source: Tutorials/2DTexture/Texture analysis of 2D data in GSAS-II.htm @ 1870

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415  <w:LsdException Locked="false" Priority="70" Name="Dark List"/>
416  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/>
417  <w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
418  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
419  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
420  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
421  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
422  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
423  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
424  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
425  <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
426  <w:LsdException Locked="false" Priority="34" QFormat="true"
427   Name="List Paragraph"/>
428  <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
429  <w:LsdException Locked="false" Priority="30" QFormat="true"
430   Name="Intense Quote"/>
431  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
432  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
433  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
434  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
435  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
436  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
437  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
438  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
439  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
440  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
441  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
442  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
443  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
444  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
445  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
446  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
447  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
448  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
449  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
450  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
451  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
452  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
453  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
454  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
455  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
456  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
457  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
458  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
459  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
460  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
461  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
462  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
463  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
464  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
465  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
466  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
467  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
468  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
469  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
470  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
471  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
472  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
473  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
474  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
475  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
476  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
477  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
478  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
479  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
480  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
481  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
482  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
483  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
484  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
485  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
486  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
487  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
488  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
489  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
490  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
491  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
492  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
493  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
494  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
495  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
496  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
497  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
498  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
499  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
500  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
501  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
502  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
503  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
504  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
505  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
506  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
507  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
508  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
509  <w:LsdException Locked="false" Priority="19" QFormat="true"
510   Name="Subtle Emphasis"/>
511  <w:LsdException Locked="false" Priority="21" QFormat="true"
512   Name="Intense Emphasis"/>
513  <w:LsdException Locked="false" Priority="31" QFormat="true"
514   Name="Subtle Reference"/>
515  <w:LsdException Locked="false" Priority="32" QFormat="true"
516   Name="Intense Reference"/>
517  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
518  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
519   UnhideWhenUsed="true" Name="Bibliography"/>
520  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
521   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
522  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
523  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
524  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
525  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
526  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
527  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
528  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
529  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
530  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
531  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
532  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
533  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
534  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
535  <w:LsdException Locked="false" Priority="46"
536   Name="Grid Table 1 Light Accent 1"/>
537  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
538  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
539  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
540  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
541  <w:LsdException Locked="false" Priority="51"
542   Name="Grid Table 6 Colorful Accent 1"/>
543  <w:LsdException Locked="false" Priority="52"
544   Name="Grid Table 7 Colorful Accent 1"/>
545  <w:LsdException Locked="false" Priority="46"
546   Name="Grid Table 1 Light Accent 2"/>
547  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
548  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
549  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
550  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
551  <w:LsdException Locked="false" Priority="51"
552   Name="Grid Table 6 Colorful Accent 2"/>
553  <w:LsdException Locked="false" Priority="52"
554   Name="Grid Table 7 Colorful Accent 2"/>
555  <w:LsdException Locked="false" Priority="46"
556   Name="Grid Table 1 Light Accent 3"/>
557  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
558  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
559  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
560  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
561  <w:LsdException Locked="false" Priority="51"
562   Name="Grid Table 6 Colorful Accent 3"/>
563  <w:LsdException Locked="false" Priority="52"
564   Name="Grid Table 7 Colorful Accent 3"/>
565  <w:LsdException Locked="false" Priority="46"
566   Name="Grid Table 1 Light Accent 4"/>
567  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
568  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
569  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
570  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
571  <w:LsdException Locked="false" Priority="51"
572   Name="Grid Table 6 Colorful Accent 4"/>
573  <w:LsdException Locked="false" Priority="52"
574   Name="Grid Table 7 Colorful Accent 4"/>
575  <w:LsdException Locked="false" Priority="46"
576   Name="Grid Table 1 Light Accent 5"/>
577  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
578  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
579  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
580  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
581  <w:LsdException Locked="false" Priority="51"
582   Name="Grid Table 6 Colorful Accent 5"/>
583  <w:LsdException Locked="false" Priority="52"
584   Name="Grid Table 7 Colorful Accent 5"/>
585  <w:LsdException Locked="false" Priority="46"
586   Name="Grid Table 1 Light Accent 6"/>
587  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
588  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
589  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
590  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
591  <w:LsdException Locked="false" Priority="51"
592   Name="Grid Table 6 Colorful Accent 6"/>
593  <w:LsdException Locked="false" Priority="52"
594   Name="Grid Table 7 Colorful Accent 6"/>
595  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
596  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
597  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
598  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
599  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
600  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
601  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
602  <w:LsdException Locked="false" Priority="46"
603   Name="List Table 1 Light Accent 1"/>
604  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
605  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
606  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
607  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
608  <w:LsdException Locked="false" Priority="51"
609   Name="List Table 6 Colorful Accent 1"/>
610  <w:LsdException Locked="false" Priority="52"
611   Name="List Table 7 Colorful Accent 1"/>
612  <w:LsdException Locked="false" Priority="46"
613   Name="List Table 1 Light Accent 2"/>
614  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
615  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
616  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
617  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
618  <w:LsdException Locked="false" Priority="51"
619   Name="List Table 6 Colorful Accent 2"/>
620  <w:LsdException Locked="false" Priority="52"
621   Name="List Table 7 Colorful Accent 2"/>
622  <w:LsdException Locked="false" Priority="46"
623   Name="List Table 1 Light Accent 3"/>
624  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
625  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
626  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
627  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
628  <w:LsdException Locked="false" Priority="51"
629   Name="List Table 6 Colorful Accent 3"/>
630  <w:LsdException Locked="false" Priority="52"
631   Name="List Table 7 Colorful Accent 3"/>
632  <w:LsdException Locked="false" Priority="46"
633   Name="List Table 1 Light Accent 4"/>
634  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
635  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
636  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
637  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
638  <w:LsdException Locked="false" Priority="51"
639   Name="List Table 6 Colorful Accent 4"/>
640  <w:LsdException Locked="false" Priority="52"
641   Name="List Table 7 Colorful Accent 4"/>
642  <w:LsdException Locked="false" Priority="46"
643   Name="List Table 1 Light Accent 5"/>
644  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
645  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
646  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
647  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
648  <w:LsdException Locked="false" Priority="51"
649   Name="List Table 6 Colorful Accent 5"/>
650  <w:LsdException Locked="false" Priority="52"
651   Name="List Table 7 Colorful Accent 5"/>
652  <w:LsdException Locked="false" Priority="46"
653   Name="List Table 1 Light Accent 6"/>
654  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
655  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
656  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
657  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
658  <w:LsdException Locked="false" Priority="51"
659   Name="List Table 6 Colorful Accent 6"/>
660  <w:LsdException Locked="false" Priority="52"
661   Name="List Table 7 Colorful Accent 6"/>
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784        mso-margin-bottom-alt:auto;
785        margin-left:0in;
786        mso-pagination:widow-orphan;
787        mso-outline-level:5;
788        font-size:12.0pt;
789        font-family:"Times New Roman",serif;
790        mso-fareast-font-family:"Times New Roman";
791        mso-fareast-theme-font:minor-fareast;
792        color:#4F4FFF;
793        font-weight:bold;}
794p.MsoTitle, li.MsoTitle, div.MsoTitle
795        {mso-style-noshow:yes;
796        mso-style-priority:10;
797        mso-style-unhide:no;
798        mso-style-qformat:yes;
799        mso-style-link:"Title Char";
800        mso-style-next:Normal;
801        margin-top:0in;
802        margin-right:0in;
803        margin-bottom:15.0pt;
804        margin-left:0in;
805        mso-add-space:auto;
806        mso-pagination:widow-orphan;
807        border:none;
808        mso-border-bottom-alt:solid #4F81BD 1.0pt;
809        mso-border-bottom-themecolor:accent1;
810        padding:0in;
811        mso-padding-alt:0in 0in 4.0pt 0in;
812        font-size:26.0pt;
813        font-family:"Cambria",serif;
814        mso-ascii-font-family:Cambria;
815        mso-ascii-theme-font:major-latin;
816        mso-fareast-font-family:"Times New Roman";
817        mso-fareast-theme-font:major-fareast;
818        mso-hansi-font-family:Cambria;
819        mso-hansi-theme-font:major-latin;
820        mso-bidi-font-family:"Times New Roman";
821        mso-bidi-theme-font:major-bidi;
822        color:#17365D;
823        mso-themecolor:text2;
824        mso-themeshade:191;
825        letter-spacing:.25pt;
826        mso-font-kerning:14.0pt;}
827p.MsoTitleCxSpFirst, li.MsoTitleCxSpFirst, div.MsoTitleCxSpFirst
828        {mso-style-noshow:yes;
829        mso-style-priority:10;
830        mso-style-unhide:no;
831        mso-style-qformat:yes;
832        mso-style-link:"Title Char";
833        mso-style-next:Normal;
834        mso-style-type:export-only;
835        margin:0in;
836        margin-bottom:.0001pt;
837        mso-add-space:auto;
838        mso-pagination:widow-orphan;
839        border:none;
840        mso-border-bottom-alt:solid #4F81BD 1.0pt;
841        mso-border-bottom-themecolor:accent1;
842        padding:0in;
843        mso-padding-alt:0in 0in 4.0pt 0in;
844        font-size:26.0pt;
845        font-family:"Cambria",serif;
846        mso-ascii-font-family:Cambria;
847        mso-ascii-theme-font:major-latin;
848        mso-fareast-font-family:"Times New Roman";
849        mso-fareast-theme-font:major-fareast;
850        mso-hansi-font-family:Cambria;
851        mso-hansi-theme-font:major-latin;
852        mso-bidi-font-family:"Times New Roman";
853        mso-bidi-theme-font:major-bidi;
854        color:#17365D;
855        mso-themecolor:text2;
856        mso-themeshade:191;
857        letter-spacing:.25pt;
858        mso-font-kerning:14.0pt;}
859p.MsoTitleCxSpMiddle, li.MsoTitleCxSpMiddle, div.MsoTitleCxSpMiddle
860        {mso-style-noshow:yes;
861        mso-style-priority:10;
862        mso-style-unhide:no;
863        mso-style-qformat:yes;
864        mso-style-link:"Title Char";
865        mso-style-next:Normal;
866        mso-style-type:export-only;
867        margin:0in;
868        margin-bottom:.0001pt;
869        mso-add-space:auto;
870        mso-pagination:widow-orphan;
871        border:none;
872        mso-border-bottom-alt:solid #4F81BD 1.0pt;
873        mso-border-bottom-themecolor:accent1;
874        padding:0in;
875        mso-padding-alt:0in 0in 4.0pt 0in;
876        font-size:26.0pt;
877        font-family:"Cambria",serif;
878        mso-ascii-font-family:Cambria;
879        mso-ascii-theme-font:major-latin;
880        mso-fareast-font-family:"Times New Roman";
881        mso-fareast-theme-font:major-fareast;
882        mso-hansi-font-family:Cambria;
883        mso-hansi-theme-font:major-latin;
884        mso-bidi-font-family:"Times New Roman";
885        mso-bidi-theme-font:major-bidi;
886        color:#17365D;
887        mso-themecolor:text2;
888        mso-themeshade:191;
889        letter-spacing:.25pt;
890        mso-font-kerning:14.0pt;}
891p.MsoTitleCxSpLast, li.MsoTitleCxSpLast, div.MsoTitleCxSpLast
892        {mso-style-noshow:yes;
893        mso-style-priority:10;
894        mso-style-unhide:no;
895        mso-style-qformat:yes;
896        mso-style-link:"Title Char";
897        mso-style-next:Normal;
898        mso-style-type:export-only;
899        margin-top:0in;
900        margin-right:0in;
901        margin-bottom:15.0pt;
902        margin-left:0in;
903        mso-add-space:auto;
904        mso-pagination:widow-orphan;
905        border:none;
906        mso-border-bottom-alt:solid #4F81BD 1.0pt;
907        mso-border-bottom-themecolor:accent1;
908        padding:0in;
909        mso-padding-alt:0in 0in 4.0pt 0in;
910        font-size:26.0pt;
911        font-family:"Cambria",serif;
912        mso-ascii-font-family:Cambria;
913        mso-ascii-theme-font:major-latin;
914        mso-fareast-font-family:"Times New Roman";
915        mso-fareast-theme-font:major-fareast;
916        mso-hansi-font-family:Cambria;
917        mso-hansi-theme-font:major-latin;
918        mso-bidi-font-family:"Times New Roman";
919        mso-bidi-theme-font:major-bidi;
920        color:#17365D;
921        mso-themecolor:text2;
922        mso-themeshade:191;
923        letter-spacing:.25pt;
924        mso-font-kerning:14.0pt;}
925a:link, span.MsoHyperlink
926        {mso-style-noshow:yes;
927        mso-style-priority:99;
928        color:blue;
929        text-decoration:underline;
930        text-underline:single;}
931a:visited, span.MsoHyperlinkFollowed
932        {mso-style-noshow:yes;
933        mso-style-priority:99;
934        color:purple;
935        text-decoration:underline;
936        text-underline:single;}
937p.MsoDocumentMap, li.MsoDocumentMap, div.MsoDocumentMap
938        {mso-style-noshow:yes;
939        mso-style-priority:99;
940        mso-style-link:"Document Map Char";
941        margin-top:0in;
942        margin-right:0in;
943        margin-bottom:4.0pt;
944        margin-left:0in;
945        mso-pagination:widow-orphan;
946        font-size:8.0pt;
947        font-family:"Tahoma",sans-serif;
948        mso-fareast-font-family:"Times New Roman";
949        mso-fareast-theme-font:minor-fareast;}
950p
951        {mso-style-noshow:yes;
952        mso-style-priority:99;
953        mso-margin-top-alt:auto;
954        margin-right:0in;
955        mso-margin-bottom-alt:auto;
956        margin-left:0in;
957        mso-pagination:widow-orphan;
958        font-size:12.0pt;
959        font-family:"Times New Roman",serif;
960        mso-fareast-font-family:"Times New Roman";
961        mso-fareast-theme-font:minor-fareast;}
962pre
963        {mso-style-noshow:yes;
964        mso-style-priority:99;
965        mso-style-link:"HTML Preformatted Char";
966        margin-top:0in;
967        margin-right:0in;
968        margin-bottom:4.0pt;
969        margin-left:0in;
970        mso-pagination:widow-orphan;
971        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;
972        font-size:10.0pt;
973        font-family:"Courier New";
974        mso-fareast-font-family:"Times New Roman";}
975p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
976        {mso-style-noshow:yes;
977        mso-style-priority:99;
978        mso-style-link:"Balloon Text Char";
979        margin-top:0in;
980        margin-right:0in;
981        margin-bottom:4.0pt;
982        margin-left:0in;
983        mso-pagination:widow-orphan;
984        font-size:8.0pt;
985        font-family:"Tahoma",sans-serif;
986        mso-fareast-font-family:"Times New Roman";
987        mso-fareast-theme-font:minor-fareast;}
988span.MsoPlaceholderText
989        {mso-style-noshow:yes;
990        mso-style-priority:99;
991        mso-style-unhide:no;
992        color:gray;}
993p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing
994        {mso-style-noshow:yes;
995        mso-style-priority:1;
996        mso-style-unhide:no;
997        mso-style-qformat:yes;
998        mso-style-parent:"";
999        margin-top:0in;
1000        margin-right:0in;
1001        margin-bottom:4.0pt;
1002        margin-left:0in;
1003        mso-pagination:widow-orphan;
1004        font-size:12.0pt;
1005        font-family:"Times New Roman",serif;
1006        mso-fareast-font-family:"Times New Roman";
1007        mso-fareast-theme-font:minor-fareast;}
1008p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
1009        {mso-style-noshow:yes;
1010        mso-style-priority:34;
1011        mso-style-unhide:no;
1012        mso-style-qformat:yes;
1013        margin-top:0in;
1014        margin-right:0in;
1015        margin-bottom:4.0pt;
1016        margin-left:.5in;
1017        mso-add-space:auto;
1018        mso-pagination:widow-orphan;
1019        font-size:12.0pt;
1020        font-family:"Times New Roman",serif;
1021        mso-fareast-font-family:"Times New Roman";
1022        mso-fareast-theme-font:minor-fareast;}
1023p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
1024        {mso-style-noshow:yes;
1025        mso-style-priority:34;
1026        mso-style-unhide:no;
1027        mso-style-qformat:yes;
1028        mso-style-type:export-only;
1029        margin-top:0in;
1030        margin-right:0in;
1031        margin-bottom:0in;
1032        margin-left:.5in;
1033        margin-bottom:.0001pt;
1034        mso-add-space:auto;
1035        mso-pagination:widow-orphan;
1036        font-size:12.0pt;
1037        font-family:"Times New Roman",serif;
1038        mso-fareast-font-family:"Times New Roman";
1039        mso-fareast-theme-font:minor-fareast;}
1040p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
1041        {mso-style-noshow:yes;
1042        mso-style-priority:34;
1043        mso-style-unhide:no;
1044        mso-style-qformat:yes;
1045        mso-style-type:export-only;
1046        margin-top:0in;
1047        margin-right:0in;
1048        margin-bottom:0in;
1049        margin-left:.5in;
1050        margin-bottom:.0001pt;
1051        mso-add-space:auto;
1052        mso-pagination:widow-orphan;
1053        font-size:12.0pt;
1054        font-family:"Times New Roman",serif;
1055        mso-fareast-font-family:"Times New Roman";
1056        mso-fareast-theme-font:minor-fareast;}
1057p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
1058        {mso-style-noshow:yes;
1059        mso-style-priority:34;
1060        mso-style-unhide:no;
1061        mso-style-qformat:yes;
1062        mso-style-type:export-only;
1063        margin-top:0in;
1064        margin-right:0in;
1065        margin-bottom:4.0pt;
1066        margin-left:.5in;
1067        mso-add-space:auto;
1068        mso-pagination:widow-orphan;
1069        font-size:12.0pt;
1070        font-family:"Times New Roman",serif;
1071        mso-fareast-font-family:"Times New Roman";
1072        mso-fareast-theme-font:minor-fareast;}
1073span.MsoIntenseReference
1074        {mso-style-priority:32;
1075        mso-style-unhide:no;
1076        mso-style-qformat:yes;
1077        font-variant:small-caps;
1078        color:#C0504D;
1079        mso-themecolor:accent2;
1080        letter-spacing:.25pt;
1081        font-weight:bold;
1082        text-decoration:underline;
1083        text-underline:single;}
1084span.Heading1Char
1085        {mso-style-name:"Heading 1 Char";
1086        mso-style-priority:9;
1087        mso-style-unhide:no;
1088        mso-style-locked:yes;
1089        mso-style-link:"Heading 1";
1090        mso-ansi-font-size:24.0pt;
1091        mso-bidi-font-size:24.0pt;
