source: Tutorials/2DTexture/Texture analysis of 2D data in GSAS-II.htm @ 1846

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Add texture tutorial

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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"/>
569  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
570  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
571  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
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"/>
591  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
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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785        mso-pagination:widow-orphan;
786        mso-outline-level:5;
787        font-size:12.0pt;
788        font-family:"Times New Roman",serif;
789        mso-fareast-font-family:"Times New Roman";
790        mso-fareast-theme-font:minor-fareast;
791        color:#4F4FFF;
792        font-weight:bold;}
793p.MsoTitle, li.MsoTitle, div.MsoTitle
794        {mso-style-noshow:yes;
795        mso-style-priority:10;
796        mso-style-unhide:no;
797        mso-style-qformat:yes;
798        mso-style-link:"Title Char";
799        mso-style-next:Normal;
800        margin-top:0in;
801        margin-right:0in;
802        margin-bottom:15.0pt;
803        margin-left:0in;
804        mso-add-space:auto;
805        mso-pagination:widow-orphan;
806        border:none;
807        mso-border-bottom-alt:solid #4F81BD 1.0pt;
808        mso-border-bottom-themecolor:accent1;
809        padding:0in;
810        mso-padding-alt:0in 0in 4.0pt 0in;
811        font-size:26.0pt;
812        font-family:"Cambria",serif;
813        mso-ascii-font-family:Cambria;
814        mso-ascii-theme-font:major-latin;
815        mso-fareast-font-family:"Times New Roman";
816        mso-fareast-theme-font:major-fareast;
817        mso-hansi-font-family:Cambria;
818        mso-hansi-theme-font:major-latin;
819        mso-bidi-font-family:"Times New Roman";
820        mso-bidi-theme-font:major-bidi;
821        color:#17365D;
822        mso-themecolor:text2;
823        mso-themeshade:191;
824        letter-spacing:.25pt;
825        mso-font-kerning:14.0pt;}
826p.MsoTitleCxSpFirst, li.MsoTitleCxSpFirst, div.MsoTitleCxSpFirst
827        {mso-style-noshow:yes;
828        mso-style-priority:10;
829        mso-style-unhide:no;
830        mso-style-qformat:yes;
831        mso-style-link:"Title Char";
832        mso-style-next:Normal;
833        mso-style-type:export-only;
834        margin:0in;
835        margin-bottom:.0001pt;
836        mso-add-space:auto;
837        mso-pagination:widow-orphan;
838        border:none;
839        mso-border-bottom-alt:solid #4F81BD 1.0pt;
840        mso-border-bottom-themecolor:accent1;
841        padding:0in;
842        mso-padding-alt:0in 0in 4.0pt 0in;
843        font-size:26.0pt;
844        font-family:"Cambria",serif;
845        mso-ascii-font-family:Cambria;
846        mso-ascii-theme-font:major-latin;
847        mso-fareast-font-family:"Times New Roman";
848        mso-fareast-theme-font:major-fareast;
849        mso-hansi-font-family:Cambria;
850        mso-hansi-theme-font:major-latin;
851        mso-bidi-font-family:"Times New Roman";
852        mso-bidi-theme-font:major-bidi;
853        color:#17365D;
854        mso-themecolor:text2;
855        mso-themeshade:191;
856        letter-spacing:.25pt;
857        mso-font-kerning:14.0pt;}
858p.MsoTitleCxSpMiddle, li.MsoTitleCxSpMiddle, div.MsoTitleCxSpMiddle
859        {mso-style-noshow:yes;
860        mso-style-priority:10;
861        mso-style-unhide:no;
862        mso-style-qformat:yes;
863        mso-style-link:"Title Char";
864        mso-style-next:Normal;
865        mso-style-type:export-only;
866        margin:0in;
867        margin-bottom:.0001pt;
868        mso-add-space:auto;
869        mso-pagination:widow-orphan;
870        border:none;
871        mso-border-bottom-alt:solid #4F81BD 1.0pt;
872        mso-border-bottom-themecolor:accent1;
873        padding:0in;
874        mso-padding-alt:0in 0in 4.0pt 0in;
875        font-size:26.0pt;
876        font-family:"Cambria",serif;
877        mso-ascii-font-family:Cambria;
878        mso-ascii-theme-font:major-latin;
879        mso-fareast-font-family:"Times New Roman";
880        mso-fareast-theme-font:major-fareast;
881        mso-hansi-font-family:Cambria;
882        mso-hansi-theme-font:major-latin;
883        mso-bidi-font-family:"Times New Roman";
884        mso-bidi-theme-font:major-bidi;
885        color:#17365D;
886        mso-themecolor:text2;
887        mso-themeshade:191;
888        letter-spacing:.25pt;
889        mso-font-kerning:14.0pt;}
890p.MsoTitleCxSpLast, li.MsoTitleCxSpLast, div.MsoTitleCxSpLast
891        {mso-style-noshow:yes;
892        mso-style-priority:10;
893        mso-style-unhide:no;
894        mso-style-qformat:yes;
895        mso-style-link:"Title Char";
896        mso-style-next:Normal;
897        mso-style-type:export-only;
898        margin-top:0in;
899        margin-right:0in;
900        margin-bottom:15.0pt;
901        margin-left:0in;
902        mso-add-space:auto;
903        mso-pagination:widow-orphan;
904        border:none;
905        mso-border-bottom-alt:solid #4F81BD 1.0pt;
906        mso-border-bottom-themecolor:accent1;
907        padding:0in;
908        mso-padding-alt:0in 0in 4.0pt 0in;
909        font-size:26.0pt;
910        font-family:"Cambria",serif;
911        mso-ascii-font-family:Cambria;
912        mso-ascii-theme-font:major-latin;
913        mso-fareast-font-family:"Times New Roman";
914        mso-fareast-theme-font:major-fareast;
915        mso-hansi-font-family:Cambria;
916        mso-hansi-theme-font:major-latin;
917        mso-bidi-font-family:"Times New Roman";
918        mso-bidi-theme-font:major-bidi;
919        color:#17365D;
920        mso-themecolor:text2;
921        mso-themeshade:191;
922        letter-spacing:.25pt;
923        mso-font-kerning:14.0pt;}
924a:link, span.MsoHyperlink
925        {mso-style-noshow:yes;
926        mso-style-priority:99;
927        color:blue;
928        text-decoration:underline;
929        text-underline:single;}
930a:visited, span.MsoHyperlinkFollowed
931        {mso-style-noshow:yes;
932        mso-style-priority:99;
933        color:purple;
934        text-decoration:underline;
935        text-underline:single;}
936p.MsoDocumentMap, li.MsoDocumentMap, div.MsoDocumentMap
937        {mso-style-noshow:yes;
938        mso-style-priority:99;
939        mso-style-link:"Document Map Char";
940        margin:0in;
941        margin-bottom:.0001pt;
942        mso-pagination:widow-orphan;
943        font-size:8.0pt;
944        font-family:"Tahoma",sans-serif;
945        mso-fareast-font-family:"Times New Roman";
946        mso-fareast-theme-font:minor-fareast;}
947p
948        {mso-style-noshow:yes;
949        mso-style-priority:99;
950        mso-margin-top-alt:auto;
951        margin-right:0in;
952        mso-margin-bottom-alt:auto;
953        margin-left:0in;
954        mso-pagination:widow-orphan;
955        font-size:12.0pt;
956        font-family:"Times New Roman",serif;
957        mso-fareast-font-family:"Times New Roman";
958        mso-fareast-theme-font:minor-fareast;}
959pre
960        {mso-style-noshow:yes;
961        mso-style-priority:99;
962        mso-style-link:"HTML Preformatted Char";
963        margin:0in;
964        margin-bottom:.0001pt;
965        mso-pagination:widow-orphan;
966        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;
967        font-size:10.0pt;
968        font-family:"Courier New";
969        mso-fareast-font-family:"Times New Roman";}
970p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
971        {mso-style-noshow:yes;
972        mso-style-priority:99;
973        mso-style-link:"Balloon Text Char";
974        margin:0in;
975        margin-bottom:.0001pt;
976        mso-pagination:widow-orphan;
977        font-size:8.0pt;
978        font-family:"Tahoma",sans-serif;
979        mso-fareast-font-family:"Times New Roman";
980        mso-fareast-theme-font:minor-fareast;}
981span.MsoPlaceholderText
982        {mso-style-noshow:yes;
983        mso-style-priority:99;
984        mso-style-unhide:no;
985        color:gray;}
986p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing
987        {mso-style-noshow:yes;
988        mso-style-priority:1;
989        mso-style-unhide:no;
990        mso-style-qformat:yes;
991        mso-style-parent:"";
992        margin:0in;
993        margin-bottom:.0001pt;
994        mso-pagination:widow-orphan;
995        font-size:12.0pt;
996        font-family:"Times New Roman",serif;
997        mso-fareast-font-family:"Times New Roman";
998        mso-fareast-theme-font:minor-fareast;}
999p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
1000        {mso-style-noshow:yes;
1001        mso-style-priority:34;
1002        mso-style-unhide:no;
1003        mso-style-qformat:yes;
1004        margin-top:0in;
1005        margin-right:0in;
1006        margin-bottom:0in;
1007        margin-left:.5in;
1008        margin-bottom:.0001pt;
1009        mso-add-space:auto;
1010        mso-pagination:widow-orphan;
1011        font-size:12.0pt;
1012        font-family:"Times New Roman",serif;
1013        mso-fareast-font-family:"Times New Roman";
1014        mso-fareast-theme-font:minor-fareast;}
1015p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
1016        {mso-style-noshow:yes;
1017        mso-style-priority:34;
1018        mso-style-unhide:no;
1019        mso-style-qformat:yes;
1020        mso-style-type:export-only;
1021        margin-top:0in;
1022        margin-right:0in;
1023        margin-bottom:0in;
1024        margin-left:.5in;
1025        margin-bottom:.0001pt;
1026        mso-add-space:auto;
1027        mso-pagination:widow-orphan;
1028        font-size:12.0pt;
1029        font-family:"Times New Roman",serif;
1030        mso-fareast-font-family:"Times New Roman";
1031        mso-fareast-theme-font:minor-fareast;}
1032p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
1033        {mso-style-noshow:yes;
1034        mso-style-priority:34;
1035        mso-style-unhide:no;
1036        mso-style-qformat:yes;
1037        mso-style-type:export-only;
1038        margin-top:0in;
1039        margin-right:0in;
1040        margin-bottom:0in;
1041        margin-left:.5in;
1042        margin-bottom:.0001pt;
1043        mso-add-space:auto;
1044        mso-pagination:widow-orphan;
1045        font-size:12.0pt;
1046        font-family:"Times New Roman",serif;
1047        mso-fareast-font-family:"Times New Roman";
1048        mso-fareast-theme-font:minor-fareast;}
1049p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
1050        {mso-style-noshow:yes;
1051        mso-style-priority:34;
1052        mso-style-unhide:no;
1053        mso-style-qformat:yes;
1054        mso-style-type:export-only;
1055        margin-top:0in;
1056        margin-right:0in;
1057        margin-bottom:0in;
1058        margin-left:.5in;
1059        margin-bottom:.0001pt;
1060        mso-add-space:auto;
1061        mso-pagination:widow-orphan;
1062        font-size:12.0pt;
1063        font-family:"Times New Roman",serif;
1064        mso-fareast-font-family:"Times New Roman";
1065        mso-fareast-theme-font:minor-fareast;}
1066span.MsoIntenseReference
1067        {mso-style-priority:32;
1068        mso-style-unhide:no;
1069        mso-style-qformat:yes;
1070        font-variant:small-caps;
1071        color:#C0504D;
1072        mso-themecolor:accent2;
1073        letter-spacing:.25pt;
1074        font-weight:bold;
1075        text-decoration:underline;
1076        text-underline:single;}
1077span.Heading1Char
1078        {mso-style-name:"Heading 1 Char";
1079        mso-style-priority:9;
1080        mso-style-unhide:no;
1081        mso-style-locked:yes;
1082        mso-style-link:"Heading 1";
1083        mso-ansi-font-size:24.0pt;
1084        mso-bidi-font-size:24.0pt;
1085        font-family:"Times New Roman",serif;
1086        mso-ascii-font-family:"Times New Roman";
1087        mso-fareast-font-family:"Times New Roman";
1088        mso-fareast-theme-font:minor-fareast;
1089        mso-hansi-font-family:"Times New Roman";
1090        mso-bidi-font-family:"Times New Roman";
1091        mso-font-kerning:18.0pt;
1092        font-weight:bold;}
1093span.Heading2Char
1094        {mso-style-name:"Heading 2 Char";
1095        mso-style-priority:9;
1096        mso-style-unhide:no;
1097        mso-style-locked:yes;
1098        mso-style-link:"Heading 2";
1099        mso-ansi-font-size:18.0pt;
1100        mso-bidi-font-size:18.0pt;
1101        font-family:"Times New Roman",serif;
1102        mso-ascii-font-family:"Times New Roman";
1103        mso-fareast-font-family:"Times New Roman";
1104        mso-fareast-theme-font:minor-fareast;
1105        mso-hansi-font-family:"Times New Roman";
1106        mso-bidi-font-family:"Times New Roman";
1107        font-weight:bold;}
1108span.Heading3Char
1109        {mso-style-name:"Heading 3 Char";
1110        mso-style-priority:9;
1111        mso-style-unhide:no;
1112        mso-style-locked:yes;
1113        mso-style-link:"Heading 3";
1114        mso-ansi-font-size:13.5pt;
1115        mso-bidi-font-size:13.5pt;
1116        font-family:"Times New Roman",serif;
1117        mso-ascii-font-family:"Times New Roman";
1118        mso-fareast-font-family:"Times New Roman";
1119        mso-fareast-theme-font:minor-fareast;
1120        mso-hansi-font-family:"Times New Roman";
1121        mso-bidi-font-family:"Times New Roman";
1122        font-weight:bold;}
1123span.Heading4Char
