source: Tutorials/2DTexture/Texture analysis of 2D data in GSAS-II.htm @ 2385

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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";}
1183p.msonormal0, li.msonormal0, div.msonormal0
1184        {mso-style-name:msonormal;
1185        mso-style-noshow:yes;
1186        mso-style-priority:99;
1187        mso-style-unhide:no;
1188        mso-margin-top-alt:auto;
1189        margin-right:0in;
1190        mso-margin-bottom-alt:auto;
1191        margin-left:0in;
1192        mso-pagination:widow-orphan;
1193        font-size:12.0pt;
1194        font-family:"Times New Roman",serif;
1195        mso-fareast-font-family:"Times New Roman";
1196        mso-fareast-theme-font:minor-fareast;}
1197span.TitleChar
1198        {mso-style-name:"Title Char";
1199        mso-style-priority:10;
1200        mso-style-unhide:no;
1201        mso-style-locked:yes;
1202        mso-style-link:Title;
1203        mso-ansi-font-size:26.0pt;
1204        mso-bidi-font-size:26.0pt;
1205        font-family:"Cambria",serif;
1206        mso-ascii-font-family:Cambria;
1207        mso-ascii-theme-font:major-latin;
1208        mso-fareast-font-family:"Times New Roman";
1209        mso-fareast-theme-font:major-fareast;
1210        mso-hansi-font-family:Cambria;
1211        mso-hansi-theme-font:major-latin;
1212        mso-bidi-font-family:"Times New Roman";
1213        mso-bidi-theme-font:major-bidi;
1214        color:#17365D;
1215        mso-themecolor:text2;
1216        mso-themeshade:191;
1217        letter-spacing:.25pt;
1218        mso-font-kerning:14.0pt;}
1219span.DocumentMapChar
1220        {mso-style-name:"Document Map Char";
1221        mso-style-noshow:yes;
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1425<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1426
1427<div class=WordSection1>
1428
1429<h1 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
14300in;line-height:115%'>Texture analysis of 2D data in GSAS-II</h1>
1431
1432<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
14330in;line-height:115%'>Introduction</h2>
1434
1435<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Texture
1436analysis using GSAS-II employs spherical harmonics modeling, as described by
1437Bunge, &quot;Texture Analysis in Materials Science&quot; (1982), and
1438implemented by Von Dreele, J. Appl. <span class=SpellE>Cryst</span>., <b
1439style='mso-bidi-font-weight:normal'>30</b>, 517-525 (1997) in GSAS. The even
1440part of the orientation distribution function (ODF) via the general axis
1441equation</p>
1442
1443<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
1444   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
1445  style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><span
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1448    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
1449    normal'><span style='font-family:"Cambria Math",serif'><m:r>h</m:r><m:r>,</m:r><m:r>y</m:r></span></i></m:e></m:d><i
1450  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
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1460      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
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1471      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
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1496    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
1497  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></m:oMathPara><![endif]--><![if !msEquation]><span
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1527
1528<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1529margin-left:0in;line-height:115%'>is used to give the intensity corrections due
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1537   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1538   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1539   normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
1540   normal'><span style='font-family:"Cambria Math",serif'><m:r>h</m:r></span></i></m:e></m:d></m:oMath><![endif]--><![if !msEquation]><span
1541style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1542"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1543top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1544EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1545 type="#_x0000_t75" style='width:32.25pt;height:26.25pt'>
1546 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image003.png"
1547  o:title="" chromakey="white"/>
1548</v:shape><![endif]--><![if !vml]><img width=43 height=35
1549src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png"
1550v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1551style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1552   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1553   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1554   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1555   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1556   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
1557   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
1558 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
1559style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1560"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1561top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1562EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1563 type="#_x0000_t75" style='width:30pt;height:26.25pt'>
1564 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png"
1565  o:title="" chromakey="white"/>
1566</v:shape><![endif]--><![if !vml]><img width=40 height=35
1567src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"
1568v:shapes="_x0000_i1025"><![endif]></span><![endif]>, take on values according
1569to the crystal and sample symmetries, respectively, and thus the two inner
1570summations are over only the resulting unique, nonzero harmonic terms. These
1571unique terms are automatically selected by <span style='mso-bidi-font-weight:
1572bold'>GSAS-II</span> according to the space group symmetry and the user chosen
1573sample symmetry. The available sample symmetries are cylindrical symmetry, 2/m,
1574mmm and no symmetry. The choice of sample symmetry profoundly affects the
1575selection of harmonic coefficients. For example, in the case of cylindrical
1576sample symmetry (fiber texture) only <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1577   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1578   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1579   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1580   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1581   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
1582   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
1583 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
1584style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1585"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1586top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1587EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1588 type="#_x0000_t75" style='width:29.25pt;height:26.25pt'>
1589 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image007.png"
1590  o:title="" chromakey="white"/>
1591</v:shape><![endif]--><![if !vml]><img width=39 height=35
1592src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image008.png"
1593v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1594style='mso-spacerun:yes'> </span>terms are nonzero so the rest are excluded
1595from the summations and the set of <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1596   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1597   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1598   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1599   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
1600   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
1601   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
1602style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1603"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1604top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1605EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1606 type="#_x0000_t75" style='width:21pt;height:26.25pt'>
1607 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image009.png"
1608  o:title="" chromakey="white"/>
1609</v:shape><![endif]--><![if !vml]><img width=28 height=35
1610src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image010.png"
1611v:shapes="_x0000_i1025"><![endif]></span><![endif]>coefficients is sufficient
1612to describe the effect on the diffraction patterns due to texture. The crystal
1613harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1614   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1615   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1616   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1617   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1618   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
1619   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
1620 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
1621style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1622"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1623top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1624EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1625 type="#_x0000_t75" style='width:32.25pt;height:26.25pt'>
1626 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image011.png"
1627  o:title="" chromakey="white"/>
1628</v:shape><![endif]--><![if !vml]><img width=43 height=35
1629src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image012.png"
1630v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined for each
1631reflection, h, <i>via</i> polar and azimuthal coordinates (<span
1632style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
1633of a unit vector coincident with h relative to the reciprocal lattice. For most
1634crystal symmetries, <span style='font-family:Symbol'>f</span> is the angle
1635between h and the n-<span class=SpellE>th</span> order major rotation axis of
1636the space group (usually the c-axis) and <span style='font-family:Symbol'>b</span>
1637is the angle between the projections of h and any secondary axis (usually the
1638a-axis) onto the normal plane.<span style='mso-spacerun:yes'>  </span>In a
1639similar way the sample harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1640   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1641   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1642   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1643   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1644   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
1645   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
1646 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
1647style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1648"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1649top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1650EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1651 type="#_x0000_t75" style='width:30pt;height:26.25pt'>
1652 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png"
1653  o:title="" chromakey="white"/>
1654</v:shape><![endif]--><![if !vml]><img width=40 height=35
1655src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png"
1656v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined according to
1657polar and azimuthal coordinates (<span style='font-family:Symbol'>y</span>, <span
1658style='font-family:Symbol'>g</span>) of a unit vector coincident with the
1659diffraction vector relative to a coordinate system attached to the external
1660form of the sample. For example, in the case of a rolled steel plate having mmm
1661symmetry, the polar angle, <span style='font-family:Symbol'>y</span>, is
1662frequently measured from the normal direction (ND) and <span style='font-family:
1663Symbol'>g</span> is then measured from the rolling direction (RD) in the TD
1664(transverse direction) - RD plane.<span style='mso-spacerun:yes'>  </span>Thus,
1665the general axis equation becomes</p>
1666
1667<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1668margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
1669   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
1670  style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><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:dPr><m:e><i style='mso-bidi-font-style:
1674    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
1675  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
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>L</m:r><m:r>=2</m:r></span></i></m:sub><m:sup><m:sSub><m:sSubPr><span
1680      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1681      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1682      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
1683      normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i
1684      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
1685      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1686      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1687      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
1688      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
1689      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
1690     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
1691    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1692    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
1693    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
1694    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
1695       m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
1696      "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
1697      "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
1698      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
1699      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
1700        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1701        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1702        normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
1703        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
1704        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
1705        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
1706      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1707      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1708      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
1709      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
1710      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
1711      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
1712      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1713      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1714      normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
1715      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
1716    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1717    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1718    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1719    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1720    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
1721    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
1722  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
1723style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1724"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
1725mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
1726 id="_x0000_i1025" type="#_x0000_t75" style='width:320.95pt;height:54pt'>
1727 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image013.png"
1728  o:title="" chromakey="white"/>
1729</v:shape><![endif]--><![if !vml]><img width=428 height=72
1730src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image014.png"
1731v:shapes="_x0000_i1025"><![endif]></span><![endif]><br style='mso-special-character:
1732line-break'>
1733<![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'>
1734<![endif]></p>
1735
1736<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In a
1737diffraction experiment the crystal reflection coordinates (<span
1738style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
1739are determined by the choice of reflection index (<span class=SpellE>hkl</span>)
1740while the sample coordinates (<span style='font-family:Symbol'>y</span>, <span
1741style='font-family:Symbol'>g</span>) are determined by the sample orientation
1742on the diffractometer.</p>
1743
1744<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1745margin-left:0in;line-height:115%'>To define the sample coordinates (<span
1746style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>),
1747we have defined an instrument coordinate system (I, J, K) such that K is normal
1748to the diffraction plane and J is coincident with the direction of the incident
1749radiation beam toward the source. We further define a standard set of
1750right-handed goniometer <span class=SpellE>eulerian</span> angles (<span
1751style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>,
1752<span style='font-family:Symbol'>F</span>) so that <span style='font-family:
1753Symbol'>W</span> and <span style='font-family:Symbol'>F</span> are rotations
1754about K and <span style='font-family:Symbol'>C</span> is a rotation about J
1755when <span style='font-family:Symbol'>W</span> <span style='font-family:Symbol'><span
1756style='mso-spacerun:yes'> </span></span>= 0.<span style='mso-spacerun:yes'> 
1757</span>Finally, as the sample may be mounted so that the sample coordinate
1758system (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>)
1759does not coincide with the instrument coordinate system (I, J, K), we define
1760three <span class=SpellE>eulerian</span> sample rotation offset angles (<span
1761style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
1762<span style='font-family:Symbol'>F</span><sub>s</sub>) that describe the
1763rotation from (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>)
1764to (I, J, K).<span style='mso-spacerun:yes'>  </span>The sample rotation angles
1765are defined so that with the goniometer angles at zero <span style='font-family:
1766Symbol'>W</span><sub>s</sub> and <span style='font-family:Symbol'>F</span><sub>s</sub>
1767are rotations about I and <span style='font-family:Symbol'>C</span><sub>s</sub>
1768is a rotation about J.<span style='mso-spacerun:yes'>  </span>The zeros of
1769these three sample rotation angles can be refined as part of the Rietveld
1770analysis to accommodate any angular offset in sample mounting. After including
1771the diffraction angle, <span style='font-family:Symbol'>Q</span>, and a
1772detector azimuthal angle, A, the full rotation matrix, <b style='mso-bidi-font-weight:
1773normal'>M</b>, is </p>
1774
1775<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1776margin-left:0in;line-height:115%'><b style='mso-bidi-font-weight:normal'>M = -</b><b
1777style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>Q</span>A</b><b
1778style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>WC</span>(</b><b
1779style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span>+</b><b
1780style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span><sub>s</sub>)</b><b
1781style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>C</span><span
1782class=SpellE><sub>s</sub><span style='font-family:Symbol'>W</span><sub>s</sub></span><o:p></o:p></b></p>
1783
1784<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1785margin-left:0in;line-height:115%'>By transformation of unit Cartesian vectors
1786(100, 010 and 001) with this rotation matrix, the sample orientation coordinates
1787(<span style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>)
1788are given by</p>
1789
1790<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1791margin-left:0in;line-height:115%'><i>cos</i>(<span style='font-family:Symbol'>y</span>)
1792= <!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span
1793 style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
1794   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1795   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1796   normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
1797         m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
1798     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1799     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1800     normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
1801      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
1802      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
1803      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
1804style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1805"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1806top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1807EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1808 type="#_x0000_t75" style='width:33.75pt;height:50.25pt'>
1809 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image015.png"
1810  o:title="" chromakey="white"/>
1811</v:shape><![endif]--><![if !vml]><img width=45 height=67
1812src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.png"
1813v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1814style='mso-spacerun:yes'> </span>and<span style='mso-spacerun:yes'>   </span><i>tan</i>(<span
1815style='font-family:Symbol'>g</span>) = <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type
1816    m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1817   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1818   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
1819   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
1820     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1821     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1822     normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
1823           m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
1824       style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1825       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1826       normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
1827        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
1828        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
1829        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
1830   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
1831     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1832     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1833     normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
1834           m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
1835       style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1836       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1837       normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
1838        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
1839        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
1840        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
