pt;height:177.75pt;visibility:visible;mso-wrap-style:square'>
1639 <v:imagedata src="LeBailSucrose.fld/image021.png" o:title="Refinement results, Rw =5"/>
1640</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=237
1641src="LeBailSucrose.fld/image021.png" alt="Refinement results, Rw =5.469"
1642v:shapes="Picture_x0020_27"><![endif]></span></p>
1643
1644<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif;
1645mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1646minor-latin'>OK</span></b>. Set the number of cycles to <b><span
1647style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1648mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>20</span></b>
1649and repeat <b><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1650minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b>
1651until the fit has converged (it may take several repeats as this part of a Le
1652Bail refinement does converge slowly). I got <span class=SpellE>Rwp</span> =
16535.26% when I quit recycling the refinement. You can now use these extracted
1654intensities to see if they can be used for a charge flipping structure solution
1655(I did get it to work once – otherwise many failures).</p>
1656
1657<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1658
1659</div>
1660
1661</body>
1662
1663</html>
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