source: Tutorials/ParameterLimits/ParameterLimitsUse.html @ 4933

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414  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
415  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
416  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
417  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
418  <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
419  <w:LsdException Locked="false" Priority="34" QFormat="true"
420   Name="List Paragraph"/>
421  <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
422  <w:LsdException Locked="false" Priority="30" QFormat="true"
423   Name="Intense Quote"/>
424  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
425  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
426  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
427  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
428  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
429  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
430  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
431  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
432  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
433  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
434  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
435  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
436  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
437  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
438  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
439  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
440  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
441  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
442  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
443  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
444  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
445  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
446  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
447  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
448  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
449  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
450  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
451  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
452  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
453  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
454  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
455  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
456  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
457  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
458  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
459  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
460  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
461  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
462  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
463  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
464  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
465  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
466  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
467  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
468  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
469  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
470  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
471  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
472  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
473  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
474  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
475  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
476  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
477  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
478  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
479  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
480  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
481  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
482  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
483  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
484  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
485  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
486  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
487  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
488  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
489  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
490  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
491  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
492  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
493  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
494  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
495  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
496  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
497  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
498  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
499  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
500  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
501  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
502  <w:LsdException Locked="false" Priority="19" QFormat="true"
503   Name="Subtle Emphasis"/>
504  <w:LsdException Locked="false" Priority="21" QFormat="true"
505   Name="Intense Emphasis"/>
506  <w:LsdException Locked="false" Priority="31" QFormat="true"
507   Name="Subtle Reference"/>
508  <w:LsdException Locked="false" Priority="32" QFormat="true"
509   Name="Intense Reference"/>
510  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
511  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
512   UnhideWhenUsed="true" Name="Bibliography"/>
513  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
514   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
515  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
516  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
517  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
518  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
519  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
520  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
521  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
522  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
523  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
524  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
525  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
526  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
527  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
528  <w:LsdException Locked="false" Priority="46"
529   Name="Grid Table 1 Light Accent 1"/>
530  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
531  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
532  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
533  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
534  <w:LsdException Locked="false" Priority="51"
535   Name="Grid Table 6 Colorful Accent 1"/>
536  <w:LsdException Locked="false" Priority="52"
537   Name="Grid Table 7 Colorful Accent 1"/>
538  <w:LsdException Locked="false" Priority="46"
539   Name="Grid Table 1 Light Accent 2"/>
540  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
541  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
542  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
543  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
544  <w:LsdException Locked="false" Priority="51"
545   Name="Grid Table 6 Colorful Accent 2"/>
546  <w:LsdException Locked="false" Priority="52"
547   Name="Grid Table 7 Colorful Accent 2"/>
548  <w:LsdException Locked="false" Priority="46"
549   Name="Grid Table 1 Light Accent 3"/>
550  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
551  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
552  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
553  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
554  <w:LsdException Locked="false" Priority="51"
555   Name="Grid Table 6 Colorful Accent 3"/>
556  <w:LsdException Locked="false" Priority="52"
557   Name="Grid Table 7 Colorful Accent 3"/>
558  <w:LsdException Locked="false" Priority="46"
559   Name="Grid Table 1 Light Accent 4"/>
560  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
561  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
562  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
563  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
564  <w:LsdException Locked="false" Priority="51"
565   Name="Grid Table 6 Colorful Accent 4"/>
566  <w:LsdException Locked="false" Priority="52"
567   Name="Grid Table 7 Colorful Accent 4"/>
568  <w:LsdException Locked="false" Priority="46"
569   Name="Grid Table 1 Light Accent 5"/>
570  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
571  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
572  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
573  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
574  <w:LsdException Locked="false" Priority="51"
575   Name="Grid Table 6 Colorful Accent 5"/>
576  <w:LsdException Locked="false" Priority="52"
577   Name="Grid Table 7 Colorful Accent 5"/>
578  <w:LsdException Locked="false" Priority="46"
579   Name="Grid Table 1 Light Accent 6"/>
580  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