1841style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1842"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1843top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1844EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1845 type="#_x0000_t75" style='width:80.25pt;height:50.25pt'>
1846 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image017.png"
1847  o:title="" chromakey="white"/>
1848</v:shape><![endif]--><![if !vml]><img width=107 height=67
1849src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.png"
1850v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
1851
1852<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1853margin-left:0in;line-height:115%'>The harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1854   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1855   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1856   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1857   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1858   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
1859   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
1860 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
1861style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1862"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1863top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1864EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1865 type="#_x0000_t75" style='width:46.5pt;height:26.25pt'>
1866 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png"
1867  o:title="" chromakey="white"/>
1868</v:shape><![endif]--><![if !vml]><img width=62 height=35
1869src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png"
1870v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1871style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1872   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1873   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1874   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1875   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1876   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
1877   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
1878 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
1879style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1880"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1881top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1882EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1883 type="#_x0000_t75" style='width:42.75pt;height:26.25pt'>
1884 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png"
1885  o:title="" chromakey="white"/>
1886</v:shape><![endif]--><![if !vml]><img width=57 height=35
1887src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.png"
1888v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are developed from</p>
1889
1890<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1891margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
1892   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
1893    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1894    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1895    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1896    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1897    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
1898    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
1899    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1900    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1901    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
1902    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
1903  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:f><m:fPr><span
1904    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1905    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1906    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
1907    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
1908       m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1909      "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1910      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
1911      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
1912    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1913    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1914    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
1915    normal'><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:e><m:sup><i
1916    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
1917    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1918    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1919    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
1920       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
1921      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1922      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1923      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
1924    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
1925    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
1926     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
1927  normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
1928    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1929    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1930    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
1931    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
1932       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
1933    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
1934  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
1935style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1936"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
1937mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
1938 id="_x0000_i1025" type="#_x0000_t75" style='width:165pt;height:42pt'>
1939 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.png"
1940  o:title="" chromakey="white"/>
1941</v:shape><![endif]--><![if !vml]><img width=220 height=56
1942src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png"
1943v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
1944
1945<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1946margin-left:0in;line-height:115%'>where the normalized associated Legendre
1947functions, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1948   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1949   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1950   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
1951      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1952     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1953     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1954     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
1955   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
1956   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
1957 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
1958style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1959"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1960top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1961EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1962 type="#_x0000_t75" style='width:33pt;height:26.25pt'>
1963 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image025.png"
1964  o:title="" chromakey="white"/>
1965</v:shape><![endif]--><![if !vml]><img width=44 height=35
1966src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image026.png"
1967v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are defined via a Fourier
1968expansion as</p>
1969
1970<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
1971margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
1972   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
1973    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1974    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1975    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
1976       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
1977      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1978      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1979      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
1980    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
1981    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
1982     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
1983    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1984    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1985    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
1986      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1987      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1988      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
1989      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
1990         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
1991      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
1992  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
1993     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
1994    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1995    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
1996    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
1997    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
1998      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1999      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2000      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
2001      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
2002      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
2003      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2004       </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
2005    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2006    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2007    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2008    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2009       m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2010    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
2011style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2012"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2013mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2014 id="_x0000_i1025" type="#_x0000_t75" style='width:154.5pt;height:52.5pt'>
2015 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image027.png"
2016  o:title="" chromakey="white"/>
2017</v:shape><![endif]--><![if !vml]><img width=206 height=70
2018src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image028.png"
2019v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2020
2021<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2022margin-left:0in;line-height:115%'>for m even and</p>
2023
2024<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2025margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2026   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
2027    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2028    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2029    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2030       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2031      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2032      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2033      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
2034    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
2035    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2036     </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
2037    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2038    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2039    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
2040      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2041      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2042      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2043      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2044         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2045      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
2046  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
2047     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2048    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2049    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2050    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
2051    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
2052      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2053      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2054      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
2055      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
2056      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
2057      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2058       </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
2059    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2060    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2061    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2062    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2063       m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2064    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
2065style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2066"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2067mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2068 id="_x0000_i1025" type="#_x0000_t75" style='width:158.25pt;height:52.5pt'>
2069 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image029.png"
2070  o:title="" chromakey="white"/>
2071</v:shape><![endif]--><![if !vml]><img width=211 height=70
2072src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image030.png"
2073v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2074
2075<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2076margin-left:0in;line-height:115%'>for m odd.<span style='mso-spacerun:yes'> 
2077</span>Each sum is only over either the even or odd values of s, respectively,
2078because of the properties of the Fourier coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2079   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2080   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2081   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2082   normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i
2083   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
2084   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2085    </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
2086style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2087"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2088top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2089EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2090 type="#_x0000_t75" style='width:24.75pt;height:26.25pt'>
2091 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image031.png"
2092  o:title="" chromakey="white"/>
2093</v:shape><![endif]--><![if !vml]><img width=33 height=35
2094src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image032.png"
2095v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
2096style='mso-spacerun:yes'>  </span>These Fourier coefficients are determined so
2097that the definition</p>
2098
2099<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2100margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2101   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><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:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2105       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2106      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2107      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2108      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
2109    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
2110    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2111     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
2112    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2113    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2114    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
2115      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2116      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2117      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2118      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2119         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2120      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
2121  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:sSubSup><m:sSubSupPr><span
2122    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2123    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2124    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2125       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2126      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2127      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2128      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
2129    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
2130    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2131     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
2132    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2133    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2134    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
2135    normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e></m:d><i
2136  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
2137     m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2138    "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2139    mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
2140      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2141      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2142      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><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:dPr><m:e><i style='mso-bidi-font-style:
2146        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
2147      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
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:dPr><m:e><i style='mso-bidi-font-style:
2151        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
2152      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
2153     m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2154    "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2155    mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><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:fPr><m:num><i style='mso-bidi-font-style:
2159      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
2160      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
2161    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2162    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2163    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
2164      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2165      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2166      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2167      normal'><span style='font-family:"Cambria Math",serif'><m:r>(-1)</m:r></span></i></m:e><m:sup><i
2168      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
2169      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2170      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2171      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2172      normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:e><m:sup><i
2173      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
2174    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
2175    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2176    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2177    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2178    normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><span
2179      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2180      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2181      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2182      normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i
2183      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
2184    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
2185       m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2186      "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2187      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
2188      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
2189      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
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:fPr><m:num><m:sSup><m:sSupPr><span
2193      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2194      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2195      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2196      normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
2197      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
2198      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2199      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2200      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2201      normal'><span style='font-family:"Cambria Math",serif'><m:r>dx</m:r></span></i></m:e><m:sup><i
2202      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
2203    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2204    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2205    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2206    normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><span
2207      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2208      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2209      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2210      normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i
2211      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
2212    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:e><m:sup><i
2213    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
2214style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2215"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2216mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2217 id="_x0000_i1025" type="#_x0000_t75" style='width:423.7pt;height:55.5pt'>
2218 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.png"
2219  o:title="" chromakey="white"/>
2220</v:shape><![endif]--><![if !vml]><img width=565 height=74
2221src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image034.png"
2222v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2223
2224<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2225margin-left:0in;line-height:115%'>is satisfied.<span style='mso-spacerun:yes'> 
2226</span>Terms of the form <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
