source: Tutorials/2DTexture/Texture analysis of 2D data in GSAS-II.htm @ 1855

Last change on this file since 1855 was 1855, checked in by vondreele, 8 years ago

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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"/>
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430   Name="Intense Quote"/>
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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"
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567  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
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570  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
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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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785        margin-left:0in;
786        mso-pagination:widow-orphan;
787        mso-outline-level:5;
788        font-size:12.0pt;
789        font-family:"Times New Roman",serif;
790        mso-fareast-font-family:"Times New Roman";
791        mso-fareast-theme-font:minor-fareast;
792        color:#4F4FFF;
793        font-weight:bold;}
794p.MsoTitle, li.MsoTitle, div.MsoTitle
795        {mso-style-noshow:yes;
796        mso-style-priority:10;
797        mso-style-unhide:no;
798        mso-style-qformat:yes;
799        mso-style-link:"Title Char";
800        mso-style-next:Normal;
801        margin-top:0in;
802        margin-right:0in;
803        margin-bottom:15.0pt;
804        margin-left:0in;
805        mso-add-space:auto;
806        mso-pagination:widow-orphan;
807        border:none;
808        mso-border-bottom-alt:solid #4F81BD 1.0pt;
809        mso-border-bottom-themecolor:accent1;
810        padding:0in;
811        mso-padding-alt:0in 0in 4.0pt 0in;
812        font-size:26.0pt;
813        font-family:"Cambria",serif;
814        mso-ascii-font-family:Cambria;
815        mso-ascii-theme-font:major-latin;
816        mso-fareast-font-family:"Times New Roman";
817        mso-fareast-theme-font:major-fareast;
818        mso-hansi-font-family:Cambria;
819        mso-hansi-theme-font:major-latin;
820        mso-bidi-font-family:"Times New Roman";
821        mso-bidi-theme-font:major-bidi;
822        color:#17365D;
823        mso-themecolor:text2;
824        mso-themeshade:191;
825        letter-spacing:.25pt;
826        mso-font-kerning:14.0pt;}
827p.MsoTitleCxSpFirst, li.MsoTitleCxSpFirst, div.MsoTitleCxSpFirst
828        {mso-style-noshow:yes;
829        mso-style-priority:10;
830        mso-style-unhide:no;
831        mso-style-qformat:yes;
832        mso-style-link:"Title Char";
833        mso-style-next:Normal;
834        mso-style-type:export-only;
835        margin:0in;
836        margin-bottom:.0001pt;
837        mso-add-space:auto;
838        mso-pagination:widow-orphan;
839        border:none;
840        mso-border-bottom-alt:solid #4F81BD 1.0pt;
841        mso-border-bottom-themecolor:accent1;
842        padding:0in;
843        mso-padding-alt:0in 0in 4.0pt 0in;
844        font-size:26.0pt;
845        font-family:"Cambria",serif;
846        mso-ascii-font-family:Cambria;
847        mso-ascii-theme-font:major-latin;
848        mso-fareast-font-family:"Times New Roman";
849        mso-fareast-theme-font:major-fareast;
850        mso-hansi-font-family:Cambria;
851        mso-hansi-theme-font:major-latin;
852        mso-bidi-font-family:"Times New Roman";
853        mso-bidi-theme-font:major-bidi;
854        color:#17365D;
855        mso-themecolor:text2;
856        mso-themeshade:191;
857        letter-spacing:.25pt;
858        mso-font-kerning:14.0pt;}
859p.MsoTitleCxSpMiddle, li.MsoTitleCxSpMiddle, div.MsoTitleCxSpMiddle
860        {mso-style-noshow:yes;
861        mso-style-priority:10;
862        mso-style-unhide:no;
863        mso-style-qformat:yes;
864        mso-style-link:"Title Char";
865        mso-style-next:Normal;
866        mso-style-type:export-only;
867        margin:0in;
868        margin-bottom:.0001pt;
869        mso-add-space:auto;
870        mso-pagination:widow-orphan;
871        border:none;
872        mso-border-bottom-alt:solid #4F81BD 1.0pt;
873        mso-border-bottom-themecolor:accent1;
874        padding:0in;
875        mso-padding-alt:0in 0in 4.0pt 0in;
876        font-size:26.0pt;
877        font-family:"Cambria",serif;
878        mso-ascii-font-family:Cambria;
879        mso-ascii-theme-font:major-latin;
880        mso-fareast-font-family:"Times New Roman";
881        mso-fareast-theme-font:major-fareast;
882        mso-hansi-font-family:Cambria;
883        mso-hansi-theme-font:major-latin;
884        mso-bidi-font-family:"Times New Roman";
885        mso-bidi-theme-font:major-bidi;
886        color:#17365D;
887        mso-themecolor:text2;
888        mso-themeshade:191;
889        letter-spacing:.25pt;
890        mso-font-kerning:14.0pt;}
891p.MsoTitleCxSpLast, li.MsoTitleCxSpLast, div.MsoTitleCxSpLast
892        {mso-style-noshow:yes;
893        mso-style-priority:10;
894        mso-style-unhide:no;
895        mso-style-qformat:yes;
896        mso-style-link:"Title Char";
897        mso-style-next:Normal;
898        mso-style-type:export-only;
899        margin-top:0in;
900        margin-right:0in;
901        margin-bottom:15.0pt;
902        margin-left:0in;
903        mso-add-space:auto;
904        mso-pagination:widow-orphan;
905        border:none;
906        mso-border-bottom-alt:solid #4F81BD 1.0pt;
907        mso-border-bottom-themecolor:accent1;
908        padding:0in;
909        mso-padding-alt:0in 0in 4.0pt 0in;
910        font-size:26.0pt;
911        font-family:"Cambria",serif;
912        mso-ascii-font-family:Cambria;
913        mso-ascii-theme-font:major-latin;
914        mso-fareast-font-family:"Times New Roman";
915        mso-fareast-theme-font:major-fareast;
916        mso-hansi-font-family:Cambria;
917        mso-hansi-theme-font:major-latin;
918        mso-bidi-font-family:"Times New Roman";
919        mso-bidi-theme-font:major-bidi;
920        color:#17365D;
921        mso-themecolor:text2;
922        mso-themeshade:191;
923        letter-spacing:.25pt;
924        mso-font-kerning:14.0pt;}
925a:link, span.MsoHyperlink
926        {mso-style-noshow:yes;
927        mso-style-priority:99;
928        color:blue;
929        text-decoration:underline;
930        text-underline:single;}
931a:visited, span.MsoHyperlinkFollowed
932        {mso-style-noshow:yes;
933        mso-style-priority:99;
934        color:purple;
935        text-decoration:underline;
936        text-underline:single;}
937p.MsoDocumentMap, li.MsoDocumentMap, div.MsoDocumentMap
938        {mso-style-noshow:yes;
939        mso-style-priority:99;
940        mso-style-link:"Document Map Char";
941        margin-top:0in;
942        margin-right:0in;
943        margin-bottom:4.0pt;
944        margin-left:0in;
945        mso-pagination:widow-orphan;
946        font-size:8.0pt;
947        font-family:"Tahoma",sans-serif;
948        mso-fareast-font-family:"Times New Roman";
949        mso-fareast-theme-font:minor-fareast;}
950p
951        {mso-style-noshow:yes;
952        mso-style-priority:99;
953        mso-margin-top-alt:auto;
954        margin-right:0in;
955        mso-margin-bottom-alt:auto;
956        margin-left:0in;
957        mso-pagination:widow-orphan;
958        font-size:12.0pt;
959        font-family:"Times New Roman",serif;
960        mso-fareast-font-family:"Times New Roman";
961        mso-fareast-theme-font:minor-fareast;}
962pre
963        {mso-style-noshow:yes;
964        mso-style-priority:99;
965        mso-style-link:"HTML Preformatted Char";
966        margin-top:0in;
967        margin-right:0in;
968        margin-bottom:4.0pt;
969        margin-left:0in;
970        mso-pagination:widow-orphan;
971        tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt;
972        font-size:10.0pt;
973        font-family:"Courier New";
974        mso-fareast-font-family:"Times New Roman";}
975p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
976        {mso-style-noshow:yes;
977        mso-style-priority:99;
978        mso-style-link:"Balloon Text Char";
979        margin-top:0in;
980        margin-right:0in;
981        margin-bottom:4.0pt;
982        margin-left:0in;
983        mso-pagination:widow-orphan;
984        font-size:8.0pt;
985        font-family:"Tahoma",sans-serif;
986        mso-fareast-font-family:"Times New Roman";
987        mso-fareast-theme-font:minor-fareast;}
988span.MsoPlaceholderText
989        {mso-style-noshow:yes;
990        mso-style-priority:99;
991        mso-style-unhide:no;
992        color:gray;}
993p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing
994        {mso-style-noshow:yes;
995        mso-style-priority:1;
996        mso-style-unhide:no;
997        mso-style-qformat:yes;
998        mso-style-parent:"";
999        margin-top:0in;
1000        margin-right:0in;
1001        margin-bottom:4.0pt;
1002        margin-left:0in;
1003        mso-pagination:widow-orphan;
1004        font-size:12.0pt;
1005        font-family:"Times New Roman",serif;
1006        mso-fareast-font-family:"Times New Roman";
1007        mso-fareast-theme-font:minor-fareast;}
1008p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
1009        {mso-style-noshow:yes;
1010        mso-style-priority:34;
1011        mso-style-unhide:no;
1012        mso-style-qformat:yes;
1013        margin-top:0in;
1014        margin-right:0in;
1015        margin-bottom:4.0pt;
1016        margin-left:.5in;
1017        mso-add-space:auto;
1018        mso-pagination:widow-orphan;
1019        font-size:12.0pt;
1020        font-family:"Times New Roman",serif;
1021        mso-fareast-font-family:"Times New Roman";
1022        mso-fareast-theme-font:minor-fareast;}
1023p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
1024        {mso-style-noshow:yes;
1025        mso-style-priority:34;
1026        mso-style-unhide:no;
1027        mso-style-qformat:yes;
1028        mso-style-type:export-only;
1029        margin-top:0in;
1030        margin-right:0in;
1031        margin-bottom:0in;
1032        margin-left:.5in;
1033        margin-bottom:.0001pt;
1034        mso-add-space:auto;
1035        mso-pagination:widow-orphan;
1036        font-size:12.0pt;
1037        font-family:"Times New Roman",serif;
1038        mso-fareast-font-family:"Times New Roman";
1039        mso-fareast-theme-font:minor-fareast;}
1040p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
1041        {mso-style-noshow:yes;
1042        mso-style-priority:34;
1043        mso-style-unhide:no;
1044        mso-style-qformat:yes;
1045        mso-style-type:export-only;
1046        margin-top:0in;
1047        margin-right:0in;
1048        margin-bottom:0in;
1049        margin-left:.5in;
1050        margin-bottom:.0001pt;
1051        mso-add-space:auto;
1052        mso-pagination:widow-orphan;
1053        font-size:12.0pt;
1054        font-family:"Times New Roman",serif;
1055        mso-fareast-font-family:"Times New Roman";
1056        mso-fareast-theme-font:minor-fareast;}
1057p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
1058        {mso-style-noshow:yes;
1059        mso-style-priority:34;
1060        mso-style-unhide:no;
1061        mso-style-qformat:yes;
1062        mso-style-type:export-only;
1063        margin-top:0in;
1064        margin-right:0in;
1065        margin-bottom:4.0pt;
1066        margin-left:.5in;
1067        mso-add-space:auto;
1068        mso-pagination:widow-orphan;
1069        font-size:12.0pt;
1070        font-family:"Times New Roman",serif;
1071        mso-fareast-font-family:"Times New Roman";
1072        mso-fareast-theme-font:minor-fareast;}
1073span.MsoIntenseReference
1074        {mso-style-priority:32;
1075        mso-style-unhide:no;
1076        mso-style-qformat:yes;
1077        font-variant:small-caps;
1078        color:#C0504D;
1079        mso-themecolor:accent2;
1080        letter-spacing:.25pt;
1081        font-weight:bold;
1082        text-decoration:underline;
1083        text-underline:single;}
1084span.Heading1Char
1085        {mso-style-name:"Heading 1 Char";
1086        mso-style-priority:9;
1087        mso-style-unhide:no;
1088        mso-style-locked:yes;
1089        mso-style-link:"Heading 1";
1090        mso-ansi-font-size:24.0pt;
1091        mso-bidi-font-size:24.0pt;
1092        font-family:"Times New Roman",serif;
1093        mso-ascii-font-family:"Times New Roman";
1094        mso-fareast-font-family:"Times New Roman";
1095        mso-fareast-theme-font:minor-fareast;
1096        mso-hansi-font-family:"Times New Roman";
1097        mso-bidi-font-family:"Times New Roman";
1098        mso-font-kerning:18.0pt;
1099        font-weight:bold;}
1100span.Heading2Char
1101        {mso-style-name:"Heading 2 Char";
1102        mso-style-noshow:yes;
1103        mso-style-priority:9;
1104        mso-style-unhide:no;
1105        mso-style-locked:yes;
1106        mso-style-link:"Heading 2";
1107        mso-ansi-font-size:18.0pt;
1108        mso-bidi-font-size:18.0pt;
1109        font-family:"Times New Roman",serif;
1110        mso-ascii-font-family:"Times New Roman";
1111        mso-fareast-font-family:"Times New Roman";
1112        mso-fareast-theme-font:minor-fareast;
1113        mso-hansi-font-family:"Times New Roman";
1114        mso-bidi-font-family:"Times New Roman";
1115        font-weight:bold;}
1116span.Heading3Char
1117        {mso-style-name:"Heading 3 Char";
1118        mso-style-noshow:yes;
1119        mso-style-priority:9;
1120        mso-style-unhide:no;
1121        mso-style-locked:yes;
1122        mso-style-link:"Heading 3";
1123        mso-ansi-font-size:13.5pt;
1124        mso-bidi-font-size:13.5pt;
1125        font-family:"Times New Roman",serif;
1126        mso-ascii-font-family:"Times New Roman";
1127        mso-fareast-font-family:"Times New Roman";
1128        mso-fareast-theme-font:minor-fareast;
1129        mso-hansi-font-family:"Times New Roman";
1130        mso-bidi-font-family:"Times New Roman";
1131        font-weight:bold;}
1132span.Heading4Char
1133        {mso-style-name:"Heading 4 Char";
1134        mso-style-noshow:yes;
1135        mso-style-priority:9;
1136        mso-style-unhide:no;
1137        mso-style-locked:yes;
1138        mso-style-link:"Heading 4";
1139        mso-ansi-font-size:13.0pt;
1140        mso-bidi-font-size:13.0pt;
1141        font-family:"Cambria",serif;
1142        mso-ascii-font-family:Cambria;
1143        mso-ascii-theme-font:major-latin;
1144        mso-fareast-font-family:"Times New Roman";
1145        mso-fareast-theme-font:major-fareast;
1146        mso-hansi-font-family:Cambria;
1147        mso-hansi-theme-font:major-latin;
1148        mso-bidi-font-family:"Times New Roman";
1149        mso-bidi-theme-font:major-bidi;
1150        color:#4F81BD;
1151        mso-themecolor:accent1;
1152        font-weight:bold;
1153        font-style:italic;}
1154span.Heading5Char
1155        {mso-style-name:"Heading 5 Char";
1156        mso-style-noshow:yes;
1157        mso-style-priority:9;
1158        mso-style-unhide:no;
1159        mso-style-locked:yes;
1160        mso-style-link:"Heading 5";
1161        mso-ansi-font-size:12.0pt;
1162        mso-bidi-font-size:12.0pt;
1163        font-family:"Times New Roman",serif;
1164        mso-ascii-font-family:"Times New Roman";
1165        mso-fareast-font-family:"Times New Roman";
1166        mso-fareast-theme-font:minor-fareast;
1167        mso-hansi-font-family:"Times New Roman";
1168        mso-bidi-font-family:"Times New Roman";
1169        color:#4F4FFF;
1170        font-weight:bold;}
1171span.HTMLPreformattedChar
1172        {mso-style-name:"HTML Preformatted Char";
1173        mso-style-noshow:yes;
1174        mso-style-priority:99;
1175        mso-style-unhide:no;
1176        mso-style-locked:yes;
1177        mso-style-link:"HTML Preformatted";
1178        font-family:"Courier New";
1179        mso-ascii-font-family:"Courier New";
1180        mso-fareast-font-family:"Times New Roman";
1181        mso-hansi-font-family:"Courier New";
