source: Tutorials/2DTexture/Texture analysis of 2D data in GSAS-II.htm @ 1849

Last change on this file since 1849 was 1849, checked in by toby, 7 years ago

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415  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/>
416  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
417  <w:LsdException Locked="false" Priority="70" Name="Dark List"/>
418  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
419  <w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
420  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
421  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
422  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
423  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
424  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
425  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
426  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
427  <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
428  <w:LsdException Locked="false" Priority="34" QFormat="true"
429   Name="List Paragraph"/>
430  <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
431  <w:LsdException Locked="false" Priority="30" QFormat="true"
432   Name="Intense Quote"/>
433  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
434  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
435  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
436  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
437  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
438  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
439  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
440  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
441  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
442  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
443  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
444  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
445  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
446  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
447  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
448  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
449  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
450  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
451  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
452  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
453  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
454  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
455  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
456  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
457  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
458  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
459  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
460  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
461  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
462  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
463  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
464  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
465  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
466  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
467  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
468  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
469  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
470  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
471  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
472  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
473  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
474  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
475  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
476  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
477  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
478  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
479  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
480  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
481  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
482  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
483  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
484  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
485  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
486  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
487  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
488  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
489  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
490  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
491  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
492  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
493  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
494  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
495  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
496  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
497  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
498  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
499  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
500  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
501  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
502  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
503  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
504  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
505  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
506  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
507  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
508  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
509  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
510  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
511  <w:LsdException Locked="false" Priority="19" QFormat="true"
512   Name="Subtle Emphasis"/>
513  <w:LsdException Locked="false" Priority="21" QFormat="true"
514   Name="Intense Emphasis"/>
515  <w:LsdException Locked="false" Priority="31" QFormat="true"
516   Name="Subtle Reference"/>
517  <w:LsdException Locked="false" Priority="32" QFormat="true"
518   Name="Intense Reference"/>
519  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
520  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
521   UnhideWhenUsed="true" Name="Bibliography"/>
522  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
523   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
524  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
525  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
526  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
527  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
528  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
529  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
530  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
531  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
532  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
533  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
534  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
535  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
536  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
537  <w:LsdException Locked="false" Priority="46"
538   Name="Grid Table 1 Light Accent 1"/>
539  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
540  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
541  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
542  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
543  <w:LsdException Locked="false" Priority="51"
544   Name="Grid Table 6 Colorful Accent 1"/>
545  <w:LsdException Locked="false" Priority="52"
546   Name="Grid Table 7 Colorful Accent 1"/>
547  <w:LsdException Locked="false" Priority="46"
548   Name="Grid Table 1 Light Accent 2"/>
549  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
550  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
551  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
552  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
553  <w:LsdException Locked="false" Priority="51"
554   Name="Grid Table 6 Colorful Accent 2"/>
555  <w:LsdException Locked="false" Priority="52"
556   Name="Grid Table 7 Colorful Accent 2"/>
557  <w:LsdException Locked="false" Priority="46"
558   Name="Grid Table 1 Light Accent 3"/>
559  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
560  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
561  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
562  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
563  <w:LsdException Locked="false" Priority="51"
564   Name="Grid Table 6 Colorful Accent 3"/>
565  <w:LsdException Locked="false" Priority="52"
566   Name="Grid Table 7 Colorful Accent 3"/>
567  <w:LsdException Locked="false" Priority="46"
568   Name="Grid Table 1 Light Accent 4"/>
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570  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
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572  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
573  <w:LsdException Locked="false" Priority="51"
574   Name="Grid Table 6 Colorful Accent 4"/>
575  <w:LsdException Locked="false" Priority="52"
576   Name="Grid Table 7 Colorful Accent 4"/>
577  <w:LsdException Locked="false" Priority="46"
578   Name="Grid Table 1 Light Accent 5"/>
579  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
580  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
581  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
582  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
583  <w:LsdException Locked="false" Priority="51"
584   Name="Grid Table 6 Colorful Accent 5"/>
585  <w:LsdException Locked="false" Priority="52"
586   Name="Grid Table 7 Colorful Accent 5"/>
587  <w:LsdException Locked="false" Priority="46"
588   Name="Grid Table 1 Light Accent 6"/>
589  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
590  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
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592  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
593  <w:LsdException Locked="false" Priority="51"
594   Name="Grid Table 6 Colorful Accent 6"/>
595  <w:LsdException Locked="false" Priority="52"
596   Name="Grid Table 7 Colorful Accent 6"/>
597  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
598  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
599  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
600  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
601  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
602  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
603  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
604  <w:LsdException Locked="false" Priority="46"
605   Name="List Table 1 Light Accent 1"/>
606  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
607  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
608  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
609  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
610  <w:LsdException Locked="false" Priority="51"
611   Name="List Table 6 Colorful Accent 1"/>
612  <w:LsdException Locked="false" Priority="52"
613   Name="List Table 7 Colorful Accent 1"/>
614  <w:LsdException Locked="false" Priority="46"
615   Name="List Table 1 Light Accent 2"/>
616  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
617  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
618  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
619  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
620  <w:LsdException Locked="false" Priority="51"
621   Name="List Table 6 Colorful Accent 2"/>
622  <w:LsdException Locked="false" Priority="52"
623   Name="List Table 7 Colorful Accent 2"/>
624  <w:LsdException Locked="false" Priority="46"
625   Name="List Table 1 Light Accent 3"/>
626  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
627  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
628  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
629  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
630  <w:LsdException Locked="false" Priority="51"
631   Name="List Table 6 Colorful Accent 3"/>
632  <w:LsdException Locked="false" Priority="52"
633   Name="List Table 7 Colorful Accent 3"/>
634  <w:LsdException Locked="false" Priority="46"
635   Name="List Table 1 Light Accent 4"/>
636  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
637  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
638  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
639  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
640  <w:LsdException Locked="false" Priority="51"
641   Name="List Table 6 Colorful Accent 4"/>
642  <w:LsdException Locked="false" Priority="52"
643   Name="List Table 7 Colorful Accent 4"/>
644  <w:LsdException Locked="false" Priority="46"
645   Name="List Table 1 Light Accent 5"/>
646  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
647  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
648  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
649  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
650  <w:LsdException Locked="false" Priority="51"
651   Name="List Table 6 Colorful Accent 5"/>
652  <w:LsdException Locked="false" Priority="52"
653   Name="List Table 7 Colorful Accent 5"/>
654  <w:LsdException Locked="false" Priority="46"
655   Name="List Table 1 Light Accent 6"/>
656  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
657  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
658  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
659  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
660  <w:LsdException Locked="false" Priority="51"
661   Name="List Table 6 Colorful Accent 6"/>
662  <w:LsdException Locked="false" Priority="52"
663   Name="List Table 7 Colorful Accent 6"/>
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784        mso-margin-top-alt:auto;
785        margin-right:0in;
786        mso-margin-bottom-alt:auto;
787        margin-left:0in;
788        mso-pagination:widow-orphan;
789        mso-outline-level:5;
790        font-size:12.0pt;
791        font-family:"Times New Roman",serif;
792        mso-fareast-font-family:"Times New Roman";
793        mso-fareast-theme-font:minor-fareast;
794        color:#4F4FFF;
795        font-weight:bold;}
796p.MsoTitle, li.MsoTitle, div.MsoTitle
797        {mso-style-noshow:yes;
798        mso-style-priority:10;
799        mso-style-unhide:no;
800        mso-style-qformat:yes;
801        mso-style-link:"Title Char";
802        mso-style-next:Normal;
803        margin-top:0in;
804        margin-right:0in;
805        margin-bottom:15.0pt;
806        margin-left:0in;
807        mso-add-space:auto;
808        mso-pagination:widow-orphan;
809        border:none;
810        mso-border-bottom-alt:solid #4F81BD 1.0pt;
811        mso-border-bottom-themecolor:accent1;
812        padding:0in;
813        mso-padding-alt:0in 0in 4.0pt 0in;
814        font-size:26.0pt;
815        font-family:"Cambria",serif;
816        mso-ascii-font-family:Cambria;
817        mso-ascii-theme-font:major-latin;
818        mso-fareast-font-family:"Times New Roman";
819        mso-fareast-theme-font:major-fareast;
820        mso-hansi-font-family:Cambria;
821        mso-hansi-theme-font:major-latin;
822        mso-bidi-font-family:"Times New Roman";
823        mso-bidi-theme-font:major-bidi;
824        color:#17365D;
825        mso-themecolor:text2;
826        mso-themeshade:191;
827        letter-spacing:.25pt;
828        mso-font-kerning:14.0pt;}
829p.MsoTitleCxSpFirst, li.MsoTitleCxSpFirst, div.MsoTitleCxSpFirst
830        {mso-style-noshow:yes;
831        mso-style-priority:10;
832        mso-style-unhide:no;
833        mso-style-qformat:yes;
834        mso-style-link:"Title Char";
835        mso-style-next:Normal;
836        mso-style-type:export-only;
837        margin:0in;
838        margin-bottom:.0001pt;
839        mso-add-space:auto;
840        mso-pagination:widow-orphan;
841        border:none;
842        mso-border-bottom-alt:solid #4F81BD 1.0pt;