581  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
582  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
583  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
584  <w:LsdException Locked="false" Priority="51"
585   Name="Grid Table 6 Colorful Accent 6"/>
586  <w:LsdException Locked="false" Priority="52"
587   Name="Grid Table 7 Colorful Accent 6"/>
588  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
589  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
590  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
591  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
592  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
593  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
594  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
595  <w:LsdException Locked="false" Priority="46"
596   Name="List Table 1 Light Accent 1"/>
597  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
598  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
599  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
600  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
601  <w:LsdException Locked="false" Priority="51"
602   Name="List Table 6 Colorful Accent 1"/>
603  <w:LsdException Locked="false" Priority="52"
604   Name="List Table 7 Colorful Accent 1"/>
605  <w:LsdException Locked="false" Priority="46"
606   Name="List Table 1 Light Accent 2"/>
607  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
608  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
609  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
610  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
611  <w:LsdException Locked="false" Priority="51"
612   Name="List Table 6 Colorful Accent 2"/>
613  <w:LsdException Locked="false" Priority="52"
614   Name="List Table 7 Colorful Accent 2"/>
615  <w:LsdException Locked="false" Priority="46"
616   Name="List Table 1 Light Accent 3"/>
617  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
618  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
619  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
620  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
621  <w:LsdException Locked="false" Priority="51"
622   Name="List Table 6 Colorful Accent 3"/>
623  <w:LsdException Locked="false" Priority="52"
624   Name="List Table 7 Colorful Accent 3"/>
625  <w:LsdException Locked="false" Priority="46"
626   Name="List Table 1 Light Accent 4"/>
627  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
628  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
629  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
630  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
631  <w:LsdException Locked="false" Priority="51"
632   Name="List Table 6 Colorful Accent 4"/>
633  <w:LsdException Locked="false" Priority="52"
634   Name="List Table 7 Colorful Accent 4"/>
635  <w:LsdException Locked="false" Priority="46"
636   Name="List Table 1 Light Accent 5"/>
637  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
638  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
639  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
640  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
641  <w:LsdException Locked="false" Priority="51"
642   Name="List Table 6 Colorful Accent 5"/>
643  <w:LsdException Locked="false" Priority="52"
644   Name="List Table 7 Colorful Accent 5"/>
645  <w:LsdException Locked="false" Priority="46"
646   Name="List Table 1 Light Accent 6"/>
647  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
648  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
649  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
650  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
651  <w:LsdException Locked="false" Priority="51"
652   Name="List Table 6 Colorful Accent 6"/>
653  <w:LsdException Locked="false" Priority="52"
654   Name="List Table 7 Colorful Accent 6"/>
655  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
656   Name="Mention"/>
657  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
658   Name="Smart Hyperlink"/>
659  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
660   Name="Hashtag"/>
661  <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
662   Name="Unresolved Mention"/>
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777        mso-bidi-theme-font:major-bidi;
778        color:#2F5496;
779        mso-themecolor:accent1;
780        mso-themeshade:191;
781        font-weight:normal;}
782p.MsoTitle, li.MsoTitle, div.MsoTitle
783        {mso-style-priority:10;
784        mso-style-unhide:no;
785        mso-style-qformat:yes;
786        mso-style-link:"Title Char";
787        mso-style-next:Normal;
788        margin:0in;
789        margin-bottom:.0001pt;
790        mso-add-space:auto;
791        mso-pagination:widow-orphan;
792        font-size:28.0pt;
793        font-family:"Calibri Light",sans-serif;
794        mso-ascii-font-family:"Calibri Light";
795        mso-ascii-theme-font:major-latin;
796        mso-fareast-font-family:"Times New Roman";
797        mso-fareast-theme-font:major-fareast;
798        mso-hansi-font-family:"Calibri Light";
799        mso-hansi-theme-font:major-latin;
800        mso-bidi-font-family:"Times New Roman";
801        mso-bidi-theme-font:major-bidi;
802        letter-spacing:-.5pt;
803        mso-font-kerning:14.0pt;}
804p.MsoTitleCxSpFirst, li.MsoTitleCxSpFirst, div.MsoTitleCxSpFirst
805        {mso-style-priority:10;
806        mso-style-unhide:no;
807        mso-style-qformat:yes;
808        mso-style-link:"Title Char";
809        mso-style-next:Normal;
810        mso-style-type:export-only;
811        margin:0in;
812        margin-bottom:.0001pt;
813        mso-add-space:auto;
814        mso-pagination:widow-orphan;
815        font-size:28.0pt;
816        font-family:"Calibri Light",sans-serif;
817        mso-ascii-font-family:"Calibri Light";
818        mso-ascii-theme-font:major-latin;
819        mso-fareast-font-family:"Times New Roman";
820        mso-fareast-theme-font:major-fareast;
821        mso-hansi-font-family:"Calibri Light";
822        mso-hansi-theme-font:major-latin;
823        mso-bidi-font-family:"Times New Roman";
824        mso-bidi-theme-font:major-bidi;
825        letter-spacing:-.5pt;
826        mso-font-kerning:14.0pt;}
827p.MsoTitleCxSpMiddle, li.MsoTitleCxSpMiddle, div.MsoTitleCxSpMiddle
828        {mso-style-priority:10;
829        mso-style-unhide:no;
830        mso-style-qformat:yes;
831        mso-style-link:"Title Char";
832        mso-style-next:Normal;
833        mso-style-type:export-only;
834        margin:0in;
835        margin-bottom:.0001pt;
836        mso-add-space:auto;
837        mso-pagination:widow-orphan;
838        font-size:28.0pt;
839        font-family:"Calibri Light",sans-serif;
840        mso-ascii-font-family:"Calibri Light";
841        mso-ascii-theme-font:major-latin;
842        mso-fareast-font-family:"Times New Roman";
843        mso-fareast-theme-font:major-fareast;
844        mso-hansi-font-family:"Calibri Light";
845        mso-hansi-theme-font:major-latin;
846        mso-bidi-font-family:"Times New Roman";
847        mso-bidi-theme-font:major-bidi;
848        letter-spacing:-.5pt;
849        mso-font-kerning:14.0pt;}
850p.MsoTitleCxSpLast, li.MsoTitleCxSpLast, div.MsoTitleCxSpLast
851        {mso-style-priority:10;
852        mso-style-unhide:no;
853        mso-style-qformat:yes;
854        mso-style-link:"Title Char";
855        mso-style-next:Normal;
856        mso-style-type:export-only;
857        margin:0in;
858        margin-bottom:.0001pt;
859        mso-add-space:auto;
860        mso-pagination:widow-orphan;
861        font-size:28.0pt;
862        font-family:"Calibri Light",sans-serif;
863        mso-ascii-font-family:"Calibri Light";
864        mso-ascii-theme-font:major-latin;
865        mso-fareast-font-family:"Times New Roman";
866        mso-fareast-theme-font:major-fareast;
867        mso-hansi-font-family:"Calibri Light";
868        mso-hansi-theme-font:major-latin;
869        mso-bidi-font-family:"Times New Roman";
870        mso-bidi-theme-font:major-bidi;
871        letter-spacing:-.5pt;
872        mso-font-kerning:14.0pt;}
873a:link, span.MsoHyperlink
874        {mso-style-noshow:yes;
875        mso-style-priority:99;
876        color:#0563C1;
877        mso-themecolor:hyperlink;
878        text-decoration:underline;
879        text-underline:single;}
880a:visited, span.MsoHyperlinkFollowed
881        {mso-style-noshow:yes;
882        mso-style-priority:99;
883        color:#954F72;
884        mso-themecolor:followedhyperlink;
885        text-decoration:underline;
886        text-underline:single;}
887p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
888        {mso-style-priority:34;
889        mso-style-unhide:no;
890        mso-style-qformat:yes;
891        margin-top:0in;
892        margin-right:0in;
893        margin-bottom:0in;
894        margin-left:.5in;
895        margin-bottom:.0001pt;
896        mso-add-space:auto;
897        mso-pagination:widow-orphan;
898        font-size:14.0pt;
899        mso-bidi-font-size:12.0pt;
900        font-family:"Calibri",sans-serif;
901        mso-ascii-font-family:Calibri;
902        mso-ascii-theme-font:minor-latin;
903        mso-fareast-font-family:Calibri;
904        mso-fareast-theme-font:minor-latin;
905        mso-hansi-font-family:Calibri;
906        mso-hansi-theme-font:minor-latin;
