source: Tutorials/SimpleMagnetic/SimpleMagnetic.htm @ 3559

Last change on this file since 3559 was 3559, checked in by toby, 3 years ago

revise tutorial web page & remove remaining refs to Exercises directory

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414  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
415  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
416  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
417  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
418  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
419  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
420  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
421  <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
422  <w:LsdException Locked="false" Priority="34" QFormat="true"
423   Name="List Paragraph"/>
424  <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
425  <w:LsdException Locked="false" Priority="30" QFormat="true"
426   Name="Intense Quote"/>
427  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
428  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
429  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
430  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
431  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
432  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
433  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
434  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
435  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
436  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
437  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
438  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
439  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
440  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
441  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
442  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
443  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
444  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
445  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
446  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
447  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
448  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
449  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
450  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
451  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
452  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
453  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
454  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
455  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
456  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
457  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
458  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
459  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
460  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
461  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
462  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
463  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
464  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
465  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
466  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
467  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
468  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
469  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
470  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
471  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
472  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
473  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
474  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
475  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
476  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
477  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
478  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
479  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
480  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
481  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
482  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
483  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
484  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
485  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
486  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
487  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
488  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
489  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
490  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
491  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
492  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
493  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
494  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
495  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
496  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
497  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
498  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
499  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
500  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
501  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
502  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
503  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
504  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
505  <w:LsdException Locked="false" Priority="19" QFormat="true"
506   Name="Subtle Emphasis"/>
507  <w:LsdException Locked="false" Priority="21" QFormat="true"
508   Name="Intense Emphasis"/>
509  <w:LsdException Locked="false" Priority="31" QFormat="true"
510   Name="Subtle Reference"/>
511  <w:LsdException Locked="false" Priority="32" QFormat="true"
512   Name="Intense Reference"/>
513  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
514  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
515   UnhideWhenUsed="true" Name="Bibliography"/>
516  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
517   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
518  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
519  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
520  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
521  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
522  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
523  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
524  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
525  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
526  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
527  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
528  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
529  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
530  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
531  <w:LsdException Locked="false" Priority="46"
532   Name="Grid Table 1 Light Accent 1"/>
533  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
534  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
535  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
536  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
537  <w:LsdException Locked="false" Priority="51"
538   Name="Grid Table 6 Colorful Accent 1"/>
539  <w:LsdException Locked="false" Priority="52"
540   Name="Grid Table 7 Colorful Accent 1"/>
541  <w:LsdException Locked="false" Priority="46"
542   Name="Grid Table 1 Light Accent 2"/>
543  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
544  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
545  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
546  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
547  <w:LsdException Locked="false" Priority="51"
548   Name="Grid Table 6 Colorful Accent 2"/>
549  <w:LsdException Locked="false" Priority="52"
550   Name="Grid Table 7 Colorful Accent 2"/>
551  <w:LsdException Locked="false" Priority="46"
552   Name="Grid Table 1 Light Accent 3"/>
553  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
554  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
555  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
556  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
557  <w:LsdException Locked="false" Priority="51"
558   Name="Grid Table 6 Colorful Accent 3"/>
559  <w:LsdException Locked="false" Priority="52"
560   Name="Grid Table 7 Colorful Accent 3"/>
561  <w:LsdException Locked="false" Priority="46"
562   Name="Grid Table 1 Light Accent 4"/>
563  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
564  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
565  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
566  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
567  <w:LsdException Locked="false" Priority="51"
568   Name="Grid Table 6 Colorful Accent 4"/>
569  <w:LsdException Locked="false" Priority="52"
570   Name="Grid Table 7 Colorful Accent 4"/>
571  <w:LsdException Locked="false" Priority="46"
572   Name="Grid Table 1 Light Accent 5"/>
573  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
574  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
575  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
576  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
577  <w:LsdException Locked="false" Priority="51"
578   Name="Grid Table 6 Colorful Accent 5"/>
579  <w:LsdException Locked="false" Priority="52"
580   Name="Grid Table 7 Colorful Accent 5"/>
581  <w:LsdException Locked="false" Priority="46"
582   Name="Grid Table 1 Light Accent 6"/>
583  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
584  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
585  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
586  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
587  <w:LsdException Locked="false" Priority="51"
588   Name="Grid Table 6 Colorful Accent 6"/>
589  <w:LsdException Locked="false" Priority="52"
590   Name="Grid Table 7 Colorful Accent 6"/>
591  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
592  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
593  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
594  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
595  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
596  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
597  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
598  <w:LsdException Locked="false" Priority="46"
599   Name="List Table 1 Light Accent 1"/>
600  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
601  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
602  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
603  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
604  <w:LsdException Locked="false" Priority="51"
605   Name="List Table 6 Colorful Accent 1"/>
606  <w:LsdException Locked="false" Priority="52"
607   Name="List Table 7 Colorful Accent 1"/>
608  <w:LsdException Locked="false" Priority="46"
609   Name="List Table 1 Light Accent 2"/>
610  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
611  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
612  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
613  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
614  <w:LsdException Locked="false" Priority="51"
615   Name="List Table 6 Colorful Accent 2"/>
616  <w:LsdException Locked="false" Priority="52"
617   Name="List Table 7 Colorful Accent 2"/>
618  <w:LsdException Locked="false" Priority="46"
619   Name="List Table 1 Light Accent 3"/>
620  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
621  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
622  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
623  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
624  <w:LsdException Locked="false" Priority="51"
625   Name="List Table 6 Colorful Accent 3"/>
626  <w:LsdException Locked="false" Priority="52"
627   Name="List Table 7 Colorful Accent 3"/>
628  <w:LsdException Locked="false" Priority="46"
629   Name="List Table 1 Light Accent 4"/>
630  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
631  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