1092        font-family:"Times New Roman",serif;
1093        mso-ascii-font-family:"Times New Roman";
1094        mso-fareast-font-family:"Times New Roman";
1095        mso-fareast-theme-font:minor-fareast;
1096        mso-hansi-font-family:"Times New Roman";
1097        mso-bidi-font-family:"Times New Roman";
1098        mso-font-kerning:18.0pt;
1099        font-weight:bold;}
1100span.Heading2Char
1101        {mso-style-name:"Heading 2 Char";
1102        mso-style-noshow:yes;
1103        mso-style-priority:9;
1104        mso-style-unhide:no;
1105        mso-style-locked:yes;
1106        mso-style-link:"Heading 2";
1107        mso-ansi-font-size:18.0pt;
1108        mso-bidi-font-size:18.0pt;
1109        font-family:"Times New Roman",serif;
1110        mso-ascii-font-family:"Times New Roman";
1111        mso-fareast-font-family:"Times New Roman";
1112        mso-fareast-theme-font:minor-fareast;
1113        mso-hansi-font-family:"Times New Roman";
1114        mso-bidi-font-family:"Times New Roman";
1115        font-weight:bold;}
1116span.Heading3Char
1117        {mso-style-name:"Heading 3 Char";
1118        mso-style-noshow:yes;
1119        mso-style-priority:9;
1120        mso-style-unhide:no;
1121        mso-style-locked:yes;
1122        mso-style-link:"Heading 3";
1123        mso-ansi-font-size:13.5pt;
1124        mso-bidi-font-size:13.5pt;
1125        font-family:"Times New Roman",serif;
1126        mso-ascii-font-family:"Times New Roman";
1127        mso-fareast-font-family:"Times New Roman";
1128        mso-fareast-theme-font:minor-fareast;
1129        mso-hansi-font-family:"Times New Roman";
1130        mso-bidi-font-family:"Times New Roman";
1131        font-weight:bold;}
1132span.Heading4Char
1133        {mso-style-name:"Heading 4 Char";
1134        mso-style-noshow:yes;
1135        mso-style-priority:9;
1136        mso-style-unhide:no;
1137        mso-style-locked:yes;
1138        mso-style-link:"Heading 4";
1139        mso-ansi-font-size:13.0pt;
1140        mso-bidi-font-size:13.0pt;
1141        font-family:"Cambria",serif;
1142        mso-ascii-font-family:Cambria;
1143        mso-ascii-theme-font:major-latin;
1144        mso-fareast-font-family:"Times New Roman";
1145        mso-fareast-theme-font:major-fareast;
1146        mso-hansi-font-family:Cambria;
1147        mso-hansi-theme-font:major-latin;
1148        mso-bidi-font-family:"Times New Roman";
1149        mso-bidi-theme-font:major-bidi;
1150        color:#4F81BD;
1151        mso-themecolor:accent1;
1152        font-weight:bold;
1153        font-style:italic;}
1154span.Heading5Char
1155        {mso-style-name:"Heading 5 Char";
1156        mso-style-noshow:yes;
1157        mso-style-priority:9;
1158        mso-style-unhide:no;
1159        mso-style-locked:yes;
1160        mso-style-link:"Heading 5";
1161        mso-ansi-font-size:12.0pt;
1162        mso-bidi-font-size:12.0pt;
1163        font-family:"Times New Roman",serif;
1164        mso-ascii-font-family:"Times New Roman";
1165        mso-fareast-font-family:"Times New Roman";
1166        mso-fareast-theme-font:minor-fareast;
1167        mso-hansi-font-family:"Times New Roman";
1168        mso-bidi-font-family:"Times New Roman";
1169        color:#4F4FFF;
1170        font-weight:bold;}
1171span.HTMLPreformattedChar
1172        {mso-style-name:"HTML Preformatted Char";
1173        mso-style-noshow:yes;
1174        mso-style-priority:99;
1175        mso-style-unhide:no;
1176        mso-style-locked:yes;
1177        mso-style-link:"HTML Preformatted";
1178        font-family:"Courier New";
1179        mso-ascii-font-family:"Courier New";
1180        mso-fareast-font-family:"Times New Roman";
1181        mso-hansi-font-family:"Courier New";
1182        mso-bidi-font-family:"Courier New";}
1183span.TitleChar
1184        {mso-style-name:"Title Char";
1185        mso-style-priority:10;
1186        mso-style-unhide:no;
1187        mso-style-locked:yes;
1188        mso-style-link:Title;
1189        mso-ansi-font-size:26.0pt;
1190        mso-bidi-font-size:26.0pt;
1191        font-family:"Cambria",serif;
1192        mso-ascii-font-family:Cambria;
1193        mso-ascii-theme-font:major-latin;
1194        mso-fareast-font-family:"Times New Roman";
1195        mso-fareast-theme-font:major-fareast;
1196        mso-hansi-font-family:Cambria;
1197        mso-hansi-theme-font:major-latin;
1198        mso-bidi-font-family:"Times New Roman";
1199        mso-bidi-theme-font:major-bidi;
1200        color:#17365D;
1201        mso-themecolor:text2;
1202        mso-themeshade:191;
1203        letter-spacing:.25pt;
1204        mso-font-kerning:14.0pt;}
1205span.DocumentMapChar
1206        {mso-style-name:"Document Map Char";
1207        mso-style-noshow:yes;
1208        mso-style-priority:99;
1209        mso-style-unhide:no;
1210        mso-style-locked:yes;
1211        mso-style-link:"Document Map";
1212        mso-ansi-font-size:8.0pt;
1213        mso-bidi-font-size:8.0pt;
1214        font-family:"Tahoma",sans-serif;
1215        mso-ascii-font-family:Tahoma;
1216        mso-fareast-font-family:"Times New Roman";
1217        mso-fareast-theme-font:minor-fareast;
1218        mso-hansi-font-family:Tahoma;
1219        mso-bidi-font-family:Tahoma;}
1220span.BalloonTextChar
1221        {mso-style-name:"Balloon Text Char";
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1413<div class=WordSection1>
1414
1415<h1 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
14160in;line-height:115%'>Texture analysis of 2D data in GSAS-II</h1>
1417
1418<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
14190in;line-height:115%'>Introduction</h2>
1420
1421<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Texture
1422analysis using GSAS-II employs spherical harmonics modeling, as described by
1423Bunge, &quot;Texture Analysis in Materials Science&quot; (1982), and
1424implemented by Von Dreele, J. Appl. <span class=SpellE>Cryst</span>., <b
1425style='mso-bidi-font-weight:normal'>30</b>, 517-525 (1997) in GSAS. The even
1426part of the orientation distribution function (ODF) via the general axis
1427equation</p>
1428
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1530EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
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1532 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image003.png"
1533  o:title="" chromakey="white"/>
1534</v:shape><![endif]--><![if !vml]><img width=43 height=35
1535src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"
1536v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1537style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1538   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1539   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1540   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1541   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1542   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1543   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
1544 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
1545style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1546"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1547top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1548EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1549 type="#_x0000_t75" style='width:30pt;height:26.25pt'>
1550 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png"
1551  o:title="" chromakey="white"/>
1552</v:shape><![endif]--><![if !vml]><img width=40 height=35
1553src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"
1554v:shapes="_x0000_i1025"><![endif]></span><![endif]>, take on values according
1555to the crystal and sample symmetries, respectively, and thus the two inner
1556summations are over only the resulting unique, nonzero harmonic terms. These
1557unique terms are automatically selected by <span style='mso-bidi-font-weight:
1558bold'>GSAS-II</span> according to the space group symmetry and the user chosen
1559sample symmetry. The available sample symmetries are cylindrical symmetry, 2/m,
1560mmm and no symmetry. The choice of sample symmetry profoundly affects the
1561selection of harmonic coefficients. For example, in the case of cylindrical
1562sample symmetry (fiber texture) only <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1563   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1564   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1565   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1566   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1567   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1568   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:sup></m:sSubSup><i
1569 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
1570style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1571"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1572top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1573EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1574 type="#_x0000_t75" style='width:29.25pt;height:26.25pt'>
1575 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image007.png"
1576  o:title="" chromakey="white"/>
1577</v:shape><![endif]--><![if !vml]><img width=39 height=35
1578src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image008.png"
1579v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1580style='mso-spacerun:yes'> </span>terms are nonzero so the rest are excluded
1581from the <span class=GramE>summations</span> and the set of <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1582   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1583   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1584   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1585   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
1586   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1587   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>0</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
1588style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1589"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1590top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1591EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1592 type="#_x0000_t75" style='width:21pt;height:26.25pt'>
1593 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image009.png"
1594  o:title="" chromakey="white"/>
1595</v:shape><![endif]--><![if !vml]><img width=28 height=35
1596src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image010.png"
1597v:shapes="_x0000_i1025"><![endif]></span><![endif]>coefficients is sufficient
1598to describe the effect on the diffraction patterns due to texture. The crystal
1599harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1600   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1601   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1602   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1603   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1604   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1605   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i
1606 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(h)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
1607style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1608"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1609top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1610EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1611 type="#_x0000_t75" style='width:32.25pt;height:26.25pt'>
1612 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image011.png"
1613  o:title="" chromakey="white"/>
1614</v:shape><![endif]--><![if !vml]><img width=43 height=35
1615src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image012.png"
1616v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined for each
1617reflection, h, <i>via</i> polar and azimuthal coordinates (<span
1618style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
1619of a unit vector coincident with h relative to the reciprocal lattice. For most
1620crystal symmetries, <span style='font-family:Symbol'>f</span> is the angle
1621between h and the n-<span class=SpellE>th</span> order major rotation axis of
1622the space group (usually the c-axis) and <span style='font-family:Symbol'>b</span>
1623is the angle between the projections of h and any secondary axis (usually the
1624a-axis) onto the normal plane.<span style='mso-spacerun:yes'>  </span>In a
1625similar way the sample harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1626   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1627   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1628   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1629   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1630   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1631   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
1632 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
1633style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1634"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1635top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1636EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1637 type="#_x0000_t75" style='width:30pt;height:26.25pt'>
1638 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png"
1639  o:title="" chromakey="white"/>
1640</v:shape><![endif]--><![if !vml]><img width=40 height=35
1641src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"
1642v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined according to
1643polar and azimuthal coordinates (<span style='font-family:Symbol'>y</span>, <span
1644style='font-family:Symbol'>g</span>) of a unit vector coincident with the
1645diffraction vector relative to a coordinate system attached to the external
1646form of the sample. For example, in the case of a rolled steel plate having mmm
1647symmetry, the polar angle, <span style='font-family:Symbol'>y</span>, is
1648frequently measured from the normal direction (ND) and <span style='font-family:
1649Symbol'>g</span> is then measured from the rolling direction (RD) in the TD
1650(transverse direction) - RD plane.<span style='mso-spacerun:yes'>  </span>Thus,
1651the general axis equation becomes</p>
1652
1653<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1654margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
1655   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
1656  style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><span
1657    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1658    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1659    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
1660    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#981;</m:r><m:r>,</m:r><m:r>&#946;</m:r><m:r>,</m:r><m:r>&#968;</m:r><m:r>,</m:r><m:r>&#947;</m:r></span></i></m:e></m:d><i
1661  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=1+</m:r></span></i><m:nary><m:naryPr><m:chr
1662     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
1663    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1664    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
1665    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>=2</m:r></span></i></m:sub><m:sup><m:sSub><m:sSubPr><span
1666      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1667      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1668      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
1669      normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i
1670      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub></m:sSub></m:sup><m:e><m:f><m:fPr><span
1671      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1672      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1673      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
1674      normal'><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r>&#960;</m:r></span></i></m:num><m:den><i
1675      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>L</m:r><m:r>+1</m:r></span></i></m:den></m:f></m:e></m:nary><m:nary><m:naryPr><m:chr
1676     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
1677    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1678    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
1679    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i
1680    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:nary><m:naryPr><m:chr
1681       m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
1682      "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
1683      "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
1684      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i
1685      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span
1686        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1687        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1688        normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
1689        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
1690        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1691        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:sSubSup><m:sSubSupPr><span
1692      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1693      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1694      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
1695      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1696      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1697      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
1698      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1699      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1700      normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
1701      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r></span></i></m:e></m:d></m:e></m:nary><m:sSubSup><m:sSubSupPr><span
1702    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1703    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1704    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1705    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1706    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1707    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
1708  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#968;</m:r><m:r>,</m:r><m:r>&#947;</m:r><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
1709style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1710"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
1711mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
1712 id="_x0000_i1025" type="#_x0000_t75" style='width:321pt;height:54pt'>
1713 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image013.png"
1714  o:title="" chromakey="white"/>
1715</v:shape><![endif]--><![if !vml]><img width=428 height=72
1716src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image014.png"
1717v:shapes="_x0000_i1025"><![endif]></span><![endif]><br style='mso-special-character:
1718line-break'>
1719<![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'>
1720<![endif]></p>
1721
1722<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In a
1723diffraction experiment the crystal reflection coordinates (<span
1724style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
1725are determined by the choice of reflection index (<span class=SpellE>hkl</span>)
1726while the sample coordinates (<span style='font-family:Symbol'>y</span>, <span
1727style='font-family:Symbol'>g</span>) are determined by the sample orientation
1728on the diffractometer.</p>
1729
1730<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1731margin-left:0in;line-height:115%'>To define the sample coordinates (<span
1732style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>),
1733we have defined an instrument coordinate system (I, J, K) such that K is normal
1734to the diffraction plane and J is coincident with the direction of the incident
1735radiation beam toward the source. We further define a standard set of
1736right-handed goniometer <span class=SpellE>eulerian</span> angles (<span
1737style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>,
1738<span style='font-family:Symbol'>F</span>) so that <span style='font-family:
1739Symbol'>W</span> and <span style='font-family:Symbol'>F</span> are rotations
1740about K and <span style='font-family:Symbol'>C</span> is a rotation about J
1741when <span style='font-family:Symbol'>W</span> <span style='font-family:Symbol'><span
1742style='mso-spacerun:yes'> </span></span>= 0.<span style='mso-spacerun:yes'> 
1743</span>Finally, as the sample may be mounted so that the sample coordinate
1744system (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>)
1745does not coincide with the instrument coordinate system (I, J, K), we define
1746three <span class=SpellE>eulerian</span> sample rotation offset angles (<span
1747style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
1748<span style='font-family:Symbol'>F</span><sub>s</sub>) that describe the
1749rotation from (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>)
1750to (I, J, K).<span style='mso-spacerun:yes'>  </span>The sample rotation angles
1751are defined so that with the goniometer angles at zero <span style='font-family:
1752Symbol'>W</span><sub>s</sub> and <span style='font-family:Symbol'>F</span><sub>s</sub>
1753are rotations about I and <span style='font-family:Symbol'>C</span><sub>s</sub>
1754is a rotation about J.<span style='mso-spacerun:yes'>  </span>The zeros of
1755these three sample rotation angles can be refined as part of the Rietveld
1756analysis to accommodate any angular offset in sample mounting. After including
1757the diffraction angle, <span style='font-family:Symbol'>Q</span>, and a
1758detector azimuthal angle, A, the full rotation matrix, <b style='mso-bidi-font-weight:
1759normal'>M</b>, is </p>
1760
1761<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1762margin-left:0in;line-height:115%'><b style='mso-bidi-font-weight:normal'>M = -</b><b
1763style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>Q</span>A</b><b
1764style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>W<span
1765class=GramE>C<span style='font-family:"Times New Roman",serif'>(</span></span>F</span>+</b><b
1766style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span><sub>s</sub>)</b><b
1767style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>C</span><span
1768class=SpellE><sub>s</sub><span style='font-family:Symbol'>W</span><sub>s</sub></span><o:p></o:p></b></p>
1769
1770<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1771margin-left:0in;line-height:115%'>By transformation of unit Cartesian vectors
1772(100, 010 and 001) with this rotation matrix, the sample orientation
1773coordinates (<span style='font-family:Symbol'>y</span>, <span style='font-family:
1774Symbol'>g</span>) are given by</p>
1775
1776<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1777margin-left:0in;line-height:115%'><span class=GramE><i>cos</i>(</span><span
1778style='font-family:Symbol'>y</span>) = <!--[if gte msEquation 12]><m:oMath><i
1779 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
1780   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1781   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1782   normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
1783         m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
1784     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1785     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1786     normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
1787      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1788      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1789      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:oMath><![endif]--><![if !msEquation]><span
1790style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1791"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1792top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1793EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1794 type="#_x0000_t75" style='width:33.75pt;height:50.25pt'>
1795 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image015.png"
1796  o:title="" chromakey="white"/>
1797</v:shape><![endif]--><![if !vml]><img width=45 height=67
1798src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.png"
1799v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1800style='mso-spacerun:yes'> </span>and<span style='mso-spacerun:yes'>   </span><i>tan</i>(<span
1801style='font-family:Symbol'>g</span>) = <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type
1802    m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1803   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1804   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
1805   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
1806     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1807     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1808     normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
1809           m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
1810       style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1811       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1812       normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