843        mso-border-bottom-themecolor:accent1;
844        padding:0in;
845        mso-padding-alt:0in 0in 4.0pt 0in;
846        font-size:26.0pt;
847        font-family:"Cambria",serif;
848        mso-ascii-font-family:Cambria;
849        mso-ascii-theme-font:major-latin;
850        mso-fareast-font-family:"Times New Roman";
851        mso-fareast-theme-font:major-fareast;
852        mso-hansi-font-family:Cambria;
853        mso-hansi-theme-font:major-latin;
854        mso-bidi-font-family:"Times New Roman";
855        mso-bidi-theme-font:major-bidi;
856        color:#17365D;
857        mso-themecolor:text2;
858        mso-themeshade:191;
859        letter-spacing:.25pt;
860        mso-font-kerning:14.0pt;}
861p.MsoTitleCxSpMiddle, li.MsoTitleCxSpMiddle, div.MsoTitleCxSpMiddle
862        {mso-style-noshow:yes;
863        mso-style-priority:10;
864        mso-style-unhide:no;
865        mso-style-qformat:yes;
866        mso-style-link:"Title Char";
867        mso-style-next:Normal;
868        mso-style-type:export-only;
869        margin:0in;
870        margin-bottom:.0001pt;
871        mso-add-space:auto;
872        mso-pagination:widow-orphan;
873        border:none;
874        mso-border-bottom-alt:solid #4F81BD 1.0pt;
875        mso-border-bottom-themecolor:accent1;
876        padding:0in;
877        mso-padding-alt:0in 0in 4.0pt 0in;
878        font-size:26.0pt;
879        font-family:"Cambria",serif;
880        mso-ascii-font-family:Cambria;
881        mso-ascii-theme-font:major-latin;
882        mso-fareast-font-family:"Times New Roman";
883        mso-fareast-theme-font:major-fareast;
884        mso-hansi-font-family:Cambria;
885        mso-hansi-theme-font:major-latin;
886        mso-bidi-font-family:"Times New Roman";
887        mso-bidi-theme-font:major-bidi;
888        color:#17365D;
889        mso-themecolor:text2;
890        mso-themeshade:191;
891        letter-spacing:.25pt;
892        mso-font-kerning:14.0pt;}
893p.MsoTitleCxSpLast, li.MsoTitleCxSpLast, div.MsoTitleCxSpLast
894        {mso-style-noshow:yes;
895        mso-style-priority:10;
896        mso-style-unhide:no;
897        mso-style-qformat:yes;
898        mso-style-link:"Title Char";
899        mso-style-next:Normal;
900        mso-style-type:export-only;
901        margin-top:0in;
902        margin-right:0in;
903        margin-bottom:15.0pt;
904        margin-left:0in;
905        mso-add-space:auto;
906        mso-pagination:widow-orphan;
907        border:none;
908        mso-border-bottom-alt:solid #4F81BD 1.0pt;
909        mso-border-bottom-themecolor:accent1;
910        padding:0in;
911        mso-padding-alt:0in 0in 4.0pt 0in;
912        font-size:26.0pt;
913        font-family:"Cambria",serif;
914        mso-ascii-font-family:Cambria;
915        mso-ascii-theme-font:major-latin;
916        mso-fareast-font-family:"Times New Roman";
917        mso-fareast-theme-font:major-fareast;
918        mso-hansi-font-family:Cambria;
919        mso-hansi-theme-font:major-latin;
920        mso-bidi-font-family:"Times New Roman";
921        mso-bidi-theme-font:major-bidi;
922        color:#17365D;
923        mso-themecolor:text2;
924        mso-themeshade:191;
925        letter-spacing:.25pt;
926        mso-font-kerning:14.0pt;}
927a:link, span.MsoHyperlink
928        {mso-style-noshow:yes;
929        mso-style-priority:99;
930        color:blue;
931        text-decoration:underline;
932        text-underline:single;}
933a:visited, span.MsoHyperlinkFollowed
934        {mso-style-noshow:yes;
935        mso-style-priority:99;
936        color:purple;
937        text-decoration:underline;
938        text-underline:single;}
939p.MsoDocumentMap, li.MsoDocumentMap, div.MsoDocumentMap
940        {mso-style-noshow:yes;
941        mso-style-priority:99;
942        mso-style-link:"Document Map Char";
943        margin:0in;
944        margin-bottom:.0001pt;
945        mso-pagination:widow-orphan;
946        font-size:8.0pt;
947        font-family:"Tahoma",sans-serif;
948        mso-fareast-font-family:"Times New Roman";
949        mso-fareast-theme-font:minor-fareast;}
950p
951        {mso-style-noshow:yes;
952        mso-style-priority:99;
953        mso-margin-top-alt:auto;
954        margin-right:0in;
955        mso-margin-bottom-alt:auto;
956        margin-left:0in;
957        mso-pagination:widow-orphan;
958        font-size:12.0pt;
959        font-family:"Times New Roman",serif;
960        mso-fareast-font-family:"Times New Roman";
961        mso-fareast-theme-font:minor-fareast;}
962pre
963        {mso-style-noshow:yes;
964        mso-style-priority:99;
965        mso-style-link:"HTML Preformatted Char";
966        margin:0in;
967        margin-bottom:.0001pt;
968        mso-pagination:widow-orphan;
969        tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt;
970        font-size:10.0pt;
971        font-family:"Courier New";
972        mso-fareast-font-family:"Times New Roman";}
973p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
974        {mso-style-noshow:yes;
975        mso-style-priority:99;
976        mso-style-link:"Balloon Text Char";
977        margin:0in;
978        margin-bottom:.0001pt;
979        mso-pagination:widow-orphan;
980        font-size:8.0pt;
981        font-family:"Tahoma",sans-serif;
982        mso-fareast-font-family:"Times New Roman";
983        mso-fareast-theme-font:minor-fareast;}
984span.MsoPlaceholderText
985        {mso-style-noshow:yes;
986        mso-style-priority:99;
987        mso-style-unhide:no;
988        color:gray;}
989p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing
990        {mso-style-noshow:yes;
991        mso-style-priority:1;
992        mso-style-unhide:no;
993        mso-style-qformat:yes;
994        mso-style-parent:"";
995        margin:0in;
996        margin-bottom:.0001pt;
997        mso-pagination:widow-orphan;
998        font-size:12.0pt;
999        font-family:"Times New Roman",serif;
1000        mso-fareast-font-family:"Times New Roman";
1001        mso-fareast-theme-font:minor-fareast;}
1002p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
1003        {mso-style-noshow:yes;
1004        mso-style-priority:34;
1005        mso-style-unhide:no;
1006        mso-style-qformat:yes;
1007        margin-top:0in;
1008        margin-right:0in;
1009        margin-bottom:0in;
1010        margin-left:.5in;
1011        margin-bottom:.0001pt;
1012        mso-add-space:auto;
1013        mso-pagination:widow-orphan;
1014        font-size:12.0pt;
1015        font-family:"Times New Roman",serif;
1016        mso-fareast-font-family:"Times New Roman";
1017        mso-fareast-theme-font:minor-fareast;}
1018p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
1019        {mso-style-noshow:yes;
1020        mso-style-priority:34;
1021        mso-style-unhide:no;
1022        mso-style-qformat:yes;
1023        mso-style-type:export-only;
1024        margin-top:0in;
1025        margin-right:0in;
1026        margin-bottom:0in;
1027        margin-left:.5in;
1028        margin-bottom:.0001pt;
1029        mso-add-space:auto;
1030        mso-pagination:widow-orphan;
1031        font-size:12.0pt;
1032        font-family:"Times New Roman",serif;
1033        mso-fareast-font-family:"Times New Roman";
1034        mso-fareast-theme-font:minor-fareast;}
1035p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
1036        {mso-style-noshow:yes;
1037        mso-style-priority:34;
1038        mso-style-unhide:no;
1039        mso-style-qformat:yes;
1040        mso-style-type:export-only;
1041        margin-top:0in;
1042        margin-right:0in;
1043        margin-bottom:0in;
1044        margin-left:.5in;
1045        margin-bottom:.0001pt;
1046        mso-add-space:auto;
1047        mso-pagination:widow-orphan;
1048        font-size:12.0pt;
1049        font-family:"Times New Roman",serif;
1050        mso-fareast-font-family:"Times New Roman";
1051        mso-fareast-theme-font:minor-fareast;}
1052p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
1053        {mso-style-noshow:yes;
1054        mso-style-priority:34;
1055        mso-style-unhide:no;
1056        mso-style-qformat:yes;
1057        mso-style-type:export-only;
1058        margin-top:0in;
1059        margin-right:0in;
1060        margin-bottom:0in;
1061        margin-left:.5in;
1062        margin-bottom:.0001pt;
1063        mso-add-space:auto;
1064        mso-pagination:widow-orphan;
1065        font-size:12.0pt;
1066        font-family:"Times New Roman",serif;
1067        mso-fareast-font-family:"Times New Roman";
1068        mso-fareast-theme-font:minor-fareast;}
1069span.MsoIntenseReference
1070        {mso-style-priority:32;
1071        mso-style-unhide:no;
1072        mso-style-qformat:yes;
1073        font-variant:small-caps;
1074        color:#C0504D;
1075        mso-themecolor:accent2;
1076        letter-spacing:.25pt;
1077        font-weight:bold;
1078        text-decoration:underline;
1079        text-underline:single;}
1080span.Heading1Char
1081        {mso-style-name:"Heading 1 Char";
1082        mso-style-priority:9;
1083        mso-style-unhide:no;
1084        mso-style-locked:yes;
1085        mso-style-link:"Heading 1";
1086        mso-ansi-font-size:24.0pt;
1087        mso-bidi-font-size:24.0pt;
1088        font-family:"Times New Roman",serif;
1089        mso-ascii-font-family:"Times New Roman";
1090        mso-fareast-font-family:"Times New Roman";
1091        mso-fareast-theme-font:minor-fareast;
1092        mso-hansi-font-family:"Times New Roman";
1093        mso-bidi-font-family:"Times New Roman";
1094        mso-font-kerning:18.0pt;
1095        font-weight:bold;}
1096span.Heading2Char
1097        {mso-style-name:"Heading 2 Char";
1098        mso-style-noshow:yes;
1099        mso-style-priority:9;
1100        mso-style-unhide:no;
1101        mso-style-locked:yes;
1102        mso-style-link:"Heading 2";
1103        mso-ansi-font-size:18.0pt;
1104        mso-bidi-font-size:18.0pt;
1105        font-family:"Times New Roman",serif;
1106        mso-ascii-font-family:"Times New Roman";
1107        mso-fareast-font-family:"Times New Roman";
1108        mso-fareast-theme-font:minor-fareast;
1109        mso-hansi-font-family:"Times New Roman";
1110        mso-bidi-font-family:"Times New Roman";
1111        font-weight:bold;}
1112span.Heading3Char
1113        {mso-style-name:"Heading 3 Char";
1114        mso-style-noshow:yes;
1115        mso-style-priority:9;
1116        mso-style-unhide:no;
1117        mso-style-locked:yes;
1118        mso-style-link:"Heading 3";
1119        mso-ansi-font-size:13.5pt;
1120        mso-bidi-font-size:13.5pt;
1121        font-family:"Times New Roman",serif;
1122        mso-ascii-font-family:"Times New Roman";
1123        mso-fareast-font-family:"Times New Roman";
1124        mso-fareast-theme-font:minor-fareast;
1125        mso-hansi-font-family:"Times New Roman";
1126        mso-bidi-font-family:"Times New Roman";
1127        font-weight:bold;}
1128span.Heading4Char
1129        {mso-style-name:"Heading 4 Char";
1130        mso-style-noshow:yes;
1131        mso-style-priority:9;
1132        mso-style-unhide:no;
1133        mso-style-locked:yes;
1134        mso-style-link:"Heading 4";
1135        mso-ansi-font-size:13.0pt;
1136        mso-bidi-font-size:13.0pt;
1137        font-family:"Cambria",serif;
1138        mso-ascii-font-family:Cambria;
1139        mso-ascii-theme-font:major-latin;
1140        mso-fareast-font-family:"Times New Roman";
1141        mso-fareast-theme-font:major-fareast;
1142        mso-hansi-font-family:Cambria;
1143        mso-hansi-theme-font:major-latin;
1144        mso-bidi-font-family:"Times New Roman";
1145        mso-bidi-theme-font:major-bidi;
1146        color:#4F81BD;
1147        mso-themecolor:accent1;
1148        font-weight:bold;
1149        font-style:italic;}
1150span.Heading5Char
1151        {mso-style-name:"Heading 5 Char";
1152        mso-style-noshow:yes;
1153        mso-style-priority:9;
1154        mso-style-unhide:no;
1155        mso-style-locked:yes;
1156        mso-style-link:"Heading 5";
1157        mso-ansi-font-size:12.0pt;
1158        mso-bidi-font-size:12.0pt;
1159        font-family:"Times New Roman",serif;
1160        mso-ascii-font-family:"Times New Roman";
1161        mso-fareast-font-family:"Times New Roman";
1162        mso-fareast-theme-font:minor-fareast;
1163        mso-hansi-font-family:"Times New Roman";
1164        mso-bidi-font-family:"Times New Roman";
1165        color:#4F4FFF;
1166        font-weight:bold;}
1167span.HTMLPreformattedChar
1168        {mso-style-name:"HTML Preformatted Char";
1169        mso-style-noshow:yes;
1170        mso-style-priority:99;
1171        mso-style-unhide:no;
1172        mso-style-locked:yes;
1173        mso-style-link:"HTML Preformatted";
1174        font-family:"Courier New";
1175        mso-ascii-font-family:"Courier New";
1176        mso-fareast-font-family:"Times New Roman";
1177        mso-hansi-font-family:"Courier New";
1178        mso-bidi-font-family:"Courier New";}
1179span.TitleChar
1180        {mso-style-name:"Title Char";
1181        mso-style-priority:10;
1182        mso-style-unhide:no;
1183        mso-style-locked:yes;
1184        mso-style-link:Title;
1185        mso-ansi-font-size:26.0pt;
1186        mso-bidi-font-size:26.0pt;
1187        font-family:"Cambria",serif;
1188        mso-ascii-font-family:Cambria;
1189        mso-ascii-theme-font:major-latin;
1190        mso-fareast-font-family:"Times New Roman";
1191        mso-fareast-theme-font:major-fareast;
1192        mso-hansi-font-family:Cambria;
1193        mso-hansi-theme-font:major-latin;
1194        mso-bidi-font-family:"Times New Roman";
1195        mso-bidi-theme-font:major-bidi;
1196        color:#17365D;
1197        mso-themecolor:text2;
1198        mso-themeshade:191;
1199        letter-spacing:.25pt;
1200        mso-font-kerning:14.0pt;}
1201span.DocumentMapChar
1202        {mso-style-name:"Document Map Char";
1203        mso-style-noshow:yes;
1204        mso-style-priority:99;
1205        mso-style-unhide:no;
1206        mso-style-locked:yes;
1207        mso-style-link:"Document Map";
1208        mso-ansi-font-size:8.0pt;
1209        mso-bidi-font-size:8.0pt;
1210        font-family:"Tahoma",sans-serif;
1211        mso-ascii-font-family:Tahoma;
1212        mso-fareast-font-family:"Times New Roman";
1213        mso-fareast-theme-font:minor-fareast;
1214        mso-hansi-font-family:Tahoma;
1215        mso-bidi-font-family:Tahoma;}
1216span.BalloonTextChar
1217        {mso-style-name:"Balloon Text Char";
1218        mso-style-noshow:yes;
1219        mso-style-priority:99;
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1407
1408<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1409
1410<div class=WordSection1>
1411
1412<h1>Texture analysis of 2D data in GSAS-II</h1>
1413
1414<h2>Introduction</h2>
1415
1416<p class=MsoNormal>Texture analysis using GSAS-II employs spherical harmonics
1417modeling, as described by Bunge, &quot;Texture Analysis in Materials
1418Science&quot; (1982), and implemented by Von Dreele, J. Appl. <span
1419class=SpellE>Cryst</span>., <b style='mso-bidi-font-weight:normal'>30</b>,
1420517-525 (1997) in GSAS. The even part of the orientation distribution function
1421(ODF) via the general axis equation</p>
1422
1423<p class=gsastext><span style='position:relative;top:14.0pt;mso-text-raise:
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1455
1456<p class=gsastext><span class=GramE>is</span> used to give the intensity
1457corrections due to texture. The two harmonic terms, <span style='position:relative;
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1459 type="#_x0000_t75" style='width:30.75pt;height:18pt' o:ole="">
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1461  o:title=""/>
1462</v:shape><![endif]--><![if !vml]><img width=41 height=24
1463src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"
1464v:shapes="_x0000_i1039"><![endif]></span><!--[if gte mso 9]><xml>
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1468</xml><![endif]--><span class=GramE>and </span><span style='position:relative;
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1470 type="#_x0000_t75" style='width:30pt;height:18pt' o:ole="">