2227   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2228   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2229   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2230   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2231      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2232   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
2233   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2234   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2235   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2236      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2237     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2238     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2239     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
2240   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
2241   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2242    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2243 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
2244   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2245   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2246   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2247   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2248      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2249   normal'><span style='font-family:"Cambria Math",serif'><m:r>m&#946;</m:r></span></i></m:e></m:func><i
2250 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
2251style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2252"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2253top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2254EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2255 type="#_x0000_t75" style='width:111pt;height:26.25pt'>
2256 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image035.png"
2257  o:title="" chromakey="white"/>
2258</v:shape><![endif]--><![if !vml]><img width=148 height=35
2259src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image036.png"
2260v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2261style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
2262   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2263   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2264   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2265   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2266      m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2267   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
2268   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2269   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2270   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2271      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2272     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2273     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2274     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
2275   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
2276   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2277    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2278 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
2279   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2280   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2281   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2282   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2283      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2284   normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
2285 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
2286style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2287"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2288top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2289EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2290 type="#_x0000_t75" style='width:100.5pt;height:26.25pt'>
2291 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image037.png"
2292  o:title="" chromakey="white"/>
2293</v:shape><![endif]--><![if !vml]><img width=134 height=35
2294src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image038.png"
2295v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2296style='mso-spacerun:yes'> </span>are combined depending on the symmetry and the
2297value of m along with appropriate normalization coefficients to give the
2298harmonic terms <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2299   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2300   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2301   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2302   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
2303   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
2304   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2305    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2306 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
2307style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2308"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2309top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2310EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2311 type="#_x0000_t75" style='width:48pt;height:26.25pt'>
2312 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
2313  o:title="" chromakey="white"/>
2314</v:shape><![endif]--><![if !vml]><img width=64 height=35
2315src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"
2316v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2317style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2318   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2319   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2320   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2321   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
2322   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
2323   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2324    </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2325 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
2326style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2327"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2328top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2329EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2330 type="#_x0000_t75" style='width:45pt;height:26.25pt'>
2331 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png"
2332  o:title="" chromakey="white"/>
2333</v:shape><![endif]--><![if !vml]><img width=60 height=35
2334src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image042.png"
2335v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
2336style='mso-spacerun:yes'>  </span>For cubic crystal symmetry, the term <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2337   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2338   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2339   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2340   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
2341   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
2342   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2343    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2344 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
2345style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2346"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2347top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2348EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2349 type="#_x0000_t75" style='width:48pt;height:26.25pt'>
2350 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
2351  o:title="" chromakey="white"/>
2352</v:shape><![endif]--><![if !vml]><img width=64 height=35
2353src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png"
2354v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2355style='mso-spacerun:yes'> </span>is obtained directly from the Fourier
2356expansion</p>
2357
2358<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2359margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2360   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
2361    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2362    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2363    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2364    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
2365    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
2366    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
2367    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2368    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2369    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
2370    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
2371  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
2372     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2373    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2374    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2375    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
2376    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
2377      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2378      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2379      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
2380      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
2381      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
2382      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
2383    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2384    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2385    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2386       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2387      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2388      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2389      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
2390    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
2391    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2392     </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2393  normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
2394    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2395    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2396    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2397    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2398       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2399    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
2400  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i><m:func><m:funcPr><span
2401    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2402    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2403    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2404    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2405       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2406    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
2407style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2408"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2409mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2410 id="_x0000_i1025" type="#_x0000_t75" style='width:193.5pt;height:52.5pt'>
2411 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image043.png"
2412  o:title="" chromakey="white"/>
2413</v:shape><![endif]--><![if !vml]><img width=258 height=70
2414src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image044.png"
2415v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2416
2417<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2418margin-left:0in;line-height:115%'>using the coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2419   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2420   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2421   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2422   normal'><span style='font-family:"Cambria Math",serif'><m:r>B</m:r></span></i></m:e><m:sub><i
2423   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
2424   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
2425style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2426"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2427top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2428EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2429 type="#_x0000_t75" style='width:22.5pt;height:26.25pt'>
2430 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image045.png"
2431  o:title="" chromakey="white"/>
2432</v:shape><![endif]--><![if !vml]><img width=30 height=35
2433src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image046.png"
2434v:shapes="_x0000_i1025"><![endif]></span><![endif]>, as tabulated by Bunge
2435(1982). </p>
2436
2437<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2438margin-left:0in;line-height:115%'>The Rietveld refinement of texture then
2439proceeds by constructing derivatives of the profile intensities with respect to
2440the allowed harmonic coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2441   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2442   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2443   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2444   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
2445   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
2446   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
2447style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2448"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2449top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2450EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2451 type="#_x0000_t75" style='width:21.75pt;height:26.25pt'>
2452 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"
2453  o:title="" chromakey="white"/>
2454</v:shape><![endif]--><![if !vml]><img width=29 height=35
2455src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
2456v:shapes="_x0000_i1025"><![endif]></span><![endif]>, and the three sample
2457orientation angles, <span style='font-family:Symbol'>W</span><sub>s</sub>, <span
2458style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:Symbol'>F</span><sub>s</sub>,
2459all of which can be adjustable parameters of the refinement. Once the
2460refinement is complete, pole figures for any reflection may be constructed by
2461use of the general axis equation, the refined values for <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2462   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2463   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2464   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2465   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
2466   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
2467   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
2468style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2469"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2470top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2471EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2472 type="#_x0000_t75" style='width:21.75pt;height:26.25pt'>
2473 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"
2474  o:title="" chromakey="white"/>
2475</v:shape><![endif]--><![if !vml]><img width=29 height=35
2476src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png"
2477v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2478style='mso-spacerun:yes'> </span>and the sample orientation angles <span
2479style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
2480<span style='font-family:Symbol'>F</span><sub>s</sub>. </p>
2481
2482<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2483margin-left:0in;line-height:115%'>The magnitude of the texture is evaluated
2484from the texture index by</p>
2485
2486<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2487margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2488   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
2489  style='font-family:"Cambria Math",serif'><m:r>J</m:r><m:r>=1+</m:r></span></i><m:nary><m:naryPr><m:chr
2490     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2491    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2492    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2493    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
2494      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2495      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2496      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
2497      normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i
2498      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
2499      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2500      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2501      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
2502      normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:num><m:den><i
2503      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
2504     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2505    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2506    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2507    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
2508    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
2509       m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
2510      "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
2511      "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2512      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
2513      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
2514        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2515        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2516        normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><m:begChr
2517           m:val="|"/><m:endChr m:val="|"/><span style='font-family:"Cambria Math",serif;
2518          mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2519          font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:sSubSup><m:sSubSupPr><span
2520            style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2521            mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2522            normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
2523            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
2524            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
2525            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
2526        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
2527style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2528"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2529mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2530 id="_x0000_i1025" type="#_x0000_t75" style='width:180.75pt;height:54pt'>
2531 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.png"
2532  o:title="" chromakey="white"/>
2533</v:shape><![endif]--><![if !vml]><img width=241 height=72
2534src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png"
2535v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2536
2537<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2538margin-left:0in;line-height:115%'>If the texture is random then J = 1, otherwise
2539J &gt; 1; for a single crystal J = <span style='font-family:Symbol'>¥.</span> </p>
2540
2541<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2542margin-left:0in;line-height:115%'>In GSAS-II the texture is defined in two ways
2543to accommodate the two possible uses of this correction. In one a suite of
2544spherical harmonics coefficients is defined for the texture of a phase in the
2545sample; this can have any of the possible sample symmetries and is the usual
2546result desired for texture analysis. The other is the suite of spherical
2547harmonics terms for cylindrical sample symmetry for each phase in each powder
2548pattern (“histogram”) and is usually used to accommodate preferred orientation
2549effects in a Rietveld refinement. The former description allows refinement of
2550the sample orientation zeros, <span style='font-family:Symbol'>W</span><sub>s</sub>,
2551<span style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:
2552Symbol'>F</span><sub>s</sub>, but the latter description does not (they are
2553assumed to be zero and not refinable). The sample orientation angles, (<span
2554style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>,
2555<span style='font-family:Symbol'>F) </span>are specified in the Sample
2556Parameters table in the GSAS-II data tree structure and are applied for either
2557description.</p>
2558
2559<p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
2560margin-left:0in;line-height:115%'>In this tutorial we will use both of these
2561descriptions to determine the texture of the two phases in a <span
2562class=SpellE>NiTi</span> shape memory alloy sample with cylindrical symmetry
2563(wire texture) as collected at APS on beam line 1ID-C (data kindly provided by
2564Paul Paradise &amp; Aaron <span class=SpellE>Stebner</span> of Colo. School of
2565Mines). Thus, there are three ways within GSAS-II that can be used for this
2566texture analysis all beginning with the same 2D area detector image. Each will
2567be described in turn after the initial setup of the GSAS-II project, image
2568input &amp; integration.</p>
2569
2570<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
25710in;line-height:115%'>Step 1. Image input &amp; integration</h2>
2572
2573<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you have
2574not done so already, <u><span style='color:#0070C0'><a
2575href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none;
2576text-underline:none'>start GSAS-II</span></a></span></u>. Note that menu
2577entries are listed in <b style='mso-bidi-font-weight:normal'><span
2578style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2579mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
2580minor-latin'>bold face</span></b> below as <b style='mso-bidi-font-weight:normal'><span
2581style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2582mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
2583minor-latin'>Help/About GSAS-II</span></b>, which lists first the name of the
2584menu (here <b style='mso-bidi-font-weight:normal'><span style='font-family:
2585"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2586minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>Help</span></b>)
2587and second the name of the entry in the menu (here <b style='mso-bidi-font-weight:
2588normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2589minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;
2590mso-bidi-theme-font:minor-latin'>About GSAS-II</span></b>). </p>
2591
2592<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Use the <b
2593style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2594mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Read image
2595data</span></b> menu item to read the data file into the current GSAS-II
2596project. A file selection dialog will be shown; its appearance will depend on
2597your OS. Change the search directory to <b style='mso-bidi-font-weight:normal'><span
2598style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2599mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
2600minor-latin'>2DTexture/data </span></b>and then select the file <b
2601style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2602mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NDC5_01588_1.ge2</span></b>.