1124        {mso-style-name:"Heading 4 Char";
1125        mso-style-noshow:yes;
1126        mso-style-priority:9;
1127        mso-style-unhide:no;
1128        mso-style-locked:yes;
1129        mso-style-link:"Heading 4";
1130        mso-ansi-font-size:13.0pt;
1131        mso-bidi-font-size:13.0pt;
1132        font-family:"Cambria",serif;
1133        mso-ascii-font-family:Cambria;
1134        mso-ascii-theme-font:major-latin;
1135        mso-fareast-font-family:"Times New Roman";
1136        mso-fareast-theme-font:major-fareast;
1137        mso-hansi-font-family:Cambria;
1138        mso-hansi-theme-font:major-latin;
1139        mso-bidi-font-family:"Times New Roman";
1140        mso-bidi-theme-font:major-bidi;
1141        color:#4F81BD;
1142        mso-themecolor:accent1;
1143        font-weight:bold;
1144        font-style:italic;}
1145span.Heading5Char
1146        {mso-style-name:"Heading 5 Char";
1147        mso-style-noshow:yes;
1148        mso-style-priority:9;
1149        mso-style-unhide:no;
1150        mso-style-locked:yes;
1151        mso-style-link:"Heading 5";
1152        mso-ansi-font-size:12.0pt;
1153        mso-bidi-font-size:12.0pt;
1154        font-family:"Times New Roman",serif;
1155        mso-ascii-font-family:"Times New Roman";
1156        mso-fareast-font-family:"Times New Roman";
1157        mso-fareast-theme-font:minor-fareast;
1158        mso-hansi-font-family:"Times New Roman";
1159        mso-bidi-font-family:"Times New Roman";
1160        color:#4F4FFF;
1161        font-weight:bold;}
1162span.HTMLPreformattedChar
1163        {mso-style-name:"HTML Preformatted Char";
1164        mso-style-noshow:yes;
1165        mso-style-priority:99;
1166        mso-style-unhide:no;
1167        mso-style-locked:yes;
1168        mso-style-link:"HTML Preformatted";
1169        font-family:"Courier New";
1170        mso-ascii-font-family:"Courier New";
1171        mso-fareast-font-family:"Times New Roman";
1172        mso-hansi-font-family:"Courier New";
1173        mso-bidi-font-family:"Courier New";}
1174span.TitleChar
1175        {mso-style-name:"Title Char";
1176        mso-style-priority:10;
1177        mso-style-unhide:no;
1178        mso-style-locked:yes;
1179        mso-style-link:Title;
1180        mso-ansi-font-size:26.0pt;
1181        mso-bidi-font-size:26.0pt;
1182        font-family:"Cambria",serif;
1183        mso-ascii-font-family:Cambria;
1184        mso-ascii-theme-font:major-latin;
1185        mso-fareast-font-family:"Times New Roman";
1186        mso-fareast-theme-font:major-fareast;
1187        mso-hansi-font-family:Cambria;
1188        mso-hansi-theme-font:major-latin;
1189        mso-bidi-font-family:"Times New Roman";
1190        mso-bidi-theme-font:major-bidi;
1191        color:#17365D;
1192        mso-themecolor:text2;
1193        mso-themeshade:191;
1194        letter-spacing:.25pt;
1195        mso-font-kerning:14.0pt;}
1196span.DocumentMapChar
1197        {mso-style-name:"Document Map Char";
1198        mso-style-noshow:yes;
1199        mso-style-priority:99;
1200        mso-style-unhide:no;
1201        mso-style-locked:yes;
1202        mso-style-link:"Document Map";
1203        mso-ansi-font-size:8.0pt;
1204        mso-bidi-font-size:8.0pt;
1205        font-family:"Tahoma",sans-serif;
1206        mso-ascii-font-family:Tahoma;
1207        mso-fareast-font-family:"Times New Roman";
1208        mso-fareast-theme-font:minor-fareast;
1209        mso-hansi-font-family:Tahoma;
1210        mso-bidi-font-family:Tahoma;}
1211span.BalloonTextChar
1212        {mso-style-name:"Balloon Text Char";
1213        mso-style-noshow:yes;
1214        mso-style-priority:99;
1215        mso-style-unhide:no;
1216        mso-style-locked:yes;
1217        mso-style-link:"Balloon Text";
1218        mso-ansi-font-size:8.0pt;
1219        mso-bidi-font-size:8.0pt;
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1401</head>
1402
1403<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1404
1405<div class=WordSection1>
1406
1407<h1>Texture analysis of 2D data in GSAS-II</h1>
1408
1409<h2>Introduction</h2>
1410
1411<p class=MsoNormal>Texture analysis using GSAS-II employs spherical harmonics
1412modeling, as described by Bunge, &quot;Texture Analysis in Materials
1413Science&quot; (1982), and implemented by Von Dreele, J. Appl. <span
1414class=SpellE>Cryst</span>., <b style='mso-bidi-font-weight:normal'>30</b>, 517-525
1415(1997) in GSAS. The even part of the orientation distribution function (ODF)
1416via the general axis equation</p>
1417
1418<p class=gsastext><span style='position:relative;top:14.0pt;mso-text-raise:
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1450
1451<p class=gsastext><span class=GramE>is</span> used to give the intensity
1452corrections due to texture. The two harmonic terms, <span style='position:relative;
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1454 type="#_x0000_t75" style='width:33.75pt;height:20.25pt' o:ole="">
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1457</v:shape><![endif]--><![if !vml]><img width=45 height=27
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1463</xml><![endif]--><span class=GramE>and </span><span style='position:relative;
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1465 type="#_x0000_t75" style='width:32.25pt;height:20.25pt' o:ole="">
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1467  o:title=""/>
1468</v:shape><![endif]--><![if !vml]><img width=43 height=27
1469src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"
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1474</xml><![endif]-->, take on values according to the crystal and sample
1475symmetries, respectively, and thus the two inner summations are over only the
1476resulting unique, nonzero harmonic terms. These unique terms are automatically
1477selected by <span style='mso-bidi-font-weight:bold'>GSAS-II</span> according to
1478the space group symmetry and the user chosen sample symmetry. The available
1479sample symmetries are cylindrical symmetry, 2/m, mmm and no symmetry. The
1480choice of sample symmetry profoundly affects the selection of harmonic
1481coefficients. For example, in the case of cylindrical sample symmetry (fiber
1482texture) only <span style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
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1493</xml><![endif]--><span style='mso-spacerun:yes'> </span>terms are nonzero so
1494the rest are excluded from the summations and the <span class=GramE>set</span>
1495of <span style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
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1505</xml><![endif]-->coefficients is sufficient to describe the effect on the
1506diffraction patterns due to texture. The crystal harmonic factor, <span
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1513src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"
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1518</xml><![endif]-->, is defined for each reflection, h, <i>via</i> polar and
1519azimuthal coordinates (<span style='font-family:Symbol'>f</span>, <span
1520style='font-family:Symbol'>b</span>) of a unit vector coincident with h
1521relative to the reciprocal lattice. For most crystal symmetries, <span
1522style='font-family:Symbol'>f</span> is the angle between h and the n-<span
1523class=SpellE>th</span> order major rotation axis of the space group (usually
1524the c-axis) and <span style='font-family:Symbol'>b</span> is the angle between
1525the projections of h and any secondary axis (usually the a-axis) onto the
1526normal plane.<span style='mso-spacerun:yes'>  </span>In a similar way the
1527sample harmonic factor, <span style='position:relative;top:5.0pt;mso-text-raise:
1528-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1031" type="#_x0000_t75"
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1533src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"
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1535 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1031"
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1538</xml><![endif]-->, is defined according to polar and azimuthal coordinates (<span
1539style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
1540of a unit vector coincident with the diffraction vector relative to a
1541coordinate system attached to the external form of the sample. For example, in
1542the case of a rolled steel plate having mmm symmetry, the polar angle, <span
1543style='font-family:Symbol'>y</span>, is frequently measured from the normal
1544direction (ND) and <span style='font-family:Symbol'>g</span> is then measured
1545from the rolling direction (RD) in the TD (transverse direction) - RD
1546plane.<span style='mso-spacerun:yes'>  </span>Thus, the general axis equation
1547becomes</p>
1548
1549<p class=gsastext><span style='position:relative;top:14.0pt;mso-text-raise:
1550-14.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75"
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1555src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image014.png"
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1561<![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'>
1562<![endif]></p>
1563
1564<p class=MsoNormal>In a diffraction experiment the crystal reflection
1565coordinates (<span style='font-family:Symbol'>f</span>, <span style='font-family:
1566Symbol'>b</span>) are determined by the choice of reflection index (<span
1567class=SpellE>hkl</span>) while the sample coordinates (<span style='font-family:
1568Symbol'>y</span>, <span style='font-family:Symbol'>g</span>) are determined by
1569the sample orientation on the diffractometer.</p>
1570
1571<p class=gsastext>To define the sample coordinates (<span style='font-family:
1572Symbol'>y</span>, <span style='font-family:Symbol'>g</span>), we have defined
1573an instrument coordinate system (I, J, K) such that K is normal to the
1574diffraction plane and J is coincident with the direction of the incident
1575radiation beam toward the source. We further define a standard set of
1576right-handed goniometer <span class=SpellE>eulerian</span> angles (<span
1577style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>,
1578<span style='font-family:Symbol'>F</span>) so that <span style='font-family:
1579Symbol'>W</span> and <span style='font-family:Symbol'>F</span> are rotations
1580about K and <span style='font-family:Symbol'>C</span> is a rotation about J
1581when <span style='font-family:Symbol'>W</span> <span style='font-family:Symbol'><span
1582style='mso-spacerun:yes'> </span></span>= 0.<span style='mso-spacerun:yes'> 
1583</span>Finally, as the sample may be mounted so that the sample coordinate
1584system (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>)
1585does not coincide with the instrument coordinate system (I, J, K), we define
1586three <span class=SpellE>eulerian</span> sample rotation offset angles (<span
1587style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
1588<span style='font-family:Symbol'>F</span><sub>s</sub>) that describe the
1589rotation from (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>)
1590to (I, J, K).<span style='mso-spacerun:yes'>  </span>The sample rotation angles
1591are defined so that with the goniometer angles at zero <span style='font-family:
1592Symbol'>W</span><sub>s</sub> and <span style='font-family:Symbol'>F</span><sub>s</sub>
1593are rotations about I and <span style='font-family:Symbol'>C</span><sub>s</sub>
1594is a rotation about J.<span style='mso-spacerun:yes'>  </span>The zeros of
1595these three sample rotation angles can be refined as part of the Rietveld
1596analysis to accommodate any angular offset in sample mounting. After including
1597the diffraction angle, <span style='font-family:Symbol'>Q</span>, and a
1598detector azimuthal angle, A, the full rotation matrix, <b style='mso-bidi-font-weight:
1599normal'>M</b>, is </p>
1600
1601<p class=gsastext><b style='mso-bidi-font-weight:normal'>M = -</b><b
1602style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>Q</span>A</b><b
1603style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>W<span
1604class=GramE>C<span style='font-family:"Times New Roman",serif'>(</span></span>F</span>+</b><b
1605style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span><sub>s</sub>)</b><b
1606style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>C</span><span
1607class=SpellE><sub>s</sub><span style='font-family:Symbol'>W</span><sub>s</sub></span><o:p></o:p></b></p>
1608
1609<p class=gsastext>By transformation of unit Cartesian vectors (100, 010 and
1610001) with this rotation matrix, the sample orientation coordinates (<span
1611style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
1612are given by</p>
1613
1614<p class=gsastext><span class=GramE><i>cos</i>(</span><span style='font-family:
1615Symbol'>y</span>) = <b style='mso-bidi-font-weight:normal'><span
1616style='position:relative;top:25.0pt;mso-text-raise:-25.0pt'><!--[if gte vml 1]><v:shape
1617 id="_x0000_i1033" type="#_x0000_t75" style='width:33.75pt;height:56.25pt'
1618 o:ole="">
1619 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image015.wmz"
1620  o:title=""/>
1621</v:shape><![endif]--><![if !vml]><img width=45 height=75
1622src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.png"
1623v:shapes="_x0000_i1033"><![endif]></span><!--[if gte mso 9]><xml>
1624 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1033"
1625  DrawAspect="Content" ObjectID="_1493033360">
1626 </o:OLEObject>
1627</xml><![endif]--></b><span style='mso-spacerun:yes'>  </span>and<span