1471 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.wmz"
1472  o:title=""/>
1473</v:shape><![endif]--><![if !vml]><img width=40 height=24
1474src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"
1475v:shapes="_x0000_i1040"><![endif]></span><!--[if gte mso 9]><xml>
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1479</xml><![endif]-->, take on values according to the crystal and sample
1480symmetries, respectively, and thus the two inner summations are over only the
1481resulting unique, nonzero harmonic terms. These unique terms are automatically
1482selected by <span style='mso-bidi-font-weight:bold'>GSAS-II</span> according to
1483the space group symmetry and the user chosen sample symmetry. The available
1484sample symmetries are cylindrical symmetry, 2/m, mmm and no symmetry. The
1485choice of sample symmetry profoundly affects the selection of harmonic
1486coefficients. For example, in the case of cylindrical sample symmetry (fiber
1487texture) only <span style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
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1491</v:shape><![endif]--><![if !vml]><img width=40 height=24
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1497</xml><![endif]--><span style='mso-spacerun:yes'> </span>terms are nonzero so
1498the rest are excluded from the summations and the set of <span
1499style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
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1509</xml><![endif]-->coefficients is sufficient to describe the effect on the
1510diffraction patterns due to texture. The crystal harmonic factor, <span
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1515</v:shape><![endif]--><![if !vml]><img width=41 height=24
1516src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"
1517v:shapes="_x0000_i1042"><![endif]></span><!--[if gte mso 9]><xml>
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1521</xml><![endif]-->, is defined for each reflection, h, <i>via</i> polar and
1522azimuthal coordinates (<span style='font-family:Symbol'>f</span>, <span
1523style='font-family:Symbol'>b</span>) of a unit vector coincident with h
1524relative to the reciprocal lattice. For most crystal symmetries, <span
1525style='font-family:Symbol'>f</span> is the angle between h and the n-<span
1526class=SpellE>th</span> order major rotation axis of the space group (usually
1527the c-axis) and <span style='font-family:Symbol'>b</span> is the angle between
1528the projections of h and any secondary axis (usually the a-axis) onto the
1529normal plane.<span style='mso-spacerun:yes'>  </span>In a similar way the
1530sample harmonic factor, <span style='position:relative;top:5.0pt;mso-text-raise:
1531-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1025" type="#_x0000_t75"
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1536src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image013.png"
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1538 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1025"
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1541</xml><![endif]-->, is defined according to polar and azimuthal coordinates (<span
1542style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
1543of a unit vector coincident with the diffraction vector relative to a
1544coordinate system attached to the external form of the sample. For example, in
1545the case of a rolled steel plate having mmm symmetry, the polar angle, <span
1546style='font-family:Symbol'>y</span>, is frequently measured from the normal
1547direction (ND) and <span style='font-family:Symbol'>g</span> is then measured
1548from the rolling direction (RD) in the TD (transverse direction) - RD
1549plane.<span style='mso-spacerun:yes'>  </span>Thus, the general axis equation
1550becomes</p>
1551
1552<p class=gsastext><span style='position:relative;top:14.0pt;mso-text-raise:
1553-14.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1044" type="#_x0000_t75"
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1558src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image015.png"
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1564<![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'>
1565<![endif]></p>
1566
1567<p class=MsoNormal>In a diffraction experiment the crystal reflection
1568coordinates (<span style='font-family:Symbol'>f</span>, <span style='font-family:
1569Symbol'>b</span>) are determined by the choice of reflection index (<span
1570class=SpellE>hkl</span>) while the sample coordinates (<span style='font-family:
1571Symbol'>y</span>, <span style='font-family:Symbol'>g</span>) are determined by
1572the sample orientation on the diffractometer.</p>
1573
1574<p class=gsastext>To define the sample coordinates (<span style='font-family:
1575Symbol'>y</span>, <span style='font-family:Symbol'>g</span>), we have defined
1576an instrument coordinate system (I, J, K) such that K is normal to the
1577diffraction plane and J is coincident with the direction of the incident
1578radiation beam toward the source. We further define a standard set of right-handed
1579goniometer <span class=SpellE>eulerian</span> angles (<span style='font-family:
1580Symbol'>W</span>, <span style='font-family:Symbol'>C</span>, <span
1581style='font-family:Symbol'>F</span>) so that <span style='font-family:Symbol'>W</span>
1582and <span style='font-family:Symbol'>F</span> are rotations about K and <span
1583style='font-family:Symbol'>C</span> is a rotation about J when <span
1584style='font-family:Symbol'>W</span> <span style='font-family:Symbol'><span
1585style='mso-spacerun:yes'> </span></span>= 0.<span style='mso-spacerun:yes'> 
1586</span>Finally, as the sample may be mounted so that the sample coordinate
1587system (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>) does
1588not coincide with the instrument coordinate system (I, J, K), we define three <span
1589class=SpellE>eulerian</span> sample rotation offset angles (<span
1590style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
1591<span style='font-family:Symbol'>F</span><sub>s</sub>) that describe the
1592rotation from (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>)
1593to (I, J, K).<span style='mso-spacerun:yes'>  </span>The sample rotation angles
1594are defined so that with the goniometer angles at zero <span style='font-family:
1595Symbol'>W</span><sub>s</sub> and <span style='font-family:Symbol'>F</span><sub>s</sub>
1596are rotations about I and <span style='font-family:Symbol'>C</span><sub>s</sub>
1597is a rotation about J.<span style='mso-spacerun:yes'>  </span>The zeros of
1598these three sample rotation angles can be refined as part of the Rietveld
1599analysis to accommodate any angular offset in sample mounting. After including
1600the diffraction angle, <span style='font-family:Symbol'>Q</span>, and a
1601detector azimuthal angle, A, the full rotation matrix, <b style='mso-bidi-font-weight:
1602normal'>M</b>, is </p>
1603
1604<p class=gsastext><b style='mso-bidi-font-weight:normal'>M = -</b><b
1605style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>Q</span>A</b><b
1606style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>W<span
1607class=GramE>C<span style='font-family:"Times New Roman",serif'>(</span></span>F</span>+</b><b
1608style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span><sub>s</sub>)</b><b
1609style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>C</span><span
1610class=SpellE><sub>s</sub><span style='font-family:Symbol'>W</span><sub>s</sub></span><o:p></o:p></b></p>
1611
1612<p class=gsastext>By transformation of unit Cartesian vectors (100, 010 and
1613001) with this rotation matrix, the sample orientation coordinates (<span
1614style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
1615are given by</p>
1616
1617<p class=gsastext><span class=GramE><i>cos</i>(</span><span style='font-family:
1618Symbol'>y</span>) = <b style='mso-bidi-font-weight:normal'><span
1619style='position:relative;top:25.0pt;mso-text-raise:-25.0pt'><!--[if gte vml 1]><v:shape
1620 id="_x0000_i1046" type="#_x0000_t75" style='width:33.75pt;height:56.25pt'
1621 o:ole="">
1622 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.wmz"
1623  o:title=""/>
1624</v:shape><![endif]--><![if !vml]><img width=45 height=75
1625src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image017.png"
1626v:shapes="_x0000_i1046"><![endif]></span><!--[if gte mso 9]><xml>
1627 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1046"
1628  DrawAspect="Content" ObjectID="_1493040247">
1629 </o:OLEObject>
1630</xml><![endif]--></b><span style='mso-spacerun:yes'>  </span>and<span
1631style='mso-spacerun:yes'>   </span><i>tan</i>(<span style='font-family:Symbol'>g</span>)
1632= <span style='position:relative;top:25.0pt;mso-text-raise:-25.0pt'><!--[if gte vml 1]><v:shape
1633 id="_x0000_i1045" type="#_x0000_t75" style='width:81.75pt;height:56.25pt'
1634 o:ole="">
1635 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.wmz"
1636  o:title=""/>
1637</v:shape><![endif]--><![if !vml]><img width=109 height=75
1638src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png"
1639v:shapes="_x0000_i1045"><![endif]></span><!--[if gte mso 9]><xml>
1640 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1045"
1641  DrawAspect="Content" ObjectID="_1493040249">
1642 </o:OLEObject>
1643</xml><![endif]--></p>
1644
1645<p class=gsastext>The harmonic terms, <span style='position:relative;
1646top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1047"
1647 type="#_x0000_t75" style='width:44.25pt;height:18pt' o:ole="">
1648 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.wmz"
1649  o:title=""/>
1650</v:shape><![endif]--><![if !vml]><img width=59 height=24
1651src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png"
1652v:shapes="_x0000_i1047"><![endif]></span><!--[if gte mso 9]><xml>
1653 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1047"
1654  DrawAspect="Content" ObjectID="_1493040250">
1655 </o:OLEObject>
1656</xml><![endif]--><span class=GramE>and </span><span style='position:relative;
1657top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1048"
1658 type="#_x0000_t75" style='width:42.75pt;height:18pt' o:ole="">
1659 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.wmz"
1660  o:title=""/>
1661</v:shape><![endif]--><![if !vml]><img width=57 height=24
1662src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.png"
1663v:shapes="_x0000_i1048"><![endif]></span><!--[if gte mso 9]><xml>
1664 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1048"
1665  DrawAspect="Content" ObjectID="_1493040251">
1666 </o:OLEObject>
1667</xml><![endif]-->, are developed from</p>
1668
1669<p class=gsastext><span style='position:relative;top:8.0pt;mso-text-raise:-8.0pt'><!--[if gte vml 1]><v:shape
1670 id="_x0000_i1049" type="#_x0000_t75" style='width:138pt;height:21pt' o:ole="">
1671 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.wmz"
1672  o:title=""/>
1673</v:shape><![endif]--><![if !vml]><img width=184 height=28
1674src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image025.png"
1675v:shapes="_x0000_i1049"><![endif]></span><!--[if gte mso 9]><xml>
1676 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1049"
1677  DrawAspect="Content" ObjectID="_1493040252">
1678 </o:OLEObject>
1679</xml><![endif]--></p>
1680
1681<p class=gsastext><span class=GramE>where</span> the normalized associated
1682Legendre functions, <span style='position:relative;top:5.0pt;mso-text-raise:
1683-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1050" type="#_x0000_t75"
1684 style='width:33.75pt;height:18pt' o:ole="">
1685 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image026.wmz"
1686  o:title=""/>
1687</v:shape><![endif]--><![if !vml]><img width=45 height=24
1688src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image027.png"
1689v:shapes="_x0000_i1050"><![endif]></span><!--[if gte mso 9]><xml>
1690 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1050"
1691  DrawAspect="Content" ObjectID="_1493040253">
1692 </o:OLEObject>
1693</xml><![endif]-->, are defined via a Fourier expansion as</p>
1694
1695<p class=gsastext><span style='position:relative;top:14.0pt;mso-text-raise:
1696-14.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1051" type="#_x0000_t75"
1697 style='width:132.75pt;height:33.75pt' o:ole="">
1698 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image028.wmz"
1699  o:title=""/>
1700</v:shape><![endif]--><![if !vml]><img width=177 height=45
1701src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image029.png"
1702v:shapes="_x0000_i1051"><![endif]></span><!--[if gte mso 9]><xml>
1703 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1051"
1704  DrawAspect="Content" ObjectID="_1493040254">
1705 </o:OLEObject>
1706</xml><![endif]--></p>
1707
1708<p class=gsastext><span class=GramE>for</span> m even and</p>
1709
1710<p class=gsastext><span style='position:relative;top:14.0pt;mso-text-raise:
1711-14.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1052" type="#_x0000_t75"
1712 style='width:132pt;height:33.75pt' o:ole="">
1713 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image030.wmz"
1714  o:title=""/>
1715</v:shape><![endif]--><![if !vml]><img width=176 height=45
1716src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image031.png"
1717v:shapes="_x0000_i1052"><![endif]></span><!--[if gte mso 9]><xml>
1718 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1052"
1719  DrawAspect="Content" ObjectID="_1493040255">
1720 </o:OLEObject>
1721</xml><![endif]--></p>
1722
1723<p class=gsastext><span class=GramE>for</span> m odd.<span
1724style='mso-spacerun:yes'>  </span>Each sum is only over either the even or odd
1725values of s, respectively, because of the properties of the Fourier
1726coefficients<span class=GramE>, </span><span style='position:relative;
1727top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1026"
1728 type="#_x0000_t75" style='width:23.25pt;height:20.25pt' o:ole="">
1729 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image032.wmz"
1730  o:title=""/>
1731</v:shape><![endif]--><![if !vml]><img width=31 height=27
1732src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.png"
1733v:shapes="_x0000_i1026"><![endif]></span><!--[if gte mso 9]><xml>
1734 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1026"
1735  DrawAspect="Content" ObjectID="_1493040256">
1736 </o:OLEObject>
1737</xml><![endif]-->.<span style='mso-spacerun:yes'>  </span>These Fourier
1738coefficients are determined so that the definition</p>
1739
1740<p class=gsastext><span style='position:relative;top:16.0pt;mso-text-raise:
1741-16.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75"
1742 style='width:356.25pt;height:38.25pt' o:ole="">
1743 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image034.wmz"
1744  o:title=""/>
1745</v:shape><![endif]--><![if !vml]><img width=475 height=51
1746src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image035.png"
1747v:shapes="_x0000_i1027"><![endif]></span><!--[if gte mso 9]><xml>
1748 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1027"
1749  DrawAspect="Content" ObjectID="_1493040257">
1750 </o:OLEObject>
1751</xml><![endif]--></p>
1752
1753<p class=gsastext><span class=GramE>is</span> satisfied.<span
1754style='mso-spacerun:yes'>  </span>Terms of the form <span style='position:relative;
1755top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1028"
1756 type="#_x0000_t75" style='width:92.25pt;height:20.25pt' o:ole="">
1757 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image036.wmz"
1758  o:title=""/>
1759</v:shape><![endif]--><![if !vml]><img width=123 height=27
1760src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image037.png"
1761v:shapes="_x0000_i1028"><![endif]></span><!--[if gte mso 9]><xml>
1762 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1028"
1763  DrawAspect="Content" ObjectID="_1493040258">
1764 </o:OLEObject>
1765</xml><![endif]--><span style='mso-spacerun:yes'> </span>and <span
1766style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