1182        mso-bidi-font-family:"Courier New";}
1183span.TitleChar
1184        {mso-style-name:"Title Char";
1185        mso-style-priority:10;
1186        mso-style-unhide:no;
1187        mso-style-locked:yes;
1188        mso-style-link:Title;
1189        mso-ansi-font-size:26.0pt;
1190        mso-bidi-font-size:26.0pt;
1191        font-family:"Cambria",serif;
1192        mso-ascii-font-family:Cambria;
1193        mso-ascii-theme-font:major-latin;
1194        mso-fareast-font-family:"Times New Roman";
1195        mso-fareast-theme-font:major-fareast;
1196        mso-hansi-font-family:Cambria;
1197        mso-hansi-theme-font:major-latin;
1198        mso-bidi-font-family:"Times New Roman";
1199        mso-bidi-theme-font:major-bidi;
1200        color:#17365D;
1201        mso-themecolor:text2;
1202        mso-themeshade:191;
1203        letter-spacing:.25pt;
1204        mso-font-kerning:14.0pt;}
1205span.DocumentMapChar
1206        {mso-style-name:"Document Map Char";
1207        mso-style-noshow:yes;
1208        mso-style-priority:99;
1209        mso-style-unhide:no;
1210        mso-style-locked:yes;
1211        mso-style-link:"Document Map";
1212        mso-ansi-font-size:8.0pt;
1213        mso-bidi-font-size:8.0pt;
1214        font-family:"Tahoma",sans-serif;
1215        mso-ascii-font-family:Tahoma;
1216        mso-fareast-font-family:"Times New Roman";
1217        mso-fareast-theme-font:minor-fareast;
1218        mso-hansi-font-family:Tahoma;
1219        mso-bidi-font-family:Tahoma;}
1220span.BalloonTextChar
1221        {mso-style-name:"Balloon Text Char";
1222        mso-style-noshow:yes;
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1416<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1417
1418<div class=WordSection1>
1419
1420<h1 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Texture analysis
1421of 2D data in GSAS-II</h1>
1422
1423<h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Introduction</h2>
1424
1425<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
1426115%'>Texture analysis using GSAS-II employs spherical harmonics modeling, as
1427described by Bunge, &quot;Texture Analysis in Materials Science&quot; (1982),
1428and implemented by Von Dreele, J. Appl. <span class=SpellE>Cryst</span>., <b
1429style='mso-bidi-font-weight:normal'>30</b>, 517-525 (1997) in GSAS. The even
1430part of the orientation distribution function (ODF) via the general axis
1431equation</p>
1432
1433<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
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1435  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><span
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1517
1518<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
1519class=GramE>is</span> used to give the intensity corrections due to texture.
1520The two harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
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1533top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1534EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1535 type="#_x0000_t75" style='width:32.25pt;height:26.25pt'>
1536 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image106.png"
1537  o:title="" chromakey="white"/>
1538</v:shape><![endif]--><![if !vml]><img width=43 height=35
1539src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image105.png"
1540v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1541style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1542   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1543   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1544   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1545   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1546   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
1547   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
1548 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
1549style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1550"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1551top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1552EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1553 type="#_x0000_t75" style='width:30pt;height:26.25pt'>
1554 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png"
1555  o:title="" chromakey="white"/>
1556</v:shape><![endif]--><![if !vml]><img width=40 height=35
1557src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image107.png"
1558v:shapes="_x0000_i1025"><![endif]></span><![endif]>, take on values according
1559to the crystal and sample symmetries, respectively, and thus the two inner
1560summations are over only the resulting unique, nonzero harmonic terms. These
1561unique terms are automatically selected by <span style='mso-bidi-font-weight:
1562bold'>GSAS-II</span> according to the space group symmetry and the user chosen
1563sample symmetry. The available sample symmetries are cylindrical symmetry, 2/m,
1564mmm and no symmetry. The choice of sample symmetry profoundly affects the
1565selection of harmonic coefficients. For example, in the case of cylindrical
1566sample symmetry (fiber texture) only <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1567   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1568   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1569   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1570   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1571   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
1572   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
1573 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
1574style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1575"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1576top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1577EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1578 type="#_x0000_t75" style='width:29.25pt;height:26.25pt'>
1579 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image007.png"
1580  o:title="" chromakey="white"/>
1581</v:shape><![endif]--><![if !vml]><img width=39 height=35
1582src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image108.png"
1583v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1584style='mso-spacerun:yes'> </span>terms are nonzero so the rest are excluded
1585from the <span class=GramE>summations</span> and the set of <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1586   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1587   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1588   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1589   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
1590   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
1591   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
1592style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1593"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1594top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1595EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1596 type="#_x0000_t75" style='width:21pt;height:26.25pt'>
1597 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image009.png"
1598  o:title="" chromakey="white"/>
1599</v:shape><![endif]--><![if !vml]><img width=28 height=35
1600src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image109.png"
1601v:shapes="_x0000_i1025"><![endif]></span><![endif]>coefficients is sufficient
1602to describe the effect on the d<span class=SpellE>iffraction</span> patterns
1603due to texture. The crystal harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1604   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1605   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1606   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1607   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1608   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
1609   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
1610 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
1611style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1612"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1613top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1614EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1615 type="#_x0000_t75" style='width:32.25pt;height:26.25pt'>
1616 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image011.png"
1617  o:title="" chromakey="white"/>
1618</v:shape><![endif]--><![if !vml]><img width=43 height=35
1619src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image110.png"
1620v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined for each
1621reflection, h, <i>via</i> polar and azimuthal coordinates (<span
1622style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
1623of a unit vector coincident with h relative to the reciprocal lattice. For most
1624crystal symmetries, <span style='font-family:Symbol'>f</span> is the angle
1625between h and the n-<span class=SpellE>th</span> order major rotation axis of
1626the space group (usually the c-axis) and <span style='font-family:Symbol'>b</span>
1627is the angle between the projections of h and any secondary axis (usually the
1628a-axis) onto the normal plane.<span style='mso-spacerun:yes'>  </span>In a
1629similar way the sample harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1630   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1631   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1632   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1633   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1634   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
1635   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
1636 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
1637style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1638"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1639top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1640EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1641 type="#_x0000_t75" style='width:30pt;height:26.25pt'>
1642 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png"
1643  o:title="" chromakey="white"/>
1644</v:shape><![endif]--><![if !vml]><img width=40 height=35
1645src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image107.png"
1646v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined according to
1647polar and azimuthal coordinates (<span style='font-family:Symbol'>y</span>, <span
1648style='font-family:Symbol'>g</span>) of a unit vector coincident with the
1649diffraction vector relative to a coordinate system attached to the external
1650form of the sample. For example, in the case of a rolled steel plate having mmm
1651symmetry, the polar angle, <span style='font-family:Symbol'>y</span>, is
1652frequently measured from the normal direction (ND) and <span style='font-family:
1653Symbol'>g</span> is then measured from the rolling direction (RD) in the TD
1654(transverse direction) - RD plane.<span style='mso-spacerun:yes'>  </span>Thus,
1655the general axis equation becomes</p>
1656
1657<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
1658   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
1659  style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><span
1660    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1661    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1662    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
1663    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
1664  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
1665     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
1666    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1667    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
1668    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
1669      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1670      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1671      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
1672      normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i
1673      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
1674      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1675      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1676      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
1677      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
1678      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
1679     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
1680    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1681    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
1682    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
1683    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
1684       m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
1685      "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
1686      "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
1687      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
1688      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
1689        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1690        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1691        normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
1692        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
1693        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
1694        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
1695      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1696      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1697      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
1698      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
1699      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
1700      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
1701      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1702      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1703      normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
1704      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
1705    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1706    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1707    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1708    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1709    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
1710    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
1711  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
1712style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1713"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
1714mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
1715 id="_x0000_i1025" type="#_x0000_t75" style='width:321pt;height:54pt'>
1716 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image013.png"
1717  o:title="" chromakey="white"/>
1718</v:shape><![endif]--><![if !vml]><img width=428 height=72
1719src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image111.png"
1720v:shapes="_x0000_i1025"><![endif]></span><![endif]><br style='mso-special-character:
1721line-break'>
1722<![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'>
1723<![endif]></p>
1724
1725<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
1726115%'>In a diffraction experiment the crystal reflection coordinates (<span
1727style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>)
1728are determined by the choice of reflection index (<span class=SpellE>hkl</span>)
1729while the sample coordinates (<span style='font-family:Symbol'>y</span>, <span
1730style='font-family:Symbol'>g</span>) are determined by the sample orientation
1731on the diffractometer.</p>
1732
1733<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>To
1734define the sample coordinates (<span style='font-family:Symbol'>y</span>, <span
1735style='font-family:Symbol'>g</span>), we have defined an instrument coordinate
1736system (I, J, K) such that K is normal to the diffraction plane and J is
1737coincident with the direction of the incident radiation beam toward the source.