1628style='mso-spacerun:yes'>   </span><i>tan</i>(<span style='font-family:Symbol'>g</span>)
1629= <span style='position:relative;top:25.0pt;mso-text-raise:-25.0pt'><!--[if gte vml 1]><v:shape
1630 id="_x0000_i1034" type="#_x0000_t75" style='width:81pt;height:56.25pt' o:ole="">
1631 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image017.wmz"
1632  o:title=""/>
1633</v:shape><![endif]--><![if !vml]><img width=108 height=75
1634src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.png"
1635v:shapes="_x0000_i1034"><![endif]></span><!--[if gte mso 9]><xml>
1636 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1034"
1637  DrawAspect="Content" ObjectID="_1493033361">
1638 </o:OLEObject>
1639</xml><![endif]--></p>
1640
1641<p class=gsastext>The harmonic terms, <span style='position:relative;
1642top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1035"
1643 type="#_x0000_t75" style='width:44.25pt;height:20.25pt' o:ole="">
1644 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.wmz"
1645  o:title=""/>
1646</v:shape><![endif]--><![if !vml]><img width=59 height=27
1647src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"
1648v:shapes="_x0000_i1035"><![endif]></span><!--[if gte mso 9]><xml>
1649 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1035"
1650  DrawAspect="Content" ObjectID="_1493033362">
1651 </o:OLEObject>
1652</xml><![endif]--><span class=GramE>and </span><span style='position:relative;
1653top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1036"
1654 type="#_x0000_t75" style='width:44.25pt;height:20.25pt' o:ole="">
1655 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.wmz"
1656  o:title=""/>
1657</v:shape><![endif]--><![if !vml]><img width=59 height=27
1658src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.png"
1659v:shapes="_x0000_i1036"><![endif]></span><!--[if gte mso 9]><xml>
1660 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1036"
1661  DrawAspect="Content" ObjectID="_1493033363">
1662 </o:OLEObject>
1663</xml><![endif]-->, are developed from</p>
1664
1665<p class=gsastext><span style='position:relative;top:10.0pt;mso-text-raise:
1666-10.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1037" type="#_x0000_t75"
1667 style='width:144.75pt;height:24.75pt' o:ole="">
1668 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.wmz"
1669  o:title=""/>
1670</v:shape><![endif]--><![if !vml]><img width=193 height=33
1671src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"
1672v:shapes="_x0000_i1037"><![endif]></span><!--[if gte mso 9]><xml>
1673 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1037"
1674  DrawAspect="Content" ObjectID="_1493033364">
1675 </o:OLEObject>
1676</xml><![endif]--></p>
1677
1678<p class=gsastext><span class=GramE>where</span> the normalized associated
1679Legendre functions, <span style='position:relative;top:5.0pt;mso-text-raise:
1680-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1038" type="#_x0000_t75"
1681 style='width:35.25pt;height:20.25pt' o:ole="">
1682 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image025.wmz"
1683  o:title=""/>
1684</v:shape><![endif]--><![if !vml]><img width=47 height=27
1685src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image026.png"
1686v:shapes="_x0000_i1038"><![endif]></span><!--[if gte mso 9]><xml>
1687 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1038"
1688  DrawAspect="Content" ObjectID="_1493033365">
1689 </o:OLEObject>
1690</xml><![endif]-->, are defined via a Fourier expansion as</p>
1691
1692<p class=gsastext><span style='position:relative;top:16.0pt;mso-text-raise:
1693-16.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1039" type="#_x0000_t75"
1694 style='width:135.75pt;height:38.25pt' o:ole="">
1695 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image027.wmz"
1696  o:title=""/>
1697</v:shape><![endif]--><![if !vml]><img width=181 height=51
1698src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image028.png"
1699v:shapes="_x0000_i1039"><![endif]></span><!--[if gte mso 9]><xml>
1700 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1039"
1701  DrawAspect="Content" ObjectID="_1493033366">
1702 </o:OLEObject>
1703</xml><![endif]--></p>
1704
1705<p class=gsastext><span class=GramE>for</span> m even and</p>
1706
1707<p class=gsastext><span style='position:relative;top:16.0pt;mso-text-raise:
1708-16.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1040" type="#_x0000_t75"
1709 style='width:134.25pt;height:38.25pt' o:ole="">
1710 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image029.wmz"
1711  o:title=""/>
1712</v:shape><![endif]--><![if !vml]><img width=179 height=51
1713src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image030.png"
1714v:shapes="_x0000_i1040"><![endif]></span><!--[if gte mso 9]><xml>
1715 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1040"
1716  DrawAspect="Content" ObjectID="_1493033367">
1717 </o:OLEObject>
1718</xml><![endif]--></p>
1719
1720<p class=gsastext><span class=GramE>for</span> m odd.<span
1721style='mso-spacerun:yes'>  </span>Each sum is only over either the even or odd
1722values of s, respectively, because of the properties of the Fourier
1723coefficients<span class=GramE>, </span><span style='position:relative;
1724top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1041"
1725 type="#_x0000_t75" style='width:23.25pt;height:20.25pt' o:ole="">
1726 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image031.wmz"
1727  o:title=""/>
1728</v:shape><![endif]--><![if !vml]><img width=31 height=27
1729src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image032.png"
1730v:shapes="_x0000_i1041"><![endif]></span><!--[if gte mso 9]><xml>
1731 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1041"
1732  DrawAspect="Content" ObjectID="_1493033368">
1733 </o:OLEObject>
1734</xml><![endif]-->.<span style='mso-spacerun:yes'>  </span>These Fourier
1735coefficients are determined so that the definition</p>
1736
1737<p class=gsastext><span style='position:relative;top:16.0pt;mso-text-raise:
1738-16.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1042" type="#_x0000_t75"
1739 style='width:356.25pt;height:38.25pt' o:ole="">
1740 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.wmz"
1741  o:title=""/>
1742</v:shape><![endif]--><![if !vml]><img width=475 height=51
1743src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image034.png"
1744v:shapes="_x0000_i1042"><![endif]></span><!--[if gte mso 9]><xml>
1745 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1042"
1746  DrawAspect="Content" ObjectID="_1493033369">
1747 </o:OLEObject>
1748</xml><![endif]--></p>
1749
1750<p class=gsastext><span class=GramE>is</span> satisfied.<span
1751style='mso-spacerun:yes'>  </span>Terms of the form <span style='position:relative;
1752top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1043"
1753 type="#_x0000_t75" style='width:92.25pt;height:20.25pt' o:ole="">
1754 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image035.wmz"
1755  o:title=""/>
1756</v:shape><![endif]--><![if !vml]><img width=123 height=27
1757src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image036.png"
1758v:shapes="_x0000_i1043"><![endif]></span><!--[if gte mso 9]><xml>
1759 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1043"
1760  DrawAspect="Content" ObjectID="_1493033370">
1761 </o:OLEObject>
1762</xml><![endif]--><span style='mso-spacerun:yes'> </span>and <span
1763style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
1764 id="_x0000_i1044" type="#_x0000_t75" style='width:90pt;height:20.25pt' o:ole="">
1765 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image037.wmz"
1766  o:title=""/>
1767</v:shape><![endif]--><![if !vml]><img width=120 height=27
1768src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image038.png"
1769v:shapes="_x0000_i1044"><![endif]></span><!--[if gte mso 9]><xml>
1770 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1044"
1771  DrawAspect="Content" ObjectID="_1493033371">
1772 </o:OLEObject>
1773</xml><![endif]-->are combined depending on the symmetry and the value of m
1774along with appropriate normalization coefficients to give the harmonic terms <span
1775style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
1776 id="_x0000_i1045" type="#_x0000_t75" style='width:44.25pt;height:20.25pt'
1777 o:ole="">
1778 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.wmz"
1779  o:title=""/>
1780</v:shape><![endif]--><![if !vml]><img width=59 height=27
1781src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"
1782v:shapes="_x0000_i1045"><![endif]></span><!--[if gte mso 9]><xml>
1783 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1045"
1784  DrawAspect="Content" ObjectID="_1493033372">
1785 </o:OLEObject>
1786</xml><![endif]--><span class=GramE>and </span><span style='position:relative;
1787top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1046"
1788 type="#_x0000_t75" style='width:44.25pt;height:20.25pt' o:ole="">
1789 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.wmz"
1790  o:title=""/>
1791</v:shape><![endif]--><![if !vml]><img width=59 height=27
1792src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.png"
1793v:shapes="_x0000_i1046"><![endif]></span><!--[if gte mso 9]><xml>
1794 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1046"
1795  DrawAspect="Content" ObjectID="_1493033373">
1796 </o:OLEObject>
1797</xml><![endif]-->.<span style='mso-spacerun:yes'>  </span>For cubic crystal
1798symmetry, the term <span style='position:relative;top:5.0pt;mso-text-raise:
1799-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1047" type="#_x0000_t75"
1800 style='width:44.25pt;height:20.25pt' o:ole="">
1801 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.wmz"
1802  o:title=""/>
1803</v:shape><![endif]--><![if !vml]><img width=59 height=27
1804src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"
1805v:shapes="_x0000_i1047"><![endif]></span><!--[if gte mso 9]><xml>
1806 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1047"
1807  DrawAspect="Content" ObjectID="_1493033374">
1808 </o:OLEObject>
1809</xml><![endif]-->is obtained directly from the Fourier expansion</p>
1810
1811<p class=gsastext><span style='position:relative;top:16.0pt;mso-text-raise:
1812-16.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1048" type="#_x0000_t75"
1813 style='width:167.25pt;height:38.25pt' o:ole="">
1814 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image042.wmz"
1815  o:title=""/>
1816</v:shape><![endif]--><![if !vml]><img width=223 height=51
1817src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image043.png"
1818v:shapes="_x0000_i1048"><![endif]></span><!--[if gte mso 9]><xml>
1819 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1048"
1820  DrawAspect="Content" ObjectID="_1493033375">
1821 </o:OLEObject>
1822</xml><![endif]--></p>
1823
1824<p class=gsastext><span class=GramE>using</span> the coefficients, <span
1825style='position:relative;top:5.0pt;mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape
1826 id="_x0000_i1049" type="#_x0000_t75" style='width:24pt;height:20.25pt' o:ole="">
1827 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image044.wmz"
1828  o:title=""/>
1829</v:shape><![endif]--><![if !vml]><img width=32 height=27
1830src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image045.png"
1831v:shapes="_x0000_i1049"><![endif]></span><!--[if gte mso 9]><xml>
1832 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1049"
1833  DrawAspect="Content" ObjectID="_1493033376">
1834 </o:OLEObject>
1835</xml><![endif]-->, as tabulated by Bunge (1982). </p>
1836
1837<p class=gsastext>The Rietveld refinement of texture then proceeds by
1838constructing derivatives of the profile intensities with respect to the allowed
1839harmonic coefficients, <span style='position:relative;top:5.0pt;mso-text-raise:
1840-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1050" type="#_x0000_t75"
1841 style='width:24pt;height:20.25pt' o:ole="">
1842 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image046.wmz"
1843  o:title=""/>
1844</v:shape><![endif]--><![if !vml]><img width=32 height=27
1845src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"
1846v:shapes="_x0000_i1050"><![endif]></span><!--[if gte mso 9]><xml>
1847 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1050"
1848  DrawAspect="Content" ObjectID="_1493033377">
1849 </o:OLEObject>
1850</xml><![endif]-->, and the three sample orientation angles, <span
1851style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
1852<span style='font-family:Symbol'>F</span><sub>s</sub>, all of which can be
1853adjustable parameters of the refinement. Once the refinement is complete, pole
1854figures for any reflection may be constructed by use of the general axis
1855equation, the refined values for <span style='position:relative;top:5.0pt;
1856mso-text-raise:-5.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1051" type="#_x0000_t75"
1857 style='width:24pt;height:20.25pt' o:ole="">
1858 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image046.wmz"
1859  o:title=""/>
1860</v:shape><![endif]--><![if !vml]><img width=32 height=27
1861src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"
1862v:shapes="_x0000_i1051"><![endif]></span><!--[if gte mso 9]><xml>
1863 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1051"
1864  DrawAspect="Content" ObjectID="_1493033378">
1865 </o:OLEObject>
1866</xml><![endif]-->and the sample orientation angles <span style='font-family:
1867Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
1868<span class=GramE><span style='font-family:Symbol'>F</span></span><sub>s</sub>.