2603A (faint) image will appear</p>
2604
2605<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2606style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_29"
2607 o:spid="_x0000_i1081" type="#_x0000_t75" style='width:525pt;height:450pt;
2608 visibility:visible;mso-wrap-style:square'>
2609 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
2610  o:title=""/>
2611</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2612src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
2613v:shapes="Picture_x0020_29"><![endif]></span></p>
2614
2615<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and the <b
2616style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2617mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2618Controls</span></b> data page will show</p>
2619
2620<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2621style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_30"
2622 o:spid="_x0000_i1080" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
2623 visibility:visible;mso-wrap-style:square'>
2624 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
2625  o:title=""/>
2626</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
2627src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
2628v:shapes="Picture_x0020_30"><![endif]></span></p>
2629
2630<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detector
2631was previously calibrated and the coefficients are stored in a file found by
2632doing <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'>Operations/Load
2634Controls</span></b> from the <b style='mso-bidi-font-weight:normal'><span
2635style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2636mso-hansi-theme-font:minor-latin'>Image Controls</span></b> menu. A file
2637selection popup will appear showing <b style='mso-bidi-font-weight:normal'><span
2638style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2639mso-hansi-theme-font:minor-latin'>NDC5.imctrl</span></b>; select it and press <b
2640style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2641mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Open</span></b>.
2642The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2643mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2644Controls</span></b> window will be repainted with the new values (do a reselect
2645of the image from the tree and then <b style='mso-bidi-font-weight:normal'><span
2646style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2647mso-hansi-theme-font:minor-latin'>Image Controls</span></b> to make sure the
2648image is up to date.)</p>
2649
2650<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2651style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_31"
2652 o:spid="_x0000_i1079" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
2653 visibility:visible;mso-wrap-style:square'>
2654 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
2655  o:title=""/>
2656</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
2657src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
2658v:shapes="Picture_x0020_31"><![endif]></span></p>
2659
2660<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detail in
2661the image can be enhanced by lowering the <b style='mso-bidi-font-weight:normal'><span
2662style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2663mso-hansi-theme-font:minor-latin'>Max intensity</span></b> (<b
2664style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2665mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>15000</span></b>
2666is suitable) and shows that the diffraction rings show the effect of texture
2667and that the image has a fairly high background. Placing the cursor in the
2668corners or inside the inner ring shows a background &gt;1700. This can be
2669suppressed by adjusting the <b style='mso-bidi-font-weight:normal'><span
2670style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2671mso-hansi-theme-font:minor-latin'>Flat <span class=SpellE>Bkg</span></span></b>
2672(I chose <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2673mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>1700</span></b>
2674for this). The image will now show the rings much more clearly.</p>
2675
2676<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2677style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32"
2678 o:spid="_x0000_i1078" type="#_x0000_t75" style='width:525pt;height:450pt;
2679 visibility:visible;mso-wrap-style:square'>
2680 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
2681  o:title=""/>
2682</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2683src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
2684v:shapes="Picture_x0020_32"><![endif]></span></p>
2685
2686<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For texture
2687analysis we will need to integrate the image into a number of slices sampling the
2688changing ring intensity with azimuthal angle. Also note that the image seems to
2689have <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2690mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>mm</span></b>
2691symmetry so that the unique part of this intensity variation covers 0-90° of
2692azimuth. In addition the ring intensity variation is such that using 10° slices
2693will capture it reasonably well. However, we want to include both 0° and 90° as
2694slice centers. Thus there will be 10 slices beginning at -5° and ending at 95°.
2695Check the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2696mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show
2697integration limits?</span></b> box and uncheck the <b style='mso-bidi-font-weight:
2698normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2699minor-latin;mso-hansi-theme-font:minor-latin'>Do full integration? </span></b>box,
2700enter <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2701mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>
2702in the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2703mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth
2704bins</span></b>, enter <b style='mso-bidi-font-weight:normal'><span
2705style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2706mso-hansi-theme-font:minor-latin'>-5</span></b> in the <b style='mso-bidi-font-weight:
2707normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2708minor-latin;mso-hansi-theme-font:minor-latin'>Start azimuth</span></b> box (it
2709will change to 355) and enter <b style='mso-bidi-font-weight:normal'><span
2710style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2711mso-hansi-theme-font:minor-latin'>455</span></b> in the <b style='mso-bidi-font-weight:
2712normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2713minor-latin;mso-hansi-theme-font:minor-latin'>End azimuth</span></b> box. In
2714addition, recall that the sample was mounted vertically and thus is aligned
2715with the defined laboratory I axis. Thus, the sample coordinate system needs to
2716be rotated by 90° to match the sample axis with the K axis; this can be done by
2717making the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2718"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2719minor-latin'>Sample goniometer axis Chi</span></b> = <b style='mso-bidi-font-weight:
2720normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2721minor-latin;mso-hansi-theme-font:minor-latin'>90</span></b>. The plot will
2722change with each entry and at the end should look like</p>
2723
2724<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2725style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_33"
2726 o:spid="_x0000_i1077" type="#_x0000_t75" style='width:525pt;height:450pt;
2727 visibility:visible;mso-wrap-style:square'>
2728 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
2729  o:title=""/>
2730</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2731src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
2732v:shapes="Picture_x0020_33"><![endif]></span></p>
2733
2734<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The <b
2735style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2736mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2737Controls</span></b> should be</p>
2738
2739<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2740style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_34"
2741 o:spid="_x0000_i1076" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
2742 visibility:visible;mso-wrap-style:square'>
2743 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
2744  o:title=""/>
2745</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
2746src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
2747v:shapes="Picture_x0020_34"><![endif]></span></p>
2748
2749<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It turns out
2750that the image contains a number of “picked bits” (very high count “zingers”);
2751these can be mostly eliminated by setting the upper threshold in Masks. Select <b
2752style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2753mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Masks</span></b>
2754and the following should appear</p>
2755
2756<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2757style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35"
2758 o:spid="_x0000_i1075" type="#_x0000_t75" style='width:297.75pt;height:99.75pt;
2759 visibility:visible;mso-wrap-style:square'>
2760 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
2761  o:title=""/>
2762</v:shape><![endif]--><![if !vml]><img border=0 width=397 height=133
2763src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
2764v:shapes="Picture_x0020_35"><![endif]></span></p>
2765
2766<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the <b
2767style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2768mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Upper
2769threshold</span></b> to <b style='mso-bidi-font-weight:normal'><span
2770style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2771mso-hansi-theme-font:minor-latin'>2500</span></b>; the image will be redrawn
2772reflecting this mask. By zooming in you may see isolated red pixels; these are
2773excluded points. Make sure the diffraction rings do not have any excluded
2774points. For example with the level set to 2200 the plot shows</p>
2775
2776<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2777style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_36"
2778 o:spid="_x0000_i1074" type="#_x0000_t75" style='width:525pt;height:450pt;
2779 visibility:visible;mso-wrap-style:square'>
2780 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
2781  o:title=""/>
2782</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2783src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
2784v:shapes="Picture_x0020_36"><![endif]></span></p>
2785
2786<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>for one ring.