1813        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1814        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1815        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:num><m:den><i
1816   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
1817     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1818     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1819     normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
1820           m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
1821       style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1822       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1823       normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
1824        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1825        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1826        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
1827style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1828"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1829top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1830EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1831 type="#_x0000_t75" style='width:80.25pt;height:50.25pt'>
1832 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image017.png"
1833  o:title="" chromakey="white"/>
1834</v:shape><![endif]--><![if !vml]><img width=107 height=67
1835src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.png"
1836v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
1837
1838<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1839margin-left:0in;line-height:115%'>The harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1840   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1841   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1842   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1843   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1844   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1845   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i
1846 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
1847style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1848"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1849top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1850EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1851 type="#_x0000_t75" style='width:46.5pt;height:26.25pt'>
1852 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png"
1853  o:title="" chromakey="white"/>
1854</v:shape><![endif]--><![if !vml]><img width=62 height=35
1855src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"
1856v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1857style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1858   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1859   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1860   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1861   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1862   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1863   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
1864 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#968;</m:r><m:r>,</m:r><m:r>&#947;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
1865style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1866"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1867top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1868EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1869 type="#_x0000_t75" style='width:42.75pt;height:26.25pt'>
1870 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png"
1871  o:title="" chromakey="white"/>
1872</v:shape><![endif]--><![if !vml]><img width=57 height=35
1873src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.png"
1874v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are developed from</p>
1875
1876<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1877margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
1878   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
1879    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1880    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1881    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1882    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1883    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1884    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
1885    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1886    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1887    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
1888    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r></span></i></m:e></m:d><i
1889  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:f><m:fPr><span
1890    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1891    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1892    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
1893    normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:num><m:den><m:rad><m:radPr><m:degHide
1894       m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1895      "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1896      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
1897      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>&#960;</m:r></span></i></m:e></m:rad></m:den></m:f><m:sSup><m:sSupPr><span
1898    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1899    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1900    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
1901    normal'><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:e><m:sup><i
1902    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>im&#946;</m:r></span></i></m:sup></m:sSup><m:sSubSup><m:sSubSupPr><span
1903    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1904    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1905    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
1906       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
1907      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1908      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1909      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
1910    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1911    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
1912     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
1913  normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
1914    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1915    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1916    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
1917    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
1918       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
1919    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
1920  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
1921style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1922"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
1923mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
1924 id="_x0000_i1025" type="#_x0000_t75" style='width:165pt;height:42pt'>
1925 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.png"
1926  o:title="" chromakey="white"/>
1927</v:shape><![endif]--><![if !vml]><img width=220 height=56
1928src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"
1929v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
1930
1931<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1932margin-left:0in;line-height:115%'><span class=GramE>where</span> the normalized
1933associated Legendre functions, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1934   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1935   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1936   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
1937      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1938     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1939     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1940     style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
1941   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1942   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i
1943 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
1944style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1945"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1946top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1947EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1948 type="#_x0000_t75" style='width:33pt;height:26.25pt'>
1949 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image025.png"
1950  o:title="" chromakey="white"/>
1951</v:shape><![endif]--><![if !vml]><img width=44 height=35
1952src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image026.png"
1953v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are defined via a Fourier
1954expansion as</p>
1955
1956<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1957margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
1958   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
1959    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1960    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1961    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
1962       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
1963      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1964      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1965      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
1966    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1967    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
1968     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
1969    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1970    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1971    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
1972      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1973      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1974      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
1975      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
1976         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
1977      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
1978  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:nary><m:naryPr><m:chr
1979     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
1980    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1981    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
1982    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>s</m:r><m:r>=0</m:r></span></i></m:sub><m:sup><i
1983    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span
1984      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1985      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1986      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
1987      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i
1988      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1989      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
1990       </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
1991    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1992    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1993    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
1994    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
1995       m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
1996    normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>s&#966;</m:r><m:r>)</m:r></span></i></m:e></m:func></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
1997style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1998"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
1999mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2000 id="_x0000_i1025" type="#_x0000_t75" style='width:154.5pt;height:52.5pt'>
2001 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image027.png"
2002  o:title="" chromakey="white"/>
2003</v:shape><![endif]--><![if !vml]><img width=206 height=70
2004src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image028.png"
2005v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2006
2007<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2008margin-left:0in;line-height:115%'><span class=GramE>for</span> m even and</p>
2009
2010<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2011margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2012   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
2013    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2014    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2015    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2016       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2017      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2018      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2019      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
2020    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2021    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2022     </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
2023    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2024    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2025    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
2026      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2027      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2028      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2029      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2030         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2031      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
2032  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:nary><m:naryPr><m:chr
2033     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2034    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2035    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2036    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>s</m:r><m:r>=1</m:r></span></i></m:sub><m:sup><i
2037    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span
2038      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2039      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2040      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
2041      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i
2042      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2043      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2044       </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
2045    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2046    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2047    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2048    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2049       m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2050    normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>s&#966;</m:r><m:r>)</m:r></span></i></m:e></m:func></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
2051style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2052"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2053mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2054 id="_x0000_i1025" type="#_x0000_t75" style='width:158.25pt;height:52.5pt'>
2055 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image029.png"
2056  o:title="" chromakey="white"/>
2057</v:shape><![endif]--><![if !vml]><img width=211 height=70
2058src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image030.png"
2059v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2060
2061<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2062margin-left:0in;line-height:115%'><span class=GramE>for</span> m odd.<span
2063style='mso-spacerun:yes'>  </span>Each sum is only over either the even or odd
2064values of s, respectively, because of the properties of the Fourier
2065coefficients<span class=GramE>, </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2066   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2067   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2068   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2069   normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i
2070   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2071   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2072    </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
2073style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2074"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2075top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2076EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2077 type="#_x0000_t75" style='width:24.75pt;height:26.25pt'>
2078 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image031.png"
2079  o:title="" chromakey="white"/>
2080</v:shape><![endif]--><![if !vml]><img width=33 height=35
2081src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image032.png"
2082v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
2083style='mso-spacerun:yes'>  </span>These Fourier coefficients are determined so
2084that the definition</p>
2085
2086<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2087margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2088   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
2089    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2090    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2091    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2092       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2093      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2094      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2095      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
2096    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2097    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2098     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
2099    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2100    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2101    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
2102      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2103      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2104      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2105      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2106         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2107      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
2108  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:sSubSup><m:sSubSupPr><span
2109    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2110    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2111    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2112       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2113      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2114      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2115      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
2116    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2117    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2118     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
2119    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2120    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2121    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
2122    normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e></m:d><i
2123  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:rad><m:radPr><m:degHide
2124     m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2125    "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2126    mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
2127      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2128      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2129      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
2130        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2131        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2132        normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
2133        normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>+</m:r><m:r>m</m:r></span></i></m:e></m:d><i
2134      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>!</m:r></span></i></m:num><m:den><m:d><m:dPr><span
2135        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2136        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2137        normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
2138        normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:e></m:d><i
2139      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>!</m:r></span></i></m:den></m:f></m:e></m:rad><m:rad><m:radPr><m:degHide
2140     m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2141    "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2142    mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
2143      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2144      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2145      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
2146      normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>L</m:r><m:r>+1</m:r></span></i></m:num><m:den><i
2147      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:den></m:f></m:e></m:rad><m:f><m:fPr><span
2148    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2149    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2150    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
2151      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2152      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2153      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2154      normal'><span style='font-family:"Cambria Math",serif'><m:r>(-1)</m:r></span></i></m:e><m:sup><i
2155      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span
2156      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2157      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2158      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2159      normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:e><m:sup><i
2160      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup></m:sSup><i
2161    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>!</m:r></span></i></m:den></m:f><m:sSup><m:sSupPr><span
2162    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2163    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2164    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2165    normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><span
2166      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2167      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2168      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2169      normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i
2170      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i
2171    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:e><m:sup><m:f><m:fPr><m:type
2172       m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2173      "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2174      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
2175      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>m</m:r></span></i></m:num><m:den><i
2176      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:den></m:f></m:sup></m:sSup><m:f><m:fPr><span
2177    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2178    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2179    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
2180      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2181      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2182      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2183      normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
2184      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span
2185      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2186      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2187      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2188      normal'><span style='font-family:"Cambria Math",serif'><m:r>dx</m:r></span></i></m:e><m:sup><i
2189      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:sup></m:sSup></m:den></m:f><m:sSup><m:sSupPr><span
2190    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2191    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2192    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2193    normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><span
2194      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2195      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2196      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2197      normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i
2198      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i
2199    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:e><m:sup><i
2200    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup></m:sSup></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