1767 id="_x0000_i1029" type="#_x0000_t75" style='width:90pt;height:20.25pt' o:ole="">
1768 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image038.wmz"
1769  o:title=""/>
1770</v:shape><![endif]--><![if !vml]><img width=120 height=27
1771src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
1772v:shapes="_x0000_i1029"><![endif]></span><!--[if gte mso 9]><xml>
1773 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1029"
1774  DrawAspect="Content" ObjectID="_1493040259">
1775 </o:OLEObject>
1776</xml><![endif]-->are combined depending on the symmetry and the value of m
1777along with appropriate normalization coefficients to give the harmonic terms <span
1778style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
1779 id="_x0000_i1030" type="#_x0000_t75" style='width:44.25pt;height:20.25pt'
1780 o:ole="">
1781 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.wmz"
1782  o:title=""/>
1783</v:shape><![endif]--><![if !vml]><img width=59 height=27
1784src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png"
1785v:shapes="_x0000_i1030"><![endif]></span><!--[if gte mso 9]><xml>
1786 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1030"
1787  DrawAspect="Content" ObjectID="_1493040260">
1788 </o:OLEObject>
1789</xml><![endif]--><span class=GramE>and </span><span style='position:relative;
1790top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1031"
1791 type="#_x0000_t75" style='width:44.25pt;height:20.25pt' o:ole="">
1792 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image042.wmz"
1793  o:title=""/>
1794</v:shape><![endif]--><![if !vml]><img width=59 height=27
1795src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image043.png"
1796v:shapes="_x0000_i1031"><![endif]></span><!--[if gte mso 9]><xml>
1797 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1031"
1798  DrawAspect="Content" ObjectID="_1493040261">
1799 </o:OLEObject>
1800</xml><![endif]-->.<span style='mso-spacerun:yes'>  </span>For cubic crystal
1801symmetry, the term <span style='position:relative;top:5.0pt;mso-text-raise:
1802-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75"
1803 style='width:44.25pt;height:20.25pt' o:ole="">
1804 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image044.wmz"
1805  o:title=""/>
1806</v:shape><![endif]--><![if !vml]><img width=59 height=27
1807src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png"
1808v:shapes="_x0000_i1032"><![endif]></span><!--[if gte mso 9]><xml>
1809 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1032"
1810  DrawAspect="Content" ObjectID="_1493040262">
1811 </o:OLEObject>
1812</xml><![endif]-->is obtained directly from the Fourier expansion</p>
1813
1814<p class=gsastext><span style='position:relative;top:16.0pt;mso-text-raise:
1815-16.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1033" type="#_x0000_t75"
1816 style='width:167.25pt;height:38.25pt' o:ole="">
1817 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image045.wmz"
1818  o:title=""/>
1819</v:shape><![endif]--><![if !vml]><img width=223 height=51
1820src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image046.png"
1821v:shapes="_x0000_i1033"><![endif]></span><!--[if gte mso 9]><xml>
1822 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1033"
1823  DrawAspect="Content" ObjectID="_1493040263">
1824 </o:OLEObject>
1825</xml><![endif]--></p>
1826
1827<p class=gsastext><span class=GramE>using</span> the coefficients, <span
1828style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
1829 id="_x0000_i1034" type="#_x0000_t75" style='width:24pt;height:20.25pt' o:ole="">
1830 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.wmz"
1831  o:title=""/>
1832</v:shape><![endif]--><![if !vml]><img width=32 height=27
1833src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
1834v:shapes="_x0000_i1034"><![endif]></span><!--[if gte mso 9]><xml>
1835 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1034"
1836  DrawAspect="Content" ObjectID="_1493040264">
1837 </o:OLEObject>
1838</xml><![endif]-->, as tabulated by Bunge (1982). </p>
1839
1840<p class=gsastext>The Rietveld refinement of texture then proceeds by
1841constructing derivatives of the profile intensities with respect to the allowed
1842harmonic coefficients, <span style='position:relative;top:5.0pt;mso-text-raise:
1843-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1035" type="#_x0000_t75"
1844 style='width:24pt;height:20.25pt' o:ole="">
1845 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.wmz"
1846  o:title=""/>
1847</v:shape><![endif]--><![if !vml]><img width=32 height=27
1848src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
1849v:shapes="_x0000_i1035"><![endif]></span><!--[if gte mso 9]><xml>
1850 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1035"
1851  DrawAspect="Content" ObjectID="_1493040265">
1852 </o:OLEObject>
1853</xml><![endif]-->, and the three sample orientation angles, <span
1854style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
1855<span style='font-family:Symbol'>F</span><sub>s</sub>, all of which can be
1856adjustable parameters of the refinement. Once the refinement is complete, pole
1857figures for any reflection may be constructed by use of the general axis
1858equation, the refined values for <span style='position:relative;top:5.0pt;
1859mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1036" type="#_x0000_t75"
1860 style='width:24pt;height:20.25pt' o:ole="">
1861 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.wmz"
1862  o:title=""/>
1863</v:shape><![endif]--><![if !vml]><img width=32 height=27
1864src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
1865v:shapes="_x0000_i1036"><![endif]></span><!--[if gte mso 9]><xml>
1866 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1036"
1867  DrawAspect="Content" ObjectID="_1493040266">
1868 </o:OLEObject>
1869</xml><![endif]-->and the sample orientation angles <span style='font-family:
1870Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
1871<span class=GramE><span style='font-family:Symbol'>F</span></span><sub>s</sub>.
1872</p>
1873
1874<p class=gsastext>The magnitude of the texture is evaluated from the texture
1875index by</p>
1876
1877<p class=gsastext><span style='position:relative;top:16.0pt;mso-text-raise:
1878-16.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1037" type="#_x0000_t75"
1879 style='width:167.25pt;height:39pt' o:ole="">
1880 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.wmz"
1881  o:title=""/>
1882</v:shape><![endif]--><![if !vml]><img width=223 height=52
1883src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
1884v:shapes="_x0000_i1037"><![endif]></span><!--[if gte mso 9]><xml>
1885 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1037"
1886  DrawAspect="Content" ObjectID="_1493040267">
1887 </o:OLEObject>
1888</xml><![endif]--></p>
1889
1890<p class=gsastext>If the texture is random then J = 1, otherwise J &gt; 1; for
1891a single crystal J = <span style='font-family:Symbol'>¥.</span> </p>
1892
1893<p class=gsastext>In GSAS-II the texture is defined in two ways to accommodate
1894the two possible uses of this correction. In one a suite of spherical harmonics
1895coefficients is defined for the texture of a phase in the sample; this can have
1896any of the possible sample symmetries and is the usual result desired for
1897texture analysis. The other is the suite of spherical harmonics terms for
1898cylindrical sample symmetry for each phase in each powder pattern (“histogram”)
1899and is usually used to accommodate preferred orientation effects in a Rietveld
1900refinement. The former description allows refinement of the sample orientation
1901zeros, <span style='font-family:Symbol'>W</span><sub>s</sub>, <span
1902style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:Symbol'>F</span><sub>s</sub>,
1903but the latter description does not (they are assumed to be zero and not
1904refinable). The sample orientation angles, (<span style='font-family:Symbol'>W</span>,
1905<span style='font-family:Symbol'>C</span>, <span style='font-family:Symbol'>F) </span>are
1906specified in the Sample Parameters table in the GSAS-II data tree structure and
1907are applied for either description.</p>
1908
1909<p class=gsastext>In this tutorial we will use both of these descriptions to
1910determine the texture of the two phases in a <span class=SpellE>NiTi</span>
1911shape memory alloy sample with cylindrical symmetry (wire texture) as collected
1912at APS on beam line 1ID-C (data kindly provided by Paul Paradise &amp; Aaron <span
1913class=SpellE>Stebner</span> of Colo. School of Mines). Thus, there are three
1914ways within GSAS-II that can be used for this texture analysis all beginning
1915with the same 2D area detector image. Each will be described in turn after the
1916initial setup of the GSAS-II project, image input &amp; integration.</p>
1917
1918<h2>Step 1. Image input &amp; integration</h2>
1919
1920<p class=MsoNormal>If you have not done so already, <u><span style='color:#0070C0'><a
1921href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none;
1922text-underline:none'>start GSAS-II</span></a></span></u>. Note that menu
1923entries are listed in <b style='mso-bidi-font-weight:normal'><span
1924style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1925mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
1926minor-latin'>bold face</span></b> below as <b style='mso-bidi-font-weight:normal'><span
1927style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1928mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
1929minor-latin'>Help/About GSAS-II</span></b>, which lists first the name of the
1930menu (here <b style='mso-bidi-font-weight:normal'><span style='font-family:
1931"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1932minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>Help</span></b>)
1933and second the name of the entry in the menu (here <b style='mso-bidi-font-weight:
1934normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1935minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;
1936mso-bidi-theme-font:minor-latin'>About GSAS-II</span></b>). </p>
1937
1938<p class=MsoNormal>Use the <b style='mso-bidi-font-weight:normal'><span
1939style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1940mso-hansi-theme-font:minor-latin'>Data/Read image data</span></b> menu item to
1941read the data file into the current GSAS-II project. A file selection dialog
1942will be shown; its appearance will depend on your OS. Change the search
1943directory to <b style='mso-bidi-font-weight:normal'><span style='font-family:
1944"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1945minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>/exercises/2DTexture
1946</span></b>and then select the file <b style='mso-bidi-font-weight:normal'><span
1947style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1948mso-hansi-theme-font:minor-latin'>NDC5_01588_1.ge2</span></b>. A (faint) image
1949will appear</p>
1950
1951<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1952 id="Picture_x0020_29" o:spid="_x0000_i1109" type="#_x0000_t75" style='width:525pt;
1953 height:450pt;visibility:visible;mso-wrap-style:square'>
1954 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
1955  o:title=""/>
1956</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1957src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
1958v:shapes="Picture_x0020_29"><![endif]></span></p>
1959
1960<p class=MsoNormal><span class=GramE>and</span> the <b style='mso-bidi-font-weight:
1961normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1962minor-latin;mso-hansi-theme-font:minor-latin'>Image Controls</span></b> data
1963page will show</p>
1964
1965<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1966 id="Picture_x0020_30" o:spid="_x0000_i1108" type="#_x0000_t75" style='width:472.5pt;
1967 height:388.5pt;visibility:visible;mso-wrap-style:square'>
1968 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
1969  o:title=""/>
1970</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
1971src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
1972v:shapes="Picture_x0020_30"><![endif]></span></p>
1973
1974<p class=MsoNormal>The detector was previously calibrated and the coefficients
1975are stored in a file found by doing <b style='mso-bidi-font-weight:normal'><span
1976style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1977mso-hansi-theme-font:minor-latin'>Operations/Load Controls</span></b> from the <b
1978style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1979mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
1980Controls</span></b> menu. A file selection popup will appear showing <b
1981style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1982mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NDC5.imctrl</span></b>;
1983select it and press <b style='mso-bidi-font-weight:normal'><span
1984style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1985mso-hansi-theme-font:minor-latin'>Open</span></b>. The <b style='mso-bidi-font-weight:
1986normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1987minor-latin;mso-hansi-theme-font:minor-latin'>Image Controls</span></b> window
1988will be repainted with the new values (do a reselect of the image from the tree
1989and then <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1990mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
1991Controls</span></b> to make sure the image is up to date.)</p>
1992
1993<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1994 id="Picture_x0020_31" o:spid="_x0000_i1107" type="#_x0000_t75" style='width:472.5pt;
1995 height:388.5pt;visibility:visible;mso-wrap-style:square'>
1996 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
1997  o:title=""/>
1998</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
1999src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
2000v:shapes="Picture_x0020_31"><![endif]></span></p>
2001
2002<p class=MsoNormal>The detail in the image can be enhanced by lowering the <b
2003style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2004mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Max
2005intensity</span></b> (<b style='mso-bidi-font-weight:normal'><span
2006style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2007mso-hansi-theme-font:minor-latin'>15000</span></b> is suitable) and shows that
2008the diffraction rings show the effect of texture and that the image has a
2009fairly high background. Placing the cursor in the corners or inside the inner
2010ring shows a background &gt;1700. This can be suppressed by adjusting the <b
2011style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2012mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Flat <span
2013class=SpellE>Bkg</span></span></b> (I chose <b style='mso-bidi-font-weight:
2014normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2015minor-latin;mso-hansi-theme-font:minor-latin'>1700</span></b> for this). The
2016image will now show the rings much more clearly.</p>
2017
2018<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2019 id="Picture_x0020_32" o:spid="_x0000_i1106" type="#_x0000_t75" style='width:525pt;
2020 height:450pt;visibility:visible;mso-wrap-style:square'>
2021 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
2022  o:title=""/>
2023</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2024src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
2025v:shapes="Picture_x0020_32"><![endif]></span></p>
2026
2027<p class=MsoNormal>For texture analysis we will need to integrate the image
2028into a number of slices sampling the changing ring intensity with azimuthal
2029angle. Also note that the image seems to have <b style='mso-bidi-font-weight:
2030normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2031minor-latin;mso-hansi-theme-font:minor-latin'>mm</span></b> symmetry so that
2032the unique part of this intensity variation covers 0-90° of azimuth. In
2033addition the ring intensity variation is such that using 10° slices will
2034capture it reasonably well. However, we want to include both 0° and 90° as
2035slice centers. Thus there will be 10 slices beginning at -5° and ending at 95°.