1738We further define a standard set of right-handed goniometer <span class=SpellE>eulerian</span>
1739angles (<span style='font-family:Symbol'>W</span>, <span style='font-family:
1740Symbol'>C</span>, <span style='font-family:Symbol'>F</span>) so that <span
1741style='font-family:Symbol'>W</span> and <span style='font-family:Symbol'>F</span>
1742are rotations about K and <span style='font-family:Symbol'>C</span> is a
1743rotation about J when <span style='font-family:Symbol'>W</span> <span
1744style='font-family:Symbol'><span style='mso-spacerun:yes'> </span></span>=
17450.<span style='mso-spacerun:yes'>  </span>Finally, as the sample may be mounted
1746so that the sample coordinate system (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>,
1747K<sub>s</sub>) does not coincide with the instrument coordinate system (I, J,
1748K), we define three <span class=SpellE>eulerian</span> sample rotation offset
1749angles (<span style='font-family:Symbol'>W</span><sub>s</sub>, <span
1750style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:Symbol'>F</span><sub>s</sub>)
1751that describe the rotation from (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>,
1752K<sub>s</sub>) to (I, J, K).<span style='mso-spacerun:yes'>  </span>The sample
1753rotation angles are defined so that with the goniometer angles at zero <span
1754style='font-family:Symbol'>W</span><sub>s</sub> and <span style='font-family:
1755Symbol'>F</span><sub>s</sub> are rotations about I and <span style='font-family:
1756Symbol'>C</span><sub>s</sub> is a rotation about J.<span
1757style='mso-spacerun:yes'>  </span>The zeros of these three sample rotation
1758angles can be refined as part of the Rietveld analysis to accommodate any
1759angular offset in sample mounting. After including the diffraction angle, <span
1760style='font-family:Symbol'>Q</span>, and a detector azimuthal angle, A, the
1761full rotation matrix, <b style='mso-bidi-font-weight:normal'>M</b>, is </p>
1762
1763<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><b
1764style='mso-bidi-font-weight:normal'>M = -</b><b style='mso-bidi-font-weight:
1765normal'><span style='font-family:Symbol'>Q</span>A</b><b style='mso-bidi-font-weight:
1766normal'><span style='font-family:Symbol'>W<span class=GramE>C<span
1767style='font-family:"Times New Roman",serif'>(</span></span>F</span>+</b><b
1768style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span><sub>s</sub>)</b><b
1769style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>C</span><span
1770class=SpellE><sub>s</sub><span style='font-family:Symbol'>W</span><sub>s</sub></span><o:p></o:p></b></p>
1771
1772<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>By
1773transformation of unit Cartesian vectors (100, 010 and 001) with this rotation
1774matrix, the sample orientation coordinates (<span style='font-family:Symbol'>y</span>,
1775<span style='font-family:Symbol'>g</span>) are given by</p>
1776
1777<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
1778class=GramE><i>cos</i>(</span><span style='font-family:Symbol'>y</span>) = <!--[if gte msEquation 12]><m:oMath><i
1779 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
1780   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1781   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1782   normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
1783         m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
1784     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1785     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1786     normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
1787      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1788      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1789      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:oMath><![endif]--><![if !msEquation]><span
1790style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1791"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1792top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1793EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1794 type="#_x0000_t75" style='width:33.75pt;height:50.25pt'>
1795 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image015.png"
1796  o:title="" chromakey="white"/>
1797</v:shape><![endif]--><![if !vml]><img width=45 height=67
1798src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image112.png"
1799v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1800style='mso-spacerun:yes'> </span>and<span style='mso-spacerun:yes'>   </span><i>tan</i>(<span
1801style='font-family:Symbol'>g</span>) = <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type
1802    m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1803   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1804   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
1805   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
1806     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1807     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1808     normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
1809           m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
1810       style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1811       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1812       normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
1813        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1814        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1815        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:num><m:den><i
1816   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span
1817     style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1818     mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1819     normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count
1820           m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span
1821       style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1822       mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1823       normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i
1824        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1825        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i
1826        style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
1827style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1828"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1829top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1830EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1831 type="#_x0000_t75" style='width:80.25pt;height:50.25pt'>
1832 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image017.png"
1833  o:title="" chromakey="white"/>
1834</v:shape><![endif]--><![if !vml]><img width=107 height=67
1835src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image113.png"
1836v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
1837
1838<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>The
1839harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1840   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1841   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1842   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1843   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1844   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1845   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i
1846 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#966;</m:r><m:r>,</m:r><m:r>&#946;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
1847style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1848"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1849top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1850EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1851 type="#_x0000_t75" style='width:46.5pt;height:26.25pt'>
1852 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png"
1853  o:title="" chromakey="white"/>
1854</v:shape><![endif]--><![if !vml]><img width=62 height=35
1855src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image114.png"
1856v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1857style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1858   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1859   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1860   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1861   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1862   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i
1863   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i
1864 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>&#968;</m:r><m:r>,</m:r><m:r>&#947;</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
1865style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1866"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1867top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1868EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1869 type="#_x0000_t75" style='width:42.75pt;height:26.25pt'>
1870 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png"
1871  o:title="" chromakey="white"/>
1872</v:shape><![endif]--><![if !vml]><img width=57 height=35
1873src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image115.png"
1874v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are developed from</p>
1875
1876<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
1877   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
1878    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1879    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1880    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
1881    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
1882    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
1883    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
1884    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1885    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1886    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
1887    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
1888  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:f><m:fPr><span
1889    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1890    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1891    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
1892    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
1893       m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1894      "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1895      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
1896      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
1897    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1898    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1899    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
1900    normal'><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:e><m:sup><i
1901    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
1902    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1903    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1904    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
1905       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
1906      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1907      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1908      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
1909    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
1910    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
1911     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
1912  normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
1913    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1914    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1915    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
1916    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
1917       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
1918    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
1919  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
1920style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1921"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
1922mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
1923 id="_x0000_i1025" type="#_x0000_t75" style='width:165pt;height:42pt'>
1924 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.png"
1925  o:title="" chromakey="white"/>
1926</v:shape><![endif]--><![if !vml]><img width=220 height=56
1927src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image116.png"
1928v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
1929
1930<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
1931class=GramE>where</span> the normalized associated Legendre functions, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
1932   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1933   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1934   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
1935      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1936     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1937     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1938     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
1939   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
1940   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
1941 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
1942style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1943"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1944top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1945EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1946 type="#_x0000_t75" style='width:33pt;height:26.25pt'>
1947 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image025.png"
1948  o:title="" chromakey="white"/>
1949</v:shape><![endif]--><![if !vml]><img width=44 height=35
1950src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image117.png"
1951v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are defin<span
1952class=SpellE>ed</span> via a Fourier expansion as</p>
1953
1954<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
1955   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
1956    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1957    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1958    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
1959       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
1960      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
1961      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1962      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
1963    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
1964    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
1965     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
1966    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1967    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1968    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
1969      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1970      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1971      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
1972      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
1973         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
1974      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
1975  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
1976     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><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:naryPr><m:sub><i
1979    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
1980    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
1981      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1982      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1983      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
1984      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
1985      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
1986      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
1987       </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
1988    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1989    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1990    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
1991    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
1992       m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
1993    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
1994style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1995"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
1996mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
1997 id="_x0000_i1025" type="#_x0000_t75" style='width:154.5pt;height:52.5pt'>
1998 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image027.png"
1999  o:title="" chromakey="white"/>
2000</v:shape><![endif]--><![if !vml]><img width=206 height=70
2001src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image118.png"
2002v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2003
2004<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
2005class=GramE>for</span> m even and</p>
2006
2007<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2008   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
2009    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2010    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2011    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2012       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2013      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2014      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2015      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
2016    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
2017    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2018     </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
2019    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2020    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2021    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
2022      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2023      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2024      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2025      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2026         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2027      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
2028  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
2029     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2030    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2031    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2032    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
2033    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
2034      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2035      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2036      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
2037      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
2038      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
2039      style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2040       </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span
2041    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2042    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2043    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2044    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2045       m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2046    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
2047style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2048"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2049mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2050 id="_x0000_i1025" type="#_x0000_t75" style='width:158.25pt;height:52.5pt'>
2051 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image029.png"
2052  o:title="" chromakey="white"/>
2053</v:shape><![endif]--><![if !vml]><img width=211 height=70
2054src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image119.png"
2055v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2056
2057<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
2058class=GramE>for</span> m odd.<span style='mso-spacerun:yes'>  </span>Each sum
2059is only over either the even or odd values of s, respectively, because of the
2060properties of the Fourier coefficients<span class=GramE>, </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2061   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2062   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2063   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2064   normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i
2065   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
2066   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2067    </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span
2068style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2069"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2070top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2071EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2072 type="#_x0000_t75" style='width:24.75pt;height:26.25pt'>
2073 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image031.png"
2074  o:title="" chromakey="white"/>
2075</v:shape><![endif]--><![if !vml]><img width=33 height=35
2076src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image120.png"
2077v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
2078style='mso-spacerun:yes'>  </span>These Fourier coefficients are determined so
2079that the definition</p>
2080
2081<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2082   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
2083    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2084    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2085    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2086       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2087      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2088      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2089      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
2090    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
2091    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2092     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
2093    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2094    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2095    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span
2096      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2097      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2098      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2099      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2100         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2101      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func></m:e></m:d><i
2102  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:sSubSup><m:sSubSupPr><span
2103    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2104    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2105    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2106       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2107      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2108      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2109      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
2110    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
2111    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2112     </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span
2113    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2114    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2115    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
2116    normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e></m:d><i
2117  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
2118     m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2119    "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2120    mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
2121      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2122      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2123      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span
2124        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2125        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2126        normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
2127        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
2128      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
2129        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2130        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2131        normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
2132        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
2133      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
2134     m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2135    "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2136    mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span
2137      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2138      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2139      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
2140      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
2141      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
2142    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2143    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2144    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
2145      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2146      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2147      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2148      normal'><span style='font-family:"Cambria Math",serif'><m:r>(-1)</m:r></span></i></m:e><m:sup><i
2149      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
2150      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2151      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2152      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2153      normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:e><m:sup><i
2154      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
2155    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
2156    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2157    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2158    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2159    normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><span
2160      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2161      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2162      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2163      normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i
2164      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
2165    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
2166       m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2167      "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2168      mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
2169      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
2170      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
2171    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2172    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2173    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
2174      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2175      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2176      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2177      normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i
2178      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
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>dx</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>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
2184    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2185    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2186    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2187    normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><span
2188      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2189      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2190      normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
2191      normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i
2192      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
2193    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:e><m:sup><i
2194    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
2195style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2196"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2197mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2198 id="_x0000_i1025" type="#_x0000_t75" style='width:423.75pt;height:55.5pt'>
2199 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.png"
2200  o:title="" chromakey="white"/>
2201</v:shape><![endif]--><![if !vml]><img width=565 height=74
2202src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image121.png"
2203v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2204
2205<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
2206class=GramE>is</span> satisfied.<span style='mso-spacerun:yes'>  </span>Terms
2207of the form <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
2208   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2209   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2210   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2211   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2212      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2213   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
2214   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2215   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2216   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2217      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2218     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2219     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2220     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
2221   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
2222   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2223    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2224 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
2225   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2226   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2227   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2228   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2229      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2230   normal'><span style='font-family:"Cambria Math",serif'><m:r>m&#946;</m:r></span></i></m:e></m:func><i
2231 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
2232style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2233"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2234top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2235EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2236 type="#_x0000_t75" style='width:111pt;height:26.25pt'>
2237 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image035.png"
2238  o:title="" chromakey="white"/>
2239</v:shape><![endif]--><![if !vml]><img width=148 height=35
2240src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image122.png"
2241v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2242style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span
2243   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2244   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2245   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2246   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2247      m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2248   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
2249   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2250   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2251   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2252      m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
2253     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
2254     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2255     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
2256   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
2257   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2258    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2259 normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
2260   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2261   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2262   normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2263   style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2264      m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2265   normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
2266 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
2267style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2268"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2269top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2270EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2271 type="#_x0000_t75" style='width:100.5pt;height:26.25pt'>
2272 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image037.png"
2273  o:title="" chromakey="white"/>
2274</v:shape><![endif]--><![if !vml]><img width=134 height=35
2275src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image123.png"
2276v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2277style='mso-spacerun:yes'> </span>are combined depending on the symmetry and the
2278value of m along with appropriate normalization coefficients to give the
2279harmonic terms <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2280   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2281   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2282   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2283   normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
2284   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
2285   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2286    </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2287 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
2288style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2289"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2290top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2291EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2292 type="#_x0000_t75" style='width:48pt;height:26.25pt'>
2293 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
2294  o:title="" chromakey="white"/>
2295</v:shape><![endif]--><![if !vml]><img width=64 height=35
2296src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image124.png"
2297v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2298style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[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>n</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>&#968;</m:r><m:r>,</m:r><m:r>&#947;</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:45pt;height:26.25pt'>
2312 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png"
2313  o:title="" chromakey="white"/>
2314</v:shape><![endif]--><![if !vml]><img width=60 height=35
2315src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image125.png"
2316v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span
2317style='mso-spacerun:yes'>  </span>For cubic crystal symmetry, the term <!--[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>m</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>&#966;</m:r><m:r>,</m:r><m:r>&#946;</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:48pt;height:26.25pt'>
2331 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png"
2332  o:title="" chromakey="white"/>
2333</v:shape><![endif]--><![if !vml]><img width=64 height=35
2334src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image124.png"
2335v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2336style='mso-spacerun:yes'> </span>is obtained direc<span class=SpellE>tly</span>
2337from the Fourier expansion</p>
2338
2339<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2340   m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span
2341    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2342    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2343    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2344    normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i
2345    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
2346    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
2347    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2348    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2349    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
2350    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
2351  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
2352     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2353    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2354    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2355    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
2356    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
2357      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2358      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2359      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
2360      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
2361      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
2362      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
2363    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2364    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2365    normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr
2366       m:val="&#773;"/><span style='font-family:"Cambria Math",serif;
2367      mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2368      font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
2369      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
2370    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
2371    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>
2372     </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style:
2373  normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span
2374    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2375    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2376    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2377    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2378       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2379    normal'><span style='font-family:"Cambria Math",serif'><m:r>&#966;</m:r></span></i></m:e></m:func><i
2380  style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i><m:func><m:funcPr><span
2381    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2382    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2383    normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
2384    style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
2385       m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
2386    normal'><span style='font-family:"Cambria Math",serif'><m:r>n&#946;</m:r></span></i></m:e></m:func></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span
2387style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2388"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2389mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2390 id="_x0000_i1025" type="#_x0000_t75" style='width:193.5pt;height:52.5pt'>
2391 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image043.png"
2392  o:title="" chromakey="white"/>
2393</v:shape><![endif]--><![if !vml]><img width=258 height=70
2394src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image126.png"
2395v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2396
2397<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><span
2398class=GramE>using</span> the coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2399   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2400   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2401   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2402   normal'><span style='font-family:"Cambria Math",serif'><m:r>B</m:r></span></i></m:e><m:sub><i
2403   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
2404   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
2405style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2406"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2407top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2408EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2409 type="#_x0000_t75" style='width:22.5pt;height:26.25pt'>
2410 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image045.png"
2411  o:title="" chromakey="white"/>
2412</v:shape><![endif]--><![if !vml]><img width=30 height=35
2413src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image127.png"
2414v:shapes="_x0000_i1025"><![endif]></span><![endif]>, as tabulated by Bunge
2415(1982). </p>
2416
2417<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>The
2418Rietveld refinement of texture then proceeds by constructing derivatives of the
2419profile intensities with respect to the allowed harmonic coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span
2420   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2421   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2422   normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style:
2423   normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i
2424   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
2425   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
2426style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2427"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
2428top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
2429EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
2430 type="#_x0000_t75" style='width:21.75pt;height:26.25pt'>
2431 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png"
2432  o:title="" chromakey="white"/>
2433</v:shape><![endif]--><![if !vml]><img width=29 height=35
2434src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image128.png"
2435v:shapes="_x0000_i1025"><![endif]></span><![endif]>, and the three sample
2436orientation angles, <span style='font-family:Symbol'>W</span><sub>s</sub>, <span
2437style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:Symbol'>F</span><sub>s</sub>,
2438all of which can be adjustable parameters of the refinement. Once the
2439refinement is complete, pole figures for any reflection may be constructed by
2440use of the general axis equation, the refined values for <!--[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/image128.png"
2456v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
2457style='mso-spacerun:yes'> </span>and the sample orientation angles <span
2458style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
2459<span class=GramE><span style='font-family:Symbol'>F</span></span><sub>s</sub>.