2787This level is too low. Return to the <b style='mso-bidi-font-weight:normal'><span
2788style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2789mso-hansi-theme-font:minor-latin'>Image Controls</span></b> item in the data
2790tree.</p>
2791
2792<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
2793ready to integrate the image; do <b style='mso-bidi-font-weight:normal'><span
2794style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2795mso-hansi-theme-font:minor-latin'>Operations/Integrate</span></b> from the <b
2796style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2797mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2798Controls</span></b> menu. When done the last powder pattern in the tree will be
2799displayed</p>
2800
2801<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2802style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_37"
2803 o:spid="_x0000_i1073" type="#_x0000_t75" style='width:525pt;height:450pt;
2804 visibility:visible;mso-wrap-style:square'>
2805 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
2806  o:title=""/>
2807</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2808src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
2809v:shapes="Picture_x0020_37"><![endif]></span></p>
2810
2811<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
28120in;line-height:115%'>Step 2. Enter <span class=SpellE>NiTi</span> phases</h2>
2813
2814<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This <span
2815class=SpellE>NiTi</span> alloy consists of two phases, cubic B2 and monoclinic
2816B19’. Their parameters are:<br>
2817B2: <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2818mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P m 3 m</span></b>,
2819a=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2820mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>3.0240</span></b>,
2821Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2822mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0,0,0</span></b>,
2823<span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span
2824style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2825mso-hansi-theme-font:minor-latin'>œ,œ,œ</span></b>, <span class=SpellE>U<sub>iso</sub></span>=<b
2826style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2827mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.005 </span></b>for
2828both.<br>
2829B19’:<span style='mso-spacerun:yes'>  </span><b style='mso-bidi-font-weight:
2830normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2831minor-latin;mso-hansi-theme-font:minor-latin'>P 1 1 21/m</span></b>, a=<b
2832style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2833mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.8853</span></b>,
2834b=<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'>4.6353</span></b>,
2836c=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2837mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.1368</span></b>,
2838&#947;=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2839mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>96.821</span></b>,
2840<span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span
2841style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2842mso-hansi-theme-font:minor-latin'>0.5787,0.2841,Œ</span></b>, Ni <b
2843style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2844mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.9700,0.8209,Œ</span></b>,
2845<span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
2846style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2847mso-hansi-theme-font:minor-latin'>0.005</span></b> for both.<br>
2848Use the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2849mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Add
2850phase</span></b> to enter the <b style='mso-bidi-font-weight:normal'><span
2851style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2852mso-hansi-theme-font:minor-latin'>B2</span></b> and <b style='mso-bidi-font-weight:
2853normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2854minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b> phases; then for
2855each enter the information given above on their respective <b style='mso-bidi-font-weight:
2856normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2857minor-latin;mso-hansi-theme-font:minor-latin'>General</span></b> and <b
2858style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2859mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms</span></b>
2860tabs. Don’t forget the spaces between the axial fields for the space group
2861symbols. On the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2862"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2863minor-latin'>Atoms</span></b> tab begin by doing <b style='mso-bidi-font-weight:
2864normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2865minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Append atom</span></b> twice
2866then fill in the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2867"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2868minor-latin'>Type</span></b> and coordinates boxes. A double click of the <b
2869style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2870mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Type</span></b>
2871entry will show a popup of the Periodic Table; select the element as
2872appropriate. NB: GSAS-II happily takes “1/2” &amp; “1/4” for coordinate values;
2873these get converted to their decimal equivalent upon entry. Note the use of a
2874nonstandard space group designation for B19’. When done the B2 Atoms table
2875should look like</p>
2876
2877<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2878style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_38"
2879 o:spid="_x0000_i1072" type="#_x0000_t75" style='width:525pt;height:166.5pt;
2880 visibility:visible;mso-wrap-style:square'>
2881 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
2882  o:title=""/>
2883</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=222
2884src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
2885v:shapes="Picture_x0020_38"><![endif]></span></p>
2886
2887<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and the B19’
2888Atoms table should be</p>
2889
2890<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2891style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_39"
2892 o:spid="_x0000_i1071" type="#_x0000_t75" style='width:525pt;height:163.5pt;
2893 visibility:visible;mso-wrap-style:square'>
2894 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2895  o:title=""/>
2896</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=218
2897src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2898v:shapes="Picture_x0020_39"><![endif]></span></p>
2899
2900<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
2901<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2902mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
2903tab for each phase; there will be a message indicating the lack of data for
2904each. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2905mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add
2906powder histograms</span></b>, do <b style='mso-bidi-font-weight:normal'><span
2907style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2908mso-hansi-theme-font:minor-latin'>Set All</span></b> on the popup selection
2909window and press <b style='mso-bidi-font-weight:normal'><span style='font-family:
2910"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2911minor-latin'>OK</span></b>. The window for B2 will change to</p>
2912
2913<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2914style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40"
2915 o:spid="_x0000_i1070" type="#_x0000_t75" style='width:342.75pt;height:375pt;
2916 visibility:visible;mso-wrap-style:square'>
2917 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2918  o:title=""/>
2919</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
2920src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2921v:shapes="Picture_x0020_40"><![endif]></span></p>
2922
2923<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and that for
2924B19’ will be</p>
2925
2926<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
2927style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_41"
2928 o:spid="_x0000_i1069" type="#_x0000_t75" style='width:370.5pt;height:375pt;
2929 visibility:visible;mso-wrap-style:square'>
2930 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
2931  o:title=""/>
2932</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
2933src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
2934v:shapes="Picture_x0020_41"><![endif]></span></p>
2935
2936<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You should now
2937save the project file (I used <span class=SpellE><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'>NiTi</span></b></span> for a
2940name); we will use this as a starting point for three different texture
2941determinations. Do a <b style='mso-bidi-font-weight:normal'><span
2942style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2943mso-hansi-theme-font:minor-latin'>File/Save project as…</span></b> and give it
2944a new name (I used <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
2945style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2946mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight:
2947normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2948minor-latin;mso-hansi-theme-font:minor-latin'>-A</span></b>); this will become
2949the new project name for the next part of this tutorial.</p>
2950
2951<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
29520in;line-height:115%'>Method A. Full refinement</h2>
2953
2954<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
29550in;line-height:115%'>Introduction</h3>
2956
2957<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In this method
2958we will do a full Rietveld refinement of the texture, profile parameters, peak
2959position variables and crystal structure parameters. This is suitable in this
2960case because of the relatively small number of histograms (10 in this case)
2961needed for the texture determination; do recall that each phase in each
2962histogram has a set of parameters (e.g. phase fraction, size, <span
2963class=SpellE>mustrain</span> &amp; hydrostatic strain) in addition to the ones
2964for each histogram (e.g. background &amp; scale factor). Consequently the total
2965number of parameters can build up very quickly in this method of analysis. The
2966other two methods seek to reduce this problem by splitting the fitting into a
2967sequential refinement (histogram by histogram) step followed by a texture
2968fitting step.</p>
2969
2970<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
29710in;line-height:115%'>Step 1. Initial refinement</h3>
2972
2973<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In the initial
2974refinement we need to vary the phase fraction for each phase/histogram and the
2975background in each histogram. To start select any <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</span></b> entry from the
2978GSAS-II data tree and select <b style='mso-bidi-font-weight:normal'><span
2979style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2980mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b> for it. Note
2981that Goniometer chi is set to 90; that came from the same entry in the Image
2982Controls during integration. Also, if you chose other than the 1<sup>st</sup>
2983PWDR data set the Detector azimuth will be some nonzero value; that is also
2984reflected in the name assigned to the histogram (e.g. <b style='mso-bidi-font-weight:
2985normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2986minor-latin;mso-hansi-theme-font:minor-latin'>PWDR NDC5_01588_1.ge2 <span
2987class=SpellE>Azm</span>= 40.00</span></b>). Uncheck the <b style='mso-bidi-font-weight:
2988normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2989minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>
2990box and then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
2991"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2992minor-latin'>Command/Copy flags</span></b>; select <b style='mso-bidi-font-weight:
2993normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2994minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b> and then press
2995<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2996mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
2997That will clear the scale factor refinement flag for all histograms; we will be
2998varying the phase fractions instead.</p>
2999
3000<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select
3001the B2 phase and pick the Data tab; you will see</p>
3002
3003<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3004style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42"
3005 o:spid="_x0000_i1068" type="#_x0000_t75" style='width:342.75pt;height:375pt;
3006 visibility:visible;mso-wrap-style:square'>
3007 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
3008  o:title=""/>
3009</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
3010src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
3011v:shapes="Picture_x0020_42"><![endif]></span></p>
3012
3013<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Select the <b
3014style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3015mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase
3016fraction</span></b> box. Then do <b style='mso-bidi-font-weight:normal'><span
3017style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3018mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b>, select <b
3019style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3020mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b>
3021&amp; press <b style='mso-bidi-font-weight:normal'><span style='font-family:
3022"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3023minor-latin'>OK</span></b> to copy these to the other histograms. Next select
3024the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3025mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3026phase and repeat this process. We are now ready for the first refinement; do <b
3027style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3028mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
3029from the main GSAS-II data tree window. A progress bar popup will appear and
3030when done a <b style='mso-bidi-font-weight:normal'><span style='font-family:
3031"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3032minor-latin'>Refinement results</span></b> popup will show with Rw~32%. Press <b
3033style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3034mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>
3035to load this result; GSAS-II will return you to the last window you were using
3036and display the 1<sup>st</sup> powder pattern showing you the fit</p>
3037
3038<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3039style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_43"
3040 o:spid="_x0000_i1067" type="#_x0000_t75" style='width:525pt;height:450pt;
3041 visibility:visible;mso-wrap-style:square'>
3042 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
3043  o:title=""/>
3044</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3045src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
3046v:shapes="Picture_x0020_43"><![endif]></span></p>
3047
3048<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is quite
3049poor. You can survey the fit successively by 1<sup>st</sup> selecting say the 1<sup>st</sup>
3050PWDR entry from the tree and then using the up/down arrow keys to step to the
3051next one; the plot will redraw at each step (NB: at full scale) and the data
3052window will show statistics of the fit. There is a substantial intensity
3053discrepancy; this is due to the texture. It is also evident that some of the
3054peaks are out of place relative to the reflection markers; this is due to
3055macroscopic strain in the drawn wire. For the <span style='font-family:"Calibri",sans-serif;
3056mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span>
3057phase select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3058"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3059minor-latin'>Texture</span></b> tab; it should look like</p>
3060
3061<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3062style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44"
3063 o:spid="_x0000_i1066" type="#_x0000_t75" style='width:456pt;height:217.5pt;
3064 visibility:visible;mso-wrap-style:square'>
3065 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
3066  o:title=""/>
3067</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290
3068src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
3069v:shapes="Picture_x0020_44"><![endif]></span></p>
3070
3071<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The texture
3072model is <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3073mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>cylindrical</span></b>
3074by default; that is what we want. Change the <b style='mso-bidi-font-weight:
3075normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3076minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to <b
3077style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3078mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>8</span></b>
3079and check both <b style='mso-bidi-font-weight:normal'><span style='font-family:
3080"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3081minor-latin'>Refine texture</span></b> and <b style='mso-bidi-font-weight:normal'><span
3082style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3083mso-hansi-theme-font:minor-latin'>Show <span class=SpellE>coeff</span></span></b>.