2036Check the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2037mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show
2038integration limits?</span></b> <span class=GramE>box</span> and uncheck the <b
2039style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2040mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Do full
2041integration? </span></b><span class=GramE>box</span>, enter <b
2042style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2043mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>
2044in the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2045mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth
2046bins</span></b>, enter <b style='mso-bidi-font-weight:normal'><span
2047style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2048mso-hansi-theme-font:minor-latin'>-5</span></b> in the <b style='mso-bidi-font-weight:
2049normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2050minor-latin;mso-hansi-theme-font:minor-latin'>Start azimuth</span></b> box (it
2051will change to 355) and enter <b style='mso-bidi-font-weight:normal'><span
2052style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2053mso-hansi-theme-font:minor-latin'>455</span></b> in the <b style='mso-bidi-font-weight:
2054normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2055minor-latin;mso-hansi-theme-font:minor-latin'>End azimuth</span></b> box. In
2056addition, recall that the sample was mounted vertically and thus is aligned
2057with the defined laboratory I axis. Thus, the sample coordinate system needs to
2058be rotated by 90° to match the sample axis with the K axis; this can be done by
2059making the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2060"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2061minor-latin'>Sample goniometer axis Chi</span></b> = <b style='mso-bidi-font-weight:
2062normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2063minor-latin;mso-hansi-theme-font:minor-latin'>90</span></b>. The plot will
2064change with each entry and at the end should look like</p>
2065
2066<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2067 id="Picture_x0020_33" o:spid="_x0000_i1105" type="#_x0000_t75" style='width:525pt;
2068 height:450pt;visibility:visible;mso-wrap-style:square'>
2069 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
2070  o:title=""/>
2071</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2072src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
2073v:shapes="Picture_x0020_33"><![endif]></span></p>
2074
2075<p class=MsoNormal>The <b style='mso-bidi-font-weight:normal'><span
2076style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2077mso-hansi-theme-font:minor-latin'>Image Controls</span></b> should be</p>
2078
2079<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2080 id="Picture_x0020_34" o:spid="_x0000_i1104" type="#_x0000_t75" style='width:472.5pt;
2081 height:388.5pt;visibility:visible;mso-wrap-style:square'>
2082 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
2083  o:title=""/>
2084</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
2085src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
2086v:shapes="Picture_x0020_34"><![endif]></span></p>
2087
2088<p class=MsoNormal>It turns out that the image contains a number of “picked
2089bits” (very high count “zingers”); these can be mostly eliminated by setting
2090the upper threshold in Masks. Select <b style='mso-bidi-font-weight:normal'><span
2091style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2092mso-hansi-theme-font:minor-latin'>Masks</span></b> and the following should
2093appear</p>
2094
2095<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2096 id="Picture_x0020_35" o:spid="_x0000_i1103" type="#_x0000_t75" style='width:297.75pt;
2097 height:99.75pt;visibility:visible;mso-wrap-style:square'>
2098 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
2099  o:title=""/>
2100</v:shape><![endif]--><![if !vml]><img border=0 width=397 height=133
2101src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
2102v:shapes="Picture_x0020_35"><![endif]></span></p>
2103
2104<p class=MsoNormal>Change the <b style='mso-bidi-font-weight:normal'><span
2105style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2106mso-hansi-theme-font:minor-latin'>Upper threshold</span></b> to <b
2107style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2108mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2500</span></b>;
2109the image will be redrawn reflecting this mask. By zooming in you may see
2110isolated red pixels; these are excluded points. Make sure the diffraction rings
2111do not have any excluded points. For example with the level set to 2200 the
2112plot shows</p>
2113
2114<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2115 id="Picture_x0020_36" o:spid="_x0000_i1102" type="#_x0000_t75" style='width:525pt;
2116 height:450pt;visibility:visible;mso-wrap-style:square'>
2117 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
2118  o:title=""/>
2119</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2120src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
2121v:shapes="Picture_x0020_36"><![endif]></span></p>
2122
2123<p class=MsoNormal><span class=GramE>for</span> one ring. This level is too
2124low. Return to the <b style='mso-bidi-font-weight:normal'><span
2125style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2126mso-hansi-theme-font:minor-latin'>Image Controls</span></b> item in the data
2127tree.</p>
2128
2129<p class=MsoNormal>We are now ready to integrate the image; do <b
2130style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2131mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Integrate</span></b>
2132from the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2133mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2134Controls</span></b> menu. When done the last powder pattern in the tree will be
2135displayed</p>
2136
2137<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2138 id="Picture_x0020_37" o:spid="_x0000_i1101" type="#_x0000_t75" style='width:525pt;
2139 height:450pt;visibility:visible;mso-wrap-style:square'>
2140 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2141  o:title=""/>
2142</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2143src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2144v:shapes="Picture_x0020_37"><![endif]></span></p>
2145
2146<h2>Step 2. Enter <span class=SpellE>NiTi</span> phases</h2>
2147
2148<p class=MsoNormal>This <span class=SpellE>NiTi</span> alloy consists of two
2149phases, cubic B2 and monoclinic B19’. Their parameters are:</p>
2150
2151<p class=MsoNormal>B2: <b style='mso-bidi-font-weight:normal'><span
2152style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2153mso-hansi-theme-font:minor-latin'>P m 3 m</span></b>, a=<b style='mso-bidi-font-weight:
2154normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2155minor-latin;mso-hansi-theme-font:minor-latin'>3.0240</span></b>, Ni <b
2156style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2157mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0<span
2158class=GramE>,0,0</span></span></b>, <span class=SpellE>Ti</span> <b
2159style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2160mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>œ,œ,œ</span></b>,
2161<span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
2162style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2163mso-hansi-theme-font:minor-latin'>0.005 </span></b>for both.</p>
2164
2165<p class=MsoNormal>B19’: <span style='mso-spacerun:yes'> </span><b
2166style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2167mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P 1 1 21/m</span></b>,
2168a=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2169mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.8853</span></b>,
2170b=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2171mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.6353</span></b>,
2172c=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2173mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.1368</span></b>,
2174&#947;=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2175mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>96.821</span></b>,
2176<span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span
2177style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2178mso-hansi-theme-font:minor-latin'>0.5787<span class=GramE>,0.2841,Œ</span></span></b>,
2179Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2180mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.9700,0.8209,Œ</span></b>,
2181<span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
2182style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2183mso-hansi-theme-font:minor-latin'>0.005</span></b> for both.</p>
2184
2185<p class=MsoNormal>Use the <b style='mso-bidi-font-weight:normal'><span
2186style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2187mso-hansi-theme-font:minor-latin'>Data/Add phase</span></b> to enter the <b
2188style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2189mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
2190and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2191mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
2192phases; then for each enter the information given above on their respective <b
2193style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2194mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>General</span></b>
2195and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2196mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms</span></b>
2197tabs. Don’t forget the spaces between the axial fields for the space group
2198symbols. On the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2199"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2200minor-latin'>Atoms</span></b> tab begin by doing <b style='mso-bidi-font-weight:
2201normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2202minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Append atom</span></b> twice
2203then fill in the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2204"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2205minor-latin'>Type</span></b> and coordinates boxes. A double click of the <b
2206style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2207mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Type</span></b>
2208entry will show a popup of the Periodic Table; select the element as
2209appropriate. NB: GSAS-II happily takes “1/2” &amp; “1/4” for coordinate values;
2210these get converted to their decimal equivalent upon entry. Note the use of a
2211nonstandard space group designation for B19’. When done the B2 Atoms table should
2212look like</p>
2213
2214<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2215 id="Picture_x0020_38" o:spid="_x0000_i1100" type="#_x0000_t75" style='width:525pt;
2216 height:166.5pt;visibility:visible;mso-wrap-style:square'>
2217 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2218  o:title=""/>
2219</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=222
2220src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2221v:shapes="Picture_x0020_38"><![endif]></span></p>
2222
2223<p class=MsoNormal><span class=GramE>and</span> the B19’ Atoms table should be</p>
2224
2225<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2226 id="Picture_x0020_39" o:spid="_x0000_i1099" type="#_x0000_t75" style='width:525pt;
2227 height:163.5pt;visibility:visible;mso-wrap-style:square'>
2228 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
2229  o:title=""/>
2230</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=218
2231src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
2232v:shapes="Picture_x0020_39"><![endif]></span></p>
2233
2234<p class=MsoNormal>Next go to the <b style='mso-bidi-font-weight:normal'><span
2235style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2236mso-hansi-theme-font:minor-latin'>Data</span></b> tab for each phase; there
2237will be a message indicating the lack of data for each. Do <b style='mso-bidi-font-weight:
2238normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2239minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add powder histograms</span></b>,
2240do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2241mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b>
2242on the popup selection window and press <b style='mso-bidi-font-weight:normal'><span
2243style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2244mso-hansi-theme-font:minor-latin'>OK</span></b>. The window for B2 will change
2245to</p>
2246
2247<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2248 id="Picture_x0020_40" o:spid="_x0000_i1098" type="#_x0000_t75" style='width:342.75pt;
2249 height:375pt;visibility:visible;mso-wrap-style:square'>
2250 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
2251  o:title=""/>
2252</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
2253src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
2254v:shapes="Picture_x0020_40"><![endif]></span></p>
2255
2256<p class=MsoNormal><span class=GramE>and</span> that for B19’ will be</p>
2257
2258<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2259 id="Picture_x0020_41" o:spid="_x0000_i1097" type="#_x0000_t75" style='width:370.5pt;
2260 height:375pt;visibility:visible;mso-wrap-style:square'>
2261 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
2262  o:title=""/>
2263</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
2264src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
2265v:shapes="Picture_x0020_41"><![endif]></span></p>
2266
2267<p class=MsoNormal>You should now save the project file (I used <span
2268class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
2269"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2270minor-latin'>NiTi</span></b></span> for a name); we will use this as a starting
2271point for three different texture determinations. Do a <b style='mso-bidi-font-weight:
2272normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2273minor-latin;mso-hansi-theme-font:minor-latin'>File/Save project as…</span></b>
2274and give it a new name (I used <span class=SpellE><b style='mso-bidi-font-weight:
2275normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2276minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b
2277style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2278mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-A</span></b>);
2279this will become the new project name for the next part of this tutorial.</p>
2280
2281<h2>Method A. Full refinement</h2>
2282
2283<h3>Introduction</h3>
2284
2285<p class=MsoNormal>In this method we will do a full Rietveld refinement of the texture,
2286profile parameters, peak position variables and crystal structure parameters.
2287This is suitable in this case because of the relatively small number of
2288histograms (10 in this case) needed for the texture determination; do recall
2289that each phase in each histogram has a set of parameters (e.g. phase fraction,
2290size, <span class=SpellE>mustrain</span> &amp; hydrostatic strain) in addition
2291to the ones for each histogram (e.g. background &amp; scale factor).