2460</p>
2461
2462<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>The
2463magnitude of the texture is evaluated from the texture index by</p>
2464
2465<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc
2466   m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span
2467  style='font-family:"Cambria Math",serif'><m:r>J</m:r><m:r>=1+</m:r></span></i><m:nary><m:naryPr><m:chr
2468     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2469    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2470    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2471    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
2472      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2473      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2474      normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style:
2475      normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i
2476      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
2477      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2478      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2479      normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
2480      normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:num><m:den><i
2481      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
2482     m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif;
2483    mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2484    font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2485    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
2486    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
2487       m:val="&#8721;"/><m:limLoc m:val="undOvr"/><span style='font-family:
2488      "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:
2489      "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i
2490      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
2491      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
2492        style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2493        mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2494        normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><m:begChr
2495           m:val="|"/><m:endChr m:val="|"/><span style='font-family:"Cambria Math",serif;
2496          mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
2497          font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:sSubSup><m:sSubSupPr><span
2498            style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
2499            mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
2500            normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i
2501            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
2502            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
2503            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
2504        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
2505style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
2506"Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US;
2507mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
2508 id="_x0000_i1025" type="#_x0000_t75" style='width:180.7pt;height:54pt'>
2509 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.png"
2510  o:title="" chromakey="white"/>
2511</v:shape><![endif]--><![if !vml]><img width=241 height=72
2512src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image129.png"
2513v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
2514
2515<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>If
2516the texture is random then J = 1, otherwise J &gt; 1; for a single crystal J = <span
2517style='font-family:Symbol'>¥.</span> </p>
2518
2519<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>In
2520GSAS-II the texture is defined in two ways to accommodate the two possible uses
2521of this correction. In one a suite of spherical harmonics coefficients is
2522defined for the texture of a phase in the sample; this can have any of the
2523possible sample symmetries and is the usual result desired for texture
2524analysis. The other is the suite of spherical harmonics terms for cylindrical
2525sample symmetry for each phase in each powder pattern (“histogram”) and is usually
2526used to accommodate preferred orientation effects in a Rietveld refinement. The
2527former description allows refinement of the sample orientation zeros, <span
2528style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>,
2529<span style='font-family:Symbol'>F</span><sub>s</sub>, but the latter
2530description does not (they are assumed to be zero and not refinable). The sample
2531orientation angles, (<span style='font-family:Symbol'>W</span>, <span
2532style='font-family:Symbol'>C</span>, <span style='font-family:Symbol'>F) </span>are
2533specified in the Sample Parameters table in the GSAS-II data tree structure and
2534are applied for either description.</p>
2535
2536<p class=gsastext style='margin:0in;margin-bottom:.0001pt;line-height:115%'>In
2537this tutorial we will use both of these descriptions to determine the texture
2538of the two phases in a <span class=SpellE>NiTi</span> shape memory alloy sample
2539with cylindrical symmetry (wire texture) as collected at APS on beam line 1ID-C
2540(data kindly provided by Paul Paradise &amp; Aaron <span class=SpellE>Stebner</span>
2541of Colo. School of Mines). Thus, there are three ways within GSAS-II that can
2542be used for this texture analysis all beginning with the same 2D area detector
2543image. Each will be described in turn after the initial setup of the GSAS-II
2544project, image input &amp; integration.</p>
2545
2546<h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 1. Image
2547input &amp; integration</h2>
2548
2549<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2550115%'>If you have not done so already, <u><span style='color:#0070C0'><a
2551href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none;
2552text-underline:none'>start GSAS-II</span></a></span></u>. Note that menu
2553entries are listed in <b style='mso-bidi-font-weight:normal'><span
2554style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2555mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
2556minor-latin'>bold face</span></b> below as <b style='mso-bidi-font-weight:normal'><span
2557style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2558mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
2559minor-latin'>Help/About GSAS-II</span></b>, which lists first the name of the
2560menu (here <b style='mso-bidi-font-weight:normal'><span style='font-family:
2561"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2562minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>Help</span></b>)
2563and second the name of the entry in the menu (here <b style='mso-bidi-font-weight:
2564normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2565minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;
2566mso-bidi-theme-font:minor-latin'>About GSAS-II</span></b>). </p>
2567
2568<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2569115%'>Use the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2570"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2571minor-latin'>Data/Read image data</span></b> menu item to read the data file
2572into the current GSAS-II project. A file selection dialog will be shown; its
2573appearance will depend on your OS. Change the search directory to <b
2574style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2575mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
2576Calibri;mso-bidi-theme-font:minor-latin'>/exercises/2DTexture </span></b>and
2577then select the file <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'>NDC5_01588_1.ge2</span></b>. A (faint) image
2580will appear</p>
2581
2582<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2583115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_29"
2584 o:spid="_x0000_i1081" type="#_x0000_t75" style='width:525pt;height:450pt;
2585 visibility:visible;mso-wrap-style:square'>
2586 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
2587  o:title=""/>
2588</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2589src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png"
2590v:shapes="Picture_x0020_29"><![endif]></span></p>
2591
2592<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2593115%'><span class=GramE>and</span> the <b style='mso-bidi-font-weight:normal'><span
2594style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2595mso-hansi-theme-font:minor-latin'>Image Controls</span></b> data page will show</p>
2596
2597<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2598115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_30"
2599 o:spid="_x0000_i1080" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
2600 visibility:visible;mso-wrap-style:square'>
2601 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
2602  o:title=""/>
2603</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
2604src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png"
2605v:shapes="Picture_x0020_30"><![endif]></span></p>
2606
2607<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2608115%'>The detector was previously calibrated and the coefficients are stored in
2609a file found by doing <b style='mso-bidi-font-weight:normal'><span
2610style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2611mso-hansi-theme-font:minor-latin'>Operations/Load Controls</span></b> from the <b
2612style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2613mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2614Controls</span></b> menu. A file selection popup will appear showing <b
2615style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2616mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NDC5.imctrl</span></b>;
2617select it and press <b style='mso-bidi-font-weight:normal'><span
2618style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2619mso-hansi-theme-font:minor-latin'>Open</span></b>. The <b style='mso-bidi-font-weight:
2620normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2621minor-latin;mso-hansi-theme-font:minor-latin'>Image Controls</span></b> window
2622will be repainted with the new values (do a reselect of the image from the tree
2623and then <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2624mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2625Controls</span></b> to make sure the image is up to date.)</p>
2626
2627<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2628115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_31"
2629 o:spid="_x0000_i1079" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
2630 visibility:visible;mso-wrap-style:square'>
2631 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
2632  o:title=""/>
2633</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
2634src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png"
2635v:shapes="Picture_x0020_31"><![endif]></span></p>
2636
2637<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2638115%'>The detail in the image can be enhanced by lowering the <b
2639style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2640mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Max
2641intensity</span></b> (<b style='mso-bidi-font-weight:normal'><span
2642style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2643mso-hansi-theme-font:minor-latin'>15000</span></b> is suitable) and shows that
2644the diffraction rings show the effect of texture and that the image has a
2645fairly high background. Placing the cursor in the corners or inside the inner
2646ring shows a background &gt;1700. This can be suppressed by adjusting the <b
2647style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2648mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Flat <span
2649class=SpellE>Bkg</span></span></b> (I chose <b style='mso-bidi-font-weight:
2650normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2651minor-latin;mso-hansi-theme-font:minor-latin'>1700</span></b> for this). The
2652image will now show the rings much more clearly.</p>
2653
2654<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2655115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32"
2656 o:spid="_x0000_i1078" type="#_x0000_t75" style='width:525pt;height:450pt;
2657 visibility:visible;mso-wrap-style:square'>
2658 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
2659  o:title=""/>
2660</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2661src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png"
2662v:shapes="Picture_x0020_32"><![endif]></span></p>
2663
2664<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2665115%'>For texture analysis we will need to integrate the image into a number of
2666slices sampling the changing ring intensity with azimuthal angle. Also note
2667that the image seems to have <b style='mso-bidi-font-weight:normal'><span
2668style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2669mso-hansi-theme-font:minor-latin'>mm</span></b> symmetry so that the unique
2670part of this intensity variation covers 0-90° of azimuth. In addition the ring
2671intensity variation is such that using 10° slices will capture it reasonably
2672well. However, we want to include both 0° and 90° as slice centers. Thus there
2673will be 10 slices beginning at -5° and ending at 95°. Check the <b
2674style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2675mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show
2676integration limits?</span></b> <span class=GramE>box</span> and uncheck the <b
2677style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2678mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Do full
2679integration? </span></b><span class=GramE>box</span>, enter <b
2680style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2681mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>
2682in the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2683mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth
2684bins</span></b>, enter <b style='mso-bidi-font-weight:normal'><span
2685style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2686mso-hansi-theme-font:minor-latin'>-5</span></b> in the <b style='mso-bidi-font-weight:
2687normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2688minor-latin;mso-hansi-theme-font:minor-latin'>Start azimuth</span></b> box (it
2689will change to 355) and enter <b style='mso-bidi-font-weight:normal'><span
2690style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2691mso-hansi-theme-font:minor-latin'>455</span></b> in the <b style='mso-bidi-font-weight:
2692normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2693minor-latin;mso-hansi-theme-font:minor-latin'>End azimuth</span></b> box. In
2694addition, recall that the sample was mounted vertically and thus is aligned
2695with the defined laboratory I axis. Thus, the sample coordinate system needs to
2696be rotated by 90° to match the sample axis with the K axis; this can be done by
2697making the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2698"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2699minor-latin'>Sample goniometer axis Chi</span></b> = <b style='mso-bidi-font-weight:
2700normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2701minor-latin;mso-hansi-theme-font:minor-latin'>90</span></b>. The plot will
2702change with each entry and at the end should look like</p>
2703
2704<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2705115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_33"
2706 o:spid="_x0000_i1077" type="#_x0000_t75" style='width:525pt;height:450pt;
2707 visibility:visible;mso-wrap-style:square'>
2708 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
2709  o:title=""/>
2710</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2711src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png"
2712v:shapes="Picture_x0020_33"><![endif]></span></p>
2713
2714<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2715115%'>The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2716mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2717Controls</span></b> should be</p>
2718
2719<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2720115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_34"
2721 o:spid="_x0000_i1076" type="#_x0000_t75" style='width:472.5pt;height:388.5pt;
2722 visibility:visible;mso-wrap-style:square'>
2723 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
2724  o:title=""/>
2725</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518
2726src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png"
2727v:shapes="Picture_x0020_34"><![endif]></span></p>
2728
2729<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2730115%'>It turns out that the image contains a number of “picked bits” (very high
2731count “zingers”); these can be mostly eliminated by setting the upper threshold
2732in Masks. Select <b style='mso-bidi-font-weight:normal'><span style='font-family:
2733"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2734minor-latin'>Masks</span></b> and the following should appear</p>
2735
2736<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2737115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35"
2738 o:spid="_x0000_i1075" type="#_x0000_t75" style='width:297.75pt;height:99.75pt;
2739 visibility:visible;mso-wrap-style:square'>
2740 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
2741  o:title=""/>
2742</v:shape><![endif]--><![if !vml]><img border=0 width=397 height=133
2743src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png"
2744v:shapes="Picture_x0020_35"><![endif]></span></p>
2745
2746<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2747115%'>Change the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2748"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2749minor-latin'>Upper threshold</span></b> to <b style='mso-bidi-font-weight:normal'><span
2750style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2751mso-hansi-theme-font:minor-latin'>2500</span></b>; the image will be redrawn
2752reflecting this mask. By zooming in you may see isolated red pixels; these are
2753excluded points. Make sure the diffraction rings do not have any excluded
2754points. For example with the level set to 2200 the plot shows</p>
2755
2756<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2757115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_36"
2758 o:spid="_x0000_i1074" type="#_x0000_t75" style='width:525pt;height:450pt;
2759 visibility:visible;mso-wrap-style:square'>
2760 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
2761  o:title=""/>