3084The window should look like</p>
3085
3086<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3087style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45"
3088 o:spid="_x0000_i1065" type="#_x0000_t75" style='width:456pt;height:250.5pt;
3089 visibility:visible;mso-wrap-style:square'>
3090 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
3091  o:title=""/>
3092</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
3093src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
3094v:shapes="Picture_x0020_45"><![endif]></span></p>
3095
3096<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the
3097<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3098mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3099tab, select <b style='mso-bidi-font-weight:normal'><span style='font-family:
3100"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3101minor-latin'>D11</span></b>; the <b style='mso-bidi-font-weight:normal'><span
3102style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3103mso-hansi-theme-font:minor-latin'>Data</span></b> window should look like (any
3104PWDR item will do)</p>
3105
3106<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3107style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_46"
3108 o:spid="_x0000_i1064" type="#_x0000_t75" style='width:342.75pt;height:375pt;
3109 visibility:visible;mso-wrap-style:square'>
3110 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
3111  o:title=""/>
3112</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
3113src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
3114v:shapes="Picture_x0020_46"><![endif]></span></p>
3115
3116<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then do <b
3117style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3118mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3119flags</span></b> to have <b style='mso-bidi-font-weight:normal'><span
3120style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3121mso-hansi-theme-font:minor-latin'>D11</span></b> refined for all PWDR data
3122sets.</p>
3123
3124<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select
3125the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3126mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3127phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3128mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
3129tab. Then select <b style='mso-bidi-font-weight:normal'><span style='font-family:
3130"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3131minor-latin'>6</span></b> for the <b style='mso-bidi-font-weight:normal'><span
3132style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3133mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> and check the two
3134boxes as before.</p>
3135
3136<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3137style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_47"
3138 o:spid="_x0000_i1063" type="#_x0000_t75" style='width:478.5pt;height:302.25pt;
3139 visibility:visible;mso-wrap-style:square'>
3140 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
3141  o:title=""/>
3142</v:shape><![endif]--><![if !vml]><img border=0 width=638 height=403
3143src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
3144v:shapes="Picture_x0020_47"><![endif]></span></p>
3145
3146<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the
3147<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3148mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3149tab for the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3150"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3151minor-latin'>B19’</span></b> phase and check all 4 of the <span class=SpellE><b
3152style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3153mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dij</span></b></span>
3154boxes and do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3155"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3156minor-latin'>Edit/Copy flags</span></b> as before. The tab will look like</p>
3157
3158<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3159style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48"
3160 o:spid="_x0000_i1062" type="#_x0000_t75" style='width:370.5pt;height:375pt;
3161 visibility:visible;mso-wrap-style:square'>
3162 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
3163  o:title=""/>
3164</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
3165src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
3166v:shapes="Picture_x0020_48"><![endif]></span></p>
3167
3168<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do <b
3169style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3170mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
3171from the main menu. The refinement will finish with <span class=SpellE>Rw</span>
3172~27%; the 1<sup>st</sup> PWDR pattern looks like</p>
3173
3174<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3175style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_49"
3176 o:spid="_x0000_i1061" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3177 visibility:visible;mso-wrap-style:square'>
3178 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
3179  o:title=""/>
3180</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3181src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
3182v:shapes="Picture_x0020_49"><![endif]></span></p>
3183
3184<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The calculated
3185peaks for both phases are too sharp. It is likely that this is a <span
3186class=SpellE>microstrain</span> effect. Select <b style='mso-bidi-font-weight:
3187normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3188minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b> 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'>B2 </span></b>phase
3191and select the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3192style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3193mso-hansi-theme-font:minor-latin'>microstrain</span></b></span> box. Then do <b
3194style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3195mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3196flags</span></b> to set it for the other PWDR data sets. Do the same for the <b
3197style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3198mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3199phase. Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3200"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3201minor-latin'>Calculate/Refine</span></b> from the main menu. The fit will be
3202substantially improved with <span class=SpellE>Rw</span> ~9.2%.</p>
3203
3204<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
32050in;line-height:115%'>Step 2. Finish refinement and examine texture</h3>
3206
3207<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Looking at the
3208individual PWDR data sets (e.g. the one for <span class=SpellE>Azm</span>=20.00)</p>
3209
3210<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3211style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_50"
3212 o:spid="_x0000_i1060" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3213 visibility:visible;mso-wrap-style:square'>
3214 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
3215  o:title=""/>
3216</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3217src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
3218v:shapes="Picture_x0020_50"><![endif]></span></p>
3219
3220<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is evident
3221that there remains intensity differences due to texture. We can increase the
3222harmonic order to more closely fit these, however one should only do this
3223carefully. Select the Texture tab for the B2 phase; the Texture tab will show</p>
3224
3225<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3226style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_18"
3227 o:spid="_x0000_i1059" type="#_x0000_t75" style='width:456pt;height:250.5pt;
3228 visibility:visible;mso-wrap-style:square'>
3229 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
3230  o:title=""/>
3231</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
3232src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
3233v:shapes="Picture_x0020_18"><![endif]></span></p>
3234
3235<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a drawing
3236of the 001 pole figure will be drawn. This is the very typical “bulls eye” for
3237cylindrical texture; of much more use is an inverse pole figure. Select that
3238from the Texture plot type; the plot will be redrawn</p>
3239
3240<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3241style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_52"
3242 o:spid="_x0000_i1058" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3243 visibility:visible;mso-wrap-style:square'>
3244 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
3245  o:title=""/>
3246</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3247src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
3248v:shapes="Picture_x0020_52"><![endif]></span></p>
3249
3250<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This shows the
3251probability of reflection vectors coinciding with the sample wire axis the high
3252spots are the 111 family of reflections. We should try the next higher Harmonic
3253order (10). </p>
3254
3255<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the
3256Texture tab for the B19’ phase. Again a bullseye pole figure is drawn; change
3257that to an Inverse pole figure.</p>
3258
3259<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3260style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_53"
3261 o:spid="_x0000_i1057" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3262 visibility:visible;mso-wrap-style:square'>
3263 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
3264  o:title=""/>
3265</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3266src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
3267v:shapes="Picture_x0020_53"><![endif]></span></p>
3268
3269<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This phase is
3270very strongly textured (the cursor shows 12-13 MRD at the peaks) along the -140
3271direction. Again we want to increment the Harmonic order to the next higher
3272level (8). Again do Calculate/Refine from the main menu; the <span
3273class=SpellE>Rwp</span> has dropped to ~7.9%. One can add the atom <span
3274class=SpellE>Uiso</span> for the Ni and <span class=SpellE>Ti</span> atoms in
3275the B2 phase and the coordinates and <span class=SpellE>Uiso</span> for the
3276B19’ phase. The <span class=SpellE>Rw</span> drops a bit further to ~7.4%.
3277Finally, we can increase the harmonic order again for the B19’ phase (it is
3278very strongly textured!) to 10 and the B2 phase to 12; the final refinement
3279converged to <span class=SpellE>Rw</span> ~6.8% and the B19’ inverse pole
3280figure has peaks at ~18 MRD (Multiple of Random Distribution) and the B2 phase
3281peaks are ~7MRD.</p>
3282
3283<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B19’
3284coefficients</p>
3285
3286<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3287style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_54"
3288 o:spid="_x0000_i1056" type="#_x0000_t75" style='width:502.5pt;height:375pt;
3289 visibility:visible;mso-wrap-style:square'>
3290 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
3291  o:title=""/>
3292</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
3293src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
3294v:shapes="Picture_x0020_54"><![endif]></span></p>
3295
3296<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and inverse
3297pole figure</p>
3298
3299<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3300style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_55"
3301 o:spid="_x0000_i1055" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3302 visibility:visible;mso-wrap-style:square'>
3303 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
3304  o:title=""/>
3305</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3306src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
3307v:shapes="Picture_x0020_55"><![endif]></span></p>
3308
3309<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B2
3310coefficients</p>
3311
3312<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3313style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_56"
3314 o:spid="_x0000_i1054" type="#_x0000_t75" style='width:480pt;height:267.75pt;
3315 visibility:visible;mso-wrap-style:square'>
3316 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
3317  o:title=""/>
3318</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3319src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
3320v:shapes="Picture_x0020_56"><![endif]></span></p>
3321
3322<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>and inverse
3323pole figure</p>
3324
3325<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3326style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_57"
3327 o:spid="_x0000_i1053" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3328 visibility:visible;mso-wrap-style:square'>
3329 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
3330  o:title=""/>
3331</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3332src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
3333v:shapes="Picture_x0020_57"><![endif]></span></p>
3334
3335<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This completes
3336the tutorial on Method A for doing texture analysis. It is useful for a case
3337like this one where there are very few data sets required for the texture analysis.