632  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
633  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
634  <w:LsdException Locked="false" Priority="51"
635   Name="List Table 6 Colorful Accent 4"/>
636  <w:LsdException Locked="false" Priority="52"
637   Name="List Table 7 Colorful Accent 4"/>
638  <w:LsdException Locked="false" Priority="46"
639   Name="List Table 1 Light Accent 5"/>
640  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
641  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
642  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
643  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
644  <w:LsdException Locked="false" Priority="51"
645   Name="List Table 6 Colorful Accent 5"/>
646  <w:LsdException Locked="false" Priority="52"
647   Name="List Table 7 Colorful Accent 5"/>
648  <w:LsdException Locked="false" Priority="46"
649   Name="List Table 1 Light Accent 6"/>
650  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
651  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
652  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
653  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
654  <w:LsdException Locked="false" Priority="51"
655   Name="List Table 6 Colorful Accent 6"/>
656  <w:LsdException Locked="false" Priority="52"
657   Name="List Table 7 Colorful Accent 6"/>
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783        mso-style-link:"Heading 5 Char";
784        mso-margin-top-alt:auto;
785        margin-right:0in;
786        mso-margin-bottom-alt:auto;
787        margin-left:0in;
788        mso-pagination:widow-orphan;
789        mso-outline-level:5;
790        font-size:12.0pt;
791        font-family:"Times New Roman",serif;
792        mso-fareast-font-family:"Times New Roman";
793        mso-fareast-theme-font:minor-fareast;
794        color:#4F4FFF;
795        font-weight:bold;}
796p.MsoTitle, li.MsoTitle, div.MsoTitle
797        {mso-style-noshow:yes;
798        mso-style-priority:10;
799        mso-style-unhide:no;
800        mso-style-qformat:yes;
801        mso-style-link:"Title Char";
802        mso-style-next:Normal;
803        margin-top:0in;
804        margin-right:0in;
805        margin-bottom:15.0pt;
806        margin-left:0in;
807        mso-add-space:auto;
808        mso-pagination:widow-orphan;
809        border:none;
810        mso-border-bottom-alt:solid #5B9BD5 1.0pt;
811        mso-border-bottom-themecolor:accent1;
812        padding:0in;
813        mso-padding-alt:0in 0in 4.0pt 0in;
814        font-size:26.0pt;
815        font-family:"Calibri Light",sans-serif;
816        mso-ascii-font-family:"Calibri Light";
817        mso-ascii-theme-font:major-latin;
818        mso-fareast-font-family:"Times New Roman";
819        mso-fareast-theme-font:major-fareast;
820        mso-hansi-font-family:"Calibri Light";
821        mso-hansi-theme-font:major-latin;
822        mso-bidi-font-family:"Times New Roman";
823        mso-bidi-theme-font:major-bidi;
824        color:#323E4F;
825        mso-themecolor:text2;
826        mso-themeshade:191;
827        letter-spacing:.25pt;
828        mso-font-kerning:14.0pt;}
829p.MsoTitleCxSpFirst, li.MsoTitleCxSpFirst, div.MsoTitleCxSpFirst
830        {mso-style-noshow:yes;
831        mso-style-priority:10;
832        mso-style-unhide:no;
833        mso-style-qformat:yes;
834        mso-style-link:"Title Char";
835        mso-style-next:Normal;
836        mso-style-type:export-only;
837        margin:0in;
838        margin-bottom:.0001pt;
839        mso-add-space:auto;
840        mso-pagination:widow-orphan;
841        border:none;
842        mso-border-bottom-alt:solid #5B9BD5 1.0pt;
843        mso-border-bottom-themecolor:accent1;
844        padding:0in;
845        mso-padding-alt:0in 0in 4.0pt 0in;
846        font-size:26.0pt;
847        font-family:"Calibri Light",sans-serif;
848        mso-ascii-font-family:"Calibri Light";
849        mso-ascii-theme-font:major-latin;
850        mso-fareast-font-family:"Times New Roman";
851        mso-fareast-theme-font:major-fareast;
852        mso-hansi-font-family:"Calibri Light";
853        mso-hansi-theme-font:major-latin;
854        mso-bidi-font-family:"Times New Roman";
855        mso-bidi-theme-font:major-bidi;
856        color:#323E4F;
857        mso-themecolor:text2;
858        mso-themeshade:191;
859        letter-spacing:.25pt;
860        mso-font-kerning:14.0pt;}
861p.MsoTitleCxSpMiddle, li.MsoTitleCxSpMiddle, div.MsoTitleCxSpMiddle
862        {mso-style-noshow:yes;
863        mso-style-priority:10;
864        mso-style-unhide:no;
865        mso-style-qformat:yes;
866        mso-style-link:"Title Char";
867        mso-style-next:Normal;
868        mso-style-type:export-only;
869        margin:0in;
870        margin-bottom:.0001pt;
871        mso-add-space:auto;
872        mso-pagination:widow-orphan;
873        border:none;
874        mso-border-bottom-alt:solid #5B9BD5 1.0pt;
875        mso-border-bottom-themecolor:accent1;
876        padding:0in;
877        mso-padding-alt:0in 0in 4.0pt 0in;
878        font-size:26.0pt;
879        font-family:"Calibri Light",sans-serif;
880        mso-ascii-font-family:"Calibri Light";
881        mso-ascii-theme-font:major-latin;
882        mso-fareast-font-family:"Times New Roman";
883        mso-fareast-theme-font:major-fareast;
884        mso-hansi-font-family:"Calibri Light";
885        mso-hansi-theme-font:major-latin;
886        mso-bidi-font-family:"Times New Roman";
887        mso-bidi-theme-font:major-bidi;
888        color:#323E4F;
889        mso-themecolor:text2;
890        mso-themeshade:191;
891        letter-spacing:.25pt;
892        mso-font-kerning:14.0pt;}
893p.MsoTitleCxSpLast, li.MsoTitleCxSpLast, div.MsoTitleCxSpLast
894        {mso-style-noshow:yes;
895        mso-style-priority:10;
896        mso-style-unhide:no;
897        mso-style-qformat:yes;
898        mso-style-link:"Title Char";
899        mso-style-next:Normal;
900        mso-style-type:export-only;
901        margin-top:0in;
902        margin-right:0in;
903        margin-bottom:15.0pt;
904        margin-left:0in;
905        mso-add-space:auto;
906        mso-pagination:widow-orphan;
907        border:none;
908        mso-border-bottom-alt:solid #5B9BD5 1.0pt;
909        mso-border-bottom-themecolor:accent1;
910        padding:0in;
911        mso-padding-alt:0in 0in 4.0pt 0in;
912        font-size:26.0pt;
913        font-family:"Calibri Light",sans-serif;
914        mso-ascii-font-family:"Calibri Light";
915        mso-ascii-theme-font:major-latin;
916        mso-fareast-font-family:"Times New Roman";
917        mso-fareast-theme-font:major-fareast;
918        mso-hansi-font-family:"Calibri Light";
919        mso-hansi-theme-font:major-latin;
920        mso-bidi-font-family:"Times New Roman";
921        mso-bidi-theme-font:major-bidi;
922        color:#323E4F;
923        mso-themecolor:text2;
924        mso-themeshade:191;
925        letter-spacing:.25pt;
926        mso-font-kerning:14.0pt;}
927a:link, span.MsoHyperlink
928        {mso-style-noshow:yes;
929        mso-style-priority:99;
930        color:blue;
931        text-decoration:underline;
932        text-underline:single;}
933a:visited, span.MsoHyperlinkFollowed
934        {mso-style-noshow:yes;
935        mso-style-priority:99;
936        color:purple;
937        text-decoration:underline;
938        text-underline:single;}
939p.MsoDocumentMap, li.MsoDocumentMap, div.MsoDocumentMap
940        {mso-style-noshow:yes;
941        mso-style-priority:99;
942        mso-style-link:"Document Map Char";
943        margin:0in;
944        margin-bottom:.0001pt;
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:0in;
967        margin-bottom:.0001pt;
968        mso-pagination:widow-orphan;
969        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;
970        font-size:10.0pt;
971        font-family:"Courier New";
972        mso-fareast-font-family:"Times New Roman";}
973p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
974        {mso-style-noshow:yes;
975        mso-style-priority:99;
976        mso-style-link:"Balloon Text Char";
977        margin:0in;
978        margin-bottom:.0001pt;
979        mso-pagination:widow-orphan;
980        font-size:8.0pt;
981        font-family:"Tahoma",sans-serif;
982        mso-fareast-font-family:"Times New Roman";
983        mso-fareast-theme-font:minor-fareast;}
984span.MsoPlaceholderText
985        {mso-style-noshow:yes;
986        mso-style-priority:99;
987        mso-style-unhide:no;
988        color:gray;}
989p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing
990        {mso-style-noshow:yes;
991        mso-style-priority:1;
992        mso-style-unhide:no;
993        mso-style-qformat:yes;
994        mso-style-parent:"";
995        margin:0in;
996        margin-bottom:.0001pt;
997        mso-pagination:widow-orphan;
998        font-size:12.0pt;
999        font-family:"Times New Roman",serif;
1000        mso-fareast-font-family:"Times New Roman";
1001        mso-fareast-theme-font:minor-fareast;}
1002p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph
1003        {mso-style-noshow:yes;
1004        mso-style-priority:34;
1005        mso-style-unhide:no;
1006        mso-style-qformat:yes;
1007        margin-top:0in;
1008        margin-right:0in;
1009        margin-bottom:0in;
1010        margin-left:.5in;
1011        margin-bottom:.0001pt;
1012        mso-add-space:auto;
1013        mso-pagination:widow-orphan;
1014        font-size:12.0pt;
1015        font-family:"Times New Roman",serif;
1016        mso-fareast-font-family:"Times New Roman";
1017        mso-fareast-theme-font:minor-fareast;}
1018p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst
1019        {mso-style-noshow:yes;
1020        mso-style-priority:34;
1021        mso-style-unhide:no;
1022        mso-style-qformat:yes;
1023        mso-style-type:export-only;
1024        margin-top:0in;
1025        margin-right:0in;
1026        margin-bottom:0in;
1027        margin-left:.5in;
1028        margin-bottom:.0001pt;
1029        mso-add-space:auto;
1030        mso-pagination:widow-orphan;
1031        font-size:12.0pt;
1032        font-family:"Times New Roman",serif;
1033        mso-fareast-font-family:"Times New Roman";
1034        mso-fareast-theme-font:minor-fareast;}
1035p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle
1036        {mso-style-noshow:yes;
1037        mso-style-priority:34;
1038        mso-style-unhide:no;
1039        mso-style-qformat:yes;
1040        mso-style-type:export-only;
1041        margin-top:0in;
1042        margin-right:0in;
1043        margin-bottom:0in;
1044        margin-left:.5in;
1045        margin-bottom:.0001pt;
1046        mso-add-space:auto;
1047        mso-pagination:widow-orphan;
1048        font-size:12.0pt;
1049        font-family:"Times New Roman",serif;
1050        mso-fareast-font-family:"Times New Roman";
1051        mso-fareast-theme-font:minor-fareast;}
1052p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast
1053        {mso-style-noshow:yes;
1054        mso-style-priority:34;
1055        mso-style-unhide:no;
1056        mso-style-qformat:yes;
1057        mso-style-type:export-only;
1058        margin-top:0in;
1059        margin-right:0in;
1060        margin-bottom:0in;
1061        margin-left:.5in;
1062        margin-bottom:.0001pt;
1063        mso-add-space:auto;
1064        mso-pagination:widow-orphan;
1065        font-size:12.0pt;
1066        font-family:"Times New Roman",serif;
1067        mso-fareast-font-family:"Times New Roman";
1068        mso-fareast-theme-font:minor-fareast;}
1069span.MsoIntenseReference
1070        {mso-style-priority:32;
1071        mso-style-unhide:no;
1072        mso-style-qformat:yes;
1073        font-variant:small-caps;
1074        color:#ED7D31;
1075        mso-themecolor:accent2;
1076        letter-spacing:.25pt;
1077        font-weight:bold;
1078        text-decoration:underline;
1079        text-underline:single;}
1080span.Heading1Char
1081        {mso-style-name:"Heading 1 Char";
1082        mso-style-priority:9;
1083        mso-style-unhide:no;
1084        mso-style-locked:yes;
1085        mso-style-link:"Heading 1";
1086        mso-ansi-font-size:24.0pt;
1087        mso-bidi-font-size:24.0pt;
1088        font-family:"Times New Roman",serif;
1089        mso-ascii-font-family:"Times New Roman";