907        mso-bidi-font-family:"Times New Roman";
908        mso-bidi-theme-font:minor-bidi;}
909p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
910        {mso-style-priority:34;
911        mso-style-unhide:no;
912        mso-style-qformat:yes;
913        mso-style-type:export-only;
914        margin-top:0in;
915        margin-right:0in;
916        margin-bottom:0in;
917        margin-left:.5in;
918        margin-bottom:.0001pt;
919        mso-add-space:auto;
920        mso-pagination:widow-orphan;
921        font-size:14.0pt;
922        mso-bidi-font-size:12.0pt;
923        font-family:"Calibri",sans-serif;
924        mso-ascii-font-family:Calibri;
925        mso-ascii-theme-font:minor-latin;
926        mso-fareast-font-family:Calibri;
927        mso-fareast-theme-font:minor-latin;
928        mso-hansi-font-family:Calibri;
929        mso-hansi-theme-font:minor-latin;
930        mso-bidi-font-family:"Times New Roman";
931        mso-bidi-theme-font:minor-bidi;}
932p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
933        {mso-style-priority:34;
934        mso-style-unhide:no;
935        mso-style-qformat:yes;
936        mso-style-type:export-only;
937        margin-top:0in;
938        margin-right:0in;
939        margin-bottom:0in;
940        margin-left:.5in;
941        margin-bottom:.0001pt;
942        mso-add-space:auto;
943        mso-pagination:widow-orphan;
944        font-size:14.0pt;
945        mso-bidi-font-size:12.0pt;
946        font-family:"Calibri",sans-serif;
947        mso-ascii-font-family:Calibri;
948        mso-ascii-theme-font:minor-latin;
949        mso-fareast-font-family:Calibri;
950        mso-fareast-theme-font:minor-latin;
951        mso-hansi-font-family:Calibri;
952        mso-hansi-theme-font:minor-latin;
953        mso-bidi-font-family:"Times New Roman";
954        mso-bidi-theme-font:minor-bidi;}
955p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
956        {mso-style-priority:34;
957        mso-style-unhide:no;
958        mso-style-qformat:yes;
959        mso-style-type:export-only;
960        margin-top:0in;
961        margin-right:0in;
962        margin-bottom:0in;
963        margin-left:.5in;
964        margin-bottom:.0001pt;
965        mso-add-space:auto;
966        mso-pagination:widow-orphan;
967        font-size:14.0pt;
968        mso-bidi-font-size:12.0pt;
969        font-family:"Calibri",sans-serif;
970        mso-ascii-font-family:Calibri;
971        mso-ascii-theme-font:minor-latin;
972        mso-fareast-font-family:Calibri;
973        mso-fareast-theme-font:minor-latin;
974        mso-hansi-font-family:Calibri;
975        mso-hansi-theme-font:minor-latin;
976        mso-bidi-font-family:"Times New Roman";
977        mso-bidi-theme-font:minor-bidi;}
978span.MsoIntenseEmphasis
979        {mso-style-priority:21;
980        mso-style-unhide:no;
981        mso-style-qformat:yes;
982        color:#4472C4;
983        mso-themecolor:accent1;
984        font-style:italic;}
985span.MsoIntenseReference
986        {mso-style-priority:32;
987        mso-style-unhide:no;
988        mso-style-qformat:yes;
989        font-variant:small-caps;
990        color:#4472C4;
991        mso-themecolor:accent1;
992        letter-spacing:.25pt;
993        font-weight:bold;}
994span.Heading1Char
995        {mso-style-name:"Heading 1 Char";
996        mso-style-priority:9;
997        mso-style-unhide:no;
998        mso-style-locked:yes;
999        mso-style-link:"Heading 1";
1000        mso-ansi-font-size:18.0pt;
1001        mso-bidi-font-size:16.0pt;
1002        font-family:"Calibri Light",sans-serif;
1003        mso-ascii-font-family:"Calibri Light";
1004        mso-ascii-theme-font:major-latin;
1005        mso-fareast-font-family:"Times New Roman";
1006        mso-fareast-theme-font:major-fareast;
1007        mso-hansi-font-family:"Calibri Light";
1008        mso-hansi-theme-font:major-latin;
1009        mso-bidi-font-family:"Times New Roman";
1010        mso-bidi-theme-font:major-bidi;
1011        color:#2F5496;
1012        mso-themecolor:accent1;
1013        mso-themeshade:191;
1014        text-decoration:underline;
1015        text-underline:single;}
1016span.Heading2Char
1017        {mso-style-name:"Heading 2 Char";
1018        mso-style-priority:9;
1019        mso-style-unhide:no;
1020        mso-style-locked:yes;
1021        mso-style-link:"Heading 2";
1022        mso-ansi-font-size:17.0pt;
1023        mso-bidi-font-size:13.0pt;
1024        font-family:"Times New Roman",serif;
1025        mso-ascii-font-family:"Times New Roman";
1026        mso-fareast-font-family:"Times New Roman";
1027        mso-fareast-theme-font:major-fareast;
1028        mso-hansi-font-family:"Times New Roman";
1029        mso-bidi-font-family:"Times New Roman";
1030        mso-bidi-theme-font:major-bidi;
1031        color:#2F5496;
1032        mso-themecolor:accent1;
1033        mso-themeshade:191;}
1034p.msonormal0, li.msonormal0, div.msonormal0
1035        {mso-style-name:msonormal;
1036        mso-style-unhide:no;
1037        mso-margin-top-alt:auto;
1038        margin-right:0in;
1039        mso-margin-bottom-alt:auto;
1040        margin-left:0in;
1041        mso-pagination:widow-orphan;
1042        font-size:12.0pt;
1043        font-family:"Times New Roman",serif;
1044        mso-fareast-font-family:"Times New Roman";
1045        mso-fareast-theme-font:minor-fareast;}
1046span.TitleChar
1047        {mso-style-name:"Title Char";
1048        mso-style-priority:10;
1049        mso-style-unhide:no;
1050        mso-style-locked:yes;
1051        mso-style-link:Title;
1052        mso-ansi-font-size:28.0pt;
1053        mso-bidi-font-size:28.0pt;
1054        font-family:"Calibri Light",sans-serif;
1055        mso-ascii-font-family:"Calibri Light";
1056        mso-ascii-theme-font:major-latin;
1057        mso-fareast-font-family:"Times New Roman";
1058        mso-fareast-theme-font:major-fareast;
1059        mso-hansi-font-family:"Calibri Light";
1060        mso-hansi-theme-font:major-latin;
1061        mso-bidi-font-family:"Times New Roman";
1062        mso-bidi-theme-font:major-bidi;
1063        letter-spacing:-.5pt;
1064        mso-font-kerning:14.0pt;}
1065span.SpellE
1066        {mso-style-name:"";
1067        mso-spl-e:yes;}
1068span.GramE
1069        {mso-style-name:"";
1070        mso-gram-e:yes;}
1071.MsoChpDefault
1072        {mso-style-type:export-only;
1073        mso-default-props:yes;
1074        font-size:10.0pt;
1075        mso-ansi-font-size:10.0pt;
1076        mso-bidi-font-size:10.0pt;
1077        mso-ascii-font-family:Calibri;
1078        mso-ascii-theme-font:minor-latin;
1079        mso-fareast-font-family:Calibri;
1080        mso-fareast-theme-font:minor-latin;
1081        mso-hansi-font-family:Calibri;
1082        mso-hansi-theme-font:minor-latin;
1083        mso-bidi-font-family:"Times New Roman";
1084        mso-bidi-theme-font:minor-bidi;}
1085@page WordSection1
1086        {size:8.5in 11.0in;
1087        margin:1.0in 1.0in 1.0in 1.0in;
1088        mso-header-margin:.5in;
1089        mso-footer-margin:.5in;
1090        mso-paper-source:0;}
1091div.WordSection1
1092        {page:WordSection1;}
1093 /* List Definitions */
1094 @list l0
1095        {mso-list-id:434594995;
1096        mso-list-type:hybrid;
1097        mso-list-template-ids:-804368520 67698689 67698691 67698693 67698689 67698691 67698693 67698689 67698691 67698693;}
1098@list l0:level1
1099        {mso-level-number-format:bullet;
1100        mso-level-text:;
1101        mso-level-tab-stop:none;
1102        mso-level-number-position:left;
1103        text-indent:-.25in;
1104        font-family:Symbol;}
1105@list l0:level2
1106        {mso-level-number-format:bullet;
1107        mso-level-text:o;
1108        mso-level-tab-stop:none;
1109        mso-level-number-position:left;
1110        text-indent:-.25in;
1111        font-family:"Courier New";}
1112@list l0:level3
1113        {mso-level-number-format:bullet;
1114        mso-level-text:;
1115        mso-level-tab-stop:none;
1116        mso-level-number-position:left;
1117        text-indent:-.25in;
1118        font-family:Wingdings;}
1119@list l0:level4
1120        {mso-level-number-format:bullet;
1121        mso-level-text:;
1122        mso-level-tab-stop:none;
1123        mso-level-number-position:left;
1124        text-indent:-.25in;
1125        font-family:Symbol;}
1126@list l0:level5
1127        {mso-level-number-format:bullet;
1128        mso-level-text:o;
1129        mso-level-tab-stop:none;
1130        mso-level-number-position:left;
1131        text-indent:-.25in;
1132        font-family:"Courier New";}
1133@list l0:level6
1134        {mso-level-number-format:bullet;
1135        mso-level-text:;
1136        mso-level-tab-stop:none;
1137        mso-level-number-position:left;
1138        text-indent:-.25in;
1139        font-family:Wingdings;}
1140@list l0:level7
1141        {mso-level-number-format:bullet;
1142        mso-level-text:;
1143        mso-level-tab-stop:none;
1144        mso-level-number-position:left;
1145        text-indent:-.25in;
1146        font-family:Symbol;}
1147@list l0:level8
1148        {mso-level-number-format:bullet;
1149        mso-level-text:o;
1150        mso-level-tab-stop:none;
1151        mso-level-number-position:left;
1152        text-indent:-.25in;
1153        font-family:"Courier New";}
1154@list l0:level9
1155        {mso-level-number-format:bullet;
1156        mso-level-text:;
1157        mso-level-tab-stop:none;