3338However, for the case of lower sample symmetry one must several dozen or even a
3339few hundred histograms and then the suite of parameters can easily be &gt; 1000
3340of which only a few dozen describe the texture. This leads to the next Methods
3341for texture analysis in GSAS-II.</p>
3342
3343<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
33440in;line-height:115%'>Method B. Sequential refinement &amp; texture analysis
3345from result</h2>
3346
3347<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
33480in;line-height:115%'>Introduction</h3>
3349
3350<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
3351the texture analysis in much the same way as Method A except that all the initial
3352refinements are done “sequentially”, that is refinements are done for the
3353parameters associated with each powder pattern to convergence in a serial
3354fashion. In this case where there are 10 PWDR data sets, there will be 10
3355refinements done in sequence. Parameters that span all the data (e.g. lattice
3356parameters, atom parameters &amp; texture) are not varied in this sequence
3357refinement. The effect of texture is modeled as a Preferred Orientation
3358correction to each histogram. To begin do <b style='mso-bidi-font-weight:normal'><span
3359style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3360mso-hansi-theme-font:minor-latin'>File/Open project…</span></b> for the <span
3361class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3362"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3363minor-latin'>NiTi.gpx</span></b></span> file created in the first step and then
3364do a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3365mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Save
3366project as…</span></b> to save it as <span class=SpellE><b style='mso-bidi-font-weight:
3367normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3368minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b
3369style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3370mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-B</span></b>.
3371This renames the project and it should have one IMG, 10 PWDR entries and two
3372phases of <span class=SpellE>NiTi</span> (B2 and B19’).</p>
3373
3374<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
33750in;line-height:115%'>Step 1. Initial refinement</h3>
3376
3377<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins
3378the same way as Method A so I’ll be brief. Do the following steps:</p>
3379
3380<p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;mso-add-space:
3381auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
3382style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
3383style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
3384any <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3385mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b>
3386entry, go to <b style='mso-bidi-font-weight:normal'><span style='font-family:
3387"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3388minor-latin'>Sample Parameters</span></b> and uncheck <b style='mso-bidi-font-weight:
3389normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3390minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>.
3391Then copy the flags to the other PWDR entries.</p>
3392
3393<p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;mso-add-space:
3394auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
3395style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
3396style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
3397the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3398mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3399phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3400mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3401tab and check the <b style='mso-bidi-font-weight:normal'><span
3402style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3403mso-hansi-theme-font:minor-latin'>Phase fraction</span></b> box and change the <b
3404style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3405mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
3406orientation model</span></b> to <b style='mso-bidi-font-weight:normal'><span
3407style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3408mso-hansi-theme-font:minor-latin'>Spherical harmonics</span></b>. Then do <b
3409style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3410mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3411data</span></b> to copy both the flag and the model to the other PWDR entries.</p>
3412
3413<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space:
3414auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
3415style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
3416style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
3417the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3418mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3419phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3420mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3421tab and check the <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'>Phase fraction box</span></b> and change the <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'>Preferred
3426orientation model</span></b> to <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'>Spherical harmonics</span></b>. Then do <b
3429style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3430mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3431data</span></b> to copy both the flag and the model to the other PWDR entries.</p>
3432
3433<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select <b
3434style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3435mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b>
3436from the GSAS-II data tree</p>
3437
3438<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3439style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_1"
3440 o:spid="_x0000_i1052" type="#_x0000_t75" style='width:330.75pt;height:153.75pt;
3441 visibility:visible;mso-wrap-style:square'>
3442 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
3443  o:title=""/>
3444</v:shape><![endif]--><![if !vml]><img border=0 width=441 height=205
3445src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
3446v:shapes="Picture_x0020_1"><![endif]></span></p>
3447
3448<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Press the <b
3449style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3450mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Select Data</span></b>
3451button for <b style='mso-bidi-font-weight:normal'><span style='font-family:
3452"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3453minor-latin'>Sequential Refinement</span></b>; a file selection popup will
3454appear. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3455"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3456minor-latin'>Set All</span></b> and press <b style='mso-bidi-font-weight:normal'><span
3457style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3458mso-hansi-theme-font:minor-latin'>OK</span></b>. The <b style='mso-bidi-font-weight:
3459normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3460minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b> page will be
3461repainted indicating that 10 data sets are selected for sequential refinement.</p>
3462
3463<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3464style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_2"
3465 o:spid="_x0000_i1051" type="#_x0000_t75" style='width:330.75pt;height:163.5pt;
3466 visibility:visible;mso-wrap-style:square'>
3467 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
3468  o:title=""/>
3469</v:shape><![endif]--><![if !vml]><img border=0 width=441 height=218
3470src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png"
3471v:shapes="Picture_x0020_2"><![endif]></span></p>
3472
3473<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You have the
3474choice of starting at the last one and for copying results from one to the
3475next. We won’t do either here. Each refinement will use the other controls
3476(e.g. <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3477mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Max cycles</span></b>)
3478as controls. We are now ready to do the 1<sup>st</sup> sequential refinement.
3479Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3480mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Sequential
3481refine</span></b> from the main menu. A progress bar popup will appear showing
3482residuals as it processes each of 10 data sets. After a few seconds the <b
3483style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3484mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refinement
3485results</span></b> popup will appear; press <b style='mso-bidi-font-weight:
3486normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3487minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to accept them. The
3488data window displays the <b style='mso-bidi-font-weight:normal'><span
3489style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3490mso-hansi-theme-font:minor-latin'>Sequential refinement results</span></b> as a
3491table.</p>
3492
3493<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3494style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3"
3495 o:spid="_x0000_i1050" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3496 visibility:visible;mso-wrap-style:square'>
3497 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
3498  o:title=""/>
3499</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3500src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
3501v:shapes="Picture_x0020_3"><![endif]></span></p>
3502
3503<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>There is a row
3504for each data set and columns for all refined parameters and some derived ones
3505along with residual and convergence indicators. The residuals are not very good
3506(we haven’t really refined much) but the &#916;&#967;<sup>2</sup> column shows
3507that convergence was achieved (NB: poor convergence will be highlighted in
3508yellow or red depending on how bad it is).</p>
3509
3510<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you examine
3511one of the PWDR entries, you’ll see that just in this point in Method A much of
3512the misfit is texture and perhaps peak position.</p>
3513
3514<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3515style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_4"
3516 o:spid="_x0000_i1049" type="#_x0000_t75" style='width:525pt;height:450pt;
3517 visibility:visible;mso-wrap-style:square'>
3518 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
3519  o:title=""/>
3520</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3521src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
3522v:shapes="Picture_x0020_4"><![endif]></span></p>
3523
3524<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>To set these
3525parameters, select the Data tab for the B2 phase</p>
3526
3527<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3528style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5"
3529 o:spid="_x0000_i1048" type="#_x0000_t75" style='width:381pt;height:375pt;
3530 visibility:visible;mso-wrap-style:square'>
3531 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
3532  o:title=""/>
3533</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=500
3534src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
3535v:shapes="Picture_x0020_5"><![endif]></span></p>
3536
3537<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Check the D11
3538box under Hydrostatic/elastic strain, set the Harmonic order to 6 and check the
3539Refine box for it (Preferred orientation). Then in two steps, do Edit/Copy
3540flags and Set All for the file selection. Then do Edit/Copy selected data; that
3541will bring up a new popup</p>
3542
3543<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3544style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_6"
3545 o:spid="_x0000_i1047" type="#_x0000_t75" style='width:240pt;height:232.5pt;
3546 visibility:visible;mso-wrap-style:square'>
3547 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
3548  o:title=""/>
3549</v:shape><![endif]--><![if !vml]><img border=0 width=320 height=310
3550src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
3551v:shapes="Picture_x0020_6"><![endif]></span></p>
3552
3553<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This allows
3554you to select which parameters to copy data and flags. Select Pref. Ori. And
3555press OK; the file selection is next. Do Set All and OK to do this copy. That
3556copies the full spherical harmonics model to the other data sets. Select one to
3557check if you’d like.</p>
3558
3559<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next do the
3560same thing for the B19’ phase; here there are 4 <span class=SpellE>Dij</span>
3561parameters to check (do all of them) and use spherical harmonics order 4. When
3562done that Data window will look like</p>
3563
3564<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3565style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_7"
3566 o:spid="_x0000_i1046" type="#_x0000_t75" style='width:381pt;height:467.25pt;
3567 visibility:visible;mso-wrap-style:square'>
3568 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
3569  o:title=""/>
3570</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=623
3571src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
3572v:shapes="Picture_x0020_7"><![endif]></span></p>
3573
3574<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now
3575ready for the next refinement; do Calculate/Sequential refine. Be careful not
3576(by habit say) pick Refine; a warning popup will appear. After it completes the
3577Sequential refinement results shows that the fit is better but convergence wasn’t
3578quite complete.</p>
3579
3580<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3581style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8"
3582 o:spid="_x0000_i1045" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3583 visibility:visible;mso-wrap-style:square'>
3584 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
3585  o:title=""/>
3586</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3587src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
3588v:shapes="Picture_x0020_8"><![endif]></span></p>
3589
3590<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is probably
3591best to do another round of sequential refinement (I had to do two) to get
3592convergence. A plot of one PWDR entry gives</p>
3593
3594<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3595style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9"
3596 o:spid="_x0000_i1044" type="#_x0000_t75" style='width:525pt;height:450pt;
3597 visibility:visible;mso-wrap-style:square'>
3598 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png"
3599  o:title=""/>
3600</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3601src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png"
3602v:shapes="Picture_x0020_9"><![endif]></span></p>
3603
3604<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>As our
3605experience in Method A, the calculated peaks are too sharp. We need to vary the
3606<span class=SpellE>mustrain</span> parameters for both phases. Go to the Data
3607tab for each phase, check the <span class=SpellE>microstrain</span> box and do
3608Edit/Copy flags for all the data sets. Then do another Calculate/Sequential
3609refine. My Sequential refinement results showed great improvement but
3610incomplete refinement</p>
3611
3612<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3613style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10"
3614 o:spid="_x0000_i1043" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3615 visibility:visible;mso-wrap-style:square'>
3616 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
3617  o:title=""/>
3618</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3619src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
3620v:shapes="Picture_x0020_10"><![endif]></span></p>
3621
3622<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Repeating the
3623sequential refinement (twice) gave convergence.</p>
3624
3625<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3626style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_11"
3627 o:spid="_x0000_i1042" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3628 visibility:visible;mso-wrap-style:square'>
3629 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png"
3630  o:title=""/>
3631</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3632src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png"
3633v:shapes="Picture_x0020_11"><![endif]></span></p>
3634
3635<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Examination of
3636the PWDR data sets showed a fairly good fit but some discrepancies (especially
3637for <span class=SpellE>Azm</span>=20.00)</p>
3638
3639<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3640style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12"
3641 o:spid="_x0000_i1041" type="#_x0000_t75" style='width:525pt;height:450pt;
3642 visibility:visible;mso-wrap-style:square'>
3643 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
3644  o:title=""/>
3645</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3646src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
3647v:shapes="Picture_x0020_12"><![endif]></span></p>
3648
3649<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Showing that
3650perhaps the B19’ phase needs high order spherical harmonics. Select the Data
3651tab for the B19’ phase and change the Harmonic order to 6. Then do Edit/Copy
3652selected data for <span class=SpellE>Pref.Ori</span>. to the other data sets.