1090        mso-fareast-font-family:"Times New Roman";
1091        mso-fareast-theme-font:minor-fareast;
1092        mso-hansi-font-family:"Times New Roman";
1093        mso-bidi-font-family:"Times New Roman";
1094        mso-font-kerning:18.0pt;
1095        font-weight:bold;}
1096span.Heading2Char
1097        {mso-style-name:"Heading 2 Char";
1098        mso-style-noshow:yes;
1099        mso-style-priority:9;
1100        mso-style-unhide:no;
1101        mso-style-locked:yes;
1102        mso-style-link:"Heading 2";
1103        mso-ansi-font-size:18.0pt;
1104        mso-bidi-font-size:18.0pt;
1105        font-family:"Times New Roman",serif;
1106        mso-ascii-font-family:"Times New Roman";
1107        mso-fareast-font-family:"Times New Roman";
1108        mso-fareast-theme-font:minor-fareast;
1109        mso-hansi-font-family:"Times New Roman";
1110        mso-bidi-font-family:"Times New Roman";
1111        font-weight:bold;}
1112span.Heading3Char
1113        {mso-style-name:"Heading 3 Char";
1114        mso-style-noshow:yes;
1115        mso-style-priority:9;
1116        mso-style-unhide:no;
1117        mso-style-locked:yes;
1118        mso-style-link:"Heading 3";
1119        mso-ansi-font-size:13.5pt;
1120        mso-bidi-font-size:13.5pt;
1121        font-family:"Times New Roman",serif;
1122        mso-ascii-font-family:"Times New Roman";
1123        mso-fareast-font-family:"Times New Roman";
1124        mso-fareast-theme-font:minor-fareast;
1125        mso-hansi-font-family:"Times New Roman";
1126        mso-bidi-font-family:"Times New Roman";
1127        font-weight:bold;}
1128span.Heading4Char
1129        {mso-style-name:"Heading 4 Char";
1130        mso-style-noshow:yes;
1131        mso-style-priority:9;
1132        mso-style-unhide:no;
1133        mso-style-locked:yes;
1134        mso-style-link:"Heading 4";
1135        mso-ansi-font-size:13.0pt;
1136        mso-bidi-font-size:13.0pt;
1137        font-family:"Calibri Light",sans-serif;
1138        mso-ascii-font-family:"Calibri Light";
1139        mso-ascii-theme-font:major-latin;
1140        mso-fareast-font-family:"Times New Roman";
1141        mso-fareast-theme-font:major-fareast;
1142        mso-hansi-font-family:"Calibri Light";
1143        mso-hansi-theme-font:major-latin;
1144        mso-bidi-font-family:"Times New Roman";
1145        mso-bidi-theme-font:major-bidi;
1146        color:#5B9BD5;
1147        mso-themecolor:accent1;
1148        font-weight:bold;
1149        font-style:italic;}
1150span.Heading5Char
1151        {mso-style-name:"Heading 5 Char";
1152        mso-style-noshow:yes;
1153        mso-style-priority:9;
1154        mso-style-unhide:no;
1155        mso-style-locked:yes;
1156        mso-style-link:"Heading 5";
1157        mso-ansi-font-size:12.0pt;
1158        mso-bidi-font-size:12.0pt;
1159        font-family:"Times New Roman",serif;
1160        mso-ascii-font-family:"Times New Roman";
1161        mso-fareast-font-family:"Times New Roman";
1162        mso-fareast-theme-font:minor-fareast;
1163        mso-hansi-font-family:"Times New Roman";
1164        mso-bidi-font-family:"Times New Roman";
1165        color:#4F4FFF;
1166        font-weight:bold;}
1167span.HTMLPreformattedChar
1168        {mso-style-name:"HTML Preformatted Char";
1169        mso-style-noshow:yes;
1170        mso-style-priority:99;
1171        mso-style-unhide:no;
1172        mso-style-locked:yes;
1173        mso-style-link:"HTML Preformatted";
1174        font-family:"Courier New";
1175        mso-ascii-font-family:"Courier New";
1176        mso-fareast-font-family:"Times New Roman";
1177        mso-hansi-font-family:"Courier New";
1178        mso-bidi-font-family:"Courier New";}
1179p.msonormal0, li.msonormal0, div.msonormal0
1180        {mso-style-name:msonormal;
1181        mso-style-noshow:yes;
1182        mso-style-priority:99;
1183        mso-style-unhide:no;
1184        mso-margin-top-alt:auto;
1185        margin-right:0in;
1186        mso-margin-bottom-alt:auto;
1187        margin-left:0in;
1188        mso-pagination:widow-orphan;
1189        font-size:12.0pt;
1190        font-family:"Times New Roman",serif;
1191        mso-fareast-font-family:"Times New Roman";
1192        mso-fareast-theme-font:minor-fareast;}
1193span.TitleChar
1194        {mso-style-name:"Title Char";
1195        mso-style-priority:10;
1196        mso-style-unhide:no;
1197        mso-style-locked:yes;
1198        mso-style-link:Title;
1199        mso-ansi-font-size:26.0pt;
1200        mso-bidi-font-size:26.0pt;
1201        font-family:"Calibri Light",sans-serif;
1202        mso-ascii-font-family:"Calibri Light";
1203        mso-ascii-theme-font:major-latin;
1204        mso-fareast-font-family:"Times New Roman";
1205        mso-fareast-theme-font:major-fareast;
1206        mso-hansi-font-family:"Calibri Light";
1207        mso-hansi-theme-font:major-latin;
1208        mso-bidi-font-family:"Times New Roman";
1209        mso-bidi-theme-font:major-bidi;
1210        color:#323E4F;
1211        mso-themecolor:text2;
1212        mso-themeshade:191;
1213        letter-spacing:.25pt;
1214        mso-font-kerning:14.0pt;}
1215span.DocumentMapChar
1216        {mso-style-name:"Document Map Char";
1217        mso-style-noshow:yes;
1218        mso-style-priority:99;
1219        mso-style-unhide:no;
1220        mso-style-locked:yes;
1221        mso-style-link:"Document Map";
1222        mso-ansi-font-size:8.0pt;
1223        mso-bidi-font-size:8.0pt;
1224        font-family:"Tahoma",sans-serif;
1225        mso-ascii-font-family:Tahoma;
1226        mso-fareast-font-family:"Times New Roman";
1227        mso-fareast-theme-font:minor-fareast;
1228        mso-hansi-font-family:Tahoma;
1229        mso-bidi-font-family:Tahoma;}
1230span.BalloonTextChar
1231        {mso-style-name:"Balloon Text Char";
1232        mso-style-noshow:yes;
1233        mso-style-priority:99;
1234        mso-style-unhide:no;
1235        mso-style-locked:yes;
1236        mso-style-link:"Balloon Text";
1237        mso-ansi-font-size:8.0pt;
1238        mso-bidi-font-size:8.0pt;
1239        font-family:"Tahoma",sans-serif;
1240        mso-ascii-font-family:Tahoma;
1241        mso-fareast-font-family:"Times New Roman";
1242        mso-fareast-theme-font:minor-fareast;
1243        mso-hansi-font-family:Tahoma;
1244        mso-bidi-font-family:Tahoma;}
1245span.SpellE
1246        {mso-style-name:"";
1247        mso-spl-e:yes;}
1248span.GramE
1249        {mso-style-name:"";
1250        mso-gram-e:yes;}
1251.MsoChpDefault
1252        {mso-style-type:export-only;
1253        mso-default-props:yes;
1254        font-size:10.0pt;
1255        mso-ansi-font-size:10.0pt;
1256        mso-bidi-font-size:10.0pt;
1257        font-family:"Calibri",sans-serif;
1258        mso-ascii-font-family:Calibri;
1259        mso-ascii-theme-font:minor-latin;
1260        mso-fareast-font-family:Calibri;
1261        mso-fareast-theme-font:minor-latin;
1262        mso-hansi-font-family:Calibri;
1263        mso-hansi-theme-font:minor-latin;
1264        mso-bidi-font-family:"Times New Roman";
1265        mso-bidi-theme-font:minor-bidi;}
1266@page WordSection1
1267        {size:8.5in 11.0in;
1268        margin:1.0in 1.0in 1.0in 1.0in;
1269        mso-header-margin:.5in;
1270        mso-footer-margin:.5in;
1271        mso-paper-source:0;}
1272div.WordSection1
1273        {page:WordSection1;}
1274 /* List Definitions */
1275 @list l0
1276        {mso-list-id:15860155;
1277        mso-list-type:hybrid;
1278        mso-list-template-ids:234676978 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
1279@list l0:level1
1280        {mso-level-tab-stop:none;
1281        mso-level-number-position:left;
1282        margin-left:.75in;
1283        text-indent:-.25in;}
1284@list l0:level2
1285        {mso-level-number-format:alpha-lower;
1286        mso-level-tab-stop:none;
1287        mso-level-number-position:left;
1288        margin-left:1.25in;
1289        text-indent:-.25in;}
1290@list l0:level3
1291        {mso-level-number-format:roman-lower;
1292        mso-level-tab-stop:none;
1293        mso-level-number-position:right;
1294        margin-left:1.75in;
1295        text-indent:-9.0pt;}
1296@list l0:level4
1297        {mso-level-tab-stop:none;
1298        mso-level-number-position:left;
1299        margin-left:2.25in;
1300        text-indent:-.25in;}
1301@list l0:level5
1302        {mso-level-number-format:alpha-lower;
1303        mso-level-tab-stop:none;
1304        mso-level-number-position:left;
1305        margin-left:2.75in;
1306        text-indent:-.25in;}
1307@list l0:level6
1308        {mso-level-number-format:roman-lower;
1309        mso-level-tab-stop:none;
1310        mso-level-number-position:right;
1311        margin-left:3.25in;
1312        text-indent:-9.0pt;}
1313@list l0:level7
1314        {mso-level-tab-stop:none;
1315        mso-level-number-position:left;
1316        margin-left:3.75in;
1317        text-indent:-.25in;}
1318@list l0:level8
1319        {mso-level-number-format:alpha-lower;
1320        mso-level-tab-stop:none;
1321        mso-level-number-position:left;
1322        margin-left:4.25in;
1323        text-indent:-.25in;}
1324@list l0:level9
1325        {mso-level-number-format:roman-lower;
1326        mso-level-tab-stop:none;
1327        mso-level-number-position:right;
1328        margin-left:4.75in;
1329        text-indent:-9.0pt;}
1330@list l1
1331        {mso-list-id:608973138;
1332        mso-list-type:hybrid;
1333        mso-list-template-ids:-1449999034 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
1334@list l1:level1
1335        {mso-level-tab-stop:none;
1336        mso-level-number-position:left;
1337        margin-left:.25in;
1338        text-indent:-.25in;}
1339@list l1:level2
1340        {mso-level-number-format:alpha-lower;
1341        mso-level-tab-stop:none;
1342        mso-level-number-position:left;
1343        margin-left:.75in;
1344        text-indent:-.25in;}
1345@list l1:level3
1346        {mso-level-number-format:roman-lower;
1347        mso-level-tab-stop:none;
1348        mso-level-number-position:right;
1349        margin-left:1.25in;
1350        text-indent:-9.0pt;}
1351@list l1:level4
1352        {mso-level-tab-stop:none;
1353        mso-level-number-position:left;
1354        margin-left:1.75in;
1355        text-indent:-.25in;}
1356@list l1:level5
1357        {mso-level-number-format:alpha-lower;
1358        mso-level-tab-stop:none;
1359        mso-level-number-position:left;
1360        margin-left:2.25in;
1361        text-indent:-.25in;}
1362@list l1:level6
1363        {mso-level-number-format:roman-lower;
1364        mso-level-tab-stop:none;
1365        mso-level-number-position:right;
1366        margin-left:2.75in;
1367        text-indent:-9.0pt;}
1368@list l1:level7
1369        {mso-level-tab-stop:none;
1370        mso-level-number-position:left;
1371        margin-left:3.25in;
1372        text-indent:-.25in;}
1373@list l1:level8
1374        {mso-level-number-format:alpha-lower;
1375        mso-level-tab-stop:none;
1376        mso-level-number-position:left;
1377        margin-left:3.75in;
1378        text-indent:-.25in;}
1379@list l1:level9
1380        {mso-level-number-format:roman-lower;
1381        mso-level-tab-stop:none;
1382        mso-level-number-position:right;
1383        margin-left:4.25in;
1384        text-indent:-9.0pt;}
1385@list l2
1386        {mso-list-id:724838487;
1387        mso-list-type:hybrid;
1388        mso-list-template-ids:-1805223932 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
1389@list l2:level1
1390        {mso-level-tab-stop:none;
1391        mso-level-number-position:left;
1392        text-indent:-.25in;}
1393@list l2:level2
1394        {mso-level-number-format:alpha-lower;
1395        mso-level-tab-stop:none;
1396        mso-level-number-position:left;
1397        text-indent:-.25in;}
1398@list l2:level3
1399        {mso-level-number-format:roman-lower;
1400        mso-level-tab-stop:none;
1401        mso-level-number-position:right;
1402        text-indent:-9.0pt;}
1403@list l2:level4
1404        {mso-level-tab-stop:none;
1405        mso-level-number-position:left;
1406        text-indent:-.25in;}
1407@list l2:level5
1408        {mso-level-number-format:alpha-lower;
1409        mso-level-tab-stop:none;
1410        mso-level-number-position:left;