1158        mso-level-number-position:left;
1159        text-indent:-.25in;
1160        font-family:Wingdings;}
1161@list l1
1162        {mso-list-id:1011375071;
1163        mso-list-type:hybrid;
1164        mso-list-template-ids:-1480444908 67698689 67698691 67698693 67698689 67698691 67698693 67698689 67698691 67698693;}
1165@list l1:level1
1166        {mso-level-number-format:bullet;
1167        mso-level-text:;
1168        mso-level-tab-stop:none;
1169        mso-level-number-position:left;
1170        text-indent:-.25in;
1171        font-family:Symbol;}
1172@list l1:level2
1173        {mso-level-number-format:bullet;
1174        mso-level-text:o;
1175        mso-level-tab-stop:none;
1176        mso-level-number-position:left;
1177        text-indent:-.25in;
1178        font-family:"Courier New";}
1179@list l1:level3
1180        {mso-level-number-format:bullet;
1181        mso-level-text:;
1182        mso-level-tab-stop:none;
1183        mso-level-number-position:left;
1184        text-indent:-.25in;
1185        font-family:Wingdings;}
1186@list l1:level4
1187        {mso-level-number-format:bullet;
1188        mso-level-text:;
1189        mso-level-tab-stop:none;
1190        mso-level-number-position:left;
1191        text-indent:-.25in;
1192        font-family:Symbol;}
1193@list l1:level5
1194        {mso-level-number-format:bullet;
1195        mso-level-text:o;
1196        mso-level-tab-stop:none;
1197        mso-level-number-position:left;
1198        text-indent:-.25in;
1199        font-family:"Courier New";}
1200@list l1:level6
1201        {mso-level-number-format:bullet;
1202        mso-level-text:;
1203        mso-level-tab-stop:none;
1204        mso-level-number-position:left;
1205        text-indent:-.25in;
1206        font-family:Wingdings;}
1207@list l1:level7
1208        {mso-level-number-format:bullet;
1209        mso-level-text:;
1210        mso-level-tab-stop:none;
1211        mso-level-number-position:left;
1212        text-indent:-.25in;
1213        font-family:Symbol;}
1214@list l1:level8
1215        {mso-level-number-format:bullet;
1216        mso-level-text:o;
1217        mso-level-tab-stop:none;
1218        mso-level-number-position:left;
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1328</head>
1329
1330<body lang=EN-US link="#0563C1" vlink="#954F72" style='tab-interval:.5in'>
1331
1332<div class=WordSection1>
1333
1334<p class=MsoTitle><a name="_GoBack"></a>Use of Parameter Limits</p>
1335
1336<p class=MsoNormal><span style='mso-bidi-font-size:14.0pt;mso-bidi-font-family:
1337Calibri;mso-bidi-theme-font:minor-latin'>Note: Exercise files are found <a
1338href="data" target="_blank">here</a><o:p></o:p></span></p>
1339
1340<h1>Introduction</h1>
1341
1342<p class=MsoNormal>It is fairly common to see parameters in Rietveld fitting
1343refine to values that do not make sense, either because the values fall in a
1344range that is not physically possible or because one has <i>a priori</i> knowledge
1345about the material being studied. When this occurs, most likely one of the
1346following cases is true: </p>
1347
1348<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1349
1350<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l2 level1 lfo2'><![if !supportLists]><span
1351style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1352Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1353</span></span></span><![endif]><span dir=LTR></span>There is a significant
1354problem with the model, for example for an x-ray fit, if an O atom is placed
1355where a S atom is actually present, the <span class=SpellE>Uiso</span> will
1356refine artificially small or the occupancy much larger than unity to try to
1357compensate for the missing electrons.</p>
1358
1359<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo2'><![if !supportLists]><span
1360style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1361Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1362</span></span></span><![endif]><span dir=LTR></span>The data are simply
1363insensitive to the parameter or combination of parameters. For example, without
1364sufficient high-Q data, the effects of occupancy and <span class=SpellE>Uiso</span>
1365value can have compensating effects, so if both are refined together
1366meaningless results are obtained. Likewise, with neutron data, vanadium atoms (at
1367natural isotopic abundance) are nearly invisible due to weak coherent
1368scattering. No parameters can be fit for a V atom with neutrons.</p>
1369
1370<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo2'><![if !supportLists]><span
1371style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1372Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1373</span></span></span><![endif]><span dir=LTR></span>The parameter is
1374non-physical (such as a negative <span class=SpellE>Uiso</span> value) but
1375within 2<span lang=EL style='mso-ansi-language:EL'>σ</span> (<span lang=EL
1376style='mso-ansi-language:EL'>σ</span><span lang=EL> </span>= standard
1377uncertainty, aka <span class=SpellE>e.s.d</span>.) of a reasonable value, in
1378which case the value is not problematic, as it is experimentally
1379indistinguishable from an expected value.</p>
1380
1381<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l2 level1 lfo2'><![if !supportLists]><span
1382style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1383Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1384</span></span></span><![endif]><span dir=LTR></span><span lang=EL
1385style='mso-ansi-language:EL'>Τ</span>here is a systematic problem with the data
1386(experimental error).</p>
1387
1388<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1389
1390<p class=MsoNormal>In all these cases, the data and fit need to be reviewed by
1391a crystallographer to decide how to best determine a structural model for these
1392data. </p>
1393
1394<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1395
1396<p class=MsoNormal>A refinement implementation could be constructed that
1397constrains parameter values to be within the expected ranges, but this is a bad
1398idea as this can hide that a systematic problem that is present. This would
1399result in a wrong model, or at best a poor result being obtained. Restraints
1400are a better choice, as they make it possible to see that the refinement is
1401being skewed in a direction that does not fit the data, but care is still
1402needed to learn this. It should be noted that is also possible in GSAS-II for
1403users to supply their own functions to restrain values to fall in a specified
1404range. This can be done by supplying an appropriate expression with the
1405&quot;General&quot; restraints. As is the case with any restraint, one must
1406probe the “final result” to understand the impact of the restraint weighting on
1407the fit. If the diffraction fit improves significantly as the restraint is
1408down-weighted, it likely indicates that the data are in conflict with the
1409restraint and something is seriously wrong. <o:p></o:p></p>
1410
1411<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1412
1413<p class=MsoNormal>What GSAS-II does now implement is a mechanism where refinement
1414limits can optionally be specified for parameters. Should a variable parameter
1415refine to a value outside that range, the value is set to the upper or lower
1416bounding value and the refine flag for that parameter will be ignored in future
1417cycles of refinement. A parameter that has refined outside its limits is
1418labeled as “frozen” and will not be refined unless the “frozen” flag is removed
1419for that parameter. This prevents a refinement from continuing with unexpected
1420values. Forcing values to remain within limits may prevent a model from falling
1421into a false minimum in the early stages of fitting or can alert the user to
1422problems in the model.</p>
1423
1424<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1425
1426<p class=MsoNormal>In this exercise we will add parameter limits to the
1427refinement used in the <a
1428href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SeqRefine/SequentialTutorial.htm">Sequential
1429Fitting tutorial</a>. </p>
1430
1431<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1432
1433<h1>Step 1. Providing parameter ranges</h1>
1434
1435<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1436
1437<p class=MsoNormal>For this step, a fairly complete refinement is supplied as
1438file <span class=SpellE><span style='font-family:Courier'>SingleHistFit.gpx</span></span>.
1439Review of this shows an excellent fit, with a GOF of 1.09 (<span lang=EL
1440style='mso-ansi-language:EL'>χ</span><sup>2</sup> = 1.2), but some minor
1441problems. One is that all <span class=SpellE>Uiso</span> values are all small,
1442with values of 0.0002(2), 0.0001(2), -0.0042(5) Å<sup>2 </sup>respectively for
1443Cu, Cr and O. (Standard uncertainties are found in the <span class=SpellE><span
1444style='font-family:Courier'>SingleHistFit.lst</span></span> file.) The reason
1445for these overall low values is unclear, but is not sample absorption or
1446extinction, nor correlation between the profile, background and <span
1447class=SpellE>Uiso</span> values, since introduction of appropriate parameters
1448and fixing the <span class=SpellE>Uiso</span> values at somewhat more
1449reasonable values, say 0.01 Å<sup>2</sup>, produces significantly worse fits.