1869</p>
1870
1871<p class=gsastext>The magnitude of the texture is evaluated from the texture
1872index by</p>
1873
1874<p class=gsastext><span style='position:relative;top:16.0pt;mso-text-raise:
1875-16.0pt'><!--[if gte vml 1]><v:shape id="_x0000_i1052" type="#_x0000_t75"
1876 style='width:167.25pt;height:39pt' o:ole="">
1877 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.wmz"
1878  o:title=""/>
1879</v:shape><![endif]--><![if !vml]><img width=223 height=52
1880src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.png"
1881v:shapes="_x0000_i1052"><![endif]></span><!--[if gte mso 9]><xml>
1882 <o:OLEObject Type="Embed" ProgID="Equation.3" ShapeID="_x0000_i1052"
1883  DrawAspect="Content" ObjectID="_1493033379">
1884 </o:OLEObject>
1885</xml><![endif]--></p>
1886
1887<p class=gsastext>If the texture is random then J = 1, otherwise J &gt; 1; for
1888a single crystal J = <span style='font-family:Symbol'>¥.</span> </p>
1889
1890<p class=gsastext>In GSAS-II the texture is defined in two ways to accommodate
1891the two possible uses of this correction. In one a suite of spherical harmonics
1892coefficients is defined for the texture of a phase in the sample; this can have
1893any of the possible sample symmetries and is the usual result desired for
1894texture analysis. The other is the suite of spherical harmonics terms for
1895cylindrical sample symmetry for each phase in each powder pattern (“histogram”)
1896and is usually used to accommodate preferred orientation effects in a Rietveld
1897refinement. The former description allows refinement of the sample orientation
1898zeros, <span style='font-family:Symbol'>W</span><sub>s</sub>, <span
1899style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:Symbol'>F</span><sub>s</sub>,
1900but the latter description does not (they are assumed to be zero and not
1901refinable). The sample orientation angles, (<span style='font-family:Symbol'>W</span>,
1902<span style='font-family:Symbol'>C</span>, <span style='font-family:Symbol'>F) </span>are
1903specified in the Sample Parameters table in the GSAS-II data tree structure and
1904are applied for either description.</p>
1905
1906<p class=gsastext>In this tutorial we will use both of these descriptions to
1907determine the texture of the two phases in a <span class=SpellE>NiTi</span>
1908shape memory alloy sample with cylindrical symmetry (wire texture) as collected
1909at APS on beam line 1ID-C (data kindly provided by Paul Paradise &amp; Aaron <span
1910class=SpellE>Stebner</span> of Colo. School of Mines). Thus, there are three
1911ways within GSAS-II that can be used for this texture analysis all beginning
1912with the same 2D area detector image. Each will be described in turn after the
1913initial setup of the GSAS-II project, image input &amp; integration.</p>
1914
1915<h2>Step 1. Image input &amp; integration</h2>
1916
1917<p class=MsoNormal>If you have not done so already, <u><span style='color:#0070C0'><a
1918href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none;
1919text-underline:none'>start GSAS-II</span></a></span></u>. Note that menu entries
1920are listed in <b style='mso-bidi-font-weight:normal'><span style='font-family:
1921"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1922minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>bold
1923face</span></b> below as <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'>Help/About GSAS-II</span></b>, which lists first the name of the
1927menu (here <b style='mso-bidi-font-weight:normal'><span style='font-family:
1928"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1929minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>Help</span></b>)
1930and second the name of the entry in the menu (here <b style='mso-bidi-font-weight:
1931normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1932minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;
1933mso-bidi-theme-font:minor-latin'>About GSAS-II</span></b>). </p>
1934
1935<p class=MsoNormal>Use the <b style='mso-bidi-font-weight:normal'><span
1936style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1937mso-hansi-theme-font:minor-latin'>Data/Read image data</span></b> menu item to
1938read the data file into the current GSAS-II project. A file selection dialog
1939will be shown; its appearance will depend on your OS. Change the search
1940directory to <b style='mso-bidi-font-weight:normal'><span style='font-family:
1941"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1942minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>/exercises/2DTexture
1943</span></b>and then select the file <b style='mso-bidi-font-weight:normal'><span
1944style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1945mso-hansi-theme-font:minor-latin'>NDC5_01588_1.ge2</span></b>. A (faint) image
1946will appear</p>
1947
1948<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1949 id="Picture_x0020_29" o:spid="_x0000_i1109" type="#_x0000_t75" style='width:525pt;
1950 height:450pt;visibility:visible;mso-wrap-style:square'>
1951 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
1952  o:title=""/>
1953</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1954src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
1955v:shapes="Picture_x0020_29"><![endif]></span></p>
1956
1957<p class=MsoNormal><span class=GramE>and</span> the <b style='mso-bidi-font-weight:
1958normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1959minor-latin;mso-hansi-theme-font:minor-latin'>Image Controls</span></b> data
1960page will show</p>
1961
1962<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1963 id="Picture_x0020_30" o:spid="_x0000_i1108" type="#_x0000_t75" style='width:472.5pt;
1964 height:388.5pt;visibility:visible;mso-wrap-style:square'>
1965 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
1966  o:title=""/>
1967</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
1968src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
1969v:shapes="Picture_x0020_30"><![endif]></span></p>
1970
1971<p class=MsoNormal>The detector was previously calibrated and the coefficients
1972are stored in a file found by doing <b style='mso-bidi-font-weight:normal'><span
1973style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1974mso-hansi-theme-font:minor-latin'>Operations/Load Controls</span></b> from the <b
1975style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1976mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
1977Controls</span></b> menu. A file selection popup will appear showing <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'>NDC5.imctrl</span></b>;
1980select it and press <b style='mso-bidi-font-weight:normal'><span
1981style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1982mso-hansi-theme-font:minor-latin'>Open</span></b>. The <b style='mso-bidi-font-weight:
1983normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1984minor-latin;mso-hansi-theme-font:minor-latin'>Image Controls</span></b> window
1985will be repainted with the new values (do a reselect of the image from the tree
1986and then <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1987mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
1988Controls</span></b> to make sure the image is up to date.)</p>
1989
1990<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1991 id="Picture_x0020_31" o:spid="_x0000_i1107" type="#_x0000_t75" style='width:472.5pt;
1992 height:388.5pt;visibility:visible;mso-wrap-style:square'>
1993 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
1994  o:title=""/>
1995</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
1996src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
1997v:shapes="Picture_x0020_31"><![endif]></span></p>
1998
1999<p class=MsoNormal>The detail in the image can be enhanced by lowering the <b
2000style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2001mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Max
2002intensity</span></b> (<b style='mso-bidi-font-weight:normal'><span
2003style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2004mso-hansi-theme-font:minor-latin'>15000</span></b> is suitable) and shows that
2005the diffraction rings show the effect of texture and that the image has a
2006fairly high background. Placing the cursor in the corners or inside the inner
2007ring shows a background &gt;1700. This can be suppressed by adjusting the <b
2008style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2009mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Flat <span
2010class=SpellE>Bkg</span></span></b> (I chose <b style='mso-bidi-font-weight:
2011normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2012minor-latin;mso-hansi-theme-font:minor-latin'>1700</span></b> for this). The
2013image will now show the rings much more clearly.</p>
2014
2015<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2016 id="Picture_x0020_32" o:spid="_x0000_i1106" type="#_x0000_t75" style='width:525pt;
2017 height:450pt;visibility:visible;mso-wrap-style:square'>
2018 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
2019  o:title=""/>
2020</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2021src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
2022v:shapes="Picture_x0020_32"><![endif]></span></p>
2023
2024<p class=MsoNormal>For texture analysis we will need to integrate the image
2025into a number of slices sampling the changing ring intensity with azimuthal
2026angle. Also note that the image seems to have <b style='mso-bidi-font-weight:
2027normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2028minor-latin;mso-hansi-theme-font:minor-latin'>mm</span></b> symmetry so that
2029the unique part of this intensity variation covers 0-90° of azimuth. In
2030addition the ring intensity variation is such that using 10° slices will
2031capture it reasonably well. However, we want to include both 0° and 90° as
2032slice centers. Thus there will be 10 slices beginning at -5° and ending at 95°.