1411        text-indent:-.25in;}
1412@list l2:level6
1413        {mso-level-number-format:roman-lower;
1414        mso-level-tab-stop:none;
1415        mso-level-number-position:right;
1416        text-indent:-9.0pt;}
1417@list l2:level7
1418        {mso-level-tab-stop:none;
1419        mso-level-number-position:left;
1420        text-indent:-.25in;}
1421@list l2:level8
1422        {mso-level-number-format:alpha-lower;
1423        mso-level-tab-stop:none;
1424        mso-level-number-position:left;
1425        text-indent:-.25in;}
1426@list l2:level9
1427        {mso-level-number-format:roman-lower;
1428        mso-level-tab-stop:none;
1429        mso-level-number-position:right;
1430        text-indent:-9.0pt;}
1431@list l3
1432        {mso-list-id:974749577;
1433        mso-list-type:hybrid;
1434        mso-list-template-ids:-1793575708 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
1435@list l3:level1
1436        {mso-level-tab-stop:none;
1437        mso-level-number-position:left;
1438        margin-left:.75in;
1439        text-indent:-.25in;}
1440@list l3:level2
1441        {mso-level-number-format:alpha-lower;
1442        mso-level-tab-stop:none;
1443        mso-level-number-position:left;
1444        margin-left:1.25in;
1445        text-indent:-.25in;}
1446@list l3:level3
1447        {mso-level-number-format:roman-lower;
1448        mso-level-tab-stop:none;
1449        mso-level-number-position:right;
1450        margin-left:1.75in;
1451        text-indent:-9.0pt;}
1452@list l3:level4
1453        {mso-level-tab-stop:none;
1454        mso-level-number-position:left;
1455        margin-left:2.25in;
1456        text-indent:-.25in;}
1457@list l3:level5
1458        {mso-level-number-format:alpha-lower;
1459        mso-level-tab-stop:none;
1460        mso-level-number-position:left;
1461        margin-left:2.75in;
1462        text-indent:-.25in;}
1463@list l3:level6
1464        {mso-level-number-format:roman-lower;
1465        mso-level-tab-stop:none;
1466        mso-level-number-position:right;
1467        margin-left:3.25in;
1468        text-indent:-9.0pt;}
1469@list l3:level7
1470        {mso-level-tab-stop:none;
1471        mso-level-number-position:left;
1472        margin-left:3.75in;
1473        text-indent:-.25in;}
1474@list l3:level8
1475        {mso-level-number-format:alpha-lower;
1476        mso-level-tab-stop:none;
1477        mso-level-number-position:left;
1478        margin-left:4.25in;
1479        text-indent:-.25in;}
1480@list l3:level9
1481        {mso-level-number-format:roman-lower;
1482        mso-level-tab-stop:none;
1483        mso-level-number-position:right;
1484        margin-left:4.75in;
1485        text-indent:-9.0pt;}
1486@list l4
1487        {mso-list-id:1479684003;
1488        mso-list-type:hybrid;
1489        mso-list-template-ids:1678017270 -1895020378 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
1490@list l4:level1
1491        {mso-level-tab-stop:none;
1492        mso-level-number-position:left;
1493        margin-left:.25in;
1494        text-indent:-.25in;}
1495@list l4:level2
1496        {mso-level-number-format:alpha-lower;
1497        mso-level-tab-stop:none;
1498        mso-level-number-position:left;
1499        margin-left:.75in;
1500        text-indent:-.25in;}
1501@list l4:level3
1502        {mso-level-number-format:roman-lower;
1503        mso-level-tab-stop:none;
1504        mso-level-number-position:right;
1505        margin-left:1.25in;
1506        text-indent:-9.0pt;}
1507@list l4:level4
1508        {mso-level-tab-stop:none;
1509        mso-level-number-position:left;
1510        margin-left:1.75in;
1511        text-indent:-.25in;}
1512@list l4:level5
1513        {mso-level-number-format:alpha-lower;
1514        mso-level-tab-stop:none;
1515        mso-level-number-position:left;
1516        margin-left:2.25in;
1517        text-indent:-.25in;}
1518@list l4:level6
1519        {mso-level-number-format:roman-lower;
1520        mso-level-tab-stop:none;
1521        mso-level-number-position:right;
1522        margin-left:2.75in;
1523        text-indent:-9.0pt;}
1524@list l4:level7
1525        {mso-level-tab-stop:none;
1526        mso-level-number-position:left;
1527        margin-left:3.25in;
1528        text-indent:-.25in;}
1529@list l4:level8
1530        {mso-level-number-format:alpha-lower;
1531        mso-level-tab-stop:none;
1532        mso-level-number-position:left;
1533        margin-left:3.75in;
1534        text-indent:-.25in;}
1535@list l4:level9
1536        {mso-level-number-format:roman-lower;
1537        mso-level-tab-stop:none;
1538        mso-level-number-position:right;
1539        margin-left:4.25in;
1540        text-indent:-9.0pt;}
1541@list l5
1542        {mso-list-id:1494641284;
1543        mso-list-type:hybrid;
1544        mso-list-template-ids:1178630220 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
1545@list l5:level1
1546        {mso-level-tab-stop:none;
1547        mso-level-number-position:left;
1548        margin-left:.25in;
1549        text-indent:-.25in;}
1550@list l5:level2
1551        {mso-level-number-format:alpha-lower;
1552        mso-level-tab-stop:none;
1553        mso-level-number-position:left;
1554        margin-left:.75in;
1555        text-indent:-.25in;}
1556@list l5:level3
1557        {mso-level-number-format:roman-lower;
1558        mso-level-tab-stop:none;
1559        mso-level-number-position:right;
1560        margin-left:1.25in;
1561        text-indent:-9.0pt;}
1562@list l5:level4
1563        {mso-level-tab-stop:none;
1564        mso-level-number-position:left;
1565        margin-left:1.75in;
1566        text-indent:-.25in;}
1567@list l5:level5
1568        {mso-level-number-format:alpha-lower;
1569        mso-level-tab-stop:none;
1570        mso-level-number-position:left;
1571        margin-left:2.25in;
1572        text-indent:-.25in;}
1573@list l5:level6
1574        {mso-level-number-format:roman-lower;
1575        mso-level-tab-stop:none;
1576        mso-level-number-position:right;
1577        margin-left:2.75in;
1578        text-indent:-9.0pt;}
1579@list l5:level7
1580        {mso-level-tab-stop:none;
1581        mso-level-number-position:left;
1582        margin-left:3.25in;
1583        text-indent:-.25in;}
1584@list l5:level8
1585        {mso-level-number-format:alpha-lower;
1586        mso-level-tab-stop:none;
1587        mso-level-number-position:left;
1588        margin-left:3.75in;
1589        text-indent:-.25in;}
1590@list l5:level9
1591        {mso-level-number-format:roman-lower;
1592        mso-level-tab-stop:none;
1593        mso-level-number-position:right;
1594        margin-left:4.25in;
1595        text-indent:-9.0pt;}
1596@list l6
1597        {mso-list-id:2054574863;
1598        mso-list-type:hybrid;
1599        mso-list-template-ids:-1794201240 2114096650 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
1600@list l6:level1
1601        {mso-level-tab-stop:none;
1602        mso-level-number-position:left;
1603        text-indent:-.25in;}
1604@list l6:level2
1605        {mso-level-number-format:alpha-lower;
1606        mso-level-tab-stop:none;
1607        mso-level-number-position:left;
1608        text-indent:-.25in;}
1609@list l6:level3
1610        {mso-level-number-format:roman-lower;
1611        mso-level-tab-stop:none;
1612        mso-level-number-position:right;
1613        text-indent:-9.0pt;}
1614@list l6:level4
1615        {mso-level-tab-stop:none;
1616        mso-level-number-position:left;
1617        text-indent:-.25in;}
1618@list l6:level5
1619        {mso-level-number-format:alpha-lower;
1620        mso-level-tab-stop:none;
1621        mso-level-number-position:left;
1622        text-indent:-.25in;}
1623@list l6:level6
1624        {mso-level-number-format:roman-lower;
1625        mso-level-tab-stop:none;
1626        mso-level-number-position:right;
1627        text-indent:-9.0pt;}
1628@list l6:level7
1629        {mso-level-tab-stop:none;
1630        mso-level-number-position:left;
1631        text-indent:-.25in;}
1632@list l6:level8
1633        {mso-level-number-format:alpha-lower;
1634        mso-level-tab-stop:none;
1635        mso-level-number-position:left;
1636        text-indent:-.25in;}
1637@list l6:level9
1638        {mso-level-number-format:roman-lower;
1639        mso-level-tab-stop:none;
1640        mso-level-number-position:right;
1641        text-indent:-9.0pt;}
1642ol
1643        {margin-bottom:0in;}
1644ul
1645        {margin-bottom:0in;}
1646-->
1647</style>
1648<!--[if gte mso 10]>
1649<style>
1650 /* Style Definitions */
1651 table.MsoNormalTable
1652        {mso-style-name:"Table Normal";
1653        mso-tstyle-rowband-size:0;
1654        mso-tstyle-colband-size:0;
1655        mso-style-noshow:yes;
1656        mso-style-priority:99;
1657        mso-style-parent:"";
1658        mso-padding-alt:0in 5.4pt 0in 5.4pt;
1659        mso-para-margin:0in;
1660        mso-para-margin-bottom:.0001pt;
1661        mso-pagination:widow-orphan;
1662        font-size:10.0pt;
1663        font-family:"Calibri",sans-serif;
1664        mso-ascii-font-family:Calibri;
1665        mso-ascii-theme-font:minor-latin;
1666        mso-hansi-font-family:Calibri;
1667        mso-hansi-theme-font:minor-latin;
1668        mso-bidi-font-family:"Times New Roman";
1669        mso-bidi-theme-font:minor-bidi;}
1670</style>
1671<![endif]--><!--[if gte mso 9]><xml>
1672 <o:shapedefaults v:ext="edit" spidmax="1026"/>
1673</xml><![endif]--><!--[if gte mso 9]><xml>
1674 <o:shapelayout v:ext="edit">
1675  <o:idmap v:ext="edit" data="1"/>
1676 </o:shapelayout></xml><![endif]-->
1677</head>
1678
1679<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1680
1681<div class=WordSection1>
1682
1683<h1>Simple Magnetic Structures in GSAS-II </h1>
1684
1685<P><B>A video version of this tutorial is available at
1686<A href="https://anl.box.com/v/SimpleMagnetic" target="_blank">
1687https://anl.box.com/v/SimpleMagnetic</A></B></P>
1688
1689<h2>Introduction</h2>
1690
1691<p class=MsoNormal>For magnetic neutron diffraction, the powder diffraction
1692structure factor consists of two non-interacting components.</p>
1693
1694<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1695
1696<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
1697 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
1698 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1699 <v:stroke joinstyle="miter"/>
1700 <v:formulas>
1701  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
1702  <v:f eqn="sum @0 1 0"/>
1703  <v:f eqn="sum 0 0 @1"/>
1704  <v:f eqn="prod @2 1 2"/>
1705  <v:f eqn="prod @3 21600 pixelWidth"/>
1706  <v:f eqn="prod @3 21600 pixelHeight"/>
1707  <v:f eqn="sum @0 0 1"/>
1708  <v:f eqn="prod @6 1 2"/>
1709  <v:f eqn="prod @7 21600 pixelWidth"/>
1710  <v:f eqn="sum @8 21600 0"/>
1711  <v:f eqn="prod @7 21600 pixelHeight"/>
1712  <v:f eqn="sum @10 21600 0"/>
1713 </v:formulas>
1714 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1715 <o:lock v:ext="edit" aspectratio="t"/>
1716</v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_i1099" type="#_x0000_t75"
1717 style='width:261pt;height:37.5pt;visibility:visible;mso-wrap-style:square'>
1718 <v:imagedata src="SimpleMagnetic_files/image001.png" o:title=""/>
1719</v:shape><![endif]--><![if !vml]><img width=348 height=50
1720src="SimpleMagnetic_files/image001.png" v:shapes="Picture_x0020_1"><![endif]></span></p>
1721
1722<p class=MsoNormal>To have this result, one assumes that the neutron beam is not
1723polarized, the sample has no texture and there is only elastic scattering. The
1724first term is the ordinary nuclear structure factor found for all crystalline
1725materials and the second is the magnetic scattering. Note that the result is a
1726sum of squares implying that the nuclear and magnetic scattering intensities
1727are summed to give the total that is measured in a magnetic powder diffraction
1728experiment. This allows us to model the structure as two separate crystalline
1729phases; one consists of the arrangement of all the atoms in the
1730crystal structure described with a conventional unit cell and space
1731group (the chemical or sometimes "nuclear" structure), and
1732the other contains only the magnetic atoms in a perhaps different unit cell
1733with a magnetic space group to describe the atom and magnetic moment
1734arrangement (the magnetic structure).