1450Noting that Cu has 29 electrons, Cr has 24 electrons and O only 8, we can
1451expect the refinement to have significantly reduced sensitivity to the O <span
1452class=SpellE>Uiso</span> value, so the slightly negative <span class=SpellE>Uiso</span>
1453value for O is a concern but not serious. </p>
1454
1455<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1456
1457<p class=MsoNormal>One other issue is that no sample broadening has been
1458introduced for the <span class=SpellE>CuO</span> impurity. To assume that this
1459phase has no sample broadening potentially skews the phase fraction.</p>
1460
1461<p class=MsoNormal align=right style='text-align:right'><span
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1487
1488<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1489
1490<h2><span class=MsoIntenseReference>1.1 Refine broadening for <span
1491class=SpellE>CoO</span><o:p></o:p></span></h2>
1492
1493<p class=MsoNormal>Without any prior knowledge, it is unclear if size or <span
1494class=SpellE>microstrain</span> broadening (or both) might be expected for <span
1495class=SpellE>CuO</span>, so initially, we might try refining both. </p>
1496
1497<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
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1501 <v:imagedata src="ParameterLimitsUse.fld/image002.png" o:title=""/>
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1504
1505<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1506
1507<p class=MsoNormal>If this is done, we see that an unreasonable (0.001 <span
1508lang=EL style='mso-ansi-language:EL'>μ</span>m) value is obtained for the size.
1509With the peaks so much wider, the phase fraction rises to an unrealistic and
1510much larger value. Note that 0.001 <span lang=EL style='mso-ansi-language:EL'>μ</span>m
1511value is the smallest that GSAS-II allows and these “hard limits” can result in
1512an unstable refinement. <span class=GramE>This results</span> are not correct
1513and should be reset. </p>
1514
1515<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1516
1517<p class=MsoNormal>One could simply reset the size parameter to the default and
1518turn off refinement, but another option is to use parameter limits to do that for
1519us. </p>
1520
1521<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1522
1523<h2><span class=MsoIntenseReference>1.2 Reset the refinement<o:p></o:p></span></h2>
1524
1525<p class=MsoNormal>Before setting parameter limits we will put the size/<span
1526class=SpellE>microstrain</span> and phase fraction back to their previous
1527values.</p>
1528
1529<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
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1535
1536<p class=MsoNormal align=right style='text-align:right'><o:p>&nbsp;</o:p></p>
1537
1538<p class=MsoNormal>Press the <u>Reset</u> button for both the <u>domain size</u>
1539and the <span class=SpellE><u>Mustrain</u></span> values. Note the size is
1540reset to the 1.0 <span lang=EL style='mso-ansi-language:EL'>μ</span>m initial
1541value and the <span class=SpellE>microstrain</span> to 1,000 (note that <span
1542class=SpellE>microstrain</span> is a fractional broadening measure, expressed
1543as <span lang=EL style='mso-ansi-language:EL'>Δ</span>Q/Q x 10<sup>6</sup>, so it
1544has no units.)<span style='mso-spacerun:yes'>  </span>Likewise, <u>reset</u>
1545the phase fraction to its approximate initial value, <u>0.03</u>.</p>
1546
1547<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
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1554
1555<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1556
1557<h2><span class=MsoIntenseReference>1.3 Set parameter limits<o:p></o:p></span></h2>
1558
1559<p class=MsoNormal>Use the Calculate<span class=GramE>/“</span>View LS <span
1560class=SpellE>parms</span>” menu command (shortcut: control-L or <span
1561style='font-family:"Cambria Math",serif;mso-bidi-font-family:"Cambria Math"'>⌘-L)
1562</span>to bring up the Least Squares Parameters window, as seen below. Note
1563this is accessible from any tree item. </p>
1564
1565<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1566yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_4" o:spid="_x0000_i1043"
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1572
1573<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1574
1575<p class=MsoNormal>The size and <span class=SpellE>microstrain</span> variables
1576are found in the Phase/<span class=SpellE>Histo</span> parameters (since there
1577is a value for every phase in each histogram), so <u>select Phase/<span
1578class=SpellE>Histo</span></u> and to further simplify choices, the <span
1579class=SpellE>CuO</span> phase (<u>phase #1</u>) only. </p>
1580
1581<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
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1588style='mso-spacerun:yes'> </span></p>
1589
1590<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1591
1592<p class=MsoNormal>Then <u>click</u> anywhere on the <u>row</u> that lists the
1593size variable for phase 1, <u><span style='font-family:Courier'>1:<span
1594class=GramE>0:Size</span>;i</span></u>, and an editing window opens, as
1595below.<span style='mso-spacerun:yes'>  </span></p>
1596
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1603src="ParameterLimitsUse.fld/image006.png" v:shapes="Picture_x0020_6"><![endif]></span></p>
1604
1605<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1606
1607<p class=MsoNormal>The reasonable range for the size requires some thought, but
1608with a minor component, even though the resolution of the instrument would
1609likely allow better, 2 <span lang=EL style='mso-ansi-language:EL'>μ</span>m is
1610a good upper limit and for a lower limit, 0.1 <span lang=EL style='mso-ansi-language:
1611EL'>μ</span>m is probably a good number, though for this purpose a larger
1612number could be used. <u>Press</u> the “<u>Add Lower limit</u>” and “<u>Add
1613Upper limit</u>” buttons, and <u>add</u> the specified <u>values</u>. </p>
1614
1615<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1616yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_7" o:spid="_x0000_i1040"
1617 type="#_x0000_t75" style='width:380pt;height:158pt;visibility:visible;
1618 mso-wrap-style:square'>
1619 <v:imagedata src="ParameterLimitsUse.fld/image007.png" o:title=""/>
1620</v:shape><![endif]--><![if !vml]><img border=0 width=380 height=158
1621src="ParameterLimitsUse.fld/image007.png" v:shapes="Picture_x0020_7"><![endif]></span></p>
1622
1623<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1624
1625<p class=MsoNormal>It will not have any effect in this particular refinement,
1626but adding limits from 1000 to 20,000 for <span class=SpellE>microstrain</span>
1627(variable <span style='font-family:Courier'>1:<span class=GramE>0:Mustrain</span>;i</span>),
1628would also make sense to constrain that variable to a reasonable range. </p>
1629
1630<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1631yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10" o:spid="_x0000_i1039"
1632 type="#_x0000_t75" style='width:559pt;height:240pt;visibility:visible;
1633 mso-wrap-style:square'>
1634 <v:imagedata src="ParameterLimitsUse.fld/image008.png" o:title=""/>
1635</v:shape><![endif]--><![if !vml]><img border=0 width=559 height=240
1636src="ParameterLimitsUse.fld/image008.png" v:shapes="Picture_x0020_10"><![endif]></span></p>
1637
1638<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1639
1640<h2><span class=MsoIntenseReference>1.4 Redo the refinement with limits in
1641place</span><b><span style='font-variant:small-caps;color:#4472C4;mso-themecolor:
1642accent1;letter-spacing:.25pt'><o:p></o:p></span></b></h2>
1643
1644<p class=MsoNormal>After the limits are set, <u>start a refinement</u> (Calculate/Refine
1645menu or shortcut: control-R or <span style='font-family:"Cambria Math",serif;
1646mso-bidi-font-family:"Cambria Math"'>⌘-</span>R). When this is done with limits
1647in place, a new message will show up in the refinement results showing that a
1648variable has been frozen:</p>
1649
1650<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1651yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_11" o:spid="_x0000_i1038"
1652 type="#_x0000_t75" style='width:270pt;height:170pt;visibility:visible;
1653 mso-wrap-style:square'>
1654 <v:imagedata src="ParameterLimitsUse.fld/image009.png" o:title=""/>
1655</v:shape><![endif]--><![if !vml]><img border=0 width=270 height=170
1656src="ParameterLimitsUse.fld/image009.png" v:shapes="Picture_x0020_11"><![endif]></span></p>
1657
1658<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1659
1660<p class=MsoNormal>Likewise, revisiting the Least Squares Parameters window, as
1661before, will now show that the size parameter has been set at the minimum value
1662and this variable is now flagged as frozen with an F in the 3<sup>rd</sup>
1663column, meaning that it will not be refined. Note that the rows of parameters that
1664are frozen are also highlighted in yellow. </p>
1665
1666<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1667yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12" o:spid="_x0000_i1037"
1668 type="#_x0000_t75" style='width:336pt;height:222pt;visibility:visible;
1669 mso-wrap-style:square'>
1670 <v:imagedata src="ParameterLimitsUse.fld/image010.png" o:title=""/>
1671</v:shape><![endif]--><![if !vml]><img border=0 width=336 height=222
1672src="ParameterLimitsUse.fld/image010.png" v:shapes="Picture_x0020_12"><![endif]></span></p>
1673
1674<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1675
1676<h2><span class=MsoIntenseReference>1.5 Final considerations</span></h2>
1677
1678<p class=MsoNormal>This has demonstrated how parameters limits are implemented.