2033Check the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2034mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show
2035integration limits?</span></b> <span class=GramE>box</span> and uncheck the <b
2036style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2037mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Do full
2038integration? </span></b><span class=GramE>box</span>, enter <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'>10</span></b>
2041in the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2042mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth
2043bins</span></b>, enter <b style='mso-bidi-font-weight:normal'><span
2044style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2045mso-hansi-theme-font:minor-latin'>-5</span></b> in the <b style='mso-bidi-font-weight:
2046normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2047minor-latin;mso-hansi-theme-font:minor-latin'>Start azimuth</span></b> box (it
2048will change to 355) and enter <b style='mso-bidi-font-weight:normal'><span
2049style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2050mso-hansi-theme-font:minor-latin'>455</span></b> in the <b style='mso-bidi-font-weight:
2051normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2052minor-latin;mso-hansi-theme-font:minor-latin'>End azimuth</span></b> box. In
2053addition, recall that the sample was mounted vertically and thus is aligned
2054with the defined laboratory I axis. Thus, the sample coordinate system needs to
2055be rotated by 90° to match the sample axis with the K axis; this can be done by
2056making the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2057"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2058minor-latin'>Sample goniometer axis Chi</span></b> = <b style='mso-bidi-font-weight:
2059normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2060minor-latin;mso-hansi-theme-font:minor-latin'>90</span></b>. The plot will
2061change with each entry and at the end should look like</p>
2062
2063<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2064 id="Picture_x0020_33" o:spid="_x0000_i1105" type="#_x0000_t75" style='width:525pt;
2065 height:450pt;visibility:visible;mso-wrap-style:square'>
2066 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
2067  o:title=""/>
2068</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2069src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
2070v:shapes="Picture_x0020_33"><![endif]></span></p>
2071
2072<p class=MsoNormal>The <b style='mso-bidi-font-weight:normal'><span
2073style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2074mso-hansi-theme-font:minor-latin'>Image Controls</span></b> should be</p>
2075
2076<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2077 id="_x0000_i1104" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
2078 visibility:visible;mso-wrap-style:square'>
2079 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
2080  o:title=""/>
2081</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
2082src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
2083v:shapes="_x0000_i1104"><![endif]></span></p>
2084
2085<p class=MsoNormal>It turns out that the image contains a number of “picked
2086bits” (very high count “zingers”); these can be mostly eliminated by setting
2087the upper threshold in Masks. Select <b style='mso-bidi-font-weight:normal'><span
2088style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2089mso-hansi-theme-font:minor-latin'>Masks</span></b> and the following should
2090appear</p>
2091
2092<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2093 id="_x0000_i1103" type="#_x0000_t75" style='width:297.75pt;height:99.75pt;
2094 visibility:visible;mso-wrap-style:square'>
2095 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
2096  o:title=""/>
2097</v:shape><![endif]--><![if !vml]><img border=0 width=397 height=133
2098src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
2099v:shapes="_x0000_i1103"><![endif]></span></p>
2100
2101<p class=MsoNormal>Change the <b style='mso-bidi-font-weight:normal'><span
2102style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2103mso-hansi-theme-font:minor-latin'>Upper threshold</span></b> to <b
2104style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2105mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2500</span></b>;
2106the image will be redrawn reflecting this mask. By zooming in you may see
2107isolated red pixels; these are excluded points. Make sure the diffraction rings
2108do not have any excluded points. For example with the level set to 2200 the
2109plot shows</p>
2110
2111<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2112 id="_x0000_i1102" type="#_x0000_t75" style='width:525pt;height:450pt;
2113 visibility:visible;mso-wrap-style:square'>
2114 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
2115  o:title=""/>
2116</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2117src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
2118v:shapes="_x0000_i1102"><![endif]></span></p>
2119
2120<p class=MsoNormal><span class=GramE>for</span> one ring. This level is too
2121low. Return to the <b style='mso-bidi-font-weight:normal'><span
2122style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2123mso-hansi-theme-font:minor-latin'>Image Controls</span></b> item in the data
2124tree.</p>
2125
2126<p class=MsoNormal>We are now ready to integrate the image; do <b
2127style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2128mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Integrate</span></b>
2129from the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2130mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2131Controls</span></b> menu. When done the last powder pattern in the tree will be
2132displayed</p>
2133
2134<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2135 id="_x0000_i1101" type="#_x0000_t75" style='width:525pt;height:450pt;
2136 visibility:visible;mso-wrap-style:square'>
2137 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
2138  o:title=""/>
2139</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2140src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
2141v:shapes="_x0000_i1101"><![endif]></span></p>
2142
2143<h2>Step 2. Enter <span class=SpellE>NiTi</span> phases</h2>
2144
2145<p class=MsoNormal>This <span class=SpellE>NiTi</span> alloy consists of two
2146phases, cubic B2 and monoclinic B19’. Their parameters are:</p>
2147
2148<p class=MsoNormal>B2: <b style='mso-bidi-font-weight:normal'><span
2149style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2150mso-hansi-theme-font:minor-latin'>P m 3 m</span></b>, a=<b style='mso-bidi-font-weight:
2151normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2152minor-latin;mso-hansi-theme-font:minor-latin'>3.0240</span></b>, Ni <b
2153style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2154mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0<span
2155class=GramE>,0,0</span></span></b>, <span class=SpellE>Ti</span> <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'>œ,œ,œ</span></b>,
2158<span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
2159style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2160mso-hansi-theme-font:minor-latin'>0.005 </span></b>for both.</p>
2161
2162<p class=MsoNormal>B19’: <span style='mso-spacerun:yes'> </span><b
2163style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2164mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P 1 1 21/m</span></b>,
2165a=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2166mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.8853</span></b>,
2167b=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2168mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.6353</span></b>,
2169c=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2170mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.1368</span></b>,
2171&#947;=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2172mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>96.821</span></b>,
2173<span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span
2174style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2175mso-hansi-theme-font:minor-latin'>0.5787<span class=GramE>,0.2841,Œ</span></span></b>,
2176Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2177mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.9700,0.8209,Œ</span></b>,
2178<span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
2179style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2180mso-hansi-theme-font:minor-latin'>0.005</span></b> for both.</p>
2181
2182<p class=MsoNormal>Use the <b style='mso-bidi-font-weight:normal'><span
2183style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2184mso-hansi-theme-font:minor-latin'>Data/Add phase</span></b> to enter the <b
2185style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2186mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
2187and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2188mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
2189phases; then for each enter the information given above on their respective <b
2190style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2191mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>General</span></b>
2192and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2193mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms</span></b>
2194tabs. Don’t forget the spaces between the axial fields for the space group
2195symbols. On the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2196"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2197minor-latin'>Atoms</span></b> tab begin by doing <b style='mso-bidi-font-weight:
2198normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2199minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Append atom</span></b> twice
2200then fill in the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2201"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2202minor-latin'>Type</span></b> and coordinates boxes. A double click of the <b
2203style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2204mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Type</span></b>
2205entry will show a popup of the Periodic Table; select the element as
2206appropriate. NB: GSAS-II happily takes “1/2” &amp; “1/4” for coordinate values;
2207these get converted to their decimal equivalent upon entry. Note the use of a
2208nonstandard space group designation for B19’. When done the B2 Atoms table should
2209look like</p>
2210
2211<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2212 id="_x0000_i1100" type="#_x0000_t75" style='width:525pt;height:166.5pt;
2213 visibility:visible;mso-wrap-style:square'>
2214 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
2215  o:title=""/>
2216</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=222
2217src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
2218v:shapes="_x0000_i1100"><![endif]></span></p>
2219
2220<p class=MsoNormal><span class=GramE>and</span> the B19’ Atoms table should be</p>
2221
2222<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2223 id="_x0000_i1099" type="#_x0000_t75" style='width:525pt;height:163.5pt;
2224 visibility:visible;mso-wrap-style:square'>
2225 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
2226  o:title=""/>
2227</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=218
2228src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
2229v:shapes="_x0000_i1099"><![endif]></span></p>
2230
2231<p class=MsoNormal>Next go to the <b style='mso-bidi-font-weight:normal'><span
2232style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2233mso-hansi-theme-font:minor-latin'>Data</span></b> tab for each phase; there will
2234be a message indicating the lack of data for each. Do <b style='mso-bidi-font-weight:
2235normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2236minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add powder histograms</span></b>,
2237do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2238mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b>
2239on the popup selection window and press <b style='mso-bidi-font-weight:normal'><span
2240style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2241mso-hansi-theme-font:minor-latin'>OK</span></b>. The window for B2 will change
2242to</p>
2243
2244<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2245 id="_x0000_i1098" type="#_x0000_t75" style='width:342.75pt;height:375pt;
2246 visibility:visible;mso-wrap-style:square'>
2247 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2248  o:title=""/>
2249</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
2250src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2251v:shapes="_x0000_i1098"><![endif]></span></p>
2252
2253<p class=MsoNormal><span class=GramE>and</span> that for B19’ will be</p>
2254
2255<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2256 id="_x0000_i1097" type="#_x0000_t75" style='width:370.5pt;height:375pt;
2257 visibility:visible;mso-wrap-style:square'>
2258 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2259  o:title=""/>
2260</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
2261src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2262v:shapes="_x0000_i1097"><![endif]></span></p>
2263
2264<p class=MsoNormal>You should now save the project file (I used <span
2265class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
2266"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2267minor-latin'>NiTi</span></b></span> for a name); we will use this as a starting
2268point for three different texture determinations. Do a <b style='mso-bidi-font-weight:
2269normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2270minor-latin;mso-hansi-theme-font:minor-latin'>File/Save project as…</span></b>
2271and give it a new name (I used <span class=SpellE><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'>NiTi</span></b></span><b
2274style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2275mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-A</span></b>);
2276this will become the new project name for the next part of this tutorial.</p>
2277
2278<h2>Method A. Full refinement</h2>
2279
2280<h3>Introduction</h3>
2281
2282<p class=MsoNormal>In this method we will do a full Rietveld refinement of the
2283texture, profile parameters, peak position variables and crystal structure
2284parameters. This is suitable in this case because of the relatively small
2285number of histograms (10 in this case) needed for the texture determination; do
2286recall that each phase in each histogram has a set of parameters (e.g. phase
2287fraction, size, <span class=SpellE>mustrain</span> &amp; hydrostatic strain) in
2288addition to the ones for each histogram (e.g. background &amp; scale factor).
2289Consequently the total number of parameters can build up very quickly in this
2290method of analysis. The other two methods seek to reduce this problem by
2291splitting the fitting into a sequential refinement (histogram by histogram)
2292step followed by a texture fitting step.</p>
2293
2294<h3>Step 1. Initial refinement</h3>
2295
2296<p class=MsoNormal>In the initial refinement we need to vary the phase fraction
2297for each phase/histogram and the background in each histogram. To start select
2298any <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2299mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b>
2300entry from the GSAS-II data tree and select <b style='mso-bidi-font-weight:
2301normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2302minor-latin;mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b> for
2303it. Note that Goniometer chi is set to 90; that came from the same entry in the
2304Image Controls during integration. Also, if you chose other than the 1<sup>st</sup>
2305PWDR data set the Detector azimuth will be some nonzero value; that is also
2306reflected in the name assigned to the histogram (e.g. <b style='mso-bidi-font-weight:
2307normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2308minor-latin;mso-hansi-theme-font:minor-latin'>PWDR NDC5_01588_1.ge2 <span
2309class=SpellE>Azm</span>= 40.00</span></b>). Uncheck the <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'>Histogram scale factor</span></b>
2312box and then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
2313"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2314minor-latin'>Command/Copy flags</span></b>; select <b style='mso-bidi-font-weight:
2315normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2316minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b> and then press
2317<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2318mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
2319That will clear the scale factor refinement flag for all histograms; we will be
2320varying the phase fractions instead.</p>
2321
2322<p class=MsoNormal>Next select the B2 phase and pick the Data tab; you will see</p>
2323
2324<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2325 id="_x0000_i1096" type="#_x0000_t75" style='width:342.75pt;height:375pt;
2326 visibility:visible;mso-wrap-style:square'>
2327 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2328  o:title=""/>
2329</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
2330src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2331v:shapes="_x0000_i1096"><![endif]></span></p>
2332
2333<p class=MsoNormal>Select the <b style='mso-bidi-font-weight:normal'><span
2334style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2335mso-hansi-theme-font:minor-latin'>Phase fraction</span></b> box. Then do <b
2336style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2337mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
2338data</span></b>, select <b style='mso-bidi-font-weight:normal'><span
2339style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2340mso-hansi-theme-font:minor-latin'>Set <span class=GramE>All</span></span></b>
2341&amp; press <b style='mso-bidi-font-weight:normal'><span style='font-family:
2342"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2343minor-latin'>OK</span></b> to copy these to the other histograms. Next select
2344the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2345mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
2346phase and repeat this process. We are now ready for the first refinement; do <b
2347style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2348mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
2349from the main GSAS-II data tree window. A progress bar popup will appear and
2350when done a <b style='mso-bidi-font-weight:normal'><span style='font-family:
2351"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2352minor-latin'>Refinement results</span></b> popup will show with Rw~32%. Press <b
2353style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2354mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>
2355to load this result; GSAS-II will return you to the last window you were using
2356and display the 1<sup>st</sup> powder pattern showing you the fit</p>
2357
2358<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2359 id="_x0000_i1095" type="#_x0000_t75" style='width:525pt;height:450pt;
2360 visibility:visible;mso-wrap-style:square'>
2361 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
2362  o:title=""/>
2363</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2364src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
2365v:shapes="_x0000_i1095"><![endif]></span></p>
2366
2367<p class=MsoNormal>This is quite poor. You can survey the fit successively by 1<sup>st</sup>
2368selecting say the 1<sup>st</sup> PWDR entry from the tree and then using the
2369up/down arrow keys to step to the next one; the plot will redraw at each step
2370(NB: at full scale) and the data window will show statistics of the fit. There
2371is a substantial intensity discrepancy; this is due to the texture. It is also
2372evident that some of the peaks are out of place relative to the reflection
2373markers; this is due to macroscopic strain in the drawn wire. For the <span
2374style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2375mso-hansi-theme-font:minor-latin'>B2</span> phase select the <b
2376style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2377mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
2378tab; it should look like</p>
2379
2380<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2381 id="_x0000_i1094" type="#_x0000_t75" style='width:456pt;height:217.5pt;
2382 visibility:visible;mso-wrap-style:square'>
2383 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
2384  o:title=""/>
2385</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290
2386src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
2387v:shapes="_x0000_i1094"><![endif]></span></p>
2388
2389<p class=MsoNormal>The texture model is <b style='mso-bidi-font-weight:normal'><span
2390style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2391mso-hansi-theme-font:minor-latin'>cylindrical</span></b> by default; that is
2392what we want. Change the <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'>Harmonic order</span></b> to <b
2395style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2396mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>8</span></b>
2397and check both <b style='mso-bidi-font-weight:normal'><span style='font-family:
2398"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2399minor-latin'>Refine texture</span></b> and <b style='mso-bidi-font-weight:normal'><span
2400style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2401mso-hansi-theme-font:minor-latin'>Show <span class=SpellE>coeff</span></span></b>.