1735Needless to say the magnetic ions only have one set of positions,
1736both phases must describe the same atomic
1737arrangement;  positions of the magnetic ions will be linked, as needed, by
1738constraints between the phases in order to maintain this arrangement.</p>
1739
1740<p class=MsoNormal>The magnetic scattering component has two factors</p>
1741
1742<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1743
1744<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1745 id="Picture_x0020_2" o:spid="_x0000_i1098" type="#_x0000_t75" style='width:103.5pt;
1746 height:48pt;visibility:visible;mso-wrap-style:square'>
1747 <v:imagedata src="SimpleMagnetic_files/image002.png" o:title=""/>
1748</v:shape><![endif]--><![if !vml]><img width=138 height=64
1749src="SimpleMagnetic_files/image002.png" v:shapes="Picture_x0020_2"><![endif]></span></p>
1750
1751<p class=MsoNormal>The second term (<i style='mso-bidi-font-style:normal'>p<sub>m</sub></i>)
1752is a scalar containing the magnetic form factor (<span class=SpellE><i
1753style='mso-bidi-font-style:normal'>f<sub>m</sub></i></span>), the magnetic
1754moment magnitude (<i style='mso-bidi-font-style:normal'>S<sub>m</sub></i>) and
1755a scaling factor ~0.539x10<sup>-12</sup> cm which is on the same scale as the
1756normal neutron scattering lengths. Thus, magnetic scattering intensities are
1757similar to those from the chemical structure. The first term (<span
1758class=SpellE><span class=GramE><b style='mso-bidi-font-weight:normal'>q<sub>m</sub></b></span></span>)
1759depends on the projection of the magnetic moment onto the scattering vector for
1760the reflection. If the scattering vector (unit vector <span class=SpellE><b
1761style='mso-bidi-font-weight:normal'>&#949;<sub>h</sub></b></span>) is parallel
1762to the magnetic (unit vector <b style='mso-bidi-font-weight:normal'>K<sub>m</sub></b>)
1763then the magnetic scattering intensity is zero and is large if the vectors are
1764perpendicular. Thus, one can anticipate the direction of the magnetic moment in
1765the structure by examining the observed magnetic intensities of low index
1766reflections.</p>
1767
1768<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1769
1770<p class=MsoNormal>In this exercise you will use GSAS-II to determine the
1771magnetic structure for a simple ferromagnet and a simple antiferromagnet. One
1772is LaMnO<sub>3</sub> which is an antiferromagnetic perovskite distorted by a
1773strong <span class=SpellE>Jahn</span>-Teller distortion to an orthorhombic
1774cell, and the other is LaMnO<sub>3</sub> doped with enough Ca to make it a
1775ferromagnet that is also orthorhombic. Neutron powder diffraction data for both
1776were obtained on BT-1 at the NIST reactor at 50K (thanks to Qingzhen Huang for
1777providing the data).</p>
1778
1779<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1780
1781<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1782
1783<h2>Simple Antiferromagnet: LaMnO<sub>3</sub></h2>
1784
1785<h3>Step 1: Read in the data file</h3>
1786
1787<p class=MsoListParagraphCxSpFirst style='margin-left:.25in;mso-add-space:auto;
1788text-indent:-.25in;mso-list:l1 level1 lfo2'><![if !supportLists]><span
1789style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
1790style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
1791the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1792mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1793minor-latin'>Import/Powder Data/from GSAS powder data file</span></b> menu item
1794to read the data file into the current GSAS-II project. This read option is set
1795to read any of the powder data formats defined for GSAS (angles in <span
1796class=SpellE>centidegrees</span>, TOF in µsec). Other submenu items will read
1797the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1798style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1799mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>cif</span></b></span>
1800format or the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1801style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1802mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>xye</span></b></span>
1803format (angles in degrees) used by <span class=SpellE>Topas</span>, etc.<span
1804style='mso-spacerun:yes'>  </span>In those cases, you would change the file
1805directory to <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1806style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1807mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>cif</span></b></span>
1808format or the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1809style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1810mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>xye</span></b></span>
1811format (angles in degrees) used by <span class=SpellE>Topas</span>, etc. to see
1812them. Because you used <span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1813minor-latin'>the </span><b style='mso-bidi-font-weight:normal'><span
1814style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1815mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font:
1816minor-latin'>Help/Download tutorial</span></b><span style='mso-fareast-font-family:
1817Calibri;mso-fareast-theme-font:minor-latin'> menu entry to open this page and
1818downloaded the exercise files (recommended), then the </span><span
1819class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1820"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
1821Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SimpleMagnetic</span></b></span><b
1822style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1823mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1824minor-latin;mso-hansi-theme-font:minor-latin'>/data/...</span></b><span
1825style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>
1826entry will bring you to the location where the files have been downloaded. (It
1827is also possible to download them manually from <a
1828href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimpleMagnetic/data/">https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimpleMagnetic/data/</a>.
1829In this case you will need to navigate to the download location manually.)<br>
1830For this tutorial you should see the data file in the file browser, but if
1831extensions on data files are not the expected ones, you may need to change the
1832file type to <b style='mso-bidi-font-weight:normal'>All files (*.*)</b> to find
1833the desired file.</span></p>
1834
1835<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
1836auto;text-indent:-.25in;mso-list:l1 level1 lfo2'><![if !supportLists]><span
1837style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
1838style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
1839the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1840mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1841minor-latin'>CaMnO3_50K.gsas</span></b><span style='font-family:"Calibri",sans-serif;
1842mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1843minor-latin'> data</span> file in the first dialog and press <b
1844style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1845mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1846minor-latin'>Open</span></b>. There will be a Dialog box asking <span
1847class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1848"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1849minor-latin;mso-bidi-theme-font:minor-latin'>Is</span></b></span><b
1850style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1851mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1852minor-latin'> this the file you want?</span></b> Press <span class=GramE><b
1853style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1854mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1855minor-latin'>Yes</span></b></span> button to proceed.</p>
1856
1857<p class=MsoListParagraphCxSpLast style='margin-left:.25in;mso-add-space:auto;
1858text-indent:-.25in;mso-list:l1 level1 lfo2'><![if !supportLists]><span
1859style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3.<span
1860style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Since
1861this data file does not define an instrument parameter file, a file dialog will
1862appear for you to select the correct instrument parameter file. Select <b
1863style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1864mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1865minor-latin'>BT1_Cu300.inst</span></b>; you may have to change the file type in
1866the file selection Dialog box to <b style='mso-bidi-font-weight:normal'><span
1867style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1868mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>GSAS <span
1869class=SpellE>iparm</span> file</span></b> to see it. At this point the <b
1870style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1871mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1872minor-latin'>GSAS-II data tree</span></b> window will have several entries </p>
1873
1874<h2><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3"
1875 o:spid="_x0000_i1097" type="#_x0000_t75" style='width:319.5pt;height:216.75pt;
1876 visibility:visible;mso-wrap-style:square'>
1877 <v:imagedata src="SimpleMagnetic_files/image005.png" o:title=""/>
1878</v:shape><![endif]--><![if !vml]><img border=0 width=426 height=289
1879src="SimpleMagnetic_files/image078.png" v:shapes="Picture_x0020_3"><![endif]></span></h2>
1880
1881<p class=MsoNormal><span class=GramE>and</span> the plot window will show the
1882powder pattern</p>
1883
1884<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1885 id="Picture_x0020_4" o:spid="_x0000_i1096" type="#_x0000_t75" style='width:468pt;
1886 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1887 <v:imagedata src="SimpleMagnetic_files/image007.png" o:title=""/>
1888</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
1889src="SimpleMagnetic_files/image080.png" v:shapes="Picture_x0020_4"><![endif]></span></p>
1890
1891<h3>Step 2: Select Limits </h3>
1892
1893<p class=MsoNormal><span style='mso-spacerun:yes'> </span>This pattern has more
1894data than we need, so it is helpful to cut down the range and one probably
1895doesn’t want to use the two very broad peaks at the upper end of the pattern as
1896they don’t contain much information for the magnetic structure. One also should
1897be careful in selecting he lower limit especially for magnetic structure
1898studies as a small peak may be hidden at low angles that can decisively
1899determine a magnetic structure (there are none in this example, but
1900this issue will be apparent in the next example). Click on the <b style='mso-bidi-font-weight:
1901normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1902minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Limits</span></b>
1903item in the <b style='mso-bidi-font-weight:normal'><span style='font-family:
1904"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>GSAS-II
1905data tree</span></b>. Use the <b style='mso-bidi-font-weight:normal'><span
1906style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1907mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>New:</span></b>
1908set of entry boxes to set <span class=SpellE><b style='mso-bidi-font-weight:
1909normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1910minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Tmin</span></b></span>
1911and <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1912style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1913mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Tmax</span></b></span>
1914to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1915mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>6 </span></b>and
1916<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1917mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1918minor-latin'>156</span></b>. Notice on the plot that the limit lines have moved
1919to these positions; the green lower limit is just below the 1<sup>st</sup> peak
1920and the red upper limit is just below that last two broad peaks. You may also
1921drag the limit lines to the desired location or place them by a left mouse
1922click on a data point for the lower limit or a right click on a data point for
1923the upper limit. The plot should look like</p>
1924
1925<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1926 id="Picture_x0020_5" o:spid="_x0000_i1095" type="#_x0000_t75" style='width:468pt;
1927 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1928 <v:imagedata src="SimpleMagnetic_files/image009.png" o:title=""/>
1929</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=535
1930src="SimpleMagnetic_files/image081.png" v:shapes="Picture_x0020_5"><![endif]></span></p>
1931
1932<h3>Step 3: Read in the chemical structure for LaMnO<sub>3</sub></h3>
1933
1934<p class=MsoListParagraphCxSpFirst style='margin-left:.25in;mso-add-space:auto;
1935text-indent:-.25in;mso-list:l3 level1 lfo4'><![if !supportLists]><span
1936style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
1937style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
1938the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1939mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1940minor-latin'>Import/Phase/from CIF file</span></b> menu item to read the phase
1941information for LaMnO<sub>3</sub> into the current GSAS-II project. This read
1942option is set to read Crystallographic Information Files (CIF). Other submenu
1943items will read phase information in other formats.<span
1944style='mso-spacerun:yes'>  </span>Because you used <span style='mso-fareast-font-family:
1945Calibri;mso-fareast-theme-font:minor-latin'>the </span><b style='mso-bidi-font-weight:
1946normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1947minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;
1948mso-hansi-theme-font:minor-latin'>Help/Download tutorial</span></b><span
1949style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>
1950menu entry to open this page and downloaded the exercise files (recommended),
1951then the </span><span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1952style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1953mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font:
1954minor-latin'>SimpleMagnetic</span></b></span><b style='mso-bidi-font-weight:
1955normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1956minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;
1957mso-hansi-theme-font:minor-latin'>/data/...</span></b><span style='mso-fareast-font-family:
1958Calibri;mso-fareast-theme-font:minor-latin'> entry will bring you to the
1959location where the files have been downloaded. (It is also possible to download
1960them manually from <a
1961href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimpleMagnetic/data/">https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimpleMagnetic/data/</a>.