1679In fact, for this histogram, once the refinement of the phase fraction and the <span
1680class=SpellE>microstrain</span> have settled into reasonable values, the freeze
1681on the size broadening can be released and then the parameter will refine to
1682yield a reasonable value. </p>
1683
1684<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1685
1686<p class=MsoNormal>There are two ways to release a frozen parameter. One is by
1687clicking on the row of the now-frozen parameter the Least Squares Parameters
1688window, where a new button is now present to remove the variable from the list
1689of frozen parameters. </p>
1690
1691<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1692yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13" o:spid="_x0000_i1036"
1693 type="#_x0000_t75" style='width:326pt;height:135pt;visibility:visible;
1694 mso-wrap-style:square'>
1695 <v:imagedata src="ParameterLimitsUse.fld/image011.png" o:title=""/>
1696</v:shape><![endif]--><![if !vml]><img border=0 width=326 height=135
1697src="ParameterLimitsUse.fld/image011.png" v:shapes="Picture_x0020_13"><![endif]></span></p>
1698
1699<p class=MsoNormal>The other way is that all frozen variables can be released
1700from the Controls tree item. </p>
1701
1702<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1703yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15" o:spid="_x0000_i1035"
1704 type="#_x0000_t75" style='width:341pt;height:106pt;visibility:visible;
1705 mso-wrap-style:square'>
1706 <v:imagedata src="ParameterLimitsUse.fld/image014.png" o:title=""/>
1707</v:shape><![endif]--><![if !vml]><img border=0 width=341 height=106
1708src="ParameterLimitsUse.fld/image014.png" v:shapes="Picture_x0020_15"><![endif]></span></p>
1709
1710<h1><o:p><span style='text-decoration:none'>&nbsp;</span></o:p></h1>
1711
1712<h1>Step 2. Sequential Fitting with Limits</h1>
1713
1714<p class=MsoNormal align=right style='text-align:right'><o:p>&nbsp;</o:p></p>
1715
1716<p class=MsoNormal>Parameter limits show an even greater value in sequential fitting,
1717where many thousands of parameters may be varied (sometimes more), since the
1718same parameter may be repeated for many histograms. In this exercise we will
1719see how to use parameter limits in a sequential refinement. </p>
1720
1721<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1722
1723<p class=MsoNormal>A starting point for a sequential fit is supplied as file <span
1724class=SpellE><span style='font-family:Courier'>AllDataStart.gpx</span></span><span
1725style='font-family:Courier'>,</span> which has the final results from Step 1
1726(where the frozen size variable has been freed). A large number of variables
1727have been turned off so that an initial fit can be used to account for the
1728changes in lattice parameters due to temperature and background, before
1729allowing any other parameters to vary. These are the steps that were performed
1730for to create this file:</p>
1731
1732<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo3'><![if !supportLists]><span
1733style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1734Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1735</span></span></span><![endif]><span dir=LTR></span>The additional 16 datasets were
1736imported. </p>
1737
1738<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo3'><![if !supportLists]><span
1739style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1740Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1741</span></span></span><![endif]><span dir=LTR></span>For CuCr<sub>2</sub>O<sub>4</sub>:
1742stop refining the cell, start refining the <span class=SpellE>D<sub>jj</sub></span>
1743(Hydrostatic strain) terms; do not refine any size or <span class=SpellE>microstrain</span>
1744terms. Turn off XU (position &amp; <span class=SpellE>U<sub>iso</sub></span>) refinement
1745for atoms</p>
1746
1747<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo3'><![if !supportLists]><span
1748style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1749Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1750</span></span></span><![endif]><span dir=LTR></span>For <span class=SpellE>CuO</span>:
1751stop refining the cell, start refining the <span class=SpellE>D<sub>jj</sub></span>
1752(Hydrostatic strain), but not the D13 term (related to the <span lang=EL
1753style='mso-ansi-language:EL'>β</span> angle); do not refine phase fraction, size
1754or <span class=SpellE>microstrain</span> terms.</p>
1755
1756<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo3'><![if !supportLists]><span
1757style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1758Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1759</span></span></span><![endif]><span dir=LTR></span>For background, do not
1760refine the background peak’s position or width. </p>
1761
1762<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo3'><![if !supportLists]><span
1763style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1764Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1765</span></span></span><![endif]><span dir=LTR></span>For sample parameters, do
1766not refine the sample displacement. </p>
1767
1768<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo3'><![if !supportLists]><span
1769style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1770Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1771</span></span></span><![endif]><span dir=LTR></span>Copy the parameters: Under
1772the main histogram tree item use Commands<span class=GramE>/“</span>Copy <span
1773class=SpellE>params</span>” to copy data limits, background, sample <span
1774class=SpellE>param</span>. flags, etc. from histogram 0 to the rest.</p>
1775
1776<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo3'><![if !supportLists]><span
1777style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1778Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1779</span></span></span><![endif]><span dir=LTR></span>For both phases, use “Copy Data”
1780in the Phases Data tab to duplicate the fit values as the initial values.</p>
1781
1782<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l1 level1 lfo3'><![if !supportLists]><span
1783style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1784Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1785</span></span></span><![endif]><span dir=LTR></span>Controls: set maximum
1786cycles to 10; select all 17 datasets for sequential refinement and set the “Copy
1787results to next histogram” flag.</p>
1788
1789<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1790
1791<h2><span class=MsoIntenseReference>2.1 Set <span class=SpellE>U<sub>iso</sub></span>
1792parameter limits<o:p></o:p></span></h2>
1793
1794<p class=MsoNormal>Here we will set limits on the size and <span class=SpellE>microstrain</span>
1795parameters in all histograms, as well as set a lower limit for the <span
1796class=SpellE>U<sub>iso</sub></span> values. </p>
1797
1798<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1799
1800<p class=MsoNormal>Open the Least Squares Parameters window (Calculate<span
1801class=GramE>/“</span><u>View LS <span class=SpellE>parms</span></u>” menu
1802command or control-L/<span style='font-family:"Cambria Math",serif;mso-bidi-font-family:
1803"Cambria Math"'>⌘-</span>L). Since none of the parameters to get limits are
1804currently being refined, we will need to set to view all parameters rather than
1805only refined parameters in the “Refinement status” radio buttons and then select
1806the specific parameters. </p>
1807
1808<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1809
1810<p class=MsoNormal>Let’s start with the <span class=SpellE>Uiso</span> value,
1811which is a phase parameter and has variables named as <span class=GramE><i>p</i><span
1812style='font-family:Courier'>::</span></span><span class=SpellE><span
1813style='font-family:Courier'>AUiso:</span><i>a</i></span>. In <u>Parameter type</u>
1814select <u>Phase</u>; then select Parameter <span class=SpellE>AUiso</span>; and
1815finally, the “<u>Refinement status</u><u>All</u> radio button. The <span
1816class=SpellE>Uiso</span> parameters for the five atoms across the two phases are
1817shown, as below. </p>
1818
1819<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1820