2201style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2202"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2203mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2204 id="_x0000_i1025" type="#_x0000_t75" style='width:423.75pt;height:55.5pt'>
2205 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.png"
2206  o:title="" chromakey="white"/>
2207</v:shape><![endif]--><![if !vml]><img width=565 height=74
2208src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image034.png"
2209v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2210
2211<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2212margin-left:0in;line-height:115%'><span class=GramE>is</span> satisfied.<span
2213style='mso-spacerun:yes'>  </span>Terms of the form <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
2214   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2215   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2216   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2217   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2218      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2219   normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>m&#946;</m:r><m:r>)</m:r></span></i></m:e></m:func><m:sSubSup><m:sSubSupPr><span
2220   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2221   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2222   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2223      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2224     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2225     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2226     style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
2227   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2228   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2229    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2230 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
2231   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2232   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2233   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2234   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2235      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2236   normal'><span style='font-family:"Cambria Math",serif'><m:r>m&#946;</m:r></span></i></m:e></m:func><i
2237 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
2238style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2239"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2240top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2241EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2242 type="#_x0000_t75" style='width:111pt;height:26.25pt'>
2243 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image035.png"
2244  o:title="" chromakey="white"/>
2245</v:shape><![endif]--><![if !vml]><img width=148 height=35
2246src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image036.png"
2247v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2248style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
2249   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2250   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2251   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2252   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2253      m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2254   normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>m&#946;</m:r><m:r>)</m:r></span></i></m:e></m:func><m:sSubSup><m:sSubSupPr><span
2255   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2256   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2257   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2258      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2259     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2260     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2261     style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
2262   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2263   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2264    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2265 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
2266   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2267   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2268   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2269   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2270      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2271   normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
2272 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
2273style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2274"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2275top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2276EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2277 type="#_x0000_t75" style='width:100.5pt;height:26.25pt'>
2278 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image037.png"
2279  o:title="" chromakey="white"/>
2280</v:shape><![endif]--><![if !vml]><img width=134 height=35
2281src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image038.png"
2282v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2283style='mso-spacerun:yes'> </span>are combined depending on the symmetry and the
2284value of m along with appropriate normalization coefficients to give the
2285harmonic terms <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2286   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2287   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2288   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2289   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
2290   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2291   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2292    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2293 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
2294style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2295"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2296top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2297EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2298 type="#_x0000_t75" style='width:48pt;height:26.25pt'>
2299 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
2300  o:title="" chromakey="white"/>
2301</v:shape><![endif]--><![if !vml]><img width=64 height=35
2302src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"
2303v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2304style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2305   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2306   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2307   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2308   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
2309   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2310   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2311    </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2312 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#968;</m:r><m:r>,</m:r><m:r>&#947;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
2313style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2314"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2315top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2316EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2317 type="#_x0000_t75" style='width:45pt;height:26.25pt'>
2318 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png"
2319  o:title="" chromakey="white"/>
2320</v:shape><![endif]--><![if !vml]><img width=60 height=35
2321src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image042.png"
2322v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
2323style='mso-spacerun:yes'>  </span>For cubic crystal symmetry, the term <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2324   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2325   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2326   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2327   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
2328   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2329   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2330    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2331 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
2332style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2333"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2334top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2335EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2336 type="#_x0000_t75" style='width:48pt;height:26.25pt'>
2337 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
2338  o:title="" chromakey="white"/>
2339</v:shape><![endif]--><![if !vml]><img width=64 height=35
2340src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"
2341v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2342style='mso-spacerun:yes'> </span>is obtained directly from the Fourier
2343expansion</p>
2344
2345<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2346margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2347   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
2348    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2349    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2350    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2351    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
2352    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2353    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
2354    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2355    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2356    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
2357    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r></span></i></m:e></m:d><i
2358  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:nary><m:naryPr><m:chr
2359     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2360    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2361    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2362    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>=0</m:r></span></i></m:sub><m:sup><i
2363    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span
2364      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2365      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2366      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
2367      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>B</m:r></span></i></m:e><m:sub><i
2368      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2369      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>nm</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:sSubSup><m:sSubSupPr><span
2370    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2371    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2372    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2373       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2374      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2375      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2376      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i
2377    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2378    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2379     </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2380  normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
2381    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2382    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2383    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2384    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2385       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2386    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
2387  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i><m:func><m:funcPr><span
2388    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2389    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2390    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2391    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2392       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2393    normal'><span style='font-family:"Cambria Math",serif'><m:r>n&#946;</m:r></span></i></m:e></m:func></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
2394style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2395"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2396mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2397 id="_x0000_i1025" type="#_x0000_t75" style='width:193.5pt;height:52.5pt'>
2398 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image043.png"
2399  o:title="" chromakey="white"/>
2400</v:shape><![endif]--><![if !vml]><img width=258 height=70
2401src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image044.png"
2402v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2403
2404<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2405margin-left:0in;line-height:115%'><span class=GramE>using</span> the
2406coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2407   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2408   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2409   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2410   normal'><span style='font-family:"Cambria Math",serif'><m:r>B</m:r></span></i></m:e><m:sub><i
2411   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2412   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>nm</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
2413style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2414"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2415top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2416EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2417 type="#_x0000_t75" style='width:22.5pt;height:26.25pt'>
2418 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image045.png"
2419  o:title="" chromakey="white"/>
2420</v:shape><![endif]--><![if !vml]><img width=30 height=35
2421src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image046.png"
2422v:shapes="_x0000_i1025"><![endif]></span><![endif]>, as tabulated by Bunge
2423(1982). </p>
2424
2425<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2426margin-left:0in;line-height:115%'>The Rietveld refinement of texture then
2427proceeds by constructing derivatives of the profile intensities with respect to
2428the allowed harmonic coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2429   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2430   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2431   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2432   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
2433   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2434   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
2435style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2436"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2437top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2438EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2439 type="#_x0000_t75" style='width:21.75pt;height:26.25pt'>
2440 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"
2441  o:title="" chromakey="white"/>
2442</v:shape><![endif]--><![if !vml]><img width=29 height=35
2443src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
2444v:shapes="_x0000_i1025"><![endif]></span><![endif]>, and the three sample
2445orientation angles, <span style='font-family:Symbol'>W</span><sub>s</sub>, <span
2446style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:Symbol'>F</span><sub>s</sub>,
2447all of which can be adjustable parameters of the refinement. Once the
2448refinement is complete, pole figures for any reflection may be constructed by
2449use of the general axis equation, the refined values for <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2450   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2451   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2452   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2453   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
2454   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2455   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
2456style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2457"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2458top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2459EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2460 type="#_x0000_t75" style='width:21.75pt;height:26.25pt'>
2461 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"
2462  o:title="" chromakey="white"/>
2463</v:shape><![endif]--><![if !vml]><img width=29 height=35
2464src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
2465v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2466style='mso-spacerun:yes'> </span>and the sample orientation angles <span
2467style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
2468<span class=GramE><span style='font-family:Symbol'>F</span></span><sub>s</sub>.
2469</p>
2470
2471<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2472margin-left:0in;line-height:115%'>The magnitude of the texture is evaluated
2473from the texture index by</p>
2474
2475<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2476margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2477   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
2478  style='font-family:"Cambria Math",serif'><m:r>J</m:r><m:r>=1+</m:r></span></i><m:nary><m:naryPr><m:chr
2479     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2480    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2481    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2482    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>=2</m:r></span></i></m:sub><m:sup><m:sSub><m:sSubPr><span
2483      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2484      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2485      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
2486      normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i
2487      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub></m:sSub></m:sup><m:e><m:f><m:fPr><span
2488      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2489      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2490      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
2491      normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:num><m:den><i
2492      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>L</m:r><m:r>+1</m:r></span></i></m:den></m:f></m:e></m:nary><m:nary><m:naryPr><m:chr
2493     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2494    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2495    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2496    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i
2497    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:nary><m:naryPr><m:chr
2498       m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
2499      "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
2500      "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2501      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i
2502      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSup><m:sSupPr><span
2503        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2504        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2505        normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><m:begChr
2506           m:val="|"/><m:endChr m:val="|"/><span style='font-family:"Cambria Math",serif;
2507          mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2508          font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:sSubSup><m:sSubSupPr><span
2509            style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2510            mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2511            normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
2512            style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
2513            style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
2514            style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:e></m:d></m:e><m:sup><i
2515        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:e></m:nary></m:e></m:nary></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
2516style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2517"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2518mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2519 id="_x0000_i1025" type="#_x0000_t75" style='width:180.75pt;height:54pt'>
2520 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.png"
2521  o:title="" chromakey="white"/>
2522</v:shape><![endif]--><![if !vml]><img width=241 height=72
2523src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
2524v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2525
2526<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2527margin-left:0in;line-height:115%'>If the texture is random then J = 1,
2528otherwise J &gt; 1; for a single crystal J = <span style='font-family:Symbol'>¥.</span>
2529</p>
2530
2531<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2532margin-left:0in;line-height:115%'>In GSAS-II the texture is defined in two ways
2533to accommodate the two possible uses of this correction. In one a suite of
2534spherical harmonics coefficients is defined for the texture of a phase in the
2535sample; this can have any of the possible sample symmetries and is the usual
2536result desired for texture analysis. The other is the suite of spherical
2537harmonics terms for cylindrical sample symmetry for each phase in each powder
2538pattern (“histogram”) and is usually used to accommodate preferred orientation
2539effects in a Rietveld refinement. The former description allows refinement of
2540the sample orientation zeros, <span style='font-family:Symbol'>W</span><sub>s</sub>,
2541<span style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:
2542Symbol'>F</span><sub>s</sub>, but the latter description does not (they are
2543assumed to be zero and not refinable). The sample orientation angles, (<span
2544style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>,
2545<span style='font-family:Symbol'>F) </span>are specified in the Sample
2546Parameters table in the GSAS-II data tree structure and are applied for either
2547description.</p>
2548
2549<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2550margin-left:0in;line-height:115%'>In this tutorial we will use both of these
2551descriptions to determine the texture of the two phases in a <span
2552class=SpellE>NiTi</span> shape memory alloy sample with cylindrical symmetry
2553(wire texture) as collected at APS on beam line 1ID-C (data kindly provided by
2554Paul Paradise &amp; Aaron <span class=SpellE>Stebner</span> of Colo. School of
2555Mines). Thus, there are three ways within GSAS-II that can be used for this
2556texture analysis all beginning with the same 2D area detector image. Each will
2557be described in turn after the initial setup of the GSAS-II project, image
2558input &amp; integration.</p>
2559
2560<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
25610in;line-height:115%'>Step 1. Image input &amp; integration</h2>
2562
2563<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you have
2564not done so already, <u><span style='color:#0070C0'><a
2565href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none;
2566text-underline:none'>start GSAS-II</span></a></span></u>. Note that menu
2567entries are listed in <b style='mso-bidi-font-weight:normal'><span
2568style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2569mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
2570minor-latin'>bold face</span></b> below as <b style='mso-bidi-font-weight:normal'><span
2571style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2572mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
2573minor-latin'>Help/About GSAS-II</span></b>, which lists first the name of the
2574menu (here <b style='mso-bidi-font-weight:normal'><span style='font-family:
2575"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2576minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>Help</span></b>)
2577and second the name of the entry in the menu (here <b style='mso-bidi-font-weight:
2578normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2579minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;
2580mso-bidi-theme-font:minor-latin'>About GSAS-II</span></b>). </p>
2581
2582<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Use the <b
2583style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2584mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Read
2585image data</span></b> menu item to read the data file into the current GSAS-II
2586project. A file selection dialog will be shown; its appearance will depend on
2587your OS. Change the search directory to <b style='mso-bidi-font-weight:normal'><span
2588style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2589mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
2590minor-latin'>/exercises/2DTexture </span></b>and then select the file <b
2591style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2592mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NDC5_01588_1.ge2</span></b>.