1962In this case you will need to navigate to the download location manually.)</span></p>
1963
1964<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
1965auto;text-indent:-.25in;mso-list:l3 level1 lfo4'><![if !supportLists]><span
1966style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
1967style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
1968the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1969mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1970minor-latin'>LaMnO3.cif</span></b><span style='font-family:"Calibri",sans-serif;
1971mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1972minor-latin'> data</span> file in the first dialog and press <b
1973style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1974mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1975minor-latin'>Open</span></b>. There will be a Dialog box asking <span
1976class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1977"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1978minor-latin;mso-bidi-theme-font:minor-latin'>Is</span></b></span><b
1979style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1980mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1981minor-latin'> this the file you want?</span></b> Press <span class=GramE><b
1982style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1983mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1984minor-latin'>Yes</span></b></span> button to proceed. You will get the
1985opportunity to change the phase name next; press <b style='mso-bidi-font-weight:
1986normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1987minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>OK</span></b>
1988to continue.</p>
1989
1990<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
1991auto;text-indent:-.25in;mso-list:l3 level1 lfo4'><![if !supportLists]><span
1992style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3.<span
1993style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Next
1994is the histogram selection window; this connects the phase to the data so it
1995can be used in subsequent calculations.<span style='mso-no-proof:yes'> </span></p>
1996
1997<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
1998auto'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_6"
1999 o:spid="_x0000_i1094" type="#_x0000_t75" style='width:283.5pt;height:228.75pt;
2000 visibility:visible;mso-wrap-style:square'>
2001 <v:imagedata src="SimpleMagnetic_files/image011.png" o:title=""/>
2002</v:shape><![endif]--><![if !vml]><img border=0 width=378 height=305
2003src="SimpleMagnetic_files/image011.png" v:shapes="Picture_x0020_6"><![endif]></span></p>
2004
2005<p class=MsoListParagraphCxSpLast style='margin-left:.25in;mso-add-space:auto'>Select
2006the histogram (or press <b style='mso-bidi-font-weight:normal'><span
2007style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2008mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Set All</span></b>)
2009and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2010mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2011minor-latin'>OK</span></b>. The General tab for the phase is shown next<br>
2012<span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_7"
2013 o:spid="_x0000_i1093" type="#_x0000_t75" style='width:404.25pt;height:208.5pt;
2014 visibility:visible;mso-wrap-style:square'>
2015 <v:imagedata src="SimpleMagnetic_files/image012.png" o:title=""/>
2016</v:shape><![endif]--><![if !vml]><img border=0 width=539 height=278
2017src="SimpleMagnetic_files/image082.png" v:shapes="Picture_x0020_7"><![endif]></span></p>
2018
2019<h3>Step 4. Check powder pattern indexing</h3>
2020
2021<p class=MsoNormal>Here the objective is to determine how the reflection
2022positions generated from the chemical (“nuclear”) crystal structure lattice
2023match up with the peaks observed for this antiferromagnet. </p>
2024
2025<p class=MsoListParagraphCxSpFirst style='margin-left:.25in;mso-add-space:auto;
2026text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
2027style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
2028style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
2029<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2030mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2031minor-latin'>Unit Cells List</span></b> from the tree entries under the
2032histogram (begins with PWDR); the Indexing controls will be shown<br>
2033<span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8"
2034 o:spid="_x0000_i1092" type="#_x0000_t75" style='width:407.25pt;height:146.25pt;
2035 visibility:visible;mso-wrap-style:square'>
2036 <v:imagedata src="SimpleMagnetic_files/image014.png" o:title=""/>
2037</v:shape><![endif]--><![if !vml]><img border=0 width=543 height=195
2038src="SimpleMagnetic_files/image083.png" v:shapes="Picture_x0020_8"><![endif]></span></p>
2039
2040<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2041auto'>This can be use lattice parameters &amp; space groups to generate
2042expected reflection positions to check against the peaks in the powder pattern.
2043</p>
2044
2045<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2046auto;text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
2047style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
2048style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>One
2049could then enter <span class=SpellE>Bravais</span> lattice, choose space group
2050&amp; enter lattice parameters by hand, but the easy way is to use the chemical
2051lattice directly. Do <b style='mso-bidi-font-weight:normal'><span
2052style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2053mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Cell
2054Index/Refine/Load Cell</span></b> from the menu; a Phase selection box will
2055appear with only one choice (<b style='mso-bidi-font-weight:normal'><span
2056style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2057mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>LaMnO3</span></b>).
2058This was taken from the Phases present in this project; there could be more
2059than one depending on what you loaded/created earlier. The <b style='mso-bidi-font-weight:
2060normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2061minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Import</span></b>
2062menu item allows you to get lattice information from any one of the other phase
2063containing files known to GSAS-II. Press <b style='mso-bidi-font-weight:normal'><span
2064style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2065mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>OK</span></b>
2066and the Indexing controls will be change<br>
2067<span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9"
2068 o:spid="_x0000_i1091" type="#_x0000_t75" style='width:411pt;height:147.75pt;
2069 visibility:visible;mso-wrap-style:square'>
2070 <v:imagedata src="SimpleMagnetic_files/image016.png" o:title=""/>
2071</v:shape><![endif]--><![if !vml]><img border=0 width=548 height=197
2072src="SimpleMagnetic_files/image084.png" v:shapes="Picture_x0020_9"><![endif]></span><br>
2073showing the lattice constants for LaMnO3 you had obtained from the <span
2074class=SpellE>cif</span> file. Note that the space group is set to that of the <span
2075class=SpellE>Bravais</span> lattice (P m <span class=SpellE>m</span> m) and not
2076the space group for LaMnO3 (P n m a).</p>
2077
2078<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2079auto;text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
2080style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3.<span
2081style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Press
2082the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2083mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2084minor-latin'>Show <span class=SpellE>hkl</span> positions</span></b> button;
2085after a short pause (while reflections are generated), the plot will show the
2086calculated reflection line positions.<br>
2087<span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10"
2088 o:spid="_x0000_i1090" type="#_x0000_t75" style='width:414pt;height:354.75pt;
2089 visibility:visible;mso-wrap-style:square'>
2090 <v:imagedata src="SimpleMagnetic_files/image018.png" o:title=""/>
2091</v:shape><![endif]--><![if !vml]><img border=0 width=552 height=473
2092src="SimpleMagnetic_files/image085.png" v:shapes="Picture_x0020_10"><![endif]></span></p>
2093
2094<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2095auto'>This is the reflection set for the <span class=SpellE>Bravais</span>
2096lattice <span class=SpellE>Pmmm</span> which includes <span class=SpellE>relections</span>
2097that may be space group extinct and/or magnetically extinct. N.B., a reflection
2098that is extinct due to the chemical structure space group could still be allowed for magnetic scattering.</p>
2099
2100<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2101auto;text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
2102style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>4.<span
2103style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Zoom
2104in on the lowest part of the pattern to see details of the indexing<br>
2105<span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_11"
2106 o:spid="_x0000_i1089" type="#_x0000_t75" style='width:411pt;height:352.5pt;
2107 visibility:visible;mso-wrap-style:square'>
2108 <v:imagedata src="SimpleMagnetic_files/image020.png" o:title=""/>
2109</v:shape><![endif]--><![if !vml]><img border=0 width=548 height=470
2110src="SimpleMagnetic_files/image086.png" v:shapes="Picture_x0020_11"><![endif]></span></p>
2111
2112<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2113auto'>Note that every observed peak is indexed (unfortunately the peak at
2114~15.69°2&#920; is probably a contaminant – it doesn’t exactly match the two
2115calculated lines that straddle it).</p>
2116
2117<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2118auto;text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
2119style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>5.<span
2120style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Change
2121the space group to <b style='mso-bidi-font-weight:normal'><span
2122style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2123mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>P n m a</span></b>
2124(near the bottom of the pull down); the indexing will immediately change<br>
2125<span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12"
2126 o:spid="_x0000_i1088" type="#_x0000_t75" style='width:408pt;height:349.5pt;
2127 visibility:visible;mso-wrap-style:square'>
2128 <v:imagedata src="SimpleMagnetic_files/image022.png" o:title=""/>
2129</v:shape><![endif]--><![if !vml]><img border=0 width=544 height=466
2130src="SimpleMagnetic_files/image087.png" v:shapes="Picture_x0020_12"><![endif]></span><br>
2131Notice that the 1<sup>st</sup> peak (as well as the contaminant) is no longer
2132indexed; this is likely to be a magnetic only peak as expected from an
2133antiferromagnet; there is another at ~34.4°2&#920;. Reset the space group to <b
2134style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2135mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2136minor-latin'>P m <span class=SpellE>m</span> <span class=SpellE>m</span></span></b>
2137and put the cursor on these two in turn; a popup box will tell you they are the
2138(0,1,0) and (0,1,2) reflections. The two straddling the contaminating peak are
2139the (1<span class=GramE>,0,0</span>) and (0,0,1) reflections; they may be
2140magnetically extinct. There are others that show for <span class=SpellE>Pmmm</span>
2141but vanish for <span class=SpellE>Pnma</span> and have no visible intensity. We
2142don’t know yet if they are magnetically allowed, but are zero because of the
2143magnetic moment direction.</p>
2144
2145<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2146auto;text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span
2147style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>6.<span
2148style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Reset
2149the space group to <b style='mso-bidi-font-weight:normal'><span
2150style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2151mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>P n m a</span></b>;
2152the reflections will again be updated. Then check the box <b style='mso-bidi-font-weight:
2153normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2154minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Magnetic?</span></b>;
2155the tab will be changed showing some more options</p>
2156
2157<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2158auto'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13"
2159 o:spid="_x0000_i1087" type="#_x0000_t75" style='width:405pt;height:146.25pt;
2160 visibility:visible;mso-wrap-style:square'>
2161 <v:imagedata src="SimpleMagnetic_files/image024.png" o:title=""/>
2162</v:shape><![endif]--><![if !vml]><img border=0 width=540 height=195
2163src="SimpleMagnetic_files/image088.png" v:shapes="Picture_x0020_13"><![endif]></span></p>
2164
2165<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2166auto'><span class=GramE>and</span> the powder indexing lines will also change
2167showing every line to be indexed for the magnetic space group “P n m a”.