2762</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2763src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png"
2764v:shapes="Picture_x0020_36"><![endif]></span></p>
2765
2766<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2767115%'><span class=GramE>for</span> one ring. This level is too low. Return to
2768the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2769mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2770Controls</span></b> item in the data tree.</p>
2771
2772<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2773115%'>We are now ready to integrate the image; do <b style='mso-bidi-font-weight:
2774normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2775minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Integrate</span></b>
2776from the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2777mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image
2778Controls</span></b> menu. When done the last powder pattern in the tree will be
2779displayed</p>
2780
2781<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2782115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_37"
2783 o:spid="_x0000_i1073" type="#_x0000_t75" style='width:525pt;height:450pt;
2784 visibility:visible;mso-wrap-style:square'>
2785 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
2786  o:title=""/>
2787</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
2788src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png"
2789v:shapes="Picture_x0020_37"><![endif]></span></p>
2790
2791<h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 2. Enter <span
2792class=SpellE>NiTi</span> phases</h2>
2793
2794<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2795115%'>This <span class=SpellE>NiTi</span> alloy consists of two phases, cubic
2796B2 and monoclinic B19’. Their parameters are:</p>
2797
2798<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2799115%'>B2: <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2800mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P m 3 m</span></b>,
2801a=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2802mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>3.0240</span></b>,
2803Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2804mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0<span
2805class=GramE>,0,0</span></span></b>, <span class=SpellE>Ti</span> <b
2806style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2807mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>œ,œ,œ</span></b>,
2808<span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
2809style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2810mso-hansi-theme-font:minor-latin'>0.005 </span></b>for both.</p>
2811
2812<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2813115%'>B19’:<span style='mso-spacerun:yes'>  </span><b style='mso-bidi-font-weight:
2814normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2815minor-latin;mso-hansi-theme-font:minor-latin'>P 1 1 21/m</span></b>, a=<b
2816style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2817mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.8853</span></b>,
2818b=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2819mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.6353</span></b>,
2820c=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2821mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.1368</span></b>,
2822&#947;=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2823mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>96.821</span></b>,
2824<span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span
2825style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2826mso-hansi-theme-font:minor-latin'>0.5787<span class=GramE>,0.2841,Œ</span></span></b>,
2827Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2828mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.9700,0.8209,Œ</span></b>,
2829<span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span
2830style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2831mso-hansi-theme-font:minor-latin'>0.005</span></b> for both.</p>
2832
2833<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2834115%'>Use the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2835"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2836minor-latin'>Data/Add phase</span></b> to enter the <b style='mso-bidi-font-weight:
2837normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2838minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> and <b
2839style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2840mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
2841phases; then for each enter the information given above on their respective <b
2842style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2843mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>General</span></b>
2844and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2845mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms</span></b>
2846tabs. Don’t forget the spaces between the axial fields for the space group
2847symbols. On the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2848"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2849minor-latin'>Atoms</span></b> tab begin by doing <b style='mso-bidi-font-weight:
2850normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2851minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Append atom</span></b> twice
2852then fill in the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2853"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2854minor-latin'>Type</span></b> and coordinates boxes. A double click of the <b
2855style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2856mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Type</span></b>
2857entry will show a popup of the Periodic Table; select the element as
2858appropriate. NB: GSAS-II happily takes “1/2” &amp; “1/4” for coordinate values;
2859these get converted to their decimal equivalent upon entry. Note the use of a
2860nonstandard space group designation for B19’. When done the B2 Atoms table
2861should look like</p>
2862
2863<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2864115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_38"
2865 o:spid="_x0000_i1072" type="#_x0000_t75" style='width:525pt;height:166.5pt;
2866 visibility:visible;mso-wrap-style:square'>
2867 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
2868  o:title=""/>
2869</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=222
2870src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png"
2871v:shapes="Picture_x0020_38"><![endif]></span></p>
2872
2873<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2874115%'><span class=GramE>and</span> the B19’ Atoms table should be</p>
2875
2876<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2877115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_39"
2878 o:spid="_x0000_i1071" type="#_x0000_t75" style='width:525pt;height:163.5pt;
2879 visibility:visible;mso-wrap-style:square'>
2880 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2881  o:title=""/>
2882</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=218
2883src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png"
2884v:shapes="Picture_x0020_39"><![endif]></span></p>
2885
2886<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2887115%'>Next go to the <b style='mso-bidi-font-weight:normal'><span
2888style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2889mso-hansi-theme-font:minor-latin'>Data</span></b> tab for each phase; there
2890will be a message indicating the lack of data for each. Do <b style='mso-bidi-font-weight:
2891normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2892minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add powder histograms</span></b>,
2893do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2894mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b>
2895on the popup selection window and press <b style='mso-bidi-font-weight:normal'><span
2896style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2897mso-hansi-theme-font:minor-latin'>OK</span></b>. The window for B2 will change
2898to</p>
2899
2900<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2901115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40"
2902 o:spid="_x0000_i1070" type="#_x0000_t75" style='width:342.75pt;height:375pt;
2903 visibility:visible;mso-wrap-style:square'>
2904 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2905  o:title=""/>
2906</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
2907src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2908v:shapes="Picture_x0020_40"><![endif]></span></p>
2909
2910<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2911115%'><span class=GramE>and</span> that for B19’ will be</p>
2912
2913<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2914115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_41"
2915 o:spid="_x0000_i1069" type="#_x0000_t75" style='width:370.5pt;height:375pt;
2916 visibility:visible;mso-wrap-style:square'>
2917 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
2918  o:title=""/>
2919</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
2920src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png"
2921v:shapes="Picture_x0020_41"><![endif]></span></p>
2922
2923<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2924115%'>You should now save the project file (I used <span class=SpellE><b
2925style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2926mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span>
2927for a name); we will use this as a starting point for three different texture
2928determinations. Do a <b style='mso-bidi-font-weight:normal'><span
2929style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2930mso-hansi-theme-font:minor-latin'>File/Save project as…</span></b> and give it
2931a new name (I used <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
2932style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2933mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight:
2934normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2935minor-latin;mso-hansi-theme-font:minor-latin'>-A</span></b>); this will become
2936the new project name for the next part of this tutorial.</p>
2937
2938<h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Method A. Full
2939refinement</h2>
2940
2941<h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Introduction</h3>
2942
2943<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2944115%'>In this method we will do a full Rietveld refinement of the texture,
2945profile parameters, peak position variables and crystal structure parameters.
2946This is suitable in this case because of the relatively small number of
2947histograms (10 in this case) needed for the texture determination; do recall
2948that each phase in each histogram has a set of parameters (e.g. phase fraction,
2949size, <span class=SpellE>mustrain</span> &amp; hydrostatic strain) in addition
2950to the ones for each histogram (e.g. background &amp; scale factor). Consequently
2951the total number of parameters can build up very quickly in this method of
2952analysis. The other two methods seek to reduce this problem by splitting the
2953fitting into a sequential refinement (histogram by histogram) step followed by
2954a texture fitting step.</p>
2955
2956<h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 1. Initial
2957refinement</h3>
2958
2959<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2960115%'>In the initial refinement we need to vary the phase fraction for each
2961phase/histogram and the background in each histogram. To start select any <b
2962style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2963mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b>
2964entry from the GSAS-II data tree and select <b style='mso-bidi-font-weight:
2965normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2966minor-latin;mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b> for
2967it. Note that Goniometer chi is set to 90; that came from the same entry in the
2968Image Controls during integration. Also, if you chose other than the 1<sup>st</sup>
2969PWDR data set the Detector azimuth will be some nonzero value; that is also
2970reflected in the name assigned to the histogram (e.g. <b style='mso-bidi-font-weight:
2971normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2972minor-latin;mso-hansi-theme-font:minor-latin'>PWDR NDC5_01588_1.ge2 <span
2973class=SpellE>Azm</span>= 40.00</span></b>). Uncheck the <b style='mso-bidi-font-weight:
2974normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2975minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>
2976box and then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
2977"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2978minor-latin'>Command/Copy flags</span></b>; select <b style='mso-bidi-font-weight:
2979normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2980minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b> and then press
2981<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2982mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
2983That will clear the scale factor refinement flag for all histograms; we will be
2984varying the phase fractions instead.</p>
2985
2986<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2987115%'>Next select the B2 phase and pick the Data tab; you will see</p>
2988
2989<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
2990115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42"
2991 o:spid="_x0000_i1068" type="#_x0000_t75" style='width:342.75pt;height:375pt;
2992 visibility:visible;mso-wrap-style:square'>
2993 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2994  o:title=""/>
2995</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
2996src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png"
2997v:shapes="Picture_x0020_42"><![endif]></span></p>
2998
2999<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3000115%'>Select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3001"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3002minor-latin'>Phase fraction</span></b> box. Then do <b style='mso-bidi-font-weight:
3003normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3004minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b>, select
3005<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3006mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set <span
3007class=GramE>All</span></span></b> &amp; press <b style='mso-bidi-font-weight:
3008normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3009minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to copy these to the
3010other histograms. Next select the <b style='mso-bidi-font-weight:normal'><span
3011style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3012mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and repeat this
3013process. We are now ready for the first refinement; do <b style='mso-bidi-font-weight:
3014normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3015minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from
3016the main GSAS-II data tree window. A progress bar popup will appear and when
3017done a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3018mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refinement
3019results</span></b> popup will show with Rw~32%. Press <b style='mso-bidi-font-weight:
3020normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3021minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to load this
3022result; GSAS-II will return you to the last window you were using and display
3023the 1<sup>st</sup> powder pattern showing you the fit</p>
3024
3025<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3026115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_43"
3027 o:spid="_x0000_i1067" type="#_x0000_t75" style='width:525pt;height:450pt;
3028 visibility:visible;mso-wrap-style:square'>
3029 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
3030  o:title=""/>
3031</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3032src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png"
3033v:shapes="Picture_x0020_43"><![endif]></span></p>
3034
3035<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3036115%'>This is quite poor. You can survey the fit successively by 1<sup>st</sup>
3037selecting say the 1<sup>st</sup> PWDR entry from the tree and then using the
3038up/down arrow keys to step to the next one; the plot will redraw at each step
3039(NB: at full scale) and the data window will show statistics of the fit. There
3040is a substantial intensity discrepancy; this is due to the texture. It is also
3041evident that some of the peaks are out of place relative to the reflection
3042markers; this is due to macroscopic strain in the drawn wire. For the <span
3043style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3044mso-hansi-theme-font:minor-latin'>B2</span> phase select the <b
3045style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3046mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
3047tab; it should look like</p>
3048
3049<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3050115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44"
3051 o:spid="_x0000_i1066" type="#_x0000_t75" style='width:456pt;height:217.5pt;
3052 visibility:visible;mso-wrap-style:square'>
3053 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
3054  o:title=""/>
3055</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290
3056src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
3057v:shapes="Picture_x0020_44"><![endif]></span></p>
3058
3059<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3060115%'>The texture model is <b style='mso-bidi-font-weight:normal'><span
3061style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3062mso-hansi-theme-font:minor-latin'>cylindrical</span></b> by default; that is
3063what we want. Change the <b style='mso-bidi-font-weight:normal'><span
3064style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3065mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to <b
3066style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3067mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>8</span></b>
3068and check both <b style='mso-bidi-font-weight:normal'><span style='font-family:
3069"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3070minor-latin'>Refine texture</span></b> and <b style='mso-bidi-font-weight:normal'><span
3071style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3072mso-hansi-theme-font:minor-latin'>Show <span class=SpellE>coeff</span></span></b>.