2292Consequently the total number of parameters can build up very quickly in this
2293method of analysis. The other two methods seek to reduce this problem by
2294splitting the fitting into a sequential refinement (histogram by histogram)
2295step followed by a texture fitting step.</p>
2296
2297<h3>Step 1. Initial refinement</h3>
2298
2299<p class=MsoNormal>In the initial refinement we need to vary the phase fraction
2300for each phase/histogram and the background in each histogram. To start select
2301any <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2302mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b>
2303entry from the GSAS-II data tree and select <b style='mso-bidi-font-weight:
2304normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2305minor-latin;mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b> for
2306it. Note that Goniometer chi is set to 90; that came from the same entry in the
2307Image Controls during integration. Also, if you chose other than the 1<sup>st</sup>
2308PWDR data set the Detector azimuth will be some nonzero value; that is also
2309reflected in the name assigned to the histogram (e.g. <b style='mso-bidi-font-weight:
2310normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2311minor-latin;mso-hansi-theme-font:minor-latin'>PWDR NDC5_01588_1.ge2 <span
2312class=SpellE>Azm</span>= 40.00</span></b>). Uncheck the <b style='mso-bidi-font-weight:
2313normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2314minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>
2315box and then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
2316"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2317minor-latin'>Command/Copy flags</span></b>; select <b style='mso-bidi-font-weight:
2318normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2319minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b> and then press
2320<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2321mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
2322That will clear the scale factor refinement flag for all histograms; we will be
2323varying the phase fractions instead.</p>
2324
2325<p class=MsoNormal>Next select the B2 phase and pick the Data tab; you will see</p>
2326
2327<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2328 id="Picture_x0020_42" o:spid="_x0000_i1096" type="#_x0000_t75" style='width:342.75pt;
2329 height:375pt;visibility:visible;mso-wrap-style:square'>
2330 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
2331  o:title=""/>
2332</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
2333src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
2334v:shapes="Picture_x0020_42"><![endif]></span></p>
2335
2336<p class=MsoNormal>Select the <b style='mso-bidi-font-weight:normal'><span
2337style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2338mso-hansi-theme-font:minor-latin'>Phase fraction</span></b> box. Then do <b
2339style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2340mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
2341data</span></b>, select <b style='mso-bidi-font-weight:normal'><span
2342style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2343mso-hansi-theme-font:minor-latin'>Set <span class=GramE>All</span></span></b>
2344&amp; press <b style='mso-bidi-font-weight:normal'><span style='font-family:
2345"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2346minor-latin'>OK</span></b> to copy these to the other histograms. Next select
2347the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2348mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
2349phase and repeat this process. We are now ready for the first refinement; do <b
2350style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2351mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
2352from the main GSAS-II data tree window. A progress bar popup will appear and
2353when done a <b style='mso-bidi-font-weight:normal'><span style='font-family:
2354"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2355minor-latin'>Refinement results</span></b> popup will show with Rw~32%. Press <b
2356style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2357mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>
2358to load this result; GSAS-II will return you to the last window you were using
2359and display the 1<sup>st</sup> powder pattern showing you the fit</p>
2360
2361<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2362 id="Picture_x0020_43" o:spid="_x0000_i1095" type="#_x0000_t75" style='width:525pt;
2363 height:450pt;visibility:visible;mso-wrap-style:square'>
2364 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
2365  o:title=""/>
2366</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2367src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
2368v:shapes="Picture_x0020_43"><![endif]></span></p>
2369
2370<p class=MsoNormal>This is quite poor. You can survey the fit successively by 1<sup>st</sup>
2371selecting say the 1<sup>st</sup> PWDR entry from the tree and then using the
2372up/down arrow keys to step to the next one; the plot will redraw at each step
2373(NB: at full scale) and the data window will show statistics of the fit. There
2374is a substantial intensity discrepancy; this is due to the texture. It is also
2375evident that some of the peaks are out of place relative to the reflection
2376markers; this is due to macroscopic strain in the drawn wire. For the <span
2377style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2378mso-hansi-theme-font:minor-latin'>B2</span> phase select the <b
2379style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2380mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
2381tab; it should look like</p>
2382
2383<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2384 id="Picture_x0020_44" o:spid="_x0000_i1094" type="#_x0000_t75" style='width:456pt;
2385 height:217.5pt;visibility:visible;mso-wrap-style:square'>
2386 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
2387  o:title=""/>
2388</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290
2389src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
2390v:shapes="Picture_x0020_44"><![endif]></span></p>
2391
2392<p class=MsoNormal>The texture model is <b style='mso-bidi-font-weight:normal'><span
2393style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2394mso-hansi-theme-font:minor-latin'>cylindrical</span></b> by default; that is
2395what we want. Change the <b style='mso-bidi-font-weight:normal'><span
2396style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2397mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to <b
2398style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2399mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>8</span></b>
2400and check both <b style='mso-bidi-font-weight:normal'><span style='font-family:
2401"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2402minor-latin'>Refine texture</span></b> and <b style='mso-bidi-font-weight:normal'><span
2403style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2404mso-hansi-theme-font:minor-latin'>Show <span class=SpellE>coeff</span></span></b>.
2405The window should look like</p>
2406
2407<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2408 id="Picture_x0020_45" o:spid="_x0000_i1093" type="#_x0000_t75" style='width:456pt;
2409 height:250.5pt;visibility:visible;mso-wrap-style:square'>
2410 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
2411  o:title=""/>
2412</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
2413src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
2414v:shapes="Picture_x0020_45"><![endif]></span></p>
2415
2416<p class=MsoNormal>Then go to the <b style='mso-bidi-font-weight:normal'><span
2417style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2418mso-hansi-theme-font:minor-latin'>Data</span></b> tab, select <b
2419style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2420mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>D11</span></b>;
2421the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2422mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
2423window should look like (any PWDR item will do)</p>
2424
2425<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2426 id="Picture_x0020_46" o:spid="_x0000_i1092" type="#_x0000_t75" style='width:342.75pt;
2427 height:375pt;visibility:visible;mso-wrap-style:square'>
2428 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
2429  o:title=""/>
2430</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
2431src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
2432v:shapes="Picture_x0020_46"><![endif]></span></p>
2433
2434<p class=MsoNormal>Then do <b style='mso-bidi-font-weight:normal'><span
2435style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2436mso-hansi-theme-font:minor-latin'>Edit/Copy flags</span></b> to have <b
2437style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2438mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>D11</span></b>
2439refined for all PWDR data sets.</p>
2440
2441<p class=MsoNormal>Next select the <b style='mso-bidi-font-weight:normal'><span
2442style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2443mso-hansi-theme-font:minor-latin'>B19’</span></b> phase <b style='mso-bidi-font-weight:
2444normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2445minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b> tab. Then
2446select <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2447mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>6</span></b>
2448for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2449mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic
2450order</span></b> and check the two boxes as before.</p>
2451
2452<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2453 id="Picture_x0020_47" o:spid="_x0000_i1091" type="#_x0000_t75" style='width:478.5pt;
2454 height:302.25pt;visibility:visible;mso-wrap-style:square'>
2455 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
2456  o:title=""/>
2457</v:shape><![endif]--><![if !vml]><img border=0 width=638 height=403
2458src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
2459v:shapes="Picture_x0020_47"><![endif]></span></p>
2460
2461<p class=MsoNormal>Then go to the <b style='mso-bidi-font-weight:normal'><span
2462style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2463mso-hansi-theme-font:minor-latin'>Data</span></b> tab for the <b
2464style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2465mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
2466phase and check all 4 of the <span class=SpellE><b style='mso-bidi-font-weight:
2467normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2468minor-latin;mso-hansi-theme-font:minor-latin'>Dij</span></b></span> boxes and
2469do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2470mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
2471flags</span></b> as before. The tab will look like</p>
2472
2473<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2474 id="Picture_x0020_48" o:spid="_x0000_i1090" type="#_x0000_t75" style='width:370.5pt;
2475 height:375pt;visibility:visible;mso-wrap-style:square'>
2476 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
2477  o:title=""/>
2478</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
2479src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
2480v:shapes="Picture_x0020_48"><![endif]></span></p>
2481
2482<p class=MsoNormal>Now do <b style='mso-bidi-font-weight:normal'><span
2483style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2484mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from the main
2485menu. The refinement will finish with <span class=SpellE>Rw</span> ~27%; the 1<sup>st</sup>
2486PWDR pattern looks like</p>
2487
2488<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2489 id="Picture_x0020_49" o:spid="_x0000_i1089" type="#_x0000_t75" style='width:525pt;
2490 height:413.25pt;visibility:visible;mso-wrap-style:square'>
2491 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
2492  o:title=""/>
2493</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2494src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
2495v:shapes="Picture_x0020_49"><![endif]></span></p>
2496
2497<p class=MsoNormal>The calculated peaks for both phases are too sharp. It is
2498likely that this is a <span class=SpellE>microstrain</span> effect. Select <b
2499style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2500mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
2501for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2502mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2 </span></b>phase
2503and select the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
2504style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2505mso-hansi-theme-font:minor-latin'>microstrain</span></b></span> box. Then do <b
2506style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2507mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
2508flags</span></b> to set it for the other PWDR data sets. Do the same for the <b
2509style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2510mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
2511phase. Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
2512"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2513minor-latin'>Calculate/Refine</span></b> from the main menu. The fit will be
2514substantially improved with <span class=SpellE>Rw</span> ~9.2%.</p>
2515
2516<h3>Step 2. Finish refinement and examine texture</h3>
2517
2518<p class=MsoNormal>Looking at the individual PWDR data sets (e.g. the one for <span
2519class=SpellE>Azm</span>=20.00)</p>
2520
2521<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2522 id="Picture_x0020_50" o:spid="_x0000_i1088" type="#_x0000_t75" style='width:525pt;
2523 height:413.25pt;visibility:visible;mso-wrap-style:square'>
2524 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
2525  o:title=""/>
2526</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2527src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
2528v:shapes="Picture_x0020_50"><![endif]></span></p>
2529
2530<p class=MsoNormal>It is evident that there remains intensity differences due
2531to texture. We can increase the harmonic order to more closely fit these,
2532however one should only do this carefully. Select the Texture tab for the B2
2533phase; the Texture tab will show</p>
2534
2535<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2536 id="Picture_x0020_18" o:spid="_x0000_i1087" type="#_x0000_t75" style='width:456pt;
2537 height:250.5pt;visibility:visible;mso-wrap-style:square'>
2538 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
2539  o:title=""/>
2540</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
2541src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
2542v:shapes="Picture_x0020_18"><![endif]></span></p>
2543
2544<p class=MsoNormal>And a drawing of the 001 pole figure will be drawn. This is
2545the very typical “bulls eye” for cylindrical texture; of much more use is an
2546inverse pole figure. Select that from the Texture plot type; the plot will be
2547redrawn</p>
2548
2549<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2550 id="Picture_x0020_52" o:spid="_x0000_i1086" type="#_x0000_t75" style='width:525pt;
2551 height:413.25pt;visibility:visible;mso-wrap-style:square'>
2552 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
2553  o:title=""/>
2554</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2555src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
2556v:shapes="Picture_x0020_52"><![endif]></span></p>
2557
2558<p class=MsoNormal>This shows the probability of reflection vectors coinciding
2559with the sample wire axis the high spots are the 111 family of reflections. We
2560should try the next higher Harmonic order (10). </p>
2561
2562<p class=MsoNormal>Next go to the Texture tab for the B19’ phase. Again a <span
2563class=SpellE>bullseye</span> pole figure is drawn; change that to an Inverse
2564pole figure.</p>
2565
2566<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2567 id="Picture_x0020_53" o:spid="_x0000_i1085" type="#_x0000_t75" style='width:525pt;
2568 height:413.25pt;visibility:visible;mso-wrap-style:square'>
2569 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
2570  o:title=""/>
2571</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2572src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
2573v:shapes="Picture_x0020_53"><![endif]></span></p>
2574
2575<p class=MsoNormal>This phase is very strongly textured (the cursor shows 12-13
2576MRD at the peaks) along the -140 direction. Again we want to increment the
2577Harmonic order to the next higher level (8). Again do Calculate/Refine from the
2578main menu; the <span class=SpellE>Rwp</span> has dropped to ~7.9%. One can add
2579the atom <span class=SpellE>Uiso</span> for the Ni and <span class=SpellE>Ti</span>
2580atoms in the B2 phase and the coordinates and <span class=SpellE>Uiso</span>
2581for the B19’ phase. The <span class=SpellE>Rw</span> drops a bit further to
2582~7.4%. Finally, we can increase the harmonic order again for the B19’ phase (it
2583is very strongly textured!) to 10 and the B2 phase to 12; the final refinement
2584converged to <span class=SpellE>Rw</span> ~6.8% and the B19’ inverse pole
2585figure has peaks at ~18 MRD (Multiple of Random Distribution) and the B2 phase
2586peaks are ~7MRD.</p>
2587
2588<p class=MsoNormal>The B19’ coefficients</p>
2589
2590<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2591 id="Picture_x0020_54" o:spid="_x0000_i1084" type="#_x0000_t75" style='width:502.5pt;
2592 height:375pt;visibility:visible;mso-wrap-style:square'>
2593 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
2594  o:title=""/>
2595</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
2596src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
2597v:shapes="Picture_x0020_54"><![endif]></span></p>
2598
2599<p class=MsoNormal><span class=GramE>and</span> inverse pole figure</p>
2600
2601<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2602 id="Picture_x0020_55" o:spid="_x0000_i1083" type="#_x0000_t75" style='width:525pt;
2603 height:413.25pt;visibility:visible;mso-wrap-style:square'>
2604 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
2605  o:title=""/>
2606</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2607src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
2608v:shapes="Picture_x0020_55"><![endif]></span></p>
2609
2610<p class=MsoNormal>The B2 coefficients</p>
2611
2612<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2613 id="Picture_x0020_56" o:spid="_x0000_i1082" type="#_x0000_t75" style='width:480pt;
2614 height:267.75pt;visibility:visible;mso-wrap-style:square'>
2615 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
2616  o:title=""/>
2617</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
2618src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
2619v:shapes="Picture_x0020_56"><![endif]></span></p>
2620
2621<p class=MsoNormal><span class=GramE>and</span> inverse pole figure</p>
2622
2623<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2624 id="Picture_x0020_57" o:spid="_x0000_i1081" type="#_x0000_t75" style='width:525pt;
2625 height:413.25pt;visibility:visible;mso-wrap-style:square'>
2626 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
2627  o:title=""/>
2628</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2629src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
2630v:shapes="Picture_x0020_57"><![endif]></span></p>
2631
2632<p class=MsoNormal>This completes the tutorial on Method A for doing texture
2633analysis. It is useful for a case like this one where there are very few data
2634sets required for the texture analysis. However, for the case of lower sample
2635symmetry one must several dozen or even a few hundred histograms and then the
2636suite of parameters can easily be &gt; 1000 of which only a few dozen describe
2637the texture. This leads to the next Methods for texture analysis in GSAS-II.</p>
2638
2639<h2>Method B. Sequential refinement &amp; texture analysis from result</h2>
2640
2641<h3>Introduction</h3>
2642
2643<p class=MsoNormal>This begins the texture analysis in much the same way as
2644Method A except that all the initial refinements are done “sequentially”, that
2645is refinements are done for the parameters associated with each powder pattern
2646to convergence in a serial fashion. In this case where there are 10 PWDR data
2647sets, there will be 10 refinements done in sequence. Parameters that span all
2648the data (e.g. lattice parameters, atom parameters &amp; texture) are not
2649varied in this sequence refinement. The effect of texture is modeled as a
2650Preferred Orientation correction to each histogram. To begin do <b
2651style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2652mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Open project…</span></b>
2653for the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
2654style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2655mso-hansi-theme-font:minor-latin'>NiTi.gpx</span></b></span> file created in
2656the first step and then do a <b style='mso-bidi-font-weight:normal'><span
2657style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2658mso-hansi-theme-font:minor-latin'>File/Save project as…</span></b> to save it
2659as <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
2660style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2661mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight:
2662normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2663minor-latin;mso-hansi-theme-font:minor-latin'>-B</span></b>. This renames the
2664project and it should have one IMG, 10 PWDR entries and two phases of <span
2665class=SpellE>NiTi</span> (B2 and B19’).</p>
2666
2667<h3>Step 1. Initial refinement</h3>
2668
2669<p class=MsoNormal>This begins the same way as Method A so I’ll be brief. Do
2670the following steps:</p>
2671
2672<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
2673style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
2674style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
2675any <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2676mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b>
2677entry, go to <b style='mso-bidi-font-weight:normal'><span style='font-family:
2678"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2679minor-latin'>Sample Parameters</span></b> and uncheck <b style='mso-bidi-font-weight:
2680normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2681minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>.