2168However there are other spin selections (8 in all!) that might be possible. We
2169have to introduce some “time reversal” operations (or “spin flips”). These are
2170given by a choice of “<b style='mso-bidi-font-weight:normal'><span
2171style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2172mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>red</span></b>”
2173or “<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2174mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2175minor-latin'>black</span></b>” for mx, my &amp; <span class=SpellE>mz</span>
2176(the 3 mirrors in <span class=SpellE>Pnma</span>). Try them out by selecting “<b
2177style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2178mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2179minor-latin'>black</span></b>” or “<b style='mso-bidi-font-weight:normal'><span
2180style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2181mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>red</span></b>”
2182for each; each time the plot will show the allowed reflections. Unfortunately
2183this is not very definitive for selecting the magnetic space group; 4 choices
2184will index the 1<sup>st</sup> line &amp; 4 will not. The allowed ones are <span
2185class=SpellE>bbb</span>, <span class=SpellE>rrr</span>, brb &amp; <span
2186class=SpellE>rbr</span> (b=black &amp; r=red). In order to reject the <span
2187class=SpellE>rrr</span> &amp; <span class=SpellE>bbb</span> choices, you have
2188to assume that the peak at ~15.69°2&#920; is a contaminant and that the two
2189reflections next to it 100 &amp; 001 are indeed absent; this leaves two
2190choices, <span class=SpellE>Pn’ma</span>’ and <span class=SpellE>Pnm’a</span>.
2191If you press the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
2192style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2193mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>ShowSpins</span></b></span><b
2194style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2195mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2196minor-latin'>?</span></b> <span class=GramE>button</span>, a popup window will
2197appear showing the magnetic symmetry operators with spin inversion ones in red.
2198For <span class=SpellE>Pn’ma</span>’ (e.g. <span class=SpellE>rbr</span>) the
2199operators are</p>
2200
2201<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2202auto'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14"
2203 o:spid="_x0000_i1086" type="#_x0000_t75" style='width:192pt;height:160.5pt;
2204 visibility:visible;mso-wrap-style:square'>
2205 <v:imagedata src="SimpleMagnetic_files/image026.png" o:title=""/>
2206</v:shape><![endif]--><![if !vml]><img border=0 width=256 height=214
2207src="SimpleMagnetic_files/image089.png" v:shapes="Picture_x0020_14"><![endif]></span></p>
2208
2209<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2210auto'><span class=GramE>and</span> the ones for <span class=SpellE>Pnm’a</span>
2211(e.g. brb) are</p>
2212
2213<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2214auto'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15"
2215 o:spid="_x0000_i1085" type="#_x0000_t75" style='width:192pt;height:160.5pt;
2216 visibility:visible;mso-wrap-style:square'>
2217 <v:imagedata src="SimpleMagnetic_files/image028.png" o:title=""/>
2218</v:shape><![endif]--><![if !vml]><img border=0 width=256 height=214
2219src="SimpleMagnetic_files/image090.png" v:shapes="Picture_x0020_15"><![endif]></span></p>
2220
2221<p class=MsoListParagraphCxSpLast style='margin-left:.25in;mso-add-space:auto'>It
2222is worthwhile noticing that the inversion operator (-1) is red in the latter
2223but not in the former since an atom at an inversion center cannot have a
2224magnetic moment if there is also spin inversion. More about this later. Press <b
2225style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2226mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2227minor-latin'>OK</span></b> to get rid of the popup box. To narrow down the
2228choice we have to examine what happens to the atoms for each choice. In some
2229cases the choice might not allow the <span class=SpellE>Mn</span> atom to have
2230a magnetic moment so it must be rejected. We will try this in the next step. </p>
2231
2232<h3>Step 5. Make the magnetic phase</h3>
2233
2234<p class=MsoNormal>In the previous step we did not have to resort to any doubling
2235of a cell axis to explain the suite of magnetic reflections, so the propagation
2236vector is zero (in case anyone asks!). To make the magnetic cell from the
2237chemical cell we will use the transform tool that is in GSAS-II in the General
2238tab for the chemical structure. That tab is</p>
2239
2240<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2241 id="Picture_x0020_16" o:spid="_x0000_i1084" type="#_x0000_t75" style='width:468pt;
2242 height:230.25pt;visibility:visible;mso-wrap-style:square'>
2243 <v:imagedata src="SimpleMagnetic_files/image030.png" o:title=""/>
2244</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=307
2245src="SimpleMagnetic_files/image091.png" v:shapes="Picture_x0020_16"><![endif]></span></p>
2246
2247<p class=MsoNormal>Under the <b style='mso-bidi-font-weight:normal'><span
2248style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2249mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Compute</span></b>
2250menu item do <b style='mso-bidi-font-weight:normal'><span style='font-family:
2251"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2252minor-latin;mso-bidi-theme-font:minor-latin'>Transform</span></b>; a new popup
2253dialog box will appear with stuff needed to effect a cell transformation.</p>
2254
2255<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2256 id="Picture_x0020_76" o:spid="_x0000_i1083" type="#_x0000_t75" style='width:274.5pt;
2257 height:327pt;visibility:visible;mso-wrap-style:square'>
2258 <v:imagedata src="SimpleMagnetic_files/image029.png" o:title=""/>
2259</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=436
2260src="SimpleMagnetic_files/image029.png" v:shapes="Picture_x0020_76"><![endif]></span></p>
2261
2262<p class=MsoNormal>The order of operations for the transformation is given at
2263the top of the window; the U vector permits applying an origin shift to the atom
2264coordinates before the transformation and the V vector is for an origin shift
2265after the transformation. The lattice parameters are transformed by changing
2266the metric tensor via</p>
2267
2268<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2269
2270<p class=MsoNormal><span class=GramE>g</span>’ = <span class=SpellE>gM</span></p>
2271
2272<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2273
2274<p class=MsoNormal>The atoms positions are transformed via</p>
2275
2276<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2277
2278<p class=MsoNormal>X’ = M*(X-U<span class=GramE>)+</span>V</p>
2279
2280<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2281
2282<p class=MsoNormal><span class=GramE>where</span> M* is the inverse of the
2283transformation matrix. The anisotropic thermal parameters are transformed via</p>
2284
2285<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2286
2287<p class=MsoNormal>U’ = M<sup>T</sup>UM/<span class=SpellE><span class=GramE>det</span></span><span
2288class=GramE>(</span>M)</p>
2289
2290<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2291
2292<p class=MsoNormal>The dialog box gives an extensive list of commonly used
2293transformations for e.g. swapping axes. In this case we are not transforming the
2294unit cell so the matrix is just the unit matrix (ones on diagonal) and we are
2295not shifting the origin so U &amp; V are zeros. We do want the new phase to be
2296magnetic so press the <b style='mso-bidi-font-weight:normal'><span
2297style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2298mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Make new
2299phase magnetic</span></b> button; the dialog will be redrawn</p>
2300
2301<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2302 id="Picture_x0020_77" o:spid="_x0000_i1082" type="#_x0000_t75" style='width:274.5pt;
2303 height:324.75pt;visibility:visible;mso-wrap-style:square'>
2304 <v:imagedata src="SimpleMagnetic_files/image031.png" o:title=""/>
2305</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=433
2306src="SimpleMagnetic_files/image031.png" v:shapes="Picture_x0020_77"><![endif]></span></p>
2307
2308<p class=MsoNormal>This allows one to select possible magnetic lattice
2309centering operations as given by the BNS nomenclature. This can be needed if
2310one had discovered a requirement of doubling a cell axis in the previous step
2311(e.g. a nonzero propagation vector). This is not required in this case and we
2312are using the space group (<span class=SpellE>Pnma</span>) for the magnetic
2313cell. Leave the box at the bottom about constraints checked as we want them to
2314tie the two phases together.<span style='mso-spacerun:yes'>  </span>Press <b
2315style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2316mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2317minor-latin'>Ok</span></b> to continue; a new popup will appear</p>
2318
2319<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2320 id="_x0000_i1081" type="#_x0000_t75" style='width:181.5pt;height:80.25pt;
2321 visibility:visible;mso-wrap-style:square'>
2322 <v:imagedata src="SimpleMagnetic_files/image034.png" o:title=""/>
2323</v:shape><![endif]--><![if !vml]><img border=0 width=242 height=107
2324src="SimpleMagnetic_files/image034.png" v:shapes="_x0000_i1081"><![endif]></span></p>
2325
2326<p class=MsoNormal>This allows one to reject certain atoms that are known to
2327not be magnetic; press <b style='mso-bidi-font-weight:normal'><span
2328style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2329mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Ok</span></b>
2330to continue. A new phase will be created and the General tab for it will be
2331shown.</p>
2332
2333<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2334 id="_x0000_i1080" type="#_x0000_t75" style='width:468pt;height:270pt;
2335 visibility:visible;mso-wrap-style:square'>
2336 <v:imagedata src="SimpleMagnetic_files/image035.png" o:title=""/>
2337</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=360
2338src="SimpleMagnetic_files/image092.png" v:shapes="_x0000_i1080"><![endif]></span></p>
2339
2340<p class=MsoNormal>The phase is named with “mag” appended to the end, the phase
2341type is magnetic and there are magnetic spin operator selections part way down
2342the page. You also can see the <span class=SpellE>Lande</span>’ g factor can be
2343changed if needed and it only contains the <span class=SpellE>Mn</span> atom.