3073The window should look like</p>
3074
3075<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3076115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45"
3077 o:spid="_x0000_i1065" type="#_x0000_t75" style='width:456pt;height:250.5pt;
3078 visibility:visible;mso-wrap-style:square'>
3079 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
3080  o:title=""/>
3081</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
3082src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
3083v:shapes="Picture_x0020_45"><![endif]></span></p>
3084
3085<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3086115%'>Then go to the <b style='mso-bidi-font-weight:normal'><span
3087style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3088mso-hansi-theme-font:minor-latin'>Data</span></b> tab, select <b
3089style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3090mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>D11</span></b>;
3091the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3092mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3093window should look like (any PWDR item will do)</p>
3094
3095<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3096115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_46"
3097 o:spid="_x0000_i1064" type="#_x0000_t75" style='width:342.75pt;height:375pt;
3098 visibility:visible;mso-wrap-style:square'>
3099 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
3100  o:title=""/>
3101</v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500
3102src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png"
3103v:shapes="Picture_x0020_46"><![endif]></span></p>
3104
3105<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3106115%'>Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3107"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3108minor-latin'>Edit/Copy flags</span></b> to have <b style='mso-bidi-font-weight:
3109normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3110minor-latin;mso-hansi-theme-font:minor-latin'>D11</span></b> refined for all
3111PWDR data sets.</p>
3112
3113<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3114115%'>Next select the <b style='mso-bidi-font-weight:normal'><span
3115style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3116mso-hansi-theme-font:minor-latin'>B19’</span></b> phase <b style='mso-bidi-font-weight:
3117normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3118minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b> tab. Then
3119select <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3120mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>6</span></b>
3121for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3122mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic
3123order</span></b> and check the two boxes as before.</p>
3124
3125<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3126115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_47"
3127 o:spid="_x0000_i1063" type="#_x0000_t75" style='width:478.5pt;height:302.25pt;
3128 visibility:visible;mso-wrap-style:square'>
3129 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
3130  o:title=""/>
3131</v:shape><![endif]--><![if !vml]><img border=0 width=638 height=403
3132src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png"
3133v:shapes="Picture_x0020_47"><![endif]></span></p>
3134
3135<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3136115%'>Then go to the <b style='mso-bidi-font-weight:normal'><span
3137style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3138mso-hansi-theme-font:minor-latin'>Data</span></b> tab for the <b
3139style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3140mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3141phase and check all 4 of the <span class=SpellE><b style='mso-bidi-font-weight:
3142normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3143minor-latin;mso-hansi-theme-font:minor-latin'>Dij</span></b></span> boxes and
3144do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3145mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3146flags</span></b> as before. The tab will look like</p>
3147
3148<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3149115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48"
3150 o:spid="_x0000_i1062" type="#_x0000_t75" style='width:370.5pt;height:375pt;
3151 visibility:visible;mso-wrap-style:square'>
3152 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
3153  o:title=""/>
3154</v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500
3155src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png"
3156v:shapes="Picture_x0020_48"><![endif]></span></p>
3157
3158<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3159115%'>Now do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3160"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3161minor-latin'>Calculate/Refine</span></b> from the main menu. The refinement
3162will finish with <span class=SpellE>Rw</span> ~27%; the 1<sup>st</sup> PWDR
3163pattern looks like</p>
3164
3165<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3166115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_49"
3167 o:spid="_x0000_i1061" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3168 visibility:visible;mso-wrap-style:square'>
3169 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
3170  o:title=""/>
3171</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3172src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png"
3173v:shapes="Picture_x0020_49"><![endif]></span></p>
3174
3175<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3176115%'>The calculated peaks for both phases are too sharp. It is likely that
3177this is a <span class=SpellE>microstrain</span> effect. Select <b
3178style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3179mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3180for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3181mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2 </span></b>phase
3182and select the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3183style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3184mso-hansi-theme-font:minor-latin'>microstrain</span></b></span> box. Then do <b
3185style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3186mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3187flags</span></b> to set it for the other PWDR data sets. Do the same for the <b
3188style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3189mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3190phase. Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3191"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3192minor-latin'>Calculate/Refine</span></b> from the main menu. The fit will be
3193substantially improved with <span class=SpellE>Rw</span> ~9.2%.</p>
3194
3195<h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 2. Finish
3196refinement and examine texture</h3>
3197
3198<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3199115%'>Looking at the individual PWDR data sets (e.g. the one for <span
3200class=SpellE>Azm</span>=20.00)</p>
3201
3202<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3203115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_50"
3204 o:spid="_x0000_i1060" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3205 visibility:visible;mso-wrap-style:square'>
3206 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
3207  o:title=""/>
3208</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3209src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png"
3210v:shapes="Picture_x0020_50"><![endif]></span></p>
3211
3212<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3213115%'>It is evident that there remains intensity differences due to texture. We
3214can increase the harmonic order to more closely fit these, however one should
3215only do this carefully. Select the Texture tab for the B2 phase; the Texture
3216tab will show</p>
3217
3218<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3219115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_18"
3220 o:spid="_x0000_i1059" type="#_x0000_t75" style='width:456pt;height:250.5pt;
3221 visibility:visible;mso-wrap-style:square'>
3222 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
3223  o:title=""/>
3224</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
3225src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png"
3226v:shapes="Picture_x0020_18"><![endif]></span></p>
3227
3228<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3229115%'>And a drawing of the 001 pole figure will be drawn. This is the very
3230typical “bulls eye” for cylindrical texture; of much more use is an inverse
3231pole figure. Select that from the Texture plot type; the plot will be redrawn</p>
3232
3233<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3234115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_52"
3235 o:spid="_x0000_i1058" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3236 visibility:visible;mso-wrap-style:square'>
3237 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
3238  o:title=""/>
3239</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3240src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png"
3241v:shapes="Picture_x0020_52"><![endif]></span></p>
3242
3243<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3244115%'>This shows the probability of reflection vectors coinciding with the
3245sample wire axis the high spots are the 111 family of reflections. We should
3246try the next higher Harmonic order (10). </p>
3247
3248<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3249115%'>Next go to the Texture tab for the B19’ phase. Again a <span
3250class=SpellE>bullseye</span> pole figure is drawn; change that to an Inverse
3251pole figure.</p>
3252
3253<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3254115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_53"
3255 o:spid="_x0000_i1057" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3256 visibility:visible;mso-wrap-style:square'>
3257 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
3258  o:title=""/>
3259</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3260src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png"
3261v:shapes="Picture_x0020_53"><![endif]></span></p>
3262
3263<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3264115%'>This phase is very strongly textured (the cursor shows 12-13 MRD at the
3265peaks) along the -140 direction. Again we want to increment the Harmonic order
3266to the next higher level (8). Again do Calculate/Refine from the main menu; the
3267<span class=SpellE>Rwp</span> has dropped to ~7.9%. One can add the atom <span
3268class=SpellE>Uiso</span> for the Ni and <span class=SpellE>Ti</span> atoms in
3269the B2 phase and the coordinates and <span class=SpellE>Uiso</span> for the
3270B19’ phase. The <span class=SpellE>Rw</span> drops a bit further to ~7.4%.
3271Finally, we can increase the harmonic order again for the B19’ phase (it is
3272very strongly textured!) to 10 and the B2 phase to 12; the final refinement
3273converged to <span class=SpellE>Rw</span> ~6.8% and the B19’ inverse pole
3274figure has peaks at ~18 MRD (Multiple of Random Distribution) and the B2 phase
3275peaks are ~7MRD.</p>
3276
3277<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3278115%'>The B19’ coefficients</p>
3279
3280<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3281115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_54"
3282 o:spid="_x0000_i1056" type="#_x0000_t75" style='width:502.5pt;height:375pt;
3283 visibility:visible;mso-wrap-style:square'>
3284 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
3285  o:title=""/>
3286</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
3287src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png"
3288v:shapes="Picture_x0020_54"><![endif]></span></p>
3289
3290<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3291115%'><span class=GramE>and</span> inverse pole figure</p>
3292
3293<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3294115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_55"
3295 o:spid="_x0000_i1055" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3296 visibility:visible;mso-wrap-style:square'>
3297 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
3298  o:title=""/>
3299</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3300src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png"
3301v:shapes="Picture_x0020_55"><![endif]></span></p>
3302
3303<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3304115%'>The B2 coefficients</p>
3305
3306<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3307115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_56"
3308 o:spid="_x0000_i1054" type="#_x0000_t75" style='width:480pt;height:267.75pt;
3309 visibility:visible;mso-wrap-style:square'>
3310 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
3311  o:title=""/>
3312</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3313src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png"
3314v:shapes="Picture_x0020_56"><![endif]></span></p>
3315
3316<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3317115%'><span class=GramE>and</span> inverse pole figure</p>
3318
3319<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3320115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_57"
3321 o:spid="_x0000_i1053" type="#_x0000_t75" style='width:525pt;height:413.25pt;
3322 visibility:visible;mso-wrap-style:square'>
3323 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
3324  o:title=""/>
3325</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551
3326src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png"
3327v:shapes="Picture_x0020_57"><![endif]></span></p>
3328
3329<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3330115%'>This completes the tutorial on Method A for doing texture analysis. It is
3331useful for a case like this one where there are very few data sets required for
3332the texture analysis. However, for the case of lower sample symmetry one must
3333several dozen or even a few hundred histograms and then the suite of parameters
3334can easily be &gt; 1000 of which only a few dozen describe the texture. This
3335leads to the next Methods for texture analysis in GSAS-II.</p>
3336
3337<h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Method B.
3338Sequential refinement &amp; texture analysis from result</h2>
3339
3340<h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Introduction</h3>
3341
3342<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3343115%'>This begins the texture analysis in much the same way as Method A except
3344that all the initial refinements are done “sequentially”, that is refinements
3345are done for the parameters associated with each powder pattern to convergence
3346in a serial fashion. In this case where there are 10 PWDR data sets, there will
3347be 10 refinements done in sequence. Parameters that span all the data (e.g.
3348lattice parameters, atom parameters &amp; texture) are not varied in this
3349sequence refinement. The effect of texture is modeled as a Preferred
3350Orientation correction to each histogram. To begin do <b style='mso-bidi-font-weight:
3351normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3352minor-latin;mso-hansi-theme-font:minor-latin'>File/Open project…</span></b> for
3353the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3354style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3355mso-hansi-theme-font:minor-latin'>NiTi.gpx</span></b></span> file created in
3356the first step and then do a <b style='mso-bidi-font-weight:normal'><span
3357style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3358mso-hansi-theme-font:minor-latin'>File/Save project as…</span></b> to save it
3359as <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3360style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3361mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight:
3362normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3363minor-latin;mso-hansi-theme-font:minor-latin'>-B</span></b>. This renames the
3364project and it should have one IMG, 10 PWDR entries and two phases of <span
3365class=SpellE>NiTi</span> (B2 and B19’).</p>
3366
3367<h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 1. Initial
3368refinement</h3>
3369
3370<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3371115%'>This begins the same way as Method A so I’ll be brief. Do the following
3372steps:</p>
3373
3374<p class=MsoListParagraphCxSpFirst style='margin-bottom:0in;margin-bottom:.0001pt;
3375mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
3376style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
3377style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
3378any <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3379mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b>
3380entry, go to <b style='mso-bidi-font-weight:normal'><span style='font-family:
3381"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3382minor-latin'>Sample Parameters</span></b> and uncheck <b style='mso-bidi-font-weight:
3383normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3384minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>.