1821<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1822yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21" o:spid="_x0000_i1034"
1823 type="#_x0000_t75" style='width:362pt;height:198pt;visibility:visible;
1824 mso-wrap-style:square'>
1825 <v:imagedata src="ParameterLimitsUse.fld/image003.png" o:title=""/>
1826</v:shape><![endif]--><![if !vml]><img border=0 width=362 height=198
1827src="ParameterLimitsUse.fld/image003.png" v:shapes="Picture_x0020_21"><![endif]></span><span
1828style='mso-spacerun:yes'> </span></p>
1829
1830<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1831
1832<p class=MsoNormal><u>Click</u> anywhere <u>in the row</u> for any of the atoms
1833in the CuCr<sub>2</sub>O<sub>4</sub> (<u>phase #0</u>) in the window shown
1834above and, as in step 1, a window opens for that parameter, as seen below: <o:p></o:p></p>
1835
1836<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1837yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_22" o:spid="_x0000_i1033"
1838 type="#_x0000_t75" style='width:330pt;height:110pt;visibility:visible;
1839 mso-wrap-style:square'>
1840 <v:imagedata src="ParameterLimitsUse.fld/image019.png" o:title=""/>
1841</v:shape><![endif]--><![if !vml]><img border=0 width=330 height=110
1842src="ParameterLimitsUse.fld/image019.png" v:shapes="Picture_x0020_22"><![endif]></span></p>
1843
1844<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1845
1846<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1847
1848<p class=MsoNormal>In that window, <u>click</u> on the “<u>Add Lower limit</u>
1849button and the window changes, as shown below. In that window, <u>set</u> the <u>limit</u>
1850to <u>0.0</u>. Also set “<u>Match all atoms</u>” so that the limit is applied
1851to all atoms in that phase. </p>
1852
1853<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1854yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_23" o:spid="_x0000_i1032"
1855 type="#_x0000_t75" style='width:328pt;height:118pt;visibility:visible;
1856 mso-wrap-style:square'>
1857 <v:imagedata src="ParameterLimitsUse.fld/image020.png" o:title=""/>
1858</v:shape><![endif]--><![if !vml]><img border=0 width=328 height=118
1859src="ParameterLimitsUse.fld/image020.png" v:shapes="Picture_x0020_23"><![endif]></span><span
1860style='mso-spacerun:yes'> </span></p>
1861
1862<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1863
1864<p class=MsoNormal>After pressing OK, note that the limits are now seen on the View
1865Parameters window for the three intended atoms, as below:</p>
1866
1867<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1868yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20" o:spid="_x0000_i1031"
1869 type="#_x0000_t75" style='width:354pt;height:201pt;visibility:visible;
1870 mso-wrap-style:square'>
1871 <v:imagedata src="ParameterLimitsUse.fld/image018.png" o:title=""/>
1872</v:shape><![endif]--><![if !vml]><img border=0 width=354 height=201
1873src="ParameterLimitsUse.fld/image018.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
1874
1875<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1876
1877<h2><span class=MsoIntenseReference>2.2 Modify Size/<span class=SpellE>microstrain</span>
1878parameter limits<o:p></o:p></span></h2>
1879
1880<p class=MsoNormal>The limits set previously for crystallite size and <span
1881lang=EL style='mso-ansi-language:EL'>μ</span>strain were previously set only
1882for the first histogram. We want to set them for all histograms. </p>
1883
1884<p class=MsoNormal>Switch to Parameter type <u>Phase/<span class=SpellE>Histo</span></u>;
1885as before the “<u>Refinement status</u>” radio button needs to be <u>All</u>; <u>Select</u>
1886Phase <u>1</u> (<span class=SpellE>CuO</span>) and for Parameter name, select “<span
1887class=SpellE><span class=GramE><span style='font-family:Courier'>Size;i</span></span></span>
1888(<span class=SpellE><span style='font-family:Courier'>i</span></span> for
1889isotropic). The window should appear as below:</p>
1890
1891<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1892yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26" o:spid="_x0000_i1030"
1893 type="#_x0000_t75" style='width:309pt;height:203pt;visibility:visible;
1894 mso-wrap-style:square'>
1895 <v:imagedata src="ParameterLimitsUse.fld/image021.png" o:title=""/>
1896</v:shape><![endif]--><![if !vml]><img border=0 width=309 height=203
1897src="ParameterLimitsUse.fld/image021.png" v:shapes="Picture_x0020_26"><![endif]></span><span
1898style='mso-spacerun:yes'> </span></p>
1899
1900<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1901
1902<p class=MsoNormal>To extend the limits to all histograms, click anywhere in
1903the first row, so that the window below opens:</p>
1904
1905<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1906yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27" o:spid="_x0000_i1029"
1907 type="#_x0000_t75" style='width:312pt;height:128pt;visibility:visible;
1908 mso-wrap-style:square'>
1909 <v:imagedata src="ParameterLimitsUse.fld/image022.png" o:title=""/>
1910</v:shape><![endif]--><![if !vml]><img border=0 width=312 height=128
1911src="ParameterLimitsUse.fld/image022.png" v:shapes="Picture_x0020_27"><![endif]></span></p>
1912
1913<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1914
1915<p class=MsoNormal>Click on the <u>two</u> “<u>Match all histograms</u>
1916buttons and <u>OK</u> and the limits now apply to all histograms:</p>
1917
1918<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
1919yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28" o:spid="_x0000_i1028"
1920 type="#_x0000_t75" style='width:320pt;height:211pt;visibility:visible;
1921 mso-wrap-style:square'>
1922 <v:imagedata src="ParameterLimitsUse.fld/image023.png" o:title=""/>
1923</v:shape><![endif]--><![if !vml]><img border=0 width=320 height=211
1924src="ParameterLimitsUse.fld/image023.png" v:shapes="Picture_x0020_28"><![endif]></span></p>
1925
1926<p class=MsoNormal align=right style='text-align:right'><o:p>&nbsp;</o:p></p>
1927
1928<p class=MsoNormal><u>Repeat</u> the above for the <u></u><span class=SpellE><span
1929class=GramE><u><span style='font-family:Courier'>Mustrain;i</span></u></span></span><u>
1930parameter</u> extending that to <u>all histograms</u>. </p>
1931
1932<h2><span class=MsoIntenseReference><o:p>&nbsp;</o:p></span></h2>
1933
1934<h2><span class=MsoIntenseReference>2.3 Refinements<o:p></o:p></span></h2>
1935
1936<p class=MsoNormal><span class=MsoIntenseReference>A)</span> For the first
1937sequential refinement, no additional parameters need to be added to the
1938refinement. Use <u>Calculate<span class=GramE>/“</span>Sequential Refine”</u>
1939(or Control-R/<span style='font-family:"Cambria Math",serif;mso-bidi-font-family:
1940"Cambria Math"'>⌘-</span>L) to start the fitting. </p>
1941
1942<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1943
1944<p class=MsoNormal><span class=MsoIntenseReference>B)</span> For the second sequential
1945refinement add the following parameters:</p>
1946
1947<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span
1948style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1949Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1950</span></span></span><![endif]><span dir=LTR></span>In one histogram, add the <u>Sample
1951X</u> displacement <u>refine</u> flag; Use Command<span class=GramE>/“</span><u>Copy
1952Flags</u>” to copy this setting to all histograms.</p>
1953
1954<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span
1955style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1956Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1957</span></span></span><![endif]><span dir=LTR></span>In the <u>CuCr2O4 phas</u>e
1958in the <u>Data tab</u>, turn on refinement of the <u>size</u> and the <u>two <span
1959class=SpellE>microstrain</span></u> flags. Use “Edit Phase”<span class=GramE>/“</span><u>Copy
1960Flags</u>” to copy this setting to all histograms.</p>
1961
1962<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span
1963style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1964Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1965</span></span></span><![endif]><span dir=LTR></span>In the <span class=SpellE><u>CuO</u></span><u>
1966phas</u>e in the <u>Data tab</u>, turn on refinement of the <u>Phase fraction </u>flag.