2682Then copy the flags to the other PWDR entries.</p>
2683
2684<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
2685style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
2686style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
2687the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2688mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
2689phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2690mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
2691tab and check the <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'>Phase fraction</span></b> box and change the <span
2694class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
2695"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2696minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span
2697style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2698mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b
2699style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2700mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical
2701harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span
2702style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2703mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the
2704flag and the model to the other PWDR entries.</p>
2705
2706<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
2707style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
2708style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
2709the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2710mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
2711phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2712mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
2713tab and check the <b style='mso-bidi-font-weight:normal'><span
2714style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2715mso-hansi-theme-font:minor-latin'>Phase fraction box</span></b> and change the <span
2716class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
2717"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2718minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span
2719style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2720mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b
2721style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2722mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical
2723harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span
2724style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2725mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the
2726flag and the model to the other PWDR entries.</p>
2727
2728<p class=MsoNormal>Now select <b style='mso-bidi-font-weight:normal'><span
2729style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2730mso-hansi-theme-font:minor-latin'>Controls</span></b> from the GSAS-II data
2731tree</p>
2732
2733<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2734 id="Picture_x0020_1" o:spid="_x0000_i1080" type="#_x0000_t75" style='width:330.75pt;
2735 height:153.75pt;visibility:visible;mso-wrap-style:square'>
2736 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
2737  o:title=""/>
2738</v:shape><![endif]--><![if !vml]><img border=0 width=441 height=205
2739src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
2740v:shapes="Picture_x0020_1"><![endif]></span></p>
2741
2742<p class=MsoNormal>Press the <b style='mso-bidi-font-weight:normal'><span
2743style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2744mso-hansi-theme-font:minor-latin'>Select Data</span></b> button for <b
2745style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2746mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Sequential
2747Refinement</span></b>; a file selection popup will appear. Do <b
2748style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2749mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b>
2750and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2751mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
2752The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2753mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b>
2754page will be repainted indicating that 10 data sets are selected for sequential
2755refinement.</p>
2756
2757<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2758 id="Picture_x0020_2" o:spid="_x0000_i1079" type="#_x0000_t75" style='width:330.75pt;
2759 height:163.5pt;visibility:visible;mso-wrap-style:square'>
2760 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
2761  o:title=""/>
2762</v:shape><![endif]--><![if !vml]><img border=0 width=441 height=218
2763src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
2764v:shapes="Picture_x0020_2"><![endif]></span></p>
2765
2766<p class=MsoNormal>You have the choice of starting at the last one and for
2767copying results from one to the next. We won’t do either here. Each refinement will
2768use the other controls (e.g. <b style='mso-bidi-font-weight:normal'><span
2769style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2770mso-hansi-theme-font:minor-latin'>Max cycles</span></b>) as controls. We are
2771now ready to do the 1<sup>st</sup> sequential refinement. Do <b
2772style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2773mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Sequential
2774refine</span></b> from the main menu. A progress bar popup will appear showing
2775residuals as it processes each of 10 data sets. After a few seconds the <b
2776style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2777mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refinement
2778results</span></b> popup will appear; press <b style='mso-bidi-font-weight:
2779normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2780minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to accept them. The
2781data window displays the <b style='mso-bidi-font-weight:normal'><span
2782style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2783mso-hansi-theme-font:minor-latin'>Sequential refinement results</span></b> as a
2784table.</p>
2785
2786<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2787 id="Picture_x0020_3" o:spid="_x0000_i1078" type="#_x0000_t75" style='width:525pt;
2788 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2789 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
2790  o:title=""/>
2791</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
2792src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
2793v:shapes="Picture_x0020_3"><![endif]></span></p>
2794
2795<p class=MsoNormal>There is a row for each data set and columns for all refined
2796parameters and some derived ones along with residual and convergence
2797indicators. The residuals are not very good (we haven’t really refined much)
2798but the &#916;&#967;<sup>2</sup> column shows that convergence was achieved
2799(NB: poor convergence will be highlighted in yellow or red depending on how bad
2800it is).</p>
2801
2802<p class=MsoNormal>If you examine one of the PWDR entries, you’ll see that just
2803in this point in Method <span class=GramE>A</span> much of the misfit is
2804texture and perhaps peak position.</p>
2805
2806<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2807 id="Picture_x0020_4" o:spid="_x0000_i1077" type="#_x0000_t75" style='width:525pt;
2808 height:450pt;visibility:visible;mso-wrap-style:square'>
2809 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
2810  o:title=""/>
2811</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2812src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
2813v:shapes="Picture_x0020_4"><![endif]></span></p>
2814
2815<p class=MsoNormal>To set these parameters, select the Data tab for the B2
2816phase</p>
2817
2818<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2819 id="Picture_x0020_5" o:spid="_x0000_i1076" type="#_x0000_t75" style='width:381pt;
2820 height:375pt;visibility:visible;mso-wrap-style:square'>
2821 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
2822  o:title=""/>
2823</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=500
2824src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
2825v:shapes="Picture_x0020_5"><![endif]></span></p>
2826
2827<p class=MsoNormal>Check the D11 box under Hydrostatic/elastic strain, set the
2828Harmonic order to 6 and check the Refine box for it (Preferred orientation).
2829Then in two steps, do Edit/Copy flags and Set All for the file selection. Then
2830do Edit/Copy selected data; that will bring up a new popup</p>
2831
2832<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2833 id="Picture_x0020_6" o:spid="_x0000_i1075" type="#_x0000_t75" style='width:240pt;
2834 height:232.5pt;visibility:visible;mso-wrap-style:square'>
2835 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
2836  o:title=""/>
2837</v:shape><![endif]--><![if !vml]><img border=0 width=320 height=310
2838src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
2839v:shapes="Picture_x0020_6"><![endif]></span></p>
2840
2841<p class=MsoNormal>This allows you to select which parameters to copy data and
2842flags. Select Pref. <span class=SpellE>Ori</span>. And press OK; the file
2843selection is next. Do Set <span class=GramE>All</span> and OK to do this copy.
2844That copies the full spherical harmonics model to the other data sets. Select
2845one to check if you’d like.</p>
2846
2847<p class=MsoNormal>Next do the same thing for the B19’ phase; here there are 4 <span
2848class=SpellE>Dij</span> parameters to check (do all of them) and use spherical
2849harmonics order 4. When done that Data window will look like</p>
2850
2851<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2852 id="Picture_x0020_7" o:spid="_x0000_i1074" type="#_x0000_t75" style='width:381pt;
2853 height:467.25pt;visibility:visible;mso-wrap-style:square'>
2854 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png"
2855  o:title=""/>
2856</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=623
2857src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png"
2858v:shapes="Picture_x0020_7"><![endif]></span></p>
2859
2860<p class=MsoNormal>We are now ready for the next refinement; do
2861Calculate/Sequential refine. Be careful not (by habit say) pick Refine; a
2862warning popup will appear. After it completes the Sequential refinement results
2863shows that the fit is better but convergence wasn’t quite complete.</p>
2864
2865<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2866 id="Picture_x0020_8" o:spid="_x0000_i1073" type="#_x0000_t75" style='width:525pt;
2867 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2868 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
2869  o:title=""/>
2870</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
2871src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
2872v:shapes="Picture_x0020_8"><![endif]></span></p>
2873
2874<p class=MsoNormal>It is probably best to do another round of sequential
2875refinement (I had to do two) to get convergence. A plot of one PWDR entry gives</p>
2876
2877<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2878 id="Picture_x0020_9" o:spid="_x0000_i1072" type="#_x0000_t75" style='width:525pt;
2879 height:450pt;visibility:visible;mso-wrap-style:square'>
2880 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png"
2881  o:title=""/>
2882</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2883src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png"
2884v:shapes="Picture_x0020_9"><![endif]></span></p>
2885
2886<p class=MsoNormal>As our experience in Method A, the calculated peaks are too
2887sharp. We need to vary the <span class=SpellE>mustrain</span> parameters for
2888both phases. Go to the Data tab for each phase, check the <span class=SpellE>microstrain</span>
2889box and do Edit/Copy flags for all the data sets. Then do another
2890Calculate/Sequential refine. My Sequential refinement results showed great
2891improvement but incomplete refinement</p>
2892
2893<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2894 id="Picture_x0020_10" o:spid="_x0000_i1071" type="#_x0000_t75" style='width:525pt;
2895 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2896 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
2897  o:title=""/>
2898</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
2899src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
2900v:shapes="Picture_x0020_10"><![endif]></span></p>
2901
2902<p class=MsoNormal>Repeating the sequential refinement (twice) gave
2903convergence.</p>
2904
2905<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2906 id="Picture_x0020_11" o:spid="_x0000_i1070" type="#_x0000_t75" style='width:525pt;
2907 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2908 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
2909  o:title=""/>
2910</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
2911src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
2912v:shapes="Picture_x0020_11"><![endif]></span></p>
2913
2914<p class=MsoNormal>Examination of the PWDR data sets showed a fairly good fit
2915but some discrepancies (especially for <span class=SpellE>Azm</span>=20.00)</p>
2916
2917<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2918 id="Picture_x0020_12" o:spid="_x0000_i1069" type="#_x0000_t75" style='width:525pt;
2919 height:450pt;visibility:visible;mso-wrap-style:square'>
2920 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
2921  o:title=""/>
2922</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2923src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
2924v:shapes="Picture_x0020_12"><![endif]></span></p>
2925
2926<p class=MsoNormal>Showing that perhaps the B19’ phase needs high order
2927spherical harmonics. Select the Data tab for the B19’ phase and change the
2928Harmonic order to 6. Then do Edit/Copy selected data for <span class=SpellE>Pref.Ori</span>.
2929<span class=GramE>to</span> the other data sets. This (after few repeats) gives
2930a further improvement in the fit</p>
2931
2932<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2933 id="Picture_x0020_13" o:spid="_x0000_i1068" type="#_x0000_t75" style='width:525pt;
2934 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2935 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png"
2936  o:title=""/>
2937</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
2938src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png"
2939v:shapes="Picture_x0020_13"><![endif]></span></p>
2940
2941<p class=MsoNormal>This fit is now sufficient for us to proceed to the next
2942step and determine the texture of the two phases.</p>
2943
2944<h3>Step 2. Texture analysis</h3>
2945
2946<p class=MsoNormal>During the sequential refinements done in Step 1, we fitted
2947the profiles allowing strain parameters (<span class=SpellE>Dij</span>) for
2948peak position shifts and <span class=SpellE>microstrain</span> for peak shape. We
2949modeled the intensity variation with a spherical harmonics preferred
2950orientation correction. If you select any PWDR entry from the GSAS-II data tree
2951and pick the Reflection List subentry (at the bottom) you can see the magnitude
2952of this correction for each reflection in each phase.</p>
2953
2954<p class=MsoNormal>For the B2 phase we see</p>
2955
2956<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2957 id="Picture_x0020_14" o:spid="_x0000_i1067" type="#_x0000_t75" style='width:659.25pt;
2958 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2959 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
2960  o:title=""/>
2961</v:shape><![endif]--><![if !vml]><img border=0 width=879 height=350
2962src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
2963v:shapes="Picture_x0020_14"><![endif]></span></p>
2964
2965<p class=MsoNormal><span class=GramE>and</span> for the B19’ phase we see</p>
2966
2967<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2968 id="Picture_x0020_15" o:spid="_x0000_i1066" type="#_x0000_t75" style='width:659.25pt;
2969 height:273pt;visibility:visible;mso-wrap-style:square'>
2970 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png"
2971  o:title=""/>
2972</v:shape><![endif]--><![if !vml]><img border=0 width=879 height=364
2973src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png"
2974v:shapes="Picture_x0020_15"><![endif]></span></p>
2975
2976<p class=MsoNormal>The preferred orientation correction is <span class=SpellE>Prfo</span>;
2977notice a few entries in red. These are nonphysical correction values (the
2978correction can’t be negative) but by in large these are small. This next step
2979uses these corrections as input data for a texture refinement. To start select
2980the Texture tab for the B2 phase; you’ll see</p>
2981
2982<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2983 id="Picture_x0020_16" o:spid="_x0000_i1065" type="#_x0000_t75" style='width:456pt;
2984 height:217.5pt;visibility:visible;mso-wrap-style:square'>
2985 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
2986  o:title=""/>
2987</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290
2988src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
2989v:shapes="Picture_x0020_16"><![endif]></span></p>
2990
2991<p class=MsoNormal>Since this sample has wire texture, we’ll use the default
2992Texture model (cylindrical). Then set the Harmonic order to 12 (what we used
2993earlier) and check the Refine and Show <span class=SpellE>coeff</span> boxes.