3653This (after few repeats) gives a further improvement in the fit</p>
3654
3655<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3656style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13"
3657 o:spid="_x0000_i1040" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3658 visibility:visible;mso-wrap-style:square'>
3659 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
3660  o:title=""/>
3661</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3662src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
3663v:shapes="Picture_x0020_13"><![endif]></span></p>
3664
3665<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This fit is
3666now sufficient for us to proceed to the next step and determine the texture of
3667the two phases.</p>
3668
3669<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
36700in;line-height:115%'>Step 2. Texture analysis</h3>
3671
3672<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>During the sequential
3673refinements done in Step 1, we fitted the profiles allowing strain parameters (<span
3674class=SpellE>Dij</span>) for peak position shifts and <span class=SpellE>microstrain</span>
3675for peak shape. We modeled the intensity variation with a spherical harmonics
3676preferred orientation correction. If you select any PWDR entry from the GSAS-II
3677data tree and pick the Reflection List subentry (at the bottom) you can see the
3678magnitude of this correction for each reflection 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%'>and for the
3694B19’ 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
3741bullseye 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 A (maybe not quite as
3768strong 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 bullseye
3786pole figure; change that to Inverse pole figure to see the texture</p>
3787
3788<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
3789style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_22"
3790 o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt;height:450pt;
3791 visibility:visible;mso-wrap-style:square'>
3792 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
3793  o:title=""/>
3794</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3795src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
3796v:shapes="Picture_x0020_22"><![endif]></span></p>
3797
3798<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Again this is very
3799similar to what we found in Method A but again not quite as strong (max MRD ~13
3800instead of ~18).</p>
3801
3802<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do a
3803File/Save project from the main menu; this saves the final texture results done
3804in Step 2 (you also will need it for Method C).</p>
3805
3806<h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
38070in;line-height:115%'>Method C. Sequential refinement &amp; full texture
3808refinement</h2>
3809
3810<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
38110in;line-height:115%'>Introduction</h3>
3812
3813<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This uses the
3814same approach as Method B except that after the sequential refinements are
3815finished we then fix almost all the parameters and then do a final texture
3816refinement with all the data. Thus, this is a replacement for Step 2 in Method
3817B. To begin do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3818"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3819minor-latin'>File/Open project…</span></b> for the <span class=SpellE><b
3820style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3821mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NiTi-B.gpx</span></b></span>
3822file created in Method B and then do a <b style='mso-bidi-font-weight:normal'><span
3823style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3824mso-hansi-theme-font:minor-latin'>File/Save project as…</span></b> to save it
3825as <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3826style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3827mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight:
3828normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3829minor-latin;mso-hansi-theme-font:minor-latin'>-C</span></b>. This renames the
3830project and it should have one IMG, 10 PWDR entries and two phases of <span
3831class=SpellE>NiTi</span> (B2 and B19’).</p>
3832
3833<h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:
38340in;line-height:115%'>Step 1. Clearing unwanted variables from sequential
3835refinement</h3>
3836
3837<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Here we want
3838to clear refinement flags for all parameters that need not be varied in a
3839texture analysis refinement. The general rule is to not refine any parameter unless
3840we expect it to affect the peak intensities. These are listed below:</p>
3841
3842<p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;mso-add-space:
3843auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3844style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
3845style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3846style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3847mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>:
3848as the background was fit during the sequential refinement we should fix it
3849here. Select any <b style='mso-bidi-font-weight:normal'><span style='font-family:
3850"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3851minor-latin'>PWDR</span></b> entry and choose the <b style='mso-bidi-font-weight:
3852normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3853minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b> subentry
3854for it. Clear the <b style='mso-bidi-font-weight:normal'><span
3855style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3856mso-hansi-theme-font:minor-latin'>Refine</span></b> flags and the do <b
3857style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3858mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Copy
3859flags</span></b> selecting all data sets. This will clear all background
3860refinement flags.</p>
3861
3862<p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;mso-add-space:
3863auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3864style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
3865style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3866style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3867mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3868phase: we do not want to refine either the <span class=SpellE>microstrain</span>,
3869D<sub>11</sub>, or preferred orientation coefficients. Select the <b
3870style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3871mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3872phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
3873"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3874minor-latin'>Data</span></b> <span class=GramE>tab.</span> Clear the <span
3875class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3876"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3877minor-latin'>microstrain</span></b></span>, <b style='mso-bidi-font-weight:
3878normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3879minor-latin;mso-hansi-theme-font:minor-latin'>D<sub>11</sub></span></b> and <b
3880style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3881mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
3882orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
3883style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3884mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
3885avoid a lot of nasty (but harmless) messages at the start of the refinement).
3886Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3887mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3888flags</span></b> selecting all data to clear all the flags and an <b
3889style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3890mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy selected
3891data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3892style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3893mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to copy the zeroed
3894out harmonic coefficients.</p>
3895
3896<p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space:
3897auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3898style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
3899style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3900style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3901mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>:
3902we do not want to refine either the <span class=SpellE>microstrain</span>, <span
3903class=SpellE>Dij</span>, or preferred orientation coefficients. Select the <b
3904style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3905mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3906phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
3907"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3908minor-latin'>Data</span></b> tab. Clear the <span class=SpellE><b
3909style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3910mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>microstrain</span></b></span>,
3911four <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3912style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3913mso-hansi-theme-font:minor-latin'>Dij</span></b></span> and <b
3914style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3915mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
3916orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
3917style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3918mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
3919avoid a lot of nasty (but harmless) messages at the start of the refinement).
3920Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3921mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3922flags</span></b> selecting all data to clear all the flags and an <b
3923style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3924mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3925selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
3926normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3927minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
3928copy the zeroed out harmonic coefficients.</p>
3929
3930<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
3931margin-left:.25in;line-height:115%'><o:p>&nbsp;</o:p></p>
3932
3933<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;
3934margin-left:.25in;line-height:115%'>Notice that we have allowed refinement of
3935the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3936mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase
3937fractions</span></b>; these may change during the texture refinement. Now
3938select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3939"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3940minor-latin'>Texture</span></b> tab for the <b style='mso-bidi-font-weight:
3941normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3942minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> phase (it may still
3943have 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>
3987<span class=GramE>tab.</span> Set 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%'>which is
4045almost identical to that from Method <span class=GramE>A.</span> 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%'>and also
4076almost identical to what was obtained in Method A; the coefficients are seen in</p>
4077
4078<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span
4079style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_58"
4080 o:spid="_x0000_i1025" type="#_x0000_t75" style='width:502.5pt;height:375pt;
4081 visibility:visible;mso-wrap-style:square'>
4082 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
4083  o:title=""/>
4084</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
4085src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
4086v:shapes="Picture_x0020_58"><![endif]></span></p>
4087
4088<p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>With this
4089Method you can add parameters (atom coordinates &amp; thermal motion
4090parameters) that could not be refined in method B. It should be clear from this
4091tutorial that in more complex textures where the data set may consist of slices
4092obtained from a suite of 2D images collected as the sample is rotated, Method C
4093will give a relatively fast determination of the texture without resorting to
4094large matrix least-squares refinements.</p>
4095
4096</div>
4097
4098</body>
4099
4100</html>
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