1967Use “Edit Phase”<span class=GramE>/“</span><u>Copy Flags</u>” to copy this
1968setting to all histograms.</p>
1969
1970<p class=MsoNormal style='margin-left:.25in'>Use <u>Calculate<span class=GramE>/“</span>Sequential
1971Refine”</u> (or Control-R/<span style='font-family:"Cambria Math",serif;
1972mso-bidi-font-family:"Cambria Math"'>⌘-</span>L) to start the fitting again.<o:p></o:p></p>
1973
1974<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1975
1976<p class=MsoNormal><span class=MsoIntenseReference>C)</span> For the third sequential
1977refinement we will add parameters that have limits:<o:p></o:p></p>
1978
1979<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span
1980style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1981Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1982</span></span></span><![endif]><span dir=LTR></span>In the <u>CuCr2O4 phas</u>e
1983in the <u>Atoms tab</u>, turn on refinement of the <u>XU</u> flags for all
1984atoms. </p>
1985
1986<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo4'><![if !supportLists]><span
1987style='font-family:Symbol;mso-fareast-font-family:Symbol;mso-bidi-font-family:
1988Symbol'><span style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1989</span></span></span><![endif]><span dir=LTR></span>In the <span class=SpellE><u>CuO</u></span><u>
1990phas</u>e in the <u>Data tab</u>, turn on refinement of the <u>Phase fraction </u>flag.
1991Use “Edit Phase”<span class=GramE>/“</span><u>Copy Flags</u>” to copy this
1992setting to all histograms.</p>
1993
1994<p class=MsoNormal style='margin-left:.25in'>Use <u>Calculate<span class=GramE>/“</span>Sequential
1995Refine”</u> (or Control-R/<span style='font-family:"Cambria Math",serif;
1996mso-bidi-font-family:"Cambria Math"'>⌘-</span>L) to start the fitting again.
1997Note that after this refinement a number of parameters are noted as frozen:<o:p></o:p></p>
1998
1999<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2000
2001<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
2002yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_29" o:spid="_x0000_i1027"
2003 type="#_x0000_t75" style='width:251pt;height:137pt;visibility:visible;
2004 mso-wrap-style:square'>
2005 <v:imagedata src="ParameterLimitsUse.fld/image015.png" o:title=""/>
2006</v:shape><![endif]--><![if !vml]><img border=0 width=251 height=137
2007src="ParameterLimitsUse.fld/image015.png" v:shapes="Picture_x0020_29"><![endif]></span></p>
2008
2009<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2010
2011<p class=MsoNormal>Also, a new column appears listing the number of frozen
2012variables in the sequential results table.</p>
2013
2014<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
2015yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_30" o:spid="_x0000_i1026"
2016 type="#_x0000_t75" style='width:365pt;height:224pt;visibility:visible;
2017 mso-wrap-style:square'>
2018 <v:imagedata src="ParameterLimitsUse.fld/image016.png" o:title=""/>
2019</v:shape><![endif]--><![if !vml]><img border=0 width=365 height=224
2020src="ParameterLimitsUse.fld/image016.png" v:shapes="Picture_x0020_30"><![endif]></span></p>
2021
2022<p class=MsoNormal align=right style='text-align:right'><o:p>&nbsp;</o:p></p>
2023
2024<p class=MsoNormal>Resting the mouse above a cell in the table where a
2025parameter is frozen will show that rather than an uncertainty (<span
2026class=SpellE>e.s.d</span>.). </p>
2027
2028<p class=MsoNormal align=right style='text-align:right'><span style='mso-no-proof:
2029yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_31" o:spid="_x0000_i1025"
2030 type="#_x0000_t75" style='width:112pt;height:158pt;visibility:visible;
2031 mso-wrap-style:square'>
2032 <v:imagedata src="ParameterLimitsUse.fld/image017.png" o:title=""/>
2033</v:shape><![endif]--><![if !vml]><img border=0 width=112 height=158
2034src="ParameterLimitsUse.fld/image017.png" v:shapes="Picture_x0020_31"><![endif]></span></p>
2035
2036<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2037
2038<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2039
2040<h2><span class=MsoIntenseReference>2.4 Finishing up<o:p></o:p></span></h2>
2041
2042<p class=MsoNormal>Based on these results, it is clear that size and <span
2043lang=EL style='mso-ansi-language:EL'>μ</span>strain cannot be refined for the <span
2044class=SpellE>CuO</span> minor impurity and the fluctuations in this are causing
2045the <span lang=EL style='mso-ansi-language:EL'>μ</span>strain and phase
2046fraction values to vary unreliably. Reset any frozen <span lang=EL
2047style='mso-ansi-language:EL'>μ</span>strain variables in the Least Squares
2048Parameter viewer. Set reasonable values for size and <span lang=EL
2049style='mso-ansi-language:EL'>μ</span>strain using the results in the first histogram
2050and turn off the size refine flag. Using “Copy Selected Data” copy the Scale,
2051Size and <span class=SpellE>Mustrain</span> to all other histograms and repeat
2052the refinement. </p>
2053
2054<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2055
2056<p class=MsoNormal>The O atoms now have their <span class=SpellE>Uiso</span>
2057values fixed at 0.0 at lower temperatures, but these values do refine as the
2058temperature increases. Weight fraction of <span class=SpellE>CuO</span> <span
2059class=GramE>and <span style='mso-spacerun:yes'> </span><span lang=EL
2060style='mso-ansi-language:EL'>μ</span></span>strain values now vary reasonably
2061smoothly (considering uncertainties). A second sequential fit causes the fit to
2062converge well, as noted by small changes <span class=GramE>in <span
2063style='mso-spacerun:yes'> </span><span class=SpellE><span lang=EL
2064style='mso-ansi-language:EL'>Δχ</span></span></span><sup>2</sup>. The final
2065result is provided as file <span class=SpellE><span style='font-family:Courier'>SeqFit.gpx</span></span>,
2066though one could contemplate adding a few more parameters to the refinement,
2067such as the width and position of the background peak and the <span
2068class=SpellE>CuO</span> D13 variable. The <span class=SpellE><span
2069style='font-family:Courier'>SeqFit.lst</span></span> file shows the final
2070goodness-of-fit values (which range from 1.0 to 1.2, corresponding to a maximum
2071reduced <span lang=EL style='mso-ansi-language:EL'>χ</span><sup>2</sup> value
2072of 1.4, so there is very little improvement to improve these models). Likewise,
2073the variables that are frozen are shown in the .<span class=SpellE>lst</span>
2074file as well. </p>
2075
2076</div>
2077
2078</body>
2079
2080</html>
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