2994The data window will be redrawn (and a blank plot will appear).</p>
2995
2996<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2997 id="Picture_x0020_17" o:spid="_x0000_i1064" type="#_x0000_t75" style='width:456pt;
2998 height:250.5pt;visibility:visible;mso-wrap-style:square'>
2999 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
3000  o:title=""/>
3001</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
3002src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
3003v:shapes="Picture_x0020_17"><![endif]></span></p>
3004
3005<p class=MsoNormal>Do Texture/Refine texture from the menu; the window will be
3006repainted and a <span class=SpellE>bullseye</span> pole figure will appear. </p>
3007
3008<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3009 id="Picture_x0020_20" o:spid="_x0000_i1063" type="#_x0000_t75" style='width:480pt;
3010 height:267.75pt;visibility:visible;mso-wrap-style:square'>
3011 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
3012  o:title=""/>
3013</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3014src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
3015v:shapes="Picture_x0020_20"><![endif]></span></p>
3016
3017<p class=MsoNormal>Change the Texture plot type to Inverse pole figure to get a
3018more useful plot</p>
3019
3020<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3021 id="Picture_x0020_19" o:spid="_x0000_i1062" type="#_x0000_t75" style='width:525pt;
3022 height:450pt;visibility:visible;mso-wrap-style:square'>
3023 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
3024  o:title=""/>
3025</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3026src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
3027v:shapes="Picture_x0020_19"><![endif]></span></p>
3028
3029<p class=MsoNormal>This is essentially the same as we obtained earlier in
3030Method <span class=GramE>A</span> (maybe not quite as strong here).</p>
3031
3032<p class=MsoNormal>Now select the Texture tab for the B19’ phase and do the
3033same; use Harmonic order 10 as we did earlier in Method A. After setting the
3034two flags and doing Texture/Refine texture we get</p>
3035
3036<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3037 id="Picture_x0020_21" o:spid="_x0000_i1061" type="#_x0000_t75" style='width:502.5pt;
3038 height:375pt;visibility:visible;mso-wrap-style:square'>
3039 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
3040  o:title=""/>
3041</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
3042src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
3043v:shapes="Picture_x0020_21"><![endif]></span></p>
3044
3045<p class=MsoNormal>And a <span class=SpellE>bullseye</span> pole figure; change
3046that to Inverse pole figure to see the texture</p>
3047
3048<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3049 id="Picture_x0020_22" o:spid="_x0000_i1060" type="#_x0000_t75" style='width:525pt;
3050 height:450pt;visibility:visible;mso-wrap-style:square'>
3051 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
3052  o:title=""/>
3053</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3054src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
3055v:shapes="Picture_x0020_22"><![endif]></span></p>
3056
3057<p class=MsoNormal>Again this is very similar to what we found in Method A but
3058again not quite as strong (max MRD ~13 instead of ~18).</p>
3059
3060<p class=MsoNormal>Now do a File/Save project from the main menu; this saves
3061the final texture results done in Step 2 (you also will need it for Method C).</p>
3062
3063<h2>Method C. Sequential refinement &amp; full texture refinement</h2>
3064
3065<h3>Introduction</h3>
3066
3067<p class=MsoNormal>This uses the same approach as Method B except that after
3068the sequential refinements are finished we then fix almost all the parameters
3069and then do a final texture refinement with all the data. Thus, this is a
3070replacement for Step 2 in Method B. To begin do <b style='mso-bidi-font-weight:
3071normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3072minor-latin;mso-hansi-theme-font:minor-latin'>File/Open project…</span></b> for
3073the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3074style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3075mso-hansi-theme-font:minor-latin'>NiTi-B.gpx</span></b></span> file created in
3076Method B and then do a <b style='mso-bidi-font-weight:normal'><span
3077style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3078mso-hansi-theme-font:minor-latin'>File/Save project as…</span></b> to save it
3079as <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3080style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3081mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight:
3082normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3083minor-latin;mso-hansi-theme-font:minor-latin'>-C</span></b>. This renames the
3084project and it should have one IMG, 10 PWDR entries and two phases of <span
3085class=SpellE>NiTi</span> (B2 and B19’).</p>
3086
3087<h3>Step 1. Clearing unwanted variables from sequential refinement</h3>
3088
3089<p class=MsoNormal>Here we want to clear refinement flags for all parameters
3090that need not be varied in a texture analysis refinement. The general rule is
3091to not refine any parameter unless we expect it to affect the peak intensities.
3092These are listed below:</p>
3093
3094<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3095style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
3096style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3097style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3098mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>:
3099as the background was fit during the sequential refinement we should fix it
3100here. Select any <b style='mso-bidi-font-weight:normal'><span style='font-family:
3101"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3102minor-latin'>PWDR</span></b> entry and choose the <b style='mso-bidi-font-weight:
3103normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3104minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b> subentry
3105for it. Clear the <b style='mso-bidi-font-weight:normal'><span
3106style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3107mso-hansi-theme-font:minor-latin'>Refine</span></b> flags and the do <b
3108style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3109mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Copy
3110flags</span></b> selecting all data sets. This will clear all background
3111refinement flags.</p>
3112
3113<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3114style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
3115style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3116style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3117mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3118phase: we do not want to refine either the <span class=SpellE>microstrain</span>,
3119D<sub>11</sub>, or preferred orientation coefficients. Select the <b
3120style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3121mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3122phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
3123"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3124minor-latin'>Data</span></b> tab. <span class=GramE>Clear</span> the <span
3125class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3126"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3127minor-latin'>microstrain</span></b></span>, <b style='mso-bidi-font-weight:
3128normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3129minor-latin;mso-hansi-theme-font:minor-latin'>D<sub>11</sub></span></b> and <b
3130style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3131mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
3132orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
3133style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3134mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
3135avoid a lot of nasty (but harmless) messages at the start of the refinement).
3136Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3137mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3138flags</span></b> selecting all data to clear all the flags and an <b
3139style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3140mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3141selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
3142normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3143minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
3144copy the zeroed out harmonic coefficients.</p>
3145
3146<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3147style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
3148style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3149style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3150mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>:
3151we do not want to refine either the <span class=SpellE>microstrain</span>, <span
3152class=SpellE>Dij</span>, or preferred orientation coefficients. Select the <b
3153style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3154mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3155phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
3156"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3157minor-latin'>Data</span></b> tab. Clear the <span class=SpellE><b
3158style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3159mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>microstrain</span></b></span>,
3160four <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3161style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3162mso-hansi-theme-font:minor-latin'>Dij</span></b></span> and <b
3163style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3164mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
3165orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
3166style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3167mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
3168avoid a lot of nasty (but harmless) messages at the start of the refinement).
3169Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3170mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3171flags</span></b> selecting all data to clear all the flags and an <b
3172style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3173mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3174selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
3175normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3176minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
3177copy the zeroed out harmonic coefficients.</p>
3178
3179<p class=MsoNormal style='margin-left:.25in'><o:p>&nbsp;</o:p></p>
3180
3181<p class=MsoNormal style='margin-left:.25in'>Notice that we have allowed
3182refinement of the <b style='mso-bidi-font-weight:normal'><span
3183style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3184mso-hansi-theme-font:minor-latin'>Phase fractions</span></b>; these may change
3185during the texture refinement. Now select the <b style='mso-bidi-font-weight:
3186normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3187minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b> tab for the <b
3188style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3189mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3190phase (it may still have values from the Method B).</p>
3191
3192<p class=MsoNormal style='margin-left:.25in'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3193 id="Picture_x0020_23" o:spid="_x0000_i1059" type="#_x0000_t75" style='width:480pt;
3194 height:267.75pt;visibility:visible;mso-wrap-style:square'>
3195 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
3196  o:title=""/>
3197</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3198src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
3199v:shapes="Picture_x0020_23"><![endif]></span></p>
3200
3201<p class=MsoNormal style='margin-left:.25in'>You can clear these by setting the
3202<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3203mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic
3204order</span></b> to zero and then back to <b style='mso-bidi-font-weight:normal'><span
3205style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3206mso-hansi-theme-font:minor-latin'>12</span></b>. Leave the <b style='mso-bidi-font-weight:
3207normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3208minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b> &amp; <b
3209style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3210mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b>
3211boxes checked.</p>
3212
3213<p class=MsoNormal style='margin-left:.25in'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3214 id="Picture_x0020_24" o:spid="_x0000_i1058" type="#_x0000_t75" style='width:480pt;
3215 height:267.75pt;visibility:visible;mso-wrap-style:square'>
3216 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
3217  o:title=""/>
3218</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3219src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
3220v:shapes="Picture_x0020_24"><![endif]></span></p>
3221
3222<p class=MsoNormal style='margin-left:.25in'>Then do the same for the <b
3223style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3224mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3225phase. Select the <b style='mso-bidi-font-weight:normal'><span
3226style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3227mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and its <b
3228style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3229mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
3230tab. <span class=GramE>Set</span> the <b style='mso-bidi-font-weight:normal'><span
3231style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3232mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero and then
3233back to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3234mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>.
3235Leave the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3236mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b>
3237and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3238mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b>
3239boxes checked. This completes the setup for the full texture refinement.</p>
3240
3241<h3>Step 2. Texture refinement</h3>
3242
3243<p class=MsoNormal>Do <b style='mso-bidi-font-weight:normal'><span
3244style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3245mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from the main
3246menu; you will see the warning message</p>
3247
3248<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3249 id="Picture_x0020_25" o:spid="_x0000_i1057" type="#_x0000_t75" style='width:363pt;
3250 height:120.75pt;visibility:visible;mso-wrap-style:square'>
3251 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
3252  o:title=""/>
3253</v:shape><![endif]--><![if !vml]><img border=0 width=484 height=161
3254src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
3255v:shapes="Picture_x0020_25"><![endif]></span></p>
3256
3257<p class=MsoNormal>In this case you do want to do a <span class=SpellE>nonsequential</span>
3258full refinement, so press the OK button. A quick look at the console will show
3259that there are 61 variables in this refinement. If yours shows more then you
3260didn’t clear all the flags in Step 1. The <b style='mso-bidi-font-weight:normal'><span
3261style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3262mso-hansi-theme-font:minor-latin'>Sequential results</span></b> entry is
3263deleted from the GSAS-II data tree. A progress bar will show giving the
3264residuals during the refinement. When finished, select the <b style='mso-bidi-font-weight:
3265normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3266minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> phase and its <b
3267style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3268mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
3269tab; if the Texture plot type is still <b style='mso-bidi-font-weight:normal'><span
3270style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3271mso-hansi-theme-font:minor-latin'>Inverse pole figure</span></b> (from Method
3272B) you should see</p>
3273
3274<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3275 id="Picture_x0020_26" o:spid="_x0000_i1056" type="#_x0000_t75" style='width:525pt;
3276 height:450pt;visibility:visible;mso-wrap-style:square'>
3277 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png"
3278  o:title=""/>
3279</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3280src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png"
3281v:shapes="Picture_x0020_26"><![endif]></span></p>
3282
3283<p class=MsoNormal><span class=GramE>which</span> is almost identical to that
3284from Method A. The coefficients are seen in</p>
3285
3286<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3287 id="Picture_x0020_27" o:spid="_x0000_i1055" type="#_x0000_t75" style='width:480pt;
3288 height:267.75pt;visibility:visible;mso-wrap-style:square'>
3289 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
3290  o:title=""/>
3291</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3292src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
3293v:shapes="Picture_x0020_27"><![endif]></span></p>
3294
3295<p class=MsoNormal>Now select the <b style='mso-bidi-font-weight:normal'><span
3296style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3297mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and its <b
3298style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3299mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
3300tab; the inverse pole figure is</p>
3301
3302<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3303 id="Picture_x0020_28" o:spid="_x0000_i1054" type="#_x0000_t75" style='width:525pt;
3304 height:450pt;visibility:visible;mso-wrap-style:square'>
3305 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image105.png"
3306  o:title=""/>
3307</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3308src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image105.png"
3309v:shapes="Picture_x0020_28"><![endif]></span></p>
3310
3311<p class=MsoNormal><span class=GramE>and</span> also almost identical to what
3312was obtained in Method A; the coefficients are seen in</p>
3313
3314<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3315 id="Picture_x0020_58" o:spid="_x0000_i1053" type="#_x0000_t75" style='width:502.5pt;
3316 height:375pt;visibility:visible;mso-wrap-style:square'>
3317 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"
3318  o:title=""/>
3319</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
3320src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"
3321v:shapes="Picture_x0020_58"><![endif]></span></p>
3322
3323<p class=MsoNormal>With this Method you can add parameters (atom coordinates
3324&amp; thermal motion parameters) that could not be refined in method B. It
3325should be clear from this tutorial that in more complex textures where the data
3326set may consist of slices obtained from a suite of 2D images collected as the
3327sample is rotated, Method C will give a relatively fast determination of the
3328texture without resorting to large matrix least-squares refinements.</p>
3329
3330</div>
3331
3332</body>
3333
3334</html>
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