2593A (faint) image will appear</p>
2594
2595<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2596style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_29"
2597 o:spid="_x0000_i1081" type="#_x0000_t75" style='width:525pt;height:450pt;
2598 visibility:visible;mso-wrap-style:square'>
2599 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
2600  o:title=""/>
2601</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2602src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
2603v:shapes="Picture_x0020_29"><![endif]></span></p>
2604
2605<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2606class=GramE>and</span> the <b style='mso-bidi-font-weight:normal'><span
2607style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2608mso-hansi-theme-font:minor-latin'>Image Controls</span></b> data page will show</p>
2609
2610<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2611style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_30"
2612 o:spid="_x0000_i1080" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
2613 visibility:visible;mso-wrap-style:square'>
2614 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
2615  o:title=""/>
2616</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
2617src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
2618v:shapes="Picture_x0020_30"><![endif]></span></p>
2619
2620<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detector
2621was previously calibrated and the coefficients are stored in a file found by
2622doing <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2623mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Load
2624Controls</span></b> from the <b style='mso-bidi-font-weight:normal'><span
2625style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2626mso-hansi-theme-font:minor-latin'>Image Controls</span></b> menu. A file
2627selection popup will appear showing <b style='mso-bidi-font-weight:normal'><span
2628style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2629mso-hansi-theme-font:minor-latin'>NDC5.imctrl</span></b>; select it and press <b
2630style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2631mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Open</span></b>.
2632The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2633mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2634Controls</span></b> window will be repainted with the new values (do a reselect
2635of the image from the tree and then <b style='mso-bidi-font-weight:normal'><span
2636style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2637mso-hansi-theme-font:minor-latin'>Image Controls</span></b> to make sure the
2638image is up to date.)</p>
2639
2640<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2641style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_31"
2642 o:spid="_x0000_i1079" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
2643 visibility:visible;mso-wrap-style:square'>
2644 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
2645  o:title=""/>
2646</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
2647src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
2648v:shapes="Picture_x0020_31"><![endif]></span></p>
2649
2650<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detail in
2651the image can be enhanced by lowering the <b style='mso-bidi-font-weight:normal'><span
2652style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2653mso-hansi-theme-font:minor-latin'>Max intensity</span></b> (<b
2654style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2655mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>15000</span></b>
2656is suitable) and shows that the diffraction rings show the effect of texture
2657and that the image has a fairly high background. Placing the cursor in the
2658corners or inside the inner ring shows a background &gt;1700. This can be suppressed
2659by adjusting the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2660"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2661minor-latin'>Flat <span class=SpellE>Bkg</span></span></b> (I chose <b
2662style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2663mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>1700</span></b>
2664for this). The image will now show the rings much more clearly.</p>
2665
2666<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2667style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32"
2668 o:spid="_x0000_i1078" type="#_x0000_t75" style='width:525pt;height:450pt;
2669 visibility:visible;mso-wrap-style:square'>
2670 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
2671  o:title=""/>
2672</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2673src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
2674v:shapes="Picture_x0020_32"><![endif]></span></p>
2675
2676<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For texture
2677analysis we will need to integrate the image into a number of slices sampling
2678the changing ring intensity with azimuthal angle. Also note that the image
2679seems to have <b style='mso-bidi-font-weight:normal'><span style='font-family:
2680"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2681minor-latin'>mm</span></b> symmetry so that the unique part of this intensity
2682variation covers 0-90° of azimuth. In addition the ring intensity variation is
2683such that using 10° slices will capture it reasonably well. However, we want to
2684include both 0° and 90° as slice centers. Thus there will be 10 slices
2685beginning at -5° and ending at 95°. Check the <b style='mso-bidi-font-weight:
2686normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2687minor-latin;mso-hansi-theme-font:minor-latin'>Show integration limits?</span></b>
2688<span class=GramE>box</span> and uncheck the <b style='mso-bidi-font-weight:
2689normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2690minor-latin;mso-hansi-theme-font:minor-latin'>Do full integration? </span></b><span
2691class=GramE>box</span>, enter <b style='mso-bidi-font-weight:normal'><span
2692style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2693mso-hansi-theme-font:minor-latin'>10</span></b> in the <b style='mso-bidi-font-weight:
2694normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2695minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth bins</span></b>,
2696enter <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2697mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-5</span></b>
2698in the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2699mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Start
2700azimuth</span></b> box (it will change to 355) and enter <b style='mso-bidi-font-weight:
2701normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2702minor-latin;mso-hansi-theme-font:minor-latin'>455</span></b> in the <b
2703style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2704mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>End azimuth</span></b>
2705box. In addition, recall that the sample was mounted vertically and thus is
2706aligned with the defined laboratory I axis. Thus, the sample coordinate system
2707needs to be rotated by 90° to match the sample axis with the K axis; this can
2708be done by making the <b style='mso-bidi-font-weight:normal'><span
2709style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2710mso-hansi-theme-font:minor-latin'>Sample goniometer axis Chi</span></b> = <b
2711style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2712mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>90</span></b>.
2713The plot will change with each entry and at the end should look like</p>
2714
2715<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2716style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_33"
2717 o:spid="_x0000_i1077" type="#_x0000_t75" style='width:525pt;height:450pt;
2718 visibility:visible;mso-wrap-style:square'>
2719 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
2720  o:title=""/>
2721</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2722src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
2723v:shapes="Picture_x0020_33"><![endif]></span></p>
2724
2725<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The <b
2726style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2727mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2728Controls</span></b> should be</p>
2729
2730<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2731style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_34"
2732 o:spid="_x0000_i1076" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
2733 visibility:visible;mso-wrap-style:square'>
2734 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
2735  o:title=""/>
2736</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
2737src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
2738v:shapes="Picture_x0020_34"><![endif]></span></p>
2739
2740<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It turns out
2741that the image contains a number of “picked bits” (very high count “zingers”);
2742these can be mostly eliminated by setting the upper threshold in Masks. Select <b
2743style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2744mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Masks</span></b>
2745and the following should appear</p>
2746
2747<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2748style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35"
2749 o:spid="_x0000_i1075" type="#_x0000_t75" style='width:297.75pt;height:99.75pt;
2750 visibility:visible;mso-wrap-style:square'>
2751 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
2752  o:title=""/>
2753</v:shape><![endif]--><![if !vml]><img border=0 width=397 height=133
2754src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
2755v:shapes="Picture_x0020_35"><![endif]></span></p>
2756
2757<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the <b
2758style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2759mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Upper
2760threshold</span></b> to <b style='mso-bidi-font-weight:normal'><span
2761style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2762mso-hansi-theme-font:minor-latin'>2500</span></b>; the image will be redrawn
2763reflecting this mask. By zooming in you may see isolated red pixels; these are
2764excluded points. Make sure the diffraction rings do not have any excluded
2765points. For example with the level set to 2200 the plot shows</p>
2766
2767<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2768style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_36"
2769 o:spid="_x0000_i1074" type="#_x0000_t75" style='width:525pt;height:450pt;
2770 visibility:visible;mso-wrap-style:square'>
2771 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
2772  o:title=""/>
2773</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2774src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
2775v:shapes="Picture_x0020_36"><![endif]></span></p>
2776
2777<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2778class=GramE>for</span> one ring. This level is too low. Return to the <b
2779style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2780mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2781Controls</span></b> item in the data tree.</p>
2782
2783<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
2784ready to integrate the image; do <b style='mso-bidi-font-weight:normal'><span
2785style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2786mso-hansi-theme-font:minor-latin'>Operations/Integrate</span></b> from the <b
2787style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2788mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2789Controls</span></b> menu. When done the last powder pattern in the tree will be
2790displayed</p>
2791
2792<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2793style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_37"
2794 o:spid="_x0000_i1073" type="#_x0000_t75" style='width:525pt;height:450pt;
2795 visibility:visible;mso-wrap-style:square'>
2796 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
2797  o:title=""/>
2798</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2799src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
2800v:shapes="Picture_x0020_37"><![endif]></span></p>
2801
2802<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
28030in;line-height:115%'>Step 2. Enter <span class=SpellE>NiTi</span> phases</h2>
2804
2805<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This <span
2806class=SpellE>NiTi</span> alloy consists of two phases, cubic B2 and monoclinic
2807B19’. Their parameters are<span class=GramE>:</span><br>
2808B2: <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2809mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P m 3 m</span></b>,
2810a=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2811mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>3.0240</span></b>,
2812Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2813mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0,0,0</span></b>,
2814<span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span
2815style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2816mso-hansi-theme-font:minor-latin'>œ,œ,œ</span></b>, <span class=SpellE>U<sub>iso</sub></span>=<b
2817style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2818mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.005 </span></b>for
2819both.<br>
2820B19’:<span style='mso-spacerun:yes'>  </span><b style='mso-bidi-font-weight:
2821normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2822minor-latin;mso-hansi-theme-font:minor-latin'>P 1 1 21/m</span></b>, a=<b
2823style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2824mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.8853</span></b>,
2825b=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2826mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.6353</span></b>,
2827c=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2828mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.1368</span></b>,
2829&#947;=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2830mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>96.821</span></b>,
2831<span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span
2832style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2833mso-hansi-theme-font:minor-latin'>0.5787<span class=GramE>,0.2841,Œ</span></span></b>,
2834Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2835mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.9700,0.8209,Œ</span></b>,
2836<span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
2837style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2838mso-hansi-theme-font:minor-latin'>0.005</span></b> for both.<br>
2839Use the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2840mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Add
2841phase</span></b> to enter the <b style='mso-bidi-font-weight:normal'><span
2842style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2843mso-hansi-theme-font:minor-latin'>B2</span></b> and <b style='mso-bidi-font-weight:
2844normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2845minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b> phases; then for
2846each enter the information given above on their respective <b style='mso-bidi-font-weight:
2847normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2848minor-latin;mso-hansi-theme-font:minor-latin'>General</span></b> and <b
2849style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2850mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms</span></b>
2851tabs. Don’t forget the spaces between the axial fields for the space group
2852symbols. On the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2853"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2854minor-latin'>Atoms</span></b> tab begin by doing <b style='mso-bidi-font-weight:
2855normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2856minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Append atom</span></b> twice
2857then fill in the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2858"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2859minor-latin'>Type</span></b> and coordinates boxes. A double click of the <b
2860style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2861mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Type</span></b>
2862entry will show a popup of the Periodic Table; select the element as
2863appropriate. NB: GSAS-II happily takes “1/2” &amp; “1/4” for coordinate values;
2864these get converted to their decimal equivalent upon entry. Note the use of a
2865nonstandard space group designation for B19’. When done the B2 Atoms table
2866should look like</p>
2867
2868<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2869style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_38"
2870 o:spid="_x0000_i1072" type="#_x0000_t75" style='width:525pt;height:166.5pt;
2871 visibility:visible;mso-wrap-style:square'>
2872 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
2873  o:title=""/>
2874</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=222
2875src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
2876v:shapes="Picture_x0020_38"><![endif]></span></p>
2877
2878<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2879class=GramE>and</span> the B19’ Atoms table should be</p>
2880
2881<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2882style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_39"
2883 o:spid="_x0000_i1071" type="#_x0000_t75" style='width:525pt;height:163.5pt;
2884 visibility:visible;mso-wrap-style:square'>
2885 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2886  o:title=""/>
2887</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=218
2888src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2889v:shapes="Picture_x0020_39"><![endif]></span></p>
2890
2891<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
2892<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2893mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
2894tab for each phase; there will be a message indicating the lack of data for
2895each. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2896mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add
2897powder histograms</span></b>, do <b style='mso-bidi-font-weight:normal'><span
2898style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2899mso-hansi-theme-font:minor-latin'>Set All</span></b> on the popup selection
2900window and press <b style='mso-bidi-font-weight:normal'><span style='font-family:
2901"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2902minor-latin'>OK</span></b>. The window for B2 will change to</p>
2903
2904<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2905style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40"
2906 o:spid="_x0000_i1070" type="#_x0000_t75" style='width:342.75pt;height:375pt;
2907 visibility:visible;mso-wrap-style:square'>
2908 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2909  o:title=""/>
2910</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
2911src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2912v:shapes="Picture_x0020_40"><![endif]></span></p>
2913
2914<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2915class=GramE>and</span> that for B19’ will be</p>
2916
2917<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2918style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_41"
2919 o:spid="_x0000_i1069" type="#_x0000_t75" style='width:370.5pt;height:375pt;
2920 visibility:visible;mso-wrap-style:square'>
2921 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
2922  o:title=""/>
2923</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
2924src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
2925v:shapes="Picture_x0020_41"><![endif]></span></p>
2926
2927<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You should now
2928save the project file (I used <span class=SpellE><b style='mso-bidi-font-weight:
2929normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2930minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span> for a
2931name); we will use this as a starting point for three different texture
2932determinations. Do a <b style='mso-bidi-font-weight:normal'><span
2933style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2934mso-hansi-theme-font:minor-latin'>File/Save project as…</span></b> and give it
2935a new name (I used <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
2936style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2937mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight:
2938normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2939minor-latin;mso-hansi-theme-font:minor-latin'>-A</span></b>); this will become
2940the new project name for the next part of this tutorial.</p>
2941
2942<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
29430in;line-height:115%'>Method A. Full refinement</h2>
2944
2945<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
29460in;line-height:115%'>Introduction</h3>
2947
2948<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In this method
2949we will do a full Rietveld refinement of the texture, profile parameters, peak
2950position variables and crystal structure parameters. This is suitable in this
2951case because of the relatively small number of histograms (10 in this case)
2952needed for the texture determination; do recall that each phase in each
2953histogram has a set of parameters (e.g. phase fraction, size, <span
2954class=SpellE>mustrain</span> &amp; hydrostatic strain) in addition to the ones
2955for each histogram (e.g. background &amp; scale factor). Consequently the total
2956number of parameters can build up very quickly in this method of analysis. The
2957other two methods seek to reduce this problem by splitting the fitting into a
2958sequential refinement (histogram by histogram) step followed by a texture
2959fitting step.</p>
2960
2961<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
29620in;line-height:115%'>Step 1. Initial refinement</h3>
2963
2964<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In the initial
2965refinement we need to vary the phase fraction for each phase/histogram and the
2966background in each histogram. To start select any <b style='mso-bidi-font-weight:
2967normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2968minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b> entry from the
2969GSAS-II data tree and select <b style='mso-bidi-font-weight:normal'><span
2970style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2971mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b> for it. Note
2972that Goniometer chi is set to 90; that came from the same entry in the Image
2973Controls during integration. Also, if you chose other than the 1<sup>st</sup>
2974PWDR data set the Detector azimuth will be some nonzero value; that is also
2975reflected in the name assigned to the histogram (e.g. <b style='mso-bidi-font-weight:
2976normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2977minor-latin;mso-hansi-theme-font:minor-latin'>PWDR NDC5_01588_1.ge2 <span
2978class=SpellE>Azm</span>= 40.00</span></b>). Uncheck the <b style='mso-bidi-font-weight:
2979normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2980minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>
2981box and then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
2982"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2983minor-latin'>Command/Copy flags</span></b>; select <b style='mso-bidi-font-weight:
2984normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2985minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b> and then press
2986<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2987mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
2988That will clear the scale factor refinement flag for all histograms; we will be
2989varying the phase fractions instead.</p>
2990
2991<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select
2992the B2 phase and pick the Data tab; you will see</p>
2993
2994<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2995style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42"
2996 o:spid="_x0000_i1068" type="#_x0000_t75" style='width:342.75pt;height:375pt;
2997 visibility:visible;mso-wrap-style:square'>
2998 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2999  o:title=""/>
3000</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
3001src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
3002v:shapes="Picture_x0020_42"><![endif]></span></p>
3003
3004<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Select the <b
3005style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3006mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase
3007fraction</span></b> box. Then do <b style='mso-bidi-font-weight:normal'><span
3008style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3009mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b>, select <b
3010style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3011mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set <span
3012class=GramE>All</span></span></b> &amp; press <b style='mso-bidi-font-weight:
3013normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3014minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to copy these to
3015the other histograms. Next select the <b style='mso-bidi-font-weight:normal'><span
3016style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3017mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and repeat this process.