3385Then copy the flags to the other PWDR entries.</p>
3386
3387<p class=MsoListParagraphCxSpMiddle style='margin-bottom:0in;margin-bottom:
3388.0001pt;mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
3389style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
3390style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
3391the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3392mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3393phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3394mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3395tab and check the <b style='mso-bidi-font-weight:normal'><span
3396style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3397mso-hansi-theme-font:minor-latin'>Phase fraction</span></b> box and change the <span
3398class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3399"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3400minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span
3401style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3402mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b
3403style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3404mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical
3405harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span
3406style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3407mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the
3408flag and the model to the other PWDR entries.</p>
3409
3410<p class=MsoListParagraphCxSpLast style='margin-bottom:0in;margin-bottom:.0001pt;
3411mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span
3412style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
3413style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
3414the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3415mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3416phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3417mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
3418tab and check the <b style='mso-bidi-font-weight:normal'><span
3419style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3420mso-hansi-theme-font:minor-latin'>Phase fraction box</span></b> and change the <span
3421class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3422"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3423minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span
3424style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3425mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b
3426style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3427mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical harmonics</span></b>.
3428Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3429mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3430data</span></b> to copy both the flag and the model to the other PWDR entries.</p>
3431
3432<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3433115%'>Now select <b style='mso-bidi-font-weight:normal'><span style='font-family:
3434"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3435minor-latin'>Controls</span></b> from the GSAS-II data tree</p>
3436
3437<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3438115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_1"
3439 o:spid="_x0000_i1052" type="#_x0000_t75" style='width:330.75pt;height:153.75pt;
3440 visibility:visible;mso-wrap-style:square'>
3441 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
3442  o:title=""/>
3443</v:shape><![endif]--><![if !vml]><img border=0 width=441 height=205
3444src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png"
3445v:shapes="Picture_x0020_1"><![endif]></span></p>
3446
3447<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3448115%'>Press the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3449"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3450minor-latin'>Select Data</span></b> button for <b style='mso-bidi-font-weight:
3451normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3452minor-latin;mso-hansi-theme-font:minor-latin'>Sequential Refinement</span></b>;
3453a file selection popup will appear. Do <b style='mso-bidi-font-weight:normal'><span
3454style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3455mso-hansi-theme-font:minor-latin'>Set All</span></b> and press <b
3456style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3457mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
3458The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3459mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b>
3460page will be repainted indicating that 10 data sets are selected for sequential
3461refinement.</p>
3462
3463<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3464115%'><span style='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:0in;margin-bottom:.0001pt;line-height:
3474115%'>You have the choice of starting at the last one and for copying results
3475from one to the next. We won’t do either here. Each refinement will use the
3476other controls (e.g. <b style='mso-bidi-font-weight:normal'><span
3477style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3478mso-hansi-theme-font:minor-latin'>Max cycles</span></b>) as controls. We are
3479now ready to do the 1<sup>st</sup> sequential refinement. Do <b
3480style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3481mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Sequential
3482refine</span></b> from the main menu. A progress bar popup will appear showing
3483residuals as it processes each of 10 data sets. After a few seconds the <b
3484style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3485mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refinement
3486results</span></b> popup will appear; press <b style='mso-bidi-font-weight:
3487normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3488minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to accept them. The
3489data window displays the <b style='mso-bidi-font-weight:normal'><span
3490style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3491mso-hansi-theme-font:minor-latin'>Sequential refinement results</span></b> as a
3492table.</p>
3493
3494<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3495115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3"
3496 o:spid="_x0000_i1050" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3497 visibility:visible;mso-wrap-style:square'>
3498 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
3499  o:title=""/>
3500</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3501src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png"
3502v:shapes="Picture_x0020_3"><![endif]></span></p>
3503
3504<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3505115%'>There is a row for each data set and columns for all refined parameters
3506and some derived ones along with residual and convergence indicators. The
3507residuals are not very good (we haven’t really refined much) but the
3508&#916;&#967;<sup>2</sup> column shows that convergence was achieved (NB: poor
3509convergence will be highlighted in yellow or red depending on how bad it is).</p>
3510
3511<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3512115%'>If you examine one of the PWDR entries, you’ll see that just in this
3513point in Method <span class=GramE>A</span> much of the misfit is texture and
3514perhaps peak position.</p>
3515
3516<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3517115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_4"
3518 o:spid="_x0000_i1049" type="#_x0000_t75" style='width:525pt;height:450pt;
3519 visibility:visible;mso-wrap-style:square'>
3520 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
3521  o:title=""/>
3522</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3523src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png"
3524v:shapes="Picture_x0020_4"><![endif]></span></p>
3525
3526<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3527115%'>To set these parameters, select the Data tab for the B2 phase</p>
3528
3529<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3530115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5"
3531 o:spid="_x0000_i1048" type="#_x0000_t75" style='width:381pt;height:375pt;
3532 visibility:visible;mso-wrap-style:square'>
3533 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
3534  o:title=""/>
3535</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=500
3536src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png"
3537v:shapes="Picture_x0020_5"><![endif]></span></p>
3538
3539<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3540115%'>Check the D11 box under Hydrostatic/elastic strain, set the Harmonic
3541order to 6 and check the Refine box for it (Preferred orientation). Then in two
3542steps, do Edit/Copy flags and Set All for the file selection. Then do Edit/Copy
3543selected data; that will bring up a new popup</p>
3544
3545<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3546115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_6"
3547 o:spid="_x0000_i1047" type="#_x0000_t75" style='width:240pt;height:232.5pt;
3548 visibility:visible;mso-wrap-style:square'>
3549 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
3550  o:title=""/>
3551</v:shape><![endif]--><![if !vml]><img border=0 width=320 height=310
3552src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png"
3553v:shapes="Picture_x0020_6"><![endif]></span></p>
3554
3555<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3556115%'>This allows you to select which parameters to copy data and flags. Select
3557Pref. <span class=SpellE>Ori</span>. And press OK; the file selection is next.
3558Do Set <span class=GramE>All</span> and OK to do this copy. That copies the
3559full spherical harmonics model to the other data sets. Select one to check if
3560you’d like.</p>
3561
3562<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3563115%'>Next do the same thing for the B19’ phase; here there are 4 <span
3564class=SpellE>Dij</span> parameters to check (do all of them) and use spherical
3565harmonics order 4. When done that Data window will look like</p>
3566
3567<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3568115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_7"
3569 o:spid="_x0000_i1046" type="#_x0000_t75" style='width:381pt;height:467.25pt;
3570 visibility:visible;mso-wrap-style:square'>
3571 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
3572  o:title=""/>
3573</v:shape><![endif]--><![if !vml]><img border=0 width=508 height=623
3574src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png"
3575v:shapes="Picture_x0020_7"><![endif]></span></p>
3576
3577<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3578115%'>We are now ready for the next refinement; do Calculate/Sequential refine.
3579Be careful not (by habit say) pick Refine; a warning popup will appear. After
3580it completes the Sequential refinement results shows that the fit is better but
3581convergence wasn’t quite complete.</p>
3582
3583<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3584115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8"
3585 o:spid="_x0000_i1045" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3586 visibility:visible;mso-wrap-style:square'>
3587 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
3588  o:title=""/>
3589</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3590src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png"
3591v:shapes="Picture_x0020_8"><![endif]></span></p>
3592
3593<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3594115%'>It is probably best to do another round of sequential refinement (I had
3595to do two) to get convergence. A plot of one PWDR entry gives</p>
3596
3597<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3598115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9"
3599 o:spid="_x0000_i1044" type="#_x0000_t75" style='width:525pt;height:450pt;
3600 visibility:visible;mso-wrap-style:square'>
3601 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png"
3602  o:title=""/>
3603</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3604src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png"
3605v:shapes="Picture_x0020_9"><![endif]></span></p>
3606
3607<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3608115%'>As our experience in Method A, the calculated peaks are too sharp. We
3609need to vary the <span class=SpellE>mustrain</span> parameters for both phases.
3610Go to the Data tab for each phase, check the <span class=SpellE>microstrain</span>
3611box and do Edit/Copy flags for all the data sets. Then do another
3612Calculate/Sequential refine. My Sequential refinement results showed great
3613improvement but incomplete refinement</p>
3614
3615<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3616115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10"
3617 o:spid="_x0000_i1043" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3618 visibility:visible;mso-wrap-style:square'>
3619 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
3620  o:title=""/>
3621</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3622src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png"
3623v:shapes="Picture_x0020_10"><![endif]></span></p>
3624
3625<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3626115%'>Repeating the sequential refinement (twice) gave convergence.</p>
3627
3628<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3629115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_11"
3630 o:spid="_x0000_i1042" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3631 visibility:visible;mso-wrap-style:square'>
3632 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png"
3633  o:title=""/>
3634</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3635src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png"
3636v:shapes="Picture_x0020_11"><![endif]></span></p>
3637
3638<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3639115%'>Examination of the PWDR data sets showed a fairly good fit but some
3640discrepancies (especially for <span class=SpellE>Azm</span>=20.00)</p>
3641
3642<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3643115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12"
3644 o:spid="_x0000_i1041" type="#_x0000_t75" style='width:525pt;height:450pt;
3645 visibility:visible;mso-wrap-style:square'>
3646 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
3647  o:title=""/>
3648</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3649src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png"
3650v:shapes="Picture_x0020_12"><![endif]></span></p>
3651
3652<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3653115%'>Showing that perhaps the B19’ phase needs high order spherical harmonics.
3654Select the Data tab for the B19’ phase and change the Harmonic order to 6. Then
3655do Edit/Copy selected data for <span class=SpellE>Pref.Ori</span>. <span
3656class=GramE>to</span> the other data sets. This (after few repeats) gives a
3657further improvement in the fit</p>
3658
3659<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3660115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13"
3661 o:spid="_x0000_i1040" type="#_x0000_t75" style='width:525pt;height:262.5pt;
3662 visibility:visible;mso-wrap-style:square'>
3663 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
3664  o:title=""/>
3665</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350
3666src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png"
3667v:shapes="Picture_x0020_13"><![endif]></span></p>
3668
3669<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3670115%'>This fit is now sufficient for us to proceed to the next step and
3671determine the texture of the two phases.</p>
3672
3673<h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 2. Texture
3674analysis</h3>
3675
3676<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3677115%'>During the sequential refinements done in Step 1, we fitted the profiles
3678allowing strain parameters (<span class=SpellE>Dij</span>) for peak position
3679shifts and <span class=SpellE>microstrain</span> for peak shape. We modeled the
3680intensity variation with a spherical harmonics preferred orientation
3681correction. If you select any PWDR entry from the GSAS-II data tree and pick
3682the Reflection List subentry (at the bottom) you can see the magnitude of this
3683correction for each reflection in each phase.</p>
3684
3685<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3686115%'>For the B2 phase we see</p>
3687
3688<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3689115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14"
3690 o:spid="_x0000_i1039" type="#_x0000_t75" style='width:659.25pt;height:262.5pt;
3691 visibility:visible;mso-wrap-style:square'>
3692 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
3693  o:title=""/>
3694</v:shape><![endif]--><![if !vml]><img border=0 width=879 height=350
3695src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png"
3696v:shapes="Picture_x0020_14"><![endif]></span></p>
3697
3698<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3699115%'><span class=GramE>and</span> for the B19’ phase we see</p>
3700
3701<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3702115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15"
3703 o:spid="_x0000_i1038" type="#_x0000_t75" style='width:659.25pt;height:273pt;
3704 visibility:visible;mso-wrap-style:square'>
3705 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png"
3706  o:title=""/>
3707</v:shape><![endif]--><![if !vml]><img border=0 width=879 height=364
3708src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png"
3709v:shapes="Picture_x0020_15"><![endif]></span></p>
3710
3711<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3712115%'>The preferred orientation correction is <span class=SpellE>Prfo</span>;
3713notice a few entries in red. These are nonphysical correction values (the
3714correction can’t be negative) but by in large these are small. This next step
3715uses these corrections as input data for a texture refinement. To start select
3716the Texture tab for the B2 phase; you’ll see</p>
3717
3718<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3719115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_16"
3720 o:spid="_x0000_i1037" type="#_x0000_t75" style='width:456pt;height:217.5pt;
3721 visibility:visible;mso-wrap-style:square'>
3722 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
3723  o:title=""/>
3724</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290
3725src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png"
3726v:shapes="Picture_x0020_16"><![endif]></span></p>
3727
3728<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3729115%'>Since this sample has wire texture, we’ll use the default Texture model
3730(cylindrical). Then set the Harmonic order to 12 (what we used earlier) and
3731check the Refine and Show <span class=SpellE>coeff</span> boxes. The data
3732window will be redrawn (and a blank plot will appear).</p>
3733
3734<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3735115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_17"
3736 o:spid="_x0000_i1036" type="#_x0000_t75" style='width:456pt;height:250.5pt;
3737 visibility:visible;mso-wrap-style:square'>
3738 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
3739  o:title=""/>
3740</v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334
3741src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png"
3742v:shapes="Picture_x0020_17"><![endif]></span></p>
3743
3744<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3745115%'>Do Texture/Refine texture from the menu; the window will be repainted and
3746a <span class=SpellE>bullseye</span> pole figure will appear. </p>
3747
3748<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3749115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20"
3750 o:spid="_x0000_i1035" type="#_x0000_t75" style='width:480pt;height:267.75pt;
3751 visibility:visible;mso-wrap-style:square'>
3752 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
3753  o:title=""/>
3754</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3755src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png"
3756v:shapes="Picture_x0020_20"><![endif]></span></p>
3757
3758<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3759115%'>Change the Texture plot type to Inverse pole figure to get a more useful
3760plot</p>
3761
3762<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3763115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_19"
3764 o:spid="_x0000_i1034" type="#_x0000_t75" style='width:525pt;height:450pt;
3765 visibility:visible;mso-wrap-style:square'>
3766 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png"
3767  o:title=""/>
3768</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3769src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png"
3770v:shapes="Picture_x0020_19"><![endif]></span></p>
3771
3772<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3773115%'>This is essentially the same as we obtained earlier in Method <span
3774class=GramE>A</span> (maybe not quite as strong here).</p>
3775
3776<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3777115%'>Now select the Texture tab for the B19’ phase and do the same; use
3778Harmonic order 10 as we did earlier in Method A. After setting the two flags
3779and doing Texture/Refine texture we get</p>
3780
3781<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3782115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21"
3783 o:spid="_x0000_i1033" type="#_x0000_t75" style='width:502.5pt;height:375pt;
3784 visibility:visible;mso-wrap-style:square'>
3785 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
3786  o:title=""/>
3787</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
3788src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png"
3789v:shapes="Picture_x0020_21"><![endif]></span></p>
3790
3791<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3792115%'>And a <span class=SpellE>bullseye</span> pole figure; change that to
3793Inverse pole figure to see the texture</p>
3794
3795<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3796115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_22"
3797 o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt;height:450pt;
3798 visibility:visible;mso-wrap-style:square'>
3799 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
3800  o:title=""/>
3801</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
3802src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png"
3803v:shapes="Picture_x0020_22"><![endif]></span></p>
3804
3805<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3806115%'>Again this is very similar to what we found in Method A but again not
3807quite as strong (max MRD ~13 instead of ~18).</p>
3808
3809<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3810115%'>Now do a File/Save project from the main menu; this saves the final texture
3811results done in Step 2 (you also will need it for Method C).</p>
3812
3813<h2 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Method C.