2402The window should look like</p>
2403
2404<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2405 id="_x0000_i1093" type="#_x0000_t75" style='width:456pt;height:250.5pt;
2406 visibility:visible;mso-wrap-style:square'>
2407 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
2408  o:title=""/>
2409</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
2410src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
2411v:shapes="_x0000_i1093"><![endif]></span></p>
2412
2413<p class=MsoNormal>Then go to the <b style='mso-bidi-font-weight:normal'><span
2414style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2415mso-hansi-theme-font:minor-latin'>Data</span></b> tab, select <b
2416style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2417mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>D11</span></b>;
2418the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2419mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
2420window should look like (any PWDR item will do)</p>
2421
2422<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2423 id="_x0000_i1092" type="#_x0000_t75" style='width:342.75pt;height:375pt;
2424 visibility:visible;mso-wrap-style:square'>
2425 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
2426  o:title=""/>
2427</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
2428src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
2429v:shapes="_x0000_i1092"><![endif]></span></p>
2430
2431<p class=MsoNormal>Then do <b style='mso-bidi-font-weight:normal'><span
2432style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2433mso-hansi-theme-font:minor-latin'>Edit/Copy flags</span></b> to have <b
2434style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2435mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>D11</span></b>
2436refined for all PWDR data sets.</p>
2437
2438<p class=MsoNormal>Next select the <b style='mso-bidi-font-weight:normal'><span
2439style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2440mso-hansi-theme-font:minor-latin'>B19’</span></b> phase <b style='mso-bidi-font-weight:
2441normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2442minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b> tab. Then
2443select <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2444mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>6</span></b>
2445for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2446mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic
2447order</span></b> and check the two boxes as before.</p>
2448
2449<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2450 id="_x0000_i1091" type="#_x0000_t75" style='width:478.5pt;height:302.25pt;
2451 visibility:visible;mso-wrap-style:square'>
2452 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
2453  o:title=""/>
2454</v:shape><![endif]--><![if !vml]><img border=0 width=638 height=403
2455src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
2456v:shapes="_x0000_i1091"><![endif]></span></p>
2457
2458<p class=MsoNormal>Then go to the <b style='mso-bidi-font-weight:normal'><span
2459style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2460mso-hansi-theme-font:minor-latin'>Data</span></b> tab for the <b
2461style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2462mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
2463phase and check all 4 of the <span class=SpellE><b style='mso-bidi-font-weight:
2464normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2465minor-latin;mso-hansi-theme-font:minor-latin'>Dij</span></b></span> boxes and
2466do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2467mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
2468flags</span></b> as before. The tab will look like</p>
2469
2470<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2471 id="_x0000_i1090" type="#_x0000_t75" style='width:370.5pt;height:375pt;
2472 visibility:visible;mso-wrap-style:square'>
2473 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
2474  o:title=""/>
2475</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
2476src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
2477v:shapes="_x0000_i1090"><![endif]></span></p>
2478
2479<p class=MsoNormal>Now do <b style='mso-bidi-font-weight:normal'><span
2480style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2481mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from the main
2482menu. The refinement will finish with <span class=SpellE>Rw</span> ~27%; the 1<sup>st</sup>
2483PWDR pattern looks like</p>
2484
2485<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2486 id="_x0000_i1089" type="#_x0000_t75" style='width:525pt;height:413.25pt;
2487 visibility:visible;mso-wrap-style:square'>
2488 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
2489  o:title=""/>
2490</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2491src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
2492v:shapes="_x0000_i1089"><![endif]></span></p>
2493
2494<p class=MsoNormal>The calculated peaks for both phases are too sharp. It is
2495likely that this is a <span class=SpellE>microstrain</span> effect. Select <b
2496style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2497mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
2498for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2499mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2 </span></b>phase
2500and select the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
2501style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2502mso-hansi-theme-font:minor-latin'>microstrain</span></b></span> box. Then do <b
2503style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2504mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
2505flags</span></b> to set it for the other PWDR data sets. Do the same for the <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'>B19’</span></b>
2508phase. Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
2509"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2510minor-latin'>Calculate/Refine</span></b> from the main menu. The fit will be
2511substantially improved with <span class=SpellE>Rw</span> ~9.2%.</p>
2512
2513<h3>Step 2. Finish refinement and examine texture</h3>
2514
2515<p class=MsoNormal>Looking at the individual PWDR data sets (e.g. the one for <span
2516class=SpellE>Azm</span>=20.00)</p>
2517
2518<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2519 id="_x0000_i1088" type="#_x0000_t75" style='width:525pt;height:413.25pt;
2520 visibility:visible;mso-wrap-style:square'>
2521 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
2522  o:title=""/>
2523</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2524src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
2525v:shapes="_x0000_i1088"><![endif]></span></p>
2526
2527<p class=MsoNormal>It is evident that there remains intensity differences due
2528to texture. We can increase the harmonic order to more closely fit these,
2529however one should only do this carefully. Select the Texture tab for the B2
2530phase; the Texture tab will show</p>
2531
2532<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2533 id="Picture_x0020_18" o:spid="_x0000_i1087" type="#_x0000_t75" style='width:456pt;
2534 height:250.5pt;visibility:visible;mso-wrap-style:square'>
2535 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
2536  o:title=""/>
2537</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
2538src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
2539v:shapes="Picture_x0020_18"><![endif]></span></p>
2540
2541<p class=MsoNormal>And a drawing of the 001 pole figure will be drawn. This is
2542the very typical “bulls eye” for cylindrical texture; of much more use is an
2543inverse pole figure. Select that from the Texture plot type; the plot will be
2544redrawn</p>
2545
2546<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2547 id="_x0000_i1086" type="#_x0000_t75" style='width:525pt;height:413.25pt;
2548 visibility:visible;mso-wrap-style:square'>
2549 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
2550  o:title=""/>
2551</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2552src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
2553v:shapes="_x0000_i1086"><![endif]></span></p>
2554
2555<p class=MsoNormal>This shows the probability of reflection vectors coinciding
2556with the sample wire axis the high spots are the 111 family of reflections. We
2557should try the next higher Harmonic order (10). </p>
2558
2559<p class=MsoNormal>Next go to the Texture tab for the B19’ phase. Again a <span
2560class=SpellE>bullseye</span> pole figure is drawn; change that to an Inverse
2561pole figure.</p>
2562
2563<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2564 id="_x0000_i1085" type="#_x0000_t75" style='width:525pt;height:413.25pt;
2565 visibility:visible;mso-wrap-style:square'>
2566 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
2567  o:title=""/>
2568</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2569src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
2570v:shapes="_x0000_i1085"><![endif]></span></p>
2571
2572<p class=MsoNormal>This phase is very strongly textured (the cursor shows 12-13
2573MRD at the peaks) along the -140 direction. Again we want to increment the
2574Harmonic order to the next higher level (8). Again do Calculate/Refine from the
2575main menu; the <span class=SpellE>Rwp</span> has dropped to ~7.9%. One can add
2576the atom <span class=SpellE>Uiso</span> for the Ni and <span class=SpellE>Ti</span>
2577atoms in the B2 phase and the coordinates and <span class=SpellE>Uiso</span>
2578for the B19’ phase. The <span class=SpellE>Rw</span> drops a bit further to
2579~7.4%. Finally, we can increase the harmonic order again for the B19’ phase (it
2580is very strongly textured!) to 10 and the B2 phase to 12; the final refinement
2581converged to <span class=SpellE>Rw</span> ~6.8% and the B19’ inverse pole
2582figure has peaks at ~18 MRD (Multiple of Random Distribution) and the B2 phase
2583peaks are ~7MRD.</p>
2584
2585<p class=MsoNormal>The B19’ coefficients</p>
2586
2587<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2588 id="_x0000_i1084" type="#_x0000_t75" style='width:502.5pt;height:375pt;
2589 visibility:visible;mso-wrap-style:square'>
2590 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
2591  o:title=""/>
2592</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
2593src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
2594v:shapes="_x0000_i1084"><![endif]></span></p>
2595
2596<p class=MsoNormal><span class=GramE>and</span> inverse pole figure</p>
2597
2598<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2599 id="_x0000_i1083" type="#_x0000_t75" style='width:525pt;height:413.25pt;
2600 visibility:visible;mso-wrap-style:square'>
2601 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
2602  o:title=""/>
2603</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2604src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
2605v:shapes="_x0000_i1083"><![endif]></span></p>
2606
2607<p class=MsoNormal>The B2 coefficients</p>
2608
2609<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2610 id="_x0000_i1082" type="#_x0000_t75" style='width:480pt;height:267.75pt;
2611 visibility:visible;mso-wrap-style:square'>
2612 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
2613  o:title=""/>
2614</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
2615src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
2616v:shapes="_x0000_i1082"><![endif]></span></p>
2617
2618<p class=MsoNormal><span class=GramE>and</span> inverse pole figure</p>
2619
2620<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2621 id="_x0000_i1081" type="#_x0000_t75" style='width:525pt;height:413.25pt;
2622 visibility:visible;mso-wrap-style:square'>
2623 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
2624  o:title=""/>
2625</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
2626src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
2627v:shapes="_x0000_i1081"><![endif]></span></p>
2628
2629<p class=MsoNormal>This completes the tutorial on Method A for doing texture
2630analysis. It is useful for a case like this one where there are very few data
2631sets required for the texture analysis. However, for the case of lower sample
2632symmetry one must several dozen or even a few hundred histograms and then the
2633suite of parameters can easily be &gt; 1000 of which only a few dozen describe
2634the texture. This leads to the next Methods for texture analysis in GSAS-II.</p>
2635
2636<h2>Method B. Sequential refinement &amp; texture analysis from result</h2>
2637
2638<h3>Introduction</h3>
2639
2640<p class=MsoNormal>This begins the texture analysis in much the same way as
2641Method A except that all the initial refinements are done “sequentially”, that
2642is refinements are done for the parameters associated with each powder pattern
2643to convergence in a serial fashion. In this case where there are 10 PWDR data
2644sets, there will be 10 refinements done in sequence. Parameters that span all
2645the data (e.g. lattice parameters, atom parameters &amp; texture) are not varied
2646in this sequence refinement. The effect of texture is modeled as a Preferred
2647Orientation correction to each histogram. To begin do <b style='mso-bidi-font-weight:
2648normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2649minor-latin;mso-hansi-theme-font:minor-latin'>File/Open project…</span></b> for
2650the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
2651style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2652mso-hansi-theme-font:minor-latin'>NiTi.gpx</span></b></span> file created in
2653the first step and then do a <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'>File/Save project as…</span></b> to save it
2656as <span class=SpellE><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'>NiTi</span></b></span><b style='mso-bidi-font-weight:
2659normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2660minor-latin;mso-hansi-theme-font:minor-latin'>-B</span></b>. This renames the project
2661and it should have one IMG, 10 PWDR entries and two phases of <span
2662class=SpellE>NiTi</span> (B2 and B19’).</p>
2663
2664<h3>Step 1. Initial refinement</h3>
2665
2666<p class=MsoNormal>This begins the same way as Method A so I’ll be brief. Do
2667the following steps:</p>
2668
2669<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
2670style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
2671style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
2672any <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2673mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b>
2674entry, go to <b style='mso-bidi-font-weight:normal'><span style='font-family:
2675"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2676minor-latin'>Sample Parameters</span></b> and uncheck <b style='mso-bidi-font-weight:
2677normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2678minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>.