3018We are now ready for the first refinement; do <b style='mso-bidi-font-weight:
3019normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3020minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from
3021the main GSAS-II data tree window. A progress bar popup will appear and when
3022done a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3023mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refinement
3024results</span></b> popup will show with Rw~32%. Press <b style='mso-bidi-font-weight:
3025normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3026minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to load this
3027result; GSAS-II will return you to the last window you were using and display
3028the 1<sup>st</sup> powder pattern showing you the fit</p>
3029
3030<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3031style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_43"
3032 o:spid="_x0000_i1067" type="#_x0000_t75" style='width:525pt;height:450pt;
3033 visibility:visible;mso-wrap-style:square'>
3034 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
3035  o:title=""/>
3036</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3037src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
3038v:shapes="Picture_x0020_43"><![endif]></span></p>
3039
3040<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is quite
3041poor. You can survey the fit successively by 1<sup>st</sup> selecting say the 1<sup>st</sup>
3042PWDR entry from the tree and then using the up/down arrow keys to step to the
3043next one; the plot will redraw at each step (NB: at full scale) and the data
3044window will show statistics of the fit. There is a substantial intensity
3045discrepancy; this is due to the texture. It is also evident that some of the
3046peaks are out of place relative to the reflection markers; this is due to
3047macroscopic strain in the drawn wire. For the <span style='font-family:"Calibri",sans-serif;
3048mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span>
3049phase select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3050"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3051minor-latin'>Texture</span></b> tab; it should look like</p>
3052
3053<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3054style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44"
3055 o:spid="_x0000_i1066" type="#_x0000_t75" style='width:456pt;height:217.5pt;
3056 visibility:visible;mso-wrap-style:square'>
3057 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
3058  o:title=""/>
3059</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290
3060src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
3061v:shapes="Picture_x0020_44"><![endif]></span></p>
3062
3063<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The texture
3064model is <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3065mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>cylindrical</span></b>
3066by default; that is what we want. Change the <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'>Harmonic order</span></b> to <b
3069style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3070mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>8</span></b>
3071and check both <b style='mso-bidi-font-weight:normal'><span style='font-family:
3072"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3073minor-latin'>Refine texture</span></b> and <b style='mso-bidi-font-weight:normal'><span
3074style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3075mso-hansi-theme-font:minor-latin'>Show <span class=SpellE>coeff</span></span></b>.
3076The window should look like</p>
3077
3078<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3079style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45"
3080 o:spid="_x0000_i1065" type="#_x0000_t75" style='width:456pt;height:250.5pt;
3081 visibility:visible;mso-wrap-style:square'>
3082 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
3083  o:title=""/>
3084</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
3085src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
3086v:shapes="Picture_x0020_45"><![endif]></span></p>
3087
3088<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the
3089<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3090mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3091tab, select <b style='mso-bidi-font-weight:normal'><span style='font-family:
3092"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3093minor-latin'>D11</span></b>; the <b style='mso-bidi-font-weight:normal'><span
3094style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3095mso-hansi-theme-font:minor-latin'>Data</span></b> window should look like (any
3096PWDR item will do)</p>
3097
3098<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3099style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_46"
3100 o:spid="_x0000_i1064" type="#_x0000_t75" style='width:342.75pt;height:375pt;
3101 visibility:visible;mso-wrap-style:square'>
3102 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
3103  o:title=""/>
3104</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
3105src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
3106v:shapes="Picture_x0020_46"><![endif]></span></p>
3107
3108<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then do <b
3109style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3110mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3111flags</span></b> to have <b style='mso-bidi-font-weight:normal'><span
3112style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3113mso-hansi-theme-font:minor-latin'>D11</span></b> refined for all PWDR data
3114sets.</p>
3115
3116<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select
3117the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3118mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3119phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3120mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
3121tab. Then select <b style='mso-bidi-font-weight:normal'><span style='font-family:
3122"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3123minor-latin'>6</span></b> for the <b style='mso-bidi-font-weight:normal'><span
3124style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3125mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> and check the two
3126boxes as before.</p>
3127
3128<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3129style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_47"
3130 o:spid="_x0000_i1063" type="#_x0000_t75" style='width:478.5pt;height:302.25pt;
3131 visibility:visible;mso-wrap-style:square'>
3132 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
3133  o:title=""/>
3134</v:shape><![endif]--><![if !vml]><img border=0 width=638 height=403
3135src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
3136v:shapes="Picture_x0020_47"><![endif]></span></p>
3137
3138<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the
3139<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3140mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3141tab for the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3142"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3143minor-latin'>B19’</span></b> phase and check all 4 of the <span class=SpellE><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'>Dij</span></b></span>
3146boxes and do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3147"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3148minor-latin'>Edit/Copy flags</span></b> as before. The tab will look like</p>
3149
3150<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3151style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48"
3152 o:spid="_x0000_i1062" type="#_x0000_t75" style='width:370.5pt;height:375pt;
3153 visibility:visible;mso-wrap-style:square'>
3154 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
3155  o:title=""/>
3156</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
3157src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
3158v:shapes="Picture_x0020_48"><![endif]></span></p>
3159
3160<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do <b
3161style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3162mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
3163from the main menu. The refinement will finish with <span class=SpellE>Rw</span>
3164~27%; the 1<sup>st</sup> PWDR pattern looks like</p>
3165
3166<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3167style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_49"
3168 o:spid="_x0000_i1061" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3169 visibility:visible;mso-wrap-style:square'>
3170 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
3171  o:title=""/>
3172</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3173src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
3174v:shapes="Picture_x0020_49"><![endif]></span></p>
3175
3176<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The calculated
3177peaks for both phases are too sharp. It is likely that this is a <span
3178class=SpellE>microstrain</span> effect. Select <b style='mso-bidi-font-weight:
3179normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3180minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b> for the <b
3181style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3182mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2 </span></b>phase
3183and select the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3184style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3185mso-hansi-theme-font:minor-latin'>microstrain</span></b></span> box. Then do <b
3186style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3187mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3188flags</span></b> to set it for the other PWDR data sets. Do the same for the <b
3189style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3190mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3191phase. Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3192"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3193minor-latin'>Calculate/Refine</span></b> from the main menu. The fit will be
3194substantially improved with <span class=SpellE>Rw</span> ~9.2%.</p>
3195
3196<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
31970in;line-height:115%'>Step 2. Finish refinement and examine texture</h3>
3198
3199<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Looking at the
3200individual PWDR data sets (e.g. the one for <span class=SpellE>Azm</span>=20.00)</p>
3201
3202<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3203style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_50"
3204 o:spid="_x0000_i1060" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3205 visibility:visible;mso-wrap-style:square'>
3206 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
3207  o:title=""/>
3208</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3209src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
3210v:shapes="Picture_x0020_50"><![endif]></span></p>
3211
3212<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is evident
3213that there remains intensity differences due to texture. We can increase the
3214harmonic order to more closely fit these, however one should only do this
3215carefully. Select the Texture tab for the B2 phase; the Texture tab will show</p>
3216
3217<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3218style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_18"
3219 o:spid="_x0000_i1059" type="#_x0000_t75" style='width:456pt;height:250.5pt;
3220 visibility:visible;mso-wrap-style:square'>
3221 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
3222  o:title=""/>
3223</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
3224src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
3225v:shapes="Picture_x0020_18"><![endif]></span></p>
3226
3227<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a drawing
3228of the 001 pole figure will be drawn. This is the very typical “bulls eye” for
3229cylindrical texture; of much more use is an inverse pole figure. Select that
3230from the Texture plot type; the plot will be redrawn</p>
3231
3232<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3233style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_52"
3234 o:spid="_x0000_i1058" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3235 visibility:visible;mso-wrap-style:square'>
3236 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
3237  o:title=""/>
3238</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3239src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
3240v:shapes="Picture_x0020_52"><![endif]></span></p>
3241
3242<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This shows the
3243probability of reflection vectors coinciding with the sample wire axis the high
3244spots are the 111 family of reflections. We should try the next higher Harmonic
3245order (10). </p>
3246
3247<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
3248Texture tab for the B19’ phase. Again a <span class=SpellE>bullseye</span> pole
3249figure is drawn; change that to an Inverse pole figure.</p>
3250
3251<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3252style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_53"
3253 o:spid="_x0000_i1057" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3254 visibility:visible;mso-wrap-style:square'>
3255 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
3256  o:title=""/>
3257</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3258src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
3259v:shapes="Picture_x0020_53"><![endif]></span></p>
3260
3261<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This phase is
3262very strongly textured (the cursor shows 12-13 MRD at the peaks) along the -140
3263direction. Again we want to increment the Harmonic order to the next higher
3264level (8). Again do Calculate/Refine from the main menu; the <span
3265class=SpellE>Rwp</span> has dropped to ~7.9%. One can add the atom <span
3266class=SpellE>Uiso</span> for the Ni and <span class=SpellE>Ti</span> atoms in
3267the B2 phase and the coordinates and <span class=SpellE>Uiso</span> for the
3268B19’ phase. The <span class=SpellE>Rw</span> drops a bit further to ~7.4%.