3814Sequential refinement &amp; full texture refinement</h2>
3815
3816<h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Introduction</h3>
3817
3818<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3819115%'>This uses the same approach as Method B except that after the sequential
3820refinements are finished we then fix almost all the parameters and then do a
3821final texture refinement with all the data. Thus, this is a replacement for
3822Step 2 in Method B. To begin do <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/Open project…</span></b> for the <span
3825class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3826"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3827minor-latin'>NiTi-B.gpx</span></b></span> file created in Method B and then do
3828a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3829mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Save
3830project as…</span></b> to save it as <span class=SpellE><b style='mso-bidi-font-weight:
3831normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3832minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b
3833style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3834mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-C</span></b>.
3835This renames the project and it should have one IMG, 10 PWDR entries and two
3836phases of <span class=SpellE>NiTi</span> (B2 and B19’).</p>
3837
3838<h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 1. Clearing
3839unwanted variables from sequential refinement</h3>
3840
3841<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
3842115%'>Here we want to clear refinement flags for all parameters that need not
3843be varied in a texture analysis refinement. The general rule is to not refine
3844any parameter unless we expect it to affect the peak intensities. These are
3845listed below:</p>
3846
3847<p class=MsoListParagraphCxSpFirst style='margin-bottom:0in;margin-bottom:.0001pt;
3848mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3849style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span
3850style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3851style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3852mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>:
3853as the background was fit during the sequential refinement we should fix it
3854here. Select any <b style='mso-bidi-font-weight:normal'><span style='font-family:
3855"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3856minor-latin'>PWDR</span></b> entry and choose the <b style='mso-bidi-font-weight:
3857normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3858minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b> subentry
3859for it. Clear the <b style='mso-bidi-font-weight:normal'><span
3860style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3861mso-hansi-theme-font:minor-latin'>Refine</span></b> flags and the do <b
3862style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3863mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Copy
3864flags</span></b> selecting all data sets. This will clear all background
3865refinement flags.</p>
3866
3867<p class=MsoListParagraphCxSpMiddle style='margin-bottom:0in;margin-bottom:
3868.0001pt;mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3869style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span
3870style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3871style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3872mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3873phase: we do not want to refine either the <span class=SpellE>microstrain</span>,
3874D<sub>11</sub>, or preferred orientation coefficients. Select the <b
3875style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3876mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3877phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
3878"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3879minor-latin'>Data</span></b> tab. <span class=GramE>Clear</span> the <span
3880class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3881"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3882minor-latin'>microstrain</span></b></span>, <b style='mso-bidi-font-weight:
3883normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3884minor-latin;mso-hansi-theme-font:minor-latin'>D<sub>11</sub></span></b> and <b
3885style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3886mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
3887orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
3888style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3889mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
3890avoid a lot of nasty (but harmless) messages at the start of the refinement).
3891Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3892mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3893flags</span></b> selecting all data to clear all the flags and an <b
3894style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3895mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3896selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
3897normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3898minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
3899copy the zeroed out harmonic coefficients.</p>
3900
3901<p class=MsoListParagraphCxSpLast style='margin-bottom:0in;margin-bottom:.0001pt;
3902mso-add-space:auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span
3903style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span
3904style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><b
3905style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3906mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>:
3907we do not want to refine either the <span class=SpellE>microstrain</span>, <span
3908class=SpellE>Dij</span>, or preferred orientation coefficients. Select the <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'>B19’</span></b>
3911phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family:
3912"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3913minor-latin'>Data</span></b> tab. Clear the <span class=SpellE><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'>microstrain</span></b></span>,
3916four <span class=SpellE><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'>Dij</span></b></span> and <b
3919style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3920mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred
3921orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span
3922style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3923mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will
3924avoid a lot of nasty (but harmless) messages at the start of the refinement).
3925Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3926mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3927flags</span></b> selecting all data to clear all the flags and an <b
3928style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3929mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy
3930selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight:
3931normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3932minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to
3933copy the zeroed out harmonic coefficients.</p>
3934
3935<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
3936margin-left:.25in;margin-bottom:.0001pt;line-height:115%'><o:p>&nbsp;</o:p></p>
3937
3938<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
3939margin-left:.25in;margin-bottom:.0001pt;line-height:115%'>Notice that we have
3940allowed refinement of the <b style='mso-bidi-font-weight:normal'><span
3941style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3942mso-hansi-theme-font:minor-latin'>Phase fractions</span></b>; these may change during
3943the texture refinement. Now select the <b style='mso-bidi-font-weight:normal'><span
3944style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3945mso-hansi-theme-font:minor-latin'>Texture</span></b> tab for the <b
3946style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3947mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b>
3948phase (it may still have values from the Method B).</p>
3949
3950<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
3951margin-left:.25in;margin-bottom:.0001pt;line-height:115%'><span
3952style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_23"
3953 o:spid="_x0000_i1031" type="#_x0000_t75" style='width:480pt;height:267.75pt;
3954 visibility:visible;mso-wrap-style:square'>
3955 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
3956  o:title=""/>
3957</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3958src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png"
3959v:shapes="Picture_x0020_23"><![endif]></span></p>
3960
3961<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
3962margin-left:.25in;margin-bottom:.0001pt;line-height:115%'>You can clear these
3963by setting the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3964"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3965minor-latin'>Harmonic order</span></b> to zero and then back to <b
3966style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3967mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>12</span></b>.
3968Leave the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3969mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b>
3970&amp; <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3971mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b>
3972boxes checked.</p>
3973
3974<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
3975margin-left:.25in;margin-bottom:.0001pt;line-height:115%'><span
3976style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_24"
3977 o:spid="_x0000_i1030" type="#_x0000_t75" style='width:480pt;height:267.75pt;
3978 visibility:visible;mso-wrap-style:square'>
3979 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
3980  o:title=""/>
3981</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
3982src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png"
3983v:shapes="Picture_x0020_24"><![endif]></span></p>
3984
3985<p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:0in;
3986margin-left:.25in;margin-bottom:.0001pt;line-height:115%'>Then do the same for
3987the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3988mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19’</span></b>
3989phase. Select the <b style='mso-bidi-font-weight:normal'><span
3990style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3991mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and its <b
3992style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3993mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
3994tab. <span class=GramE>Set</span> the <b style='mso-bidi-font-weight:normal'><span
3995style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3996mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero and then
3997back to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3998mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>.
3999Leave the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
4000mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b>
4001and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
4002mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b>
4003boxes checked. This completes the setup for the full texture refinement.</p>
4004
4005<h3 style='margin:0in;margin-bottom:.0001pt;line-height:115%'>Step 2. Texture
4006refinement</h3>
4007
4008<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
4009115%'>Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
4010mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
4011from the main menu; you will see the warning message</p>
4012
4013<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
4014115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_25"
4015 o:spid="_x0000_i1029" type="#_x0000_t75" style='width:363pt;height:120.75pt;
4016 visibility:visible;mso-wrap-style:square'>
4017 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
4018  o:title=""/>
4019</v:shape><![endif]--><![if !vml]><img border=0 width=484 height=161
4020src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png"
4021v:shapes="Picture_x0020_25"><![endif]></span></p>
4022
4023<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
4024115%'>In this case you do want to do a <span class=SpellE>nonsequential</span>
4025full refinement, so press the OK button. A quick look at the console will show
4026that there are 61 variables in this refinement. If yours shows more then you
4027didn’t clear all the flags in Step 1. The <b style='mso-bidi-font-weight:normal'><span
4028style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
4029mso-hansi-theme-font:minor-latin'>Sequential results</span></b> entry is
4030deleted from the GSAS-II data tree. A progress bar will show giving the
4031residuals during the refinement. When finished, select the <b style='mso-bidi-font-weight:
4032normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
4033minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> phase and its <b
4034style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
4035mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
4036tab; if the Texture plot type is still <b style='mso-bidi-font-weight:normal'><span
4037style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
4038mso-hansi-theme-font:minor-latin'>Inverse pole figure</span></b> (from Method
4039B) you should see</p>
4040
4041<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
4042115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26"
4043 o:spid="_x0000_i1028" type="#_x0000_t75" style='width:525pt;height:450pt;
4044 visibility:visible;mso-wrap-style:square'>
4045 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
4046  o:title=""/>
4047</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
4048src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png"
4049v:shapes="Picture_x0020_26"><![endif]></span></p>
4050
4051<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
4052115%'><span class=GramE>which</span> is almost identical to that from Method A.
4053The coefficients are seen in</p>
4054
4055<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
4056115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27"
4057 o:spid="_x0000_i1027" type="#_x0000_t75" style='width:480pt;height:267.75pt;
4058 visibility:visible;mso-wrap-style:square'>
4059 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
4060  o:title=""/>
4061</v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357
4062src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png"
4063v:shapes="Picture_x0020_27"><![endif]></span></p>
4064
4065<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
4066115%'>Now select the <b style='mso-bidi-font-weight:normal'><span
4067style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
4068mso-hansi-theme-font:minor-latin'>B19’</span></b> phase and its <b
4069style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
4070mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b>
4071tab; the inverse pole figure is</p>
4072
4073<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
4074115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28"
4075 o:spid="_x0000_i1026" type="#_x0000_t75" style='width:525pt;height:450pt;
4076 visibility:visible;mso-wrap-style:square'>
4077 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png"
4078  o:title=""/>
4079</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
4080src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png"
4081v:shapes="Picture_x0020_28"><![endif]></span></p>
4082
4083<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
4084115%'><span class=GramE>and</span> also almost identical to what was obtained
4085in Method A; the coefficients are seen in</p>
4086
4087<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
4088115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_58"
4089 o:spid="_x0000_i1025" type="#_x0000_t75" style='width:502.5pt;height:375pt;
4090 visibility:visible;mso-wrap-style:square'>
4091 <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
4092  o:title=""/>
4093</v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500
4094src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png"
4095v:shapes="Picture_x0020_58"><![endif]></span></p>
4096
4097<p class=MsoNormal style='margin-bottom:0in;margin-bottom:.0001pt;line-height:
4098115%'>With this Method you can add parameters (atom coordinates &amp; thermal
4099motion parameters) that could not be refined in method B. It should be clear
4100from this tutorial that in more complex textures where the data set may consist
4101of slices obtained from a suite of 2D images collected as the sample is
4102rotated, Method C will give a relatively fast determination of the texture
4103without resorting to large matrix least-squares refinements.</p>
4104
4105</div>
4106
4107</body>
4108
4109</html>
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