2679Then copy the flags to the other PWDR entries.</p>
2680
2681<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
2682style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
2683style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
2684the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2685mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
2686phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2687mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
2688tab and check the <b style='mso-bidi-font-weight:normal'><span
2689style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2690mso-hansi-theme-font:minor-latin'>Phase fraction</span></b> box and change the <span
2691class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
2692"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2693minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span
2694style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2695mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b
2696style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2697mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical
2698harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span
2699style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2700mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the
2701flag and the model to the other PWDR entries.</p>
2702
2703<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
2704style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
2705style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
2706the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2707mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
2708phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2709mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
2710tab and check the <b style='mso-bidi-font-weight:normal'><span
2711style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2712mso-hansi-theme-font:minor-latin'>Phase fraction box</span></b> and change the <span
2713class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
2714"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2715minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span
2716style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2717mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b
2718style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2719mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical
2720harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span
2721style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2722mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the
2723flag and the model to the other PWDR entries.</p>
2724
2725<p class=MsoNormal>Now select <b style='mso-bidi-font-weight:normal'><span
2726style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2727mso-hansi-theme-font:minor-latin'>Controls</span></b> from the GSAS-II data
2728tree</p>
2729
2730<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2731 id="Picture_x0020_1" o:spid="_x0000_i1080" type="#_x0000_t75" style='width:330.75pt;
2732 height:153.75pt;visibility:visible;mso-wrap-style:square'>
2733 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
2734  o:title=""/>
2735</v:shape><![endif]--><![if !vml]><img border=0 width=441 height=205
2736src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
2737v:shapes="Picture_x0020_1"><![endif]></span></p>
2738
2739<p class=MsoNormal>Press the <b style='mso-bidi-font-weight:normal'><span
2740style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2741mso-hansi-theme-font:minor-latin'>Select Data</span></b> button for <b
2742style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2743mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Sequential
2744Refinement</span></b>; a file selection popup will appear. Do <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'>Set All</span></b>
2747and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2748mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
2749The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2750mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b>
2751page will be repainted indicating that 10 data sets are selected for sequential
2752refinement.</p>
2753
2754<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2755 id="Picture_x0020_2" o:spid="_x0000_i1079" type="#_x0000_t75" style='width:330.75pt;
2756 height:163.5pt;visibility:visible;mso-wrap-style:square'>
2757 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
2758  o:title=""/>
2759</v:shape><![endif]--><![if !vml]><img border=0 width=441 height=218
2760src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
2761v:shapes="Picture_x0020_2"><![endif]></span></p>
2762
2763<p class=MsoNormal>You have the choice of starting at the last one and for
2764copying results from one to the next. We won’t do either here. Each refinement
2765will use the other controls (e.g. <b style='mso-bidi-font-weight:normal'><span
2766style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2767mso-hansi-theme-font:minor-latin'>Max cycles</span></b>) as controls. We are
2768now ready to do the 1<sup>st</sup> sequential refinement. Do <b
2769style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2770mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Sequential
2771refine</span></b> from the main menu. A progress bar popup will appear showing
2772residuals as it processes each of 10 data sets. After a few seconds the <b
2773style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2774mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refinement
2775results</span></b> popup will appear; press <b style='mso-bidi-font-weight:
2776normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2777minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to accept them. The
2778data window displays the <b style='mso-bidi-font-weight:normal'><span
2779style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2780mso-hansi-theme-font:minor-latin'>Sequential refinement results</span></b> as a
2781table.</p>
2782
2783<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2784 id="Picture_x0020_3" o:spid="_x0000_i1078" type="#_x0000_t75" style='width:525pt;
2785 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2786 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
2787  o:title=""/>
2788</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
2789src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
2790v:shapes="Picture_x0020_3"><![endif]></span></p>
2791
2792<p class=MsoNormal>There is a row for each data set and columns for all refined
2793parameters and some derived ones along with residual and convergence
2794indicators. The residuals are not very good (we haven’t really refined much)
2795but the &#916;&#967;<sup>2</sup> column shows that convergence was achieved
2796(NB: poor convergence will be highlighted in yellow or red depending on how bad
2797it is).</p>
2798
2799<p class=MsoNormal>If you examine one of the PWDR entries, you’ll see that just
2800in this point in Method <span class=GramE>A</span> much of the misfit is
2801texture and perhaps peak position.</p>
2802
2803<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2804 id="Picture_x0020_4" o:spid="_x0000_i1077" type="#_x0000_t75" style='width:525pt;
2805 height:450pt;visibility:visible;mso-wrap-style:square'>
2806 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
2807  o:title=""/>
2808</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2809src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
2810v:shapes="Picture_x0020_4"><![endif]></span></p>
2811
2812<p class=MsoNormal>To set these parameters, select the Data tab for the B2
2813phase</p>
2814
2815<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2816 id="Picture_x0020_5" o:spid="_x0000_i1076" type="#_x0000_t75" style='width:381pt;
2817 height:375pt;visibility:visible;mso-wrap-style:square'>
2818 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
2819  o:title=""/>
2820</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=500
2821src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
2822v:shapes="Picture_x0020_5"><![endif]></span></p>
2823
2824<p class=MsoNormal>Check the D11 box under Hydrostatic/elastic strain, set the
2825Harmonic order to 6 and check the Refine box for it (Preferred orientation).
2826Then in two steps, do Edit/Copy flags and Set All for the file selection. Then
2827do Edit/Copy selected data; that will bring up a new popup</p>
2828
2829<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2830 id="Picture_x0020_6" o:spid="_x0000_i1075" type="#_x0000_t75" style='width:240pt;
2831 height:232.5pt;visibility:visible;mso-wrap-style:square'>
2832 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
2833  o:title=""/>
2834</v:shape><![endif]--><![if !vml]><img border=0 width=320 height=310
2835src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
2836v:shapes="Picture_x0020_6"><![endif]></span></p>
2837
2838<p class=MsoNormal>This allows you to select which parameters to copy data and
2839flags. Select Pref. <span class=SpellE>Ori</span>. And press OK; the file
2840selection is next. Do Set <span class=GramE>All</span> and OK to do this copy.
2841That copies the full spherical harmonics model to the other data sets. Select
2842one to check if you’d like.</p>
2843
2844<p class=MsoNormal>Next do the same thing for the B19’ phase; here there are 4 <span
2845class=SpellE>Dij</span> parameters to check (do all of them) and use spherical
2846harmonics order 4. When done that Data window will look like</p>
2847
2848<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2849 id="Picture_x0020_7" o:spid="_x0000_i1074" type="#_x0000_t75" style='width:381pt;
2850 height:467.25pt;visibility:visible;mso-wrap-style:square'>
2851 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
2852  o:title=""/>
2853</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=623
2854src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
2855v:shapes="Picture_x0020_7"><![endif]></span></p>
2856
2857<p class=MsoNormal>We are now ready for the next refinement; do Calculate/Sequential
2858refine. Be careful not (by habit say) pick Refine; a warning popup will appear.
2859After it completes the Sequential refinement results shows that the fit is
2860better but convergence wasn’t quite complete.</p>
2861
2862<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2863 id="Picture_x0020_8" o:spid="_x0000_i1073" type="#_x0000_t75" style='width:525pt;
2864 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2865 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
2866  o:title=""/>
2867</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
2868src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
2869v:shapes="Picture_x0020_8"><![endif]></span></p>
2870
2871<p class=MsoNormal>It is probably best to do another round of sequential
2872refinement (I had to do two) to get convergence. A plot of one PWDR entry gives</p>
2873
2874<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2875 id="Picture_x0020_9" o:spid="_x0000_i1072" type="#_x0000_t75" style='width:525pt;
2876 height:450pt;visibility:visible;mso-wrap-style:square'>
2877 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
2878  o:title=""/>
2879</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2880src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
2881v:shapes="Picture_x0020_9"><![endif]></span></p>
2882
2883<p class=MsoNormal>As our experience in Method A, the calculated peaks are too
2884sharp. We need to vary the <span class=SpellE>mustrain</span> parameters for
2885both phases. Go to the Data tab for each phase, check the <span class=SpellE>microstrain</span>
2886box and do Edit/Copy flags for all the data sets. Then do another
2887Calculate/Sequential refine. My Sequential refinement results showed great
2888improvement but incomplete refinement</p>
2889
2890<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2891 id="Picture_x0020_10" o:spid="_x0000_i1071" type="#_x0000_t75" style='width:525pt;
2892 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2893 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png"
2894  o:title=""/>
2895</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
2896src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png"
2897v:shapes="Picture_x0020_10"><![endif]></span></p>
2898
2899<p class=MsoNormal>Repeating the sequential refinement (twice) gave convergence.</p>
2900
2901<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2902 id="Picture_x0020_11" o:spid="_x0000_i1070" type="#_x0000_t75" style='width:525pt;
2903 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2904 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
2905  o:title=""/>
2906</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
2907src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
2908v:shapes="Picture_x0020_11"><![endif]></span></p>
2909
2910<p class=MsoNormal>Examination of the PWDR data sets showed a fairly good fit
2911but some discrepancies (especially for <span class=SpellE>Azm</span>=20.00)</p>
2912
2913<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2914 id="Picture_x0020_12" o:spid="_x0000_i1069" type="#_x0000_t75" style='width:525pt;
2915 height:450pt;visibility:visible;mso-wrap-style:square'>
2916 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png"
2917  o:title=""/>
2918</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2919src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png"
2920v:shapes="Picture_x0020_12"><![endif]></span></p>
2921
2922<p class=MsoNormal>Showing that perhaps the B19’ phase needs high order
2923spherical harmonics. Select the Data tab for the B19’ phase and change the
2924Harmonic order to 6. Then do Edit/Copy selected data for <span class=SpellE>Pref.Ori</span>.
2925<span class=GramE>to</span> the other data sets. This (after few repeats) gives
2926a further improvement in the fit</p>
2927
2928<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2929 id="Picture_x0020_13" o:spid="_x0000_i1068" type="#_x0000_t75" style='width:525pt;
2930 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2931 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
2932  o:title=""/>
2933</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
2934src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
2935v:shapes="Picture_x0020_13"><![endif]></span></p>
2936
2937<p class=MsoNormal>This fit is now sufficient for us to proceed to the next
2938step and determine the texture of the two phases.</p>
2939
2940<h3>Step 2. Texture analysis</h3>
2941
2942<p class=MsoNormal>During the sequential refinements done in Step 1, we fitted
2943the profiles allowing strain parameters (<span class=SpellE>Dij</span>) for
2944peak position shifts and <span class=SpellE>microstrain</span> for peak shape.
2945We modeled the intensity variation with a spherical harmonics preferred
2946orientation correction. If you select any PWDR entry from the GSAS-II data tree
2947and pick the Reflection List subentry (at the bottom) you can see the magnitude
2948of this correction for each reflection in each phase.</p>
2949
2950<p class=MsoNormal>For the B2 phase we see</p>
2951
2952<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2953 id="Picture_x0020_14" o:spid="_x0000_i1067" type="#_x0000_t75" style='width:659.25pt;
2954 height:262.5pt;visibility:visible;mso-wrap-style:square'>
2955 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
2956  o:title=""/>
2957</v:shape><![endif]--><![if !vml]><img border=0 width=879 height=350
2958src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
2959v:shapes="Picture_x0020_14"><![endif]></span></p>
2960
2961<p class=MsoNormal><span class=GramE>and</span> for the B19’ phase we see</p>
2962
2963<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2964 id="Picture_x0020_15" o:spid="_x0000_i1066" type="#_x0000_t75" style='width:659.25pt;
2965 height:273pt;visibility:visible;mso-wrap-style:square'>
2966 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
2967  o:title=""/>
2968</v:shape><![endif]--><![if !vml]><img border=0 width=879 height=364
2969src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
2970v:shapes="Picture_x0020_15"><![endif]></span></p>
2971
2972<p class=MsoNormal>The preferred orientation correction is <span class=SpellE>Prfo</span>;
2973notice a few entries in red. These are nonphysical correction values (the
2974correction can’t be negative) but by in large these are small. This next step
2975uses these corrections as input data for a texture refinement. To start select
2976the Texture tab for the B2 phase; you’ll see</p>
2977
2978<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2979 id="Picture_x0020_16" o:spid="_x0000_i1065" type="#_x0000_t75" style='width:456pt;
2980 height:217.5pt;visibility:visible;mso-wrap-style:square'>
2981 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
2982  o:title=""/>
2983</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290
2984src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
2985v:shapes="Picture_x0020_16"><![endif]></span></p>
2986
2987<p class=MsoNormal>Since this sample has wire texture, we’ll use the default
2988Texture model (cylindrical). Then set the Harmonic order to 12 (what we used
2989earlier) and check the Refine and Show <span class=SpellE>coeff</span> boxes.