3269Finally, we can increase the harmonic order again for the B19’ phase (it is
3270very strongly textured!) to 10 and the B2 phase to 12; the final refinement
3271converged to <span class=SpellE>Rw</span> ~6.8% and the B19’ inverse pole
3272figure has peaks at ~18 MRD (Multiple of Random Distribution) and the B2 phase
3273peaks are ~7MRD.</p>
3274
3275<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B19’
3276coefficients</p>
3277
3278<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3279style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_54"
3280 o:spid="_x0000_i1056" type="#_x0000_t75" style='width:502.5pt;height:375pt;
3281 visibility:visible;mso-wrap-style:square'>
3282 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
3283  o:title=""/>
3284</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
3285src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
3286v:shapes="Picture_x0020_54"><![endif]></span></p>
3287
3288<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3289class=GramE>and</span> inverse pole figure</p>
3290
3291<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3292style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_55"
3293 o:spid="_x0000_i1055" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3294 visibility:visible;mso-wrap-style:square'>
3295 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
3296  o:title=""/>
3297</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3298src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
3299v:shapes="Picture_x0020_55"><![endif]></span></p>
3300
3301<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B2
3302coefficients</p>
3303
3304<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3305style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_56"
3306 o:spid="_x0000_i1054" type="#_x0000_t75" style='width:480pt;height:267.75pt;
3307 visibility:visible;mso-wrap-style:square'>
3308 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
3309  o:title=""/>
3310</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3311src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
3312v:shapes="Picture_x0020_56"><![endif]></span></p>
3313
3314<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3315class=GramE>and</span> inverse pole figure</p>
3316
3317<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3318style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_57"
3319 o:spid="_x0000_i1053" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3320 visibility:visible;mso-wrap-style:square'>
3321 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
3322  o:title=""/>
3323</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3324src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
3325v:shapes="Picture_x0020_57"><![endif]></span></p>
3326
3327<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This completes
3328the tutorial on Method A for doing texture analysis. It is useful for a case
3329like this one where there are very few data sets required for the texture
3330analysis. However, for the case of lower sample symmetry one must several dozen
3331or even a few hundred histograms and then the suite of parameters can easily be
3332&gt; 1000 of which only a few dozen describe the texture. This leads to the
3333next Methods for texture analysis in GSAS-II.</p>
3334
3335<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
33360in;line-height:115%'>Method B. Sequential refinement &amp; texture analysis
3337from result</h2>
3338
3339<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
33400in;line-height:115%'>Introduction</h3>
3341
3342<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
3343the texture analysis in much the same way as Method A except that all the
3344initial refinements are done “sequentially”, that is refinements are done for
3345the parameters associated with each powder pattern to convergence in a serial
3346fashion. In this case where there are 10 PWDR data sets, there will be 10
3347refinements done in sequence. Parameters that span all the data (e.g. lattice
3348parameters, atom parameters &amp; texture) are not varied in this sequence
3349refinement. The effect of texture is modeled as a Preferred Orientation
3350correction to each histogram. To begin do <b style='mso-bidi-font-weight:normal'><span
3351style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3352mso-hansi-theme-font:minor-latin'>File/Open project…</span></b> for the <span
3353class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3354"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3355minor-latin'>NiTi.gpx</span></b></span> file created in the first step and then
3356do a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3357mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Save
3358project as…</span></b> to save it as <span class=SpellE><b style='mso-bidi-font-weight:
3359normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3360minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b
3361style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3362mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-B</span></b>.
3363This renames the project and it should have one IMG, 10 PWDR entries and two
3364phases of <span class=SpellE>NiTi</span> (B2 and B19’).</p>
3365
3366<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
33670in;line-height:115%'>Step 1. Initial refinement</h3>
3368
3369<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
3370the same way as Method A so I’ll be brief. Do the following steps:</p>
3371
3372<p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;mso-add-space:
3373auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
3374style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
3375style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
3376any <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3377mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b>
3378entry, go to <b style='mso-bidi-font-weight:normal'><span style='font-family:
3379"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3380minor-latin'>Sample Parameters</span></b> and uncheck <b style='mso-bidi-font-weight:
3381normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3382minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>.
3383Then copy the flags to the other PWDR entries.</p>
3384
3385<p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;mso-add-space:
3386auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
3387style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
3388style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
3389the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3390mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3391phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3392mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3393tab and check the <b style='mso-bidi-font-weight:normal'><span
3394style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3395mso-hansi-theme-font:minor-latin'>Phase fraction</span></b> box and change the <span
3396class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3397"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3398minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span
3399style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3400mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b
3401style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3402mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical
3403harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span
3404style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3405mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the
3406flag and the model to the other PWDR entries.</p>
3407
3408<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space:
3409auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
3410style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
3411style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
3412the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3413mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3414phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3415mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3416tab and check the <b style='mso-bidi-font-weight:normal'><span
3417style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3418mso-hansi-theme-font:minor-latin'>Phase fraction box</span></b> and change the <span
3419class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3420"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3421minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span
3422style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3423mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b
3424style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3425mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical
3426harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span
3427style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3428mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the
3429flag and the model to the other PWDR entries.</p>
3430
3431<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select <b
3432style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3433mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b>
3434from the GSAS-II data tree</p>
3435
3436<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3437style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_1"
3438 o:spid="_x0000_i1052" type="#_x0000_t75" style='width:330.75pt;height:153.75pt;
3439 visibility:visible;mso-wrap-style:square'>
3440 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
3441  o:title=""/>
3442</v:shape><![endif]--><![if !vml]><img border=0 width=441 height=205
3443src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
3444v:shapes="Picture_x0020_1"><![endif]></span></p>
3445
3446<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Press the <b
3447style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3448mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Select Data</span></b>
3449button for <b style='mso-bidi-font-weight:normal'><span style='font-family:
3450"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3451minor-latin'>Sequential Refinement</span></b>; a file selection popup will
3452appear. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3453"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3454minor-latin'>Set All</span></b> and press <b style='mso-bidi-font-weight:normal'><span
3455style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3456mso-hansi-theme-font:minor-latin'>OK</span></b>. The <b style='mso-bidi-font-weight:
3457normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3458minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b> page will be
3459repainted indicating that 10 data sets are selected for sequential refinement.</p>
3460
3461<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3462style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_2"
3463 o:spid="_x0000_i1051" type="#_x0000_t75" style='width:330.75pt;height:163.5pt;
3464 visibility:visible;mso-wrap-style:square'>
3465 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
3466  o:title=""/>
3467</v:shape><![endif]--><![if !vml]><img border=0 width=441 height=218
3468src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
3469v:shapes="Picture_x0020_2"><![endif]></span></p>
3470
3471<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You have the
3472choice of starting at the last one and for copying results from one to the
3473next. We won’t do either here. Each refinement will use the other controls
3474(e.g. <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3475mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Max cycles</span></b>)
3476as controls. We are now ready to do the 1<sup>st</sup> sequential refinement.
3477Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3478mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Sequential
3479refine</span></b> from the main menu. A progress bar popup will appear showing
3480residuals as it processes each of 10 data sets. After a few seconds the <b
3481style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3482mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refinement
3483results</span></b> popup will appear; press <b style='mso-bidi-font-weight:
3484normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3485minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to accept them. The
3486data window displays the <b style='mso-bidi-font-weight:normal'><span
3487style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3488mso-hansi-theme-font:minor-latin'>Sequential refinement results</span></b> as a
3489table.</p>
3490
3491<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3492style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3"
3493 o:spid="_x0000_i1050" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3494 visibility:visible;mso-wrap-style:square'>
3495 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
3496  o:title=""/>
3497</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3498src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
3499v:shapes="Picture_x0020_3"><![endif]></span></p>
3500
3501<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>There is a row
3502for each data set and columns for all refined parameters and some derived ones
3503along with residual and convergence indicators. The residuals are not very good
3504(we haven’t really refined much) but the &#916;&#967;<sup>2</sup> column shows
3505that convergence was achieved (NB: poor convergence will be highlighted in
3506yellow or red depending on how bad it is).</p>
3507
3508<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you examine
3509one of the PWDR entries, you’ll see that just in this point in Method <span
3510class=GramE>A</span> much of the misfit is texture and perhaps peak position.</p>
3511
3512<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3513style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_4"
3514 o:spid="_x0000_i1049" type="#_x0000_t75" style='width:525pt;height:450pt;
3515 visibility:visible;mso-wrap-style:square'>
3516 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
3517  o:title=""/>
3518</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3519src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
3520v:shapes="Picture_x0020_4"><![endif]></span></p>
3521
3522<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>To set these
3523parameters, select the Data tab for the B2 phase</p>
3524
3525<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3526style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5"
3527 o:spid="_x0000_i1048" type="#_x0000_t75" style='width:381pt;height:375pt;
3528 visibility:visible;mso-wrap-style:square'>
3529 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
3530  o:title=""/>
3531</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=500
3532src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
3533v:shapes="Picture_x0020_5"><![endif]></span></p>
3534
3535<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Check the D11
3536box under Hydrostatic/elastic strain, set the Harmonic order to 6 and check the
3537Refine box for it (Preferred orientation). Then in two steps, do Edit/Copy
3538flags and Set All for the file selection. Then do Edit/Copy selected data; that
3539will bring up a new popup</p>
3540
3541<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3542style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_6"
3543 o:spid="_x0000_i1047" type="#_x0000_t75" style='width:240pt;height:232.5pt;
3544 visibility:visible;mso-wrap-style:square'>
3545 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
3546  o:title=""/>
3547</v:shape><![endif]--><![if !vml]><img border=0 width=320 height=310
3548src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
3549v:shapes="Picture_x0020_6"><![endif]></span></p>
3550
3551<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This allows
3552you to select which parameters to copy data and flags. Select Pref. <span
3553class=SpellE>Ori</span>. And press OK; the file selection is next. Do Set <span
3554class=GramE>All</span> and OK to do this copy. That copies the full spherical
3555harmonics model to the other data sets. Select one to check if you’d like.</p>
3556
3557<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next do the
3558same thing for the B19’ phase; here there are 4 <span class=SpellE>Dij</span>
3559parameters to check (do all of them) and use spherical harmonics order 4. When
3560done that Data window will look like</p>
3561
3562<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3563style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_7"
3564 o:spid="_x0000_i1046" type="#_x0000_t75" style='width:381pt;height:467.25pt;
3565 visibility:visible;mso-wrap-style:square'>
3566 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
3567  o:title=""/>
3568</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=623
3569src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
3570v:shapes="Picture_x0020_7"><![endif]></span></p>
3571
3572<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
3573ready for the next refinement; do Calculate/Sequential refine. Be careful not
3574(by habit say) pick Refine; a warning popup will appear. After it completes the
3575Sequential refinement results shows that the fit is better but convergence
3576wasn’t quite complete.</p>
3577
3578<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3579style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8"
3580 o:spid="_x0000_i1045" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3581 visibility:visible;mso-wrap-style:square'>
3582 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
3583  o:title=""/>
3584</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3585src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
3586v:shapes="Picture_x0020_8"><![endif]></span></p>
3587
3588<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is probably
3589best to do another round of sequential refinement (I had to do two) to get
3590convergence. A plot of one PWDR entry gives</p>
3591
3592<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3593style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9"
3594 o:spid="_x0000_i1044" type="#_x0000_t75" style='width:525pt;height:450pt;
3595 visibility:visible;mso-wrap-style:square'>
3596 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png"
3597  o:title=""/>
3598</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3599src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png"
3600v:shapes="Picture_x0020_9"><![endif]></span></p>
3601
3602<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>As our
3603experience in Method A, the calculated peaks are too sharp. We need to vary the
3604<span class=SpellE>mustrain</span> parameters for both phases. Go to the Data
3605tab for each phase, check the <span class=SpellE>microstrain</span> box and do
3606Edit/Copy flags for all the data sets. Then do another Calculate/Sequential
3607refine. My Sequential refinement results showed great improvement but
3608incomplete refinement</p>
3609
3610<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3611style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10"
3612 o:spid="_x0000_i1043" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3613 visibility:visible;mso-wrap-style:square'>
3614 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
3615  o:title=""/>
3616</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3617src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
3618v:shapes="Picture_x0020_10"><![endif]></span></p>
3619
3620<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Repeating the
3621sequential refinement (twice) gave convergence.</p>
3622
3623<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3624style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_11"
3625 o:spid="_x0000_i1042" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3626 visibility:visible;mso-wrap-style:square'>
3627 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png"
3628  o:title=""/>
3629</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3630src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png"
3631v:shapes="Picture_x0020_11"><![endif]></span></p>
3632
3633<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Examination of
3634the PWDR data sets showed a fairly good fit but some discrepancies (especially
3635for <span class=SpellE>Azm</span>=20.00)</p>
3636
3637<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3638style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12"
3639 o:spid="_x0000_i1041" type="#_x0000_t75" style='width:525pt;height:450pt;
3640 visibility:visible;mso-wrap-style:square'>
3641 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
3642  o:title=""/>
3643</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3644src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
3645v:shapes="Picture_x0020_12"><![endif]></span></p>
3646
3647<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Showing that
3648perhaps the B19’ phase needs high order spherical harmonics. Select the Data
3649tab for the B19’ phase and change the Harmonic order to 6. Then do Edit/Copy
3650selected data for <span class=SpellE>Pref.Ori</span>. <span class=GramE>to</span>
3651the other data sets. This (after few repeats) gives a further improvement in
3652the fit</p>
3653
3654<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3655style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13"
3656 o:spid="_x0000_i1040" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3657 visibility:visible;mso-wrap-style:square'>
3658 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
3659  o:title=""/>
3660</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3661src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
3662v:shapes="Picture_x0020_13"><![endif]></span></p>
3663
3664<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This fit is
3665now sufficient for us to proceed to the next step and determine the texture of
3666the two phases.</p>
3667
3668<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
36690in;line-height:115%'>Step 2. Texture analysis</h3>
3670
3671<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>During the
3672sequential refinements done in Step 1, we fitted the profiles allowing strain
3673parameters (<span class=SpellE>Dij</span>) for peak position shifts and <span
3674class=SpellE>microstrain</span> for peak shape. We modeled the intensity
3675variation with a spherical harmonics preferred orientation correction. If you
3676select any PWDR entry from the GSAS-II data tree and pick the Reflection List
3677subentry (at the bottom) you can see the magnitude of this correction for each
3678reflection in each phase.</p>
3679
3680<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For the B2
3681phase we see</p>
3682
3683<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3684style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14"
3685 o:spid="_x0000_i1039" type="#_x0000_t75" style='width:659.25pt;height:262.5pt;
3686 visibility:visible;mso-wrap-style:square'>
3687 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
3688  o:title=""/>
3689</v:shape><![endif]--><![if !vml]><img border=0 width=879 height=350
3690src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
3691v:shapes="Picture_x0020_14"><![endif]></span></p>
3692
3693<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3694class=GramE>and</span> for the B19’ phase we see</p>
3695
3696<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3697style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15"
3698 o:spid="_x0000_i1038" type="#_x0000_t75" style='width:659.25pt;height:273pt;
3699 visibility:visible;mso-wrap-style:square'>
3700 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png"
3701  o:title=""/>
3702</v:shape><![endif]--><![if !vml]><img border=0 width=879 height=364
3703src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png"
3704v:shapes="Picture_x0020_15"><![endif]></span></p>
3705
3706<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The preferred
3707orientation correction is <span class=SpellE>Prfo</span>; notice a few entries
3708in red. These are nonphysical correction values (the correction can’t be
3709negative) but by in large these are small. This next step uses these
3710corrections as input data for a texture refinement. To start select the Texture
3711tab for the B2 phase; you’ll see</p>
3712
3713<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3714style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_16"
3715 o:spid="_x0000_i1037" type="#_x0000_t75" style='width:456pt;height:217.5pt;
3716 visibility:visible;mso-wrap-style:square'>
3717 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
3718  o:title=""/>
3719</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290
3720src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
3721v:shapes="Picture_x0020_16"><![endif]></span></p>
3722
3723<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Since this
3724sample has wire texture, we’ll use the default Texture model (cylindrical).