2990The data window will be redrawn (and a blank plot will appear).</p>
2991
2992<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2993 id="Picture_x0020_17" o:spid="_x0000_i1064" type="#_x0000_t75" style='width:456pt;
2994 height:250.5pt;visibility:visible;mso-wrap-style:square'>
2995 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
2996  o:title=""/>
2997</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
2998src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
2999v:shapes="Picture_x0020_17"><![endif]></span></p>
3000
3001<p class=MsoNormal>Do Texture/Refine texture from the menu; the window will be
3002repainted and a <span class=SpellE>bullseye</span> pole figure will appear. </p>
3003
3004<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3005 id="Picture_x0020_20" o:spid="_x0000_i1063" type="#_x0000_t75" style='width:480pt;
3006 height:267.75pt;visibility:visible;mso-wrap-style:square'>
3007 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png"
3008  o:title=""/>
3009</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3010src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png"
3011v:shapes="Picture_x0020_20"><![endif]></span></p>
3012
3013<p class=MsoNormal>Change the Texture plot type to Inverse pole figure to get a
3014more useful plot</p>
3015
3016<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3017 id="Picture_x0020_19" o:spid="_x0000_i1062" type="#_x0000_t75" style='width:525pt;
3018 height:450pt;visibility:visible;mso-wrap-style:square'>
3019 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
3020  o:title=""/>
3021</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3022src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
3023v:shapes="Picture_x0020_19"><![endif]></span></p>
3024
3025<p class=MsoNormal>This is essentially the same as we obtained earlier in
3026Method <span class=GramE>A</span> (maybe not quite as strong here).</p>
3027
3028<p class=MsoNormal>Now select the Texture tab for the B19’ phase and do the
3029same; use Harmonic order 10 as we did earlier in Method A. After setting the two
3030flags and doing Texture/Refine texture we get</p>
3031
3032<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3033 id="Picture_x0020_21" o:spid="_x0000_i1061" type="#_x0000_t75" style='width:502.5pt;
3034 height:375pt;visibility:visible;mso-wrap-style:square'>
3035 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png"
3036  o:title=""/>
3037</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
3038src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png"
3039v:shapes="Picture_x0020_21"><![endif]></span></p>
3040
3041<p class=MsoNormal>And a <span class=SpellE>bullseye</span> pole figure; change
3042that to Inverse pole figure to see the texture</p>
3043
3044<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3045 id="Picture_x0020_22" o:spid="_x0000_i1060" type="#_x0000_t75" style='width:525pt;
3046 height:450pt;visibility:visible;mso-wrap-style:square'>
3047 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
3048  o:title=""/>
3049</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3050src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
3051v:shapes="Picture_x0020_22"><![endif]></span></p>
3052
3053<p class=MsoNormal>Again this is very similar to what we found in Method A but
3054again not quite as strong (max MRD ~13 instead of ~18).</p>
3055
3056<p class=MsoNormal>Now do a File/Save project from the main menu; this saves the
3057final texture results done in Step 2 (you also will need it for Method C).</p>
3058
3059<h2>Method C. Sequential refinement &amp; full texture refinement</h2>
3060
3061<h3>Introduction</h3>
3062
3063<p class=MsoNormal>This uses the same approach as Method B except that after
3064the sequential refinements are finished we then fix almost all the parameters
3065and then do a final texture refinement with all the data. Thus, this is a
3066replacement for Step 2 in Method B. To begin do <b style='mso-bidi-font-weight:
3067normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3068minor-latin;mso-hansi-theme-font:minor-latin'>File/Open project…</span></b> for
3069the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3070style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3071mso-hansi-theme-font:minor-latin'>NiTi-B.gpx</span></b></span> file created in Method
3072B and then do a <b style='mso-bidi-font-weight:normal'><span style='font-family:
3073"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3074minor-latin'>File/Save project as…</span></b> to save it as <span class=SpellE><b
3075style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3076mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b
3077style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3078mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-C</span></b>.
3079This renames the project and it should have one IMG, 10 PWDR entries and two
3080phases of <span class=SpellE>NiTi</span> (B2 and B19’).</p>
3081
3082<h3>Step 1. Clearing unwanted variables from sequential refinement</h3>
3083
3084<p class=MsoNormal>Here we want to clear refinement flags for all parameters
3085that need not be varied in a texture analysis refinement. The general rule is
3086to not refine any parameter unless we expect it to affect the peak intensities.
3087These are listed below:</p>
3088
3089<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo3'><![if !supportLists]><span
3090style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
3091style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3092style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3093mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>:
3094as the background was fit during the sequential refinement we should fix it
3095here. Select any <b style='mso-bidi-font-weight:normal'><span style='font-family:
3096"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3097minor-latin'>PWDR</span></b> entry and choose the <b style='mso-bidi-font-weight:
3098normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3099minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b> subentry
3100for it. Clear the <b style='mso-bidi-font-weight:normal'><span
3101style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3102mso-hansi-theme-font:minor-latin'>Refine</span></b> flags and the do <b
3103style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3104mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Copy
3105flags</span></b> selecting all data sets. This will clear all background
3106refinement flags.</p>
3107
3108<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo3'><![if !supportLists]><span
3109style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
3110style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3111style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3112mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3113phase: we do not want to refine either the <span class=SpellE>microstrain</span>,
3114D<sub>11</sub>, or preferred orientation coefficients. Select the <b
3115style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3116mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3117phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
3118"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3119minor-latin'>Data</span></b> tab. <span class=GramE>Clear</span> the <span
3120class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3121"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3122minor-latin'>microstrain</span></b></span>, <b style='mso-bidi-font-weight:
3123normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3124minor-latin;mso-hansi-theme-font:minor-latin'>D<sub>11</sub></span></b> and <b
3125style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3126mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
3127orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
3128style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3129mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
3130avoid a lot of nasty (but harmless) messages at the start of the refinement). Then
3131do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3132mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3133flags</span></b> selecting all data to clear all the flags and an <b
3134style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3135mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3136selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
3137normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3138minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
3139copy the zeroed out harmonic coefficients.</p>
3140
3141<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l1 level1 lfo3'><![if !supportLists]><span
3142style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
3143style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3144style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3145mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>:
3146we do not want to refine either the <span class=SpellE>microstrain</span>, <span
3147class=SpellE>Dij</span>, or preferred orientation coefficients. Select the <b
3148style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3149mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3150phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
3151"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3152minor-latin'>Data</span></b> tab. Clear the <span class=SpellE><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'>microstrain</span></b></span>,
3155four <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3156style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3157mso-hansi-theme-font:minor-latin'>Dij</span></b></span> and <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'>Preferred
3160orientation</span></b> boxes. Also set the <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'>Harmonic order</span></b> to zero (this will
3163avoid a lot of nasty (but harmless) messages at the start of the refinement).
3164Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3165mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3166flags</span></b> selecting all data to clear all the flags and an <b
3167style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3168mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3169selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
3170normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3171minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
3172copy the zeroed out harmonic coefficients.<o:p></o:p></p>
3173
3174<p class=MsoNormal style='margin-left:.25in'><o:p>&nbsp;</o:p></p>
3175
3176<p class=MsoNormal style='margin-left:.25in'>Notice that we have allowed
3177refinement of the <b style='mso-bidi-font-weight:normal'><span
3178style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3179mso-hansi-theme-font:minor-latin'>Phase fractions</span></b>; these may change
3180during the texture refinement. Now select the <b style='mso-bidi-font-weight:
3181normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3182minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b> tab for the <b
3183style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3184mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3185phase (it may still have values from the Method B).</p>
3186
3187<p class=MsoNormal style='margin-left:.25in'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3188 id="Picture_x0020_23" o:spid="_x0000_i1059" type="#_x0000_t75" style='width:480pt;
3189 height:267.75pt;visibility:visible;mso-wrap-style:square'>
3190 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
3191  o:title=""/>
3192</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3193src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
3194v:shapes="Picture_x0020_23"><![endif]></span></p>
3195
3196<p class=MsoNormal style='margin-left:.25in'>You can clear these by setting the
3197<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3198mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic
3199order</span></b> to zero and then back to <b style='mso-bidi-font-weight:normal'><span
3200style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3201mso-hansi-theme-font:minor-latin'>12</span></b>. Leave the <b style='mso-bidi-font-weight:
3202normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3203minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b> &amp; <b
3204style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3205mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b>
3206boxes checked.</p>
3207
3208<p class=MsoNormal style='margin-left:.25in'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3209 id="Picture_x0020_24" o:spid="_x0000_i1058" type="#_x0000_t75" style='width:480pt;
3210 height:267.75pt;visibility:visible;mso-wrap-style:square'>
3211 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
3212  o:title=""/>
3213</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3214src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
3215v:shapes="Picture_x0020_24"><![endif]></span></p>
3216
3217<p class=MsoNormal style='margin-left:.25in'>Then do the same for the <b
3218style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3219mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3220phase. Select the <b style='mso-bidi-font-weight:normal'><span
3221style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3222mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and its <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'>Texture</span></b>
3225tab. <span class=GramE>Set</span> 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'>Harmonic order</span></b> to zero and then
3228back to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3229mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>.
3230Leave the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3231mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b>
3232and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3233mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b>
3234boxes checked. This completes the setup for the full texture refinement.</p>
3235
3236<h3>Step 2. Texture refinement</h3>
3237
3238<p class=MsoNormal>Do <b style='mso-bidi-font-weight:normal'><span
3239style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3240mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from the main
3241menu; you will see the warning message</p>
3242
3243<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3244 id="Picture_x0020_25" o:spid="_x0000_i1057" type="#_x0000_t75" style='width:363pt;
3245 height:120.75pt;visibility:visible;mso-wrap-style:square'>
3246 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
3247  o:title=""/>
3248</v:shape><![endif]--><![if !vml]><img border=0 width=484 height=161
3249src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
3250v:shapes="Picture_x0020_25"><![endif]></span></p>
3251
3252<p class=MsoNormal>In this case you do want to do a <span class=SpellE>nonsequential</span>
3253full refinement, so press the OK button. A quick look at the console will show
3254that there are 61 variables in this refinement. If yours shows more then you
3255didn’t clear all the flags in Step 1. The <b style='mso-bidi-font-weight:normal'><span
3256style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3257mso-hansi-theme-font:minor-latin'>Sequential results</span></b> entry is
3258deleted from the GSAS-II data tree. A progress bar will show giving the
3259residuals during the refinement. When finished, select the <b style='mso-bidi-font-weight:
3260normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3261minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> phase and its <b
3262style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3263mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
3264tab; if the Texture plot type is still <b style='mso-bidi-font-weight:normal'><span
3265style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3266mso-hansi-theme-font:minor-latin'>Inverse pole figure</span></b> (from Method
3267B) you should see</p>
3268
3269<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3270 id="Picture_x0020_26" o:spid="_x0000_i1056" type="#_x0000_t75" style='width:525pt;
3271 height:450pt;visibility:visible;mso-wrap-style:square'>
3272 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
3273  o:title=""/>
3274</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3275src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
3276v:shapes="Picture_x0020_26"><![endif]></span></p>
3277
3278<p class=MsoNormal><span class=GramE>which</span> is almost identical to that
3279from Method A. The coefficients are seen in</p>
3280
3281<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3282 id="Picture_x0020_27" o:spid="_x0000_i1055" type="#_x0000_t75" style='width:480pt;
3283 height:267.75pt;visibility:visible;mso-wrap-style:square'>
3284 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
3285  o:title=""/>
3286</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3287src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
3288v:shapes="Picture_x0020_27"><![endif]></span></p>
3289
3290<p class=MsoNormal>Now select the <b style='mso-bidi-font-weight:normal'><span
3291style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3292mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and its <b
3293style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3294mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
3295tab; the inverse pole figure is</p>
3296
3297<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3298 id="Picture_x0020_28" o:spid="_x0000_i1054" type="#_x0000_t75" style='width:525pt;
3299 height:450pt;visibility:visible;mso-wrap-style:square'>
3300 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
3301  o:title=""/>
3302</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3303src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
3304v:shapes="Picture_x0020_28"><![endif]></span><o:p></o:p></p>
3305
3306<p class=MsoNormal><span class=GramE>and</span> also almost identical to what
3307was obtained in Method A; the coefficients are seen in</p>
3308
3309<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3310 id="Picture_x0020_58" o:spid="_x0000_i1053" type="#_x0000_t75" style='width:502.5pt;
3311 height:375pt;visibility:visible;mso-wrap-style:square'>
3312 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png"
3313  o:title=""/>
3314</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
3315src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png"
3316v:shapes="Picture_x0020_58"><![endif]></span></p>
3317
3318<p class=MsoNormal>With this Method you can add parameters (atom coordinates
3319&amp; thermal motion parameters) that could not be refined in method B. It
3320should be clear from this tutorial that in more complex textures where the data
3321set may consist of slices obtained from a suite of 2D images collected as the
3322sample is rotated, Method C will give a relatively fast determination of the
3323texture without resorting to large matrix least-squares refinements.</p>
3324
3325</div>
3326
3327</body>
3328
3329</html>
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