3725Then set the Harmonic order to 12 (what we used earlier) and check the Refine
3726and Show <span class=SpellE>coeff</span> boxes. The data window will be redrawn
3727(and a blank plot will appear).</p>
3728
3729<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3730style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_17"
3731 o:spid="_x0000_i1036" type="#_x0000_t75" style='width:456pt;height:250.5pt;
3732 visibility:visible;mso-wrap-style:square'>
3733 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
3734  o:title=""/>
3735</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
3736src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
3737v:shapes="Picture_x0020_17"><![endif]></span></p>
3738
3739<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do
3740Texture/Refine texture from the menu; the window will be repainted and a <span
3741class=SpellE>bullseye</span> pole figure will appear. </p>
3742
3743<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3744style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20"
3745 o:spid="_x0000_i1035" type="#_x0000_t75" style='width:480pt;height:267.75pt;
3746 visibility:visible;mso-wrap-style:square'>
3747 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
3748  o:title=""/>
3749</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3750src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
3751v:shapes="Picture_x0020_20"><![endif]></span></p>
3752
3753<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the
3754Texture plot type to Inverse pole figure to get a more useful plot</p>
3755
3756<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3757style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_19"
3758 o:spid="_x0000_i1034" type="#_x0000_t75" style='width:525pt;height:450pt;
3759 visibility:visible;mso-wrap-style:square'>
3760 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png"
3761  o:title=""/>
3762</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3763src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png"
3764v:shapes="Picture_x0020_19"><![endif]></span></p>
3765
3766<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is
3767essentially the same as we obtained earlier in Method <span class=GramE>A</span>
3768(maybe not quite as strong here).</p>
3769
3770<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the
3771Texture tab for the B19’ phase and do the same; use Harmonic order 10 as we did
3772earlier in Method A. After setting the two flags and doing Texture/Refine
3773texture we get</p>
3774
3775<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3776style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21"
3777 o:spid="_x0000_i1033" type="#_x0000_t75" style='width:502.5pt;height:375pt;
3778 visibility:visible;mso-wrap-style:square'>
3779 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
3780  o:title=""/>
3781</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
3782src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
3783v:shapes="Picture_x0020_21"><![endif]></span></p>
3784
3785<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a <span
3786class=SpellE>bullseye</span> pole figure; change that to Inverse pole figure to
3787see the texture</p>
3788
3789<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3790style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_22"
3791 o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt;height:450pt;
3792 visibility:visible;mso-wrap-style:square'>
3793 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
3794  o:title=""/>
3795</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3796src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
3797v:shapes="Picture_x0020_22"><![endif]></span></p>
3798
3799<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Again this is
3800very similar to what we found in Method A but again not quite as strong (max
3801MRD ~13 instead of ~18).</p>
3802
3803<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do a
3804File/Save project from the main menu; this saves the final texture results done
3805in Step 2 (you also will need it for Method C).</p>
3806
3807<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
38080in;line-height:115%'>Method C. Sequential refinement &amp; full texture
3809refinement</h2>
3810
3811<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
38120in;line-height:115%'>Introduction</h3>
3813
3814<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This uses the
3815same approach as Method B except that after the sequential refinements are
3816finished we then fix almost all the parameters and then do a final texture
3817refinement with all the data. Thus, this is a replacement for Step 2 in Method
3818B. To begin do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3819"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3820minor-latin'>File/Open project…</span></b> for the <span class=SpellE><b
3821style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3822mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NiTi-B.gpx</span></b></span>
3823file created in Method B and then do a <b style='mso-bidi-font-weight:normal'><span
3824style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3825mso-hansi-theme-font:minor-latin'>File/Save project as…</span></b> to save it
3826as <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3827style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3828mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight:
3829normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3830minor-latin;mso-hansi-theme-font:minor-latin'>-C</span></b>. This renames the
3831project and it should have one IMG, 10 PWDR entries and two phases of <span
3832class=SpellE>NiTi</span> (B2 and B19’).</p>
3833
3834<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
38350in;line-height:115%'>Step 1. Clearing unwanted variables from sequential
3836refinement</h3>
3837
3838<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Here we want
3839to clear refinement flags for all parameters that need not be varied in a
3840texture analysis refinement. The general rule is to not refine any parameter
3841unless we expect it to affect the peak intensities. These are listed below:</p>
3842
3843<p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;mso-add-space:
3844auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3845style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
3846style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3847style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3848mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>:
3849as the background was fit during the sequential refinement we should fix it
3850here. Select any <b style='mso-bidi-font-weight:normal'><span style='font-family:
3851"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3852minor-latin'>PWDR</span></b> entry and choose the <b style='mso-bidi-font-weight:
3853normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3854minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b> subentry
3855for it. Clear the <b style='mso-bidi-font-weight:normal'><span
3856style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3857mso-hansi-theme-font:minor-latin'>Refine</span></b> flags and the do <b
3858style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3859mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Copy
3860flags</span></b> selecting all data sets. This will clear all background
3861refinement flags.</p>
3862
3863<p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;mso-add-space:
3864auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3865style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
3866style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3867style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3868mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3869phase: we do not want to refine either the <span class=SpellE>microstrain</span>,
3870D<sub>11</sub>, or preferred orientation coefficients. Select the <b
3871style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3872mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3873phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
3874"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3875minor-latin'>Data</span></b> tab. <span class=GramE>Clear</span> the <span
3876class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3877"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3878minor-latin'>microstrain</span></b></span>, <b style='mso-bidi-font-weight:
3879normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3880minor-latin;mso-hansi-theme-font:minor-latin'>D<sub>11</sub></span></b> and <b
3881style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3882mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
3883orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
3884style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3885mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
3886avoid a lot of nasty (but harmless) messages at the start of the refinement).
3887Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3888mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3889flags</span></b> selecting all data to clear all the flags and an <b
3890style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3891mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3892selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
3893normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3894minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
3895copy the zeroed out harmonic coefficients.</p>
3896
3897<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space:
3898auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3899style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
3900style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3901style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3902mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>:
3903we do not want to refine either the <span class=SpellE>microstrain</span>, <span
3904class=SpellE>Dij</span>, or preferred orientation coefficients. Select the <b
3905style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3906mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3907phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
3908"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3909minor-latin'>Data</span></b> tab. Clear the <span class=SpellE><b
3910style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3911mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>microstrain</span></b></span>,
3912four <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3913style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3914mso-hansi-theme-font:minor-latin'>Dij</span></b></span> and <b
3915style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3916mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
3917orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
3918style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3919mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
3920avoid a lot of nasty (but harmless) messages at the start of the refinement).
3921Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3922mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3923flags</span></b> selecting all data to clear all the flags and an <b
3924style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3925mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3926selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
3927normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3928minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
3929copy the zeroed out harmonic coefficients.</p>
3930
3931<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
3932margin-left:.25in;line-height:115%'><o:p>&nbsp;</o:p></p>
3933
3934<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
3935margin-left:.25in;line-height:115%'>Notice that we have allowed refinement of
3936the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3937mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase fractions</span></b>;
3938these may change during the texture refinement. Now select the <b
3939style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3940mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
3941tab for the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3942"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3943minor-latin'>B2</span></b> phase (it may still have values from the Method B).</p>
3944
3945<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
3946margin-left:.25in;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3947 id="Picture_x0020_23" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:480pt;
3948 height:267.75pt;visibility:visible;mso-wrap-style:square'>
3949 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
3950  o:title=""/>
3951</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3952src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
3953v:shapes="Picture_x0020_23"><![endif]></span></p>
3954
3955<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
3956margin-left:.25in;line-height:115%'>You can clear these by setting the <b
3957style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3958mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic
3959order</span></b> to zero and then back to <b style='mso-bidi-font-weight:normal'><span
3960style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3961mso-hansi-theme-font:minor-latin'>12</span></b>. Leave the <b style='mso-bidi-font-weight:
3962normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3963minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b> &amp; <b
3964style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3965mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b>
3966boxes checked.</p>
3967
3968<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
3969margin-left:.25in;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3970 id="Picture_x0020_24" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:480pt;
3971 height:267.75pt;visibility:visible;mso-wrap-style:square'>
3972 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
3973  o:title=""/>
3974</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3975src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
3976v:shapes="Picture_x0020_24"><![endif]></span></p>
3977
3978<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
3979margin-left:.25in;line-height:115%'>Then do the same for the <b
3980style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3981mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3982phase. Select the <b style='mso-bidi-font-weight:normal'><span
3983style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3984mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and its <b
3985style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3986mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
3987tab. <span class=GramE>Set</span> the <b style='mso-bidi-font-weight:normal'><span
3988style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3989mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero and then
3990back to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3991mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>.
3992Leave the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3993mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b>
3994and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3995mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b>
3996boxes checked. This completes the setup for the full texture refinement.</p>
3997
3998<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
39990in;line-height:115%'>Step 2. Texture refinement</h3>
4000
4001<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do <b
4002style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
4003mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
4004from the main menu; you will see the warning message</p>
4005
4006<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
4007style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_25"
4008 o:spid="_x0000_i1029" type="#_x0000_t75" style='width:363pt;height:120.75pt;
4009 visibility:visible;mso-wrap-style:square'>
4010 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
4011  o:title=""/>
4012</v:shape><![endif]--><![if !vml]><img border=0 width=484 height=161
4013src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
4014v:shapes="Picture_x0020_25"><![endif]></span></p>
4015
4016<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In this case
4017you do want to do a <span class=SpellE>nonsequential</span> full refinement, so
4018press the OK button. A quick look at the console will show that there are 61
4019variables in this refinement. If yours shows more then you didn’t clear all the
4020flags in Step 1. The <b style='mso-bidi-font-weight:normal'><span
4021style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
4022mso-hansi-theme-font:minor-latin'>Sequential results</span></b> entry is
4023deleted from the GSAS-II data tree. A progress bar will show giving the
4024residuals during the refinement. When finished, select the <b style='mso-bidi-font-weight:
4025normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
4026minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> phase and its <b
4027style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
4028mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
4029tab; if the Texture plot type is still <b style='mso-bidi-font-weight:normal'><span
4030style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
4031mso-hansi-theme-font:minor-latin'>Inverse pole figure</span></b> (from Method
4032B) you should see</p>
4033
4034<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
4035style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26"
4036 o:spid="_x0000_i1028" type="#_x0000_t75" style='width:525pt;height:450pt;
4037 visibility:visible;mso-wrap-style:square'>
4038 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
4039  o:title=""/>
4040</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
4041src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
4042v:shapes="Picture_x0020_26"><![endif]></span></p>
4043
4044<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
4045class=GramE>which</span> is almost identical to that from Method A. The
4046coefficients are seen in</p>
4047
4048<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
4049style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27"
4050 o:spid="_x0000_i1027" type="#_x0000_t75" style='width:480pt;height:267.75pt;
4051 visibility:visible;mso-wrap-style:square'>
4052 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
4053  o:title=""/>
4054</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
4055src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
4056v:shapes="Picture_x0020_27"><![endif]></span></p>
4057
4058<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the
4059<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
4060mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
4061phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
4062"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
4063minor-latin'>Texture</span></b> tab; the inverse pole figure is</p>
4064
4065<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
4066style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28"
4067 o:spid="_x0000_i1026" type="#_x0000_t75" style='width:525pt;height:450pt;
4068 visibility:visible;mso-wrap-style:square'>
4069 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png"
4070  o:title=""/>
4071</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
4072src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png"
4073v:shapes="Picture_x0020_28"><![endif]></span></p>
4074
4075<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
4076class=GramE>and</span> also almost identical to what was obtained in Method A;
4077the coefficients are seen in</p>
4078
4079<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
4080style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_58"
4081 o:spid="_x0000_i1025" type="#_x0000_t75" style='width:502.5pt;height:375pt;
4082 visibility:visible;mso-wrap-style:square'>
4083 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
4084  o:title=""/>
4085</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
4086src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
4087v:shapes="Picture_x0020_58"><![endif]></span></p>
4088
4089<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>With this
4090Method you can add parameters (atom coordinates &amp; thermal motion
4091parameters) that could not be refined in method B. It should be clear from this
4092tutorial that in more complex textures where the data set may consist of slices
4093obtained from a suite of 2D images collected as the sample is rotated, Method C
4094will give a relatively fast determination of the texture without resorting to large
4095matrix least-squares refinements.</p>
4096
4097</div>
4098
4099</body>
4100
4101</html>
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