2344To see what happened with respect to constraints, select <b style='mso-bidi-font-weight:
2345normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2346minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Constraints</span></b>
2347from the main part of the GSAS-II data tree. The ones for phases will be shown</p>
2348
2349<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2350 id="_x0000_i1079" type="#_x0000_t75" style='width:387.75pt;height:264.75pt;
2351 visibility:visible;mso-wrap-style:square'>
2352 <v:imagedata src="SimpleMagnetic_files/image037.png" o:title=""/>
2353</v:shape><![endif]--><![if !vml]><img border=0 width=517 height=353
2354src="SimpleMagnetic_files/image093.png" v:shapes="_x0000_i1079"><![endif]></span></p>
2355
2356<p class=MsoNormal>This shows all the possible required constraints between the
2357chemical structure and the magnetic one. The first eight are for the <span
2358class=SpellE>Mn</span> atom; only the <span class=SpellE>Uiso</span> one is
2359probably necessary for this analysis but the others will do no harm. The last
2360three tie the lattices together. Select the <span class=SpellE><b
2361style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2362mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2363minor-latin'>Histgram</span></b></span><b style='mso-bidi-font-weight:normal'><span
2364style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2365mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>/Phase</span></b>
2366tab</p>
2367
2368<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2369 id="Picture_x0020_32" o:spid="_x0000_i1078" type="#_x0000_t75" style='width:386.25pt;
2370 height:139.5pt;visibility:visible;mso-wrap-style:square'>
2371 <v:imagedata src="SimpleMagnetic_files/image039.png" o:title=""/>
2372</v:shape><![endif]--><![if !vml]><img border=0 width=515 height=186
2373src="SimpleMagnetic_files/image095.png" v:shapes="Picture_x0020_32"><![endif]></span></p>
2374
2375<p class=MsoNormal>This gives the constraints between the two phases for scale factors
2376(e.g. phase fractions) and the size &amp; mustrain sample broadening terms. NB:
2377this assumes isotropic modelling of both because the original LaMnO<sub>3</sub>
2378was modeled that way. If you want to use one of the more complex sample
2379broadening models, you will have to revisit this tab and put in the appropriate
2380entries to tie those parameters together.</p>
2381
2382<h3>Step 6. Select spin configuration</h3>
2383
2384<p class=MsoNormal>Recall that we had found 2 spin configurations that were
2385consistent with the observed peaks; <span class=SpellE>Pn’ma</span>’ and <span
2386class=SpellE>Pnm’a</span> (there was also the possibility of <span
2387class=SpellE>Pnma</span> or <span class=SpellE>Pn’m’a</span>’ if one chose not
2388to ignore that contaminating peak at ~15.69°2&#920;). First let’s try <span
2389class=SpellE>Pnm’a</span>; select “<b style='mso-bidi-font-weight:normal'><span
2390style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2391mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>red</span></b>”
2392for the middle spin selector (<b style='mso-bidi-font-weight:normal'><span
2393style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2394mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>my</span></b>);
2395the window will be refreshed. Then select the <b style='mso-bidi-font-weight:
2396normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2397minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Atoms</span></b>
2398tab; it will show</p>
2399
2400<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2401 id="Picture_x0020_23" o:spid="_x0000_i1077" type="#_x0000_t75" style='width:468pt;
2402 height:111.75pt;visibility:visible;mso-wrap-style:square'>
2403 <v:imagedata src="SimpleMagnetic_files/image041.png" o:title=""/>
2404</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=149
2405src="SimpleMagnetic_files/image097.png" v:shapes="Picture_x0020_23"><![endif]></span></p>
2406
2407<p class=MsoNormal>The boxes that carry the magnetic moment components (<span
2408class=SpellE>Mx</span>, My &amp; <span class=SpellE>Mz</span>) are grey
2409indicating that no magnetic moment is allowed for the <span class=SpellE>Mn</span>
2410atom site in the space group <span class=SpellE>Pnm’a</span>. The site symmetry
2411is marked as -1’ indicating an inversion center with spin inversion; this
2412precludes a magnetic moment. So we need to try the other choice, <span
2413class=SpellE>Pn’ma</span>’. Return to the <b style='mso-bidi-font-weight:normal'><span
2414style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2415mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>General</span></b>
2416tab and change the <b style='mso-bidi-font-weight:normal'><span
2417style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2418mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>mx</span></b>,
2419<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2420mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2421minor-latin'>my</span></b> &amp; <span class=SpellE><b style='mso-bidi-font-weight:
2422normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2423minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>mz</span></b></span>
2424spin operators to “<b style='mso-bidi-font-weight:normal'><span
2425style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2426mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>red</span></b>”,
2427“<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2428mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2429minor-latin'>black</span></b>” &amp; “<b style='mso-bidi-font-weight:normal'><span
2430style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2431mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>red</span></b>”,
2432respectively. The tab will refresh at each change. When done it should look
2433like</p>
2434
2435<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2436 id="Picture_x0020_24" o:spid="_x0000_i1076" type="#_x0000_t75" style='width:468pt;
2437 height:231pt;visibility:visible;mso-wrap-style:square'>
2438 <v:imagedata src="SimpleMagnetic_files/image043.png" o:title=""/>
2439</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=308
2440src="SimpleMagnetic_files/image098.png" v:shapes="Picture_x0020_24"><![endif]></span></p>
2441
2442<p class=MsoNormal>It now shows the magnetic space group as <span class=SpellE>Pn’ma</span>’.
2443The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2444mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2445minor-latin'>Atoms</span></b> tab now shows</p>
2446
2447<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2448 id="Picture_x0020_25" o:spid="_x0000_i1075" type="#_x0000_t75" style='width:468pt;
2449 height:121.5pt;visibility:visible;mso-wrap-style:square'>
2450 <v:imagedata src="SimpleMagnetic_files/image045.png" o:title=""/>
2451</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=162
2452src="SimpleMagnetic_files/image099.png" v:shapes="Picture_x0020_25"><![endif]></span></p>
2453
2454<p class=MsoNormal><span class=GramE>with</span> 0.0 in each of the magnetic
2455moment components, because the site symmetry is -1 which allows a magnetic
2456moment. We can now give the <span class=SpellE>Mn</span> atom a magnetic
2457moment. You can also try the other two choices, <span class=SpellE>Pnma</span>
2458and <span class=SpellE>Pn’m’a</span>’. The latter can be rejected immediately
2459because the -1 operator has spin inversion (use the <b style='mso-bidi-font-weight:
2460normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2461minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Show
2462spins?</span></b> button to show the operators), leaving only <span
2463class=SpellE>Pnma</span> as a possibility along with <span class=SpellE>Pn’ma</span>’.
2464Both allow the <span class=SpellE>Mn</span> site to have a magnetic moment. Put
2465the choice to <span class=SpellE>Pn’ma</span>’ (“red”, “black” &amp; “red”);
2466we’ll test <span class=SpellE>Pnma</span> later. This might be a good place to
2467save the project; I called it “<b style='mso-bidi-font-weight:normal'><span
2468style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2469mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>LaMnO3.gpx</span></b>”.</p>
2470
2471<h3>Step 7. Solving the magnetic structure</h3>
2472
2473<h4 style='margin-left:.25in;text-indent:-.25in;mso-list:l5 level1 lfo8'><![if !supportLists]><span
2474style='mso-fareast-font-family:"Calibri Light";mso-fareast-theme-font:major-latin;
2475mso-bidi-font-family:"Calibri Light";mso-bidi-theme-font:major-latin'><span
2476style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
2477</span></span></span><![endif]>Test the <span class=SpellE>Pn’ma</span>’ model</h4>
2478
2479<p class=MsoNormal>So now we have one or maybe two spin arrangements to
2480consider, <span class=SpellE>Pn’ma</span>’ and possibly <span class=SpellE>Pnma</span>,
2481but we do not know the magnetic moment components, <span class=SpellE>Mx</span>,
2482My &amp; <span class=SpellE>Mz</span>. However, since the 1<sup>st </sup>reflection
2483(the 010) is magnetic and strong, it is likely that the value of <span
2484class=GramE>My=</span>0. We can force this (to avoid refinement problems) by
2485making a ‘hold’ on its value. Select the <b style='mso-bidi-font-weight:normal'><span
2486style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2487mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Constraints</span></b>
2488item from the GSAS-II tree; it will show the constraints generated when the
2489magnetic phase was made</p>
2490
2491<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2492 id="Picture_x0020_26" o:spid="_x0000_i1074" type="#_x0000_t75" style='width:315.75pt;
2493 height:230.25pt;visibility:visible;mso-wrap-style:square'>
2494 <v:imagedata src="SimpleMagnetic_files/image047.png" o:title=""/>
2495</v:shape><![endif]--><![if !vml]><img border=0 width=421 height=307
2496src="SimpleMagnetic_files/image100.png" v:shapes="Picture_x0020_26"><![endif]></span></p>
2497
2498<p class=MsoNormal>Under the <b style='mso-bidi-font-weight:normal'><span
2499style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2500mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Edit <span
2501class=SpellE>Costr</span>.</span></b> <span class=GramE>menu</span> item do <b
2502style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2503mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2504minor-latin'>Add hold</span></b>; a Hold phase variable window will appear</p>
2505
2506<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2507 id="Picture_x0020_34" o:spid="_x0000_i1073" type="#_x0000_t75" style='width:333pt;
2508 height:168.75pt;visibility:visible;mso-wrap-style:square'>
2509 <v:imagedata src="SimpleMagnetic_files/image049.png" o:title=""/>
2510</v:shape><![endif]--><![if !vml]><img border=0 width=444 height=225
2511src="SimpleMagnetic_files/image101.png" v:shapes="Picture_x0020_34"><![endif]></span></p>
2512
2513<p class=MsoNormal>Scroll down to the bottom and select <b style='mso-bidi-font-weight:
2514normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2515minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>1:<span
2516class=GramE>:AMy:0</span></span></b> and press <b style='mso-bidi-font-weight:
2517normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2518minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>OK</span></b>.
2519The constraints will have a new entry giving the hold on <span class=GramE>My</span>
2520for the <span class=SpellE>Mn</span> atom at the bottom of the list. </p>
2521
2522<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2523 id="Picture_x0020_35" o:spid="_x0000_i1072" type="#_x0000_t75" style='width:312pt;
2524 height:227.25pt;visibility:visible;mso-wrap-style:square'>
2525 <v:imagedata src="SimpleMagnetic_files/image051.png" o:title=""/>
2526</v:shape><![endif]--><![if !vml]><img border=0 width=416 height=303
2527src="SimpleMagnetic_files/image102.png" v:shapes="Picture_x0020_35"><![endif]></span></p>
2528
2529<p class=MsoNormal>Now return to phases and select <b style='mso-bidi-font-weight:
2530normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2531minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>La
2532<span class=SpellE>Mn</span> O3 mag</span></b> and the <b style='mso-bidi-font-weight:
2533normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2534minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Atoms</span></b>
2535tab; you should see</p>
2536
2537<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2538 id="Picture_x0020_37" o:spid="_x0000_i1071" type="#_x0000_t75" style='width:366.75pt;
2539 height:75.75pt;visibility:visible;mso-wrap-style:square'>
2540 <v:imagedata src="SimpleMagnetic_files/image053.png" o:title=""/>
2541</v:shape><![endif]--><![if !vml]><img border=0 width=489 height=101
2542src="SimpleMagnetic_files/image103.png" v:shapes="Picture_x0020_37"><![endif]></span></p>
2543
2544<p class=MsoNormal>The least squares will not begin a refinement of <span
2545class=SpellE>Mx</span> &amp; <span class=SpellE>Mz</span> starting from zero
2546since either +/- values are equally possible; the result will be a singularity.
2547So these values must be offset so set them to <b style='mso-bidi-font-weight:
2548normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2549minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>1.0</span></b>
2550each. Save the project as <b style='mso-bidi-font-weight:normal'><span
2551style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2552mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>LaMnO3 try1</span></b>.
2553Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2554mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2555minor-latin'>Calculate/Refine</span></b>; the refinement will quickly converge
2556to <span class=SpellE>Rwp</span> ~14% and the powder plot will look like</p>
2557
2558<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2559 id="Picture_x0020_30" o:spid="_x0000_i1070" type="#_x0000_t75" style='width:463.5pt;
2560 height:425.25pt;visibility:visible;mso-wrap-style:square'>
2561 <v:imagedata src="SimpleMagnetic_files/image055.png" o:title=""/>
2562</v:shape><![endif]--><![if !vml]><img border=0 width=618 height=567
2563src="SimpleMagnetic_files/image105.png" v:shapes="Picture_x0020_30"><![endif]></span></p>
2564
2565<p class=MsoNormal>There does not appear to be any calculated magnetic
2566intensity, but a zoom onto the low angle (10-30°2&#920;) part of the pattern
2567shows that some intensity was obtained, but clearly not enough.</p>
2568
2569<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2570 id="Picture_x0020_31" o:spid="_x0000_i1069" type="#_x0000_t75" style='width:463.5pt;
2571 height:425.25pt;visibility:visible;mso-wrap-style:square'>
2572 <v:imagedata src="SimpleMagnetic_files/image057.png" o:title=""/>
2573</v:shape><![endif]--><![if !vml]><img border=0 width=618 height=567
2574src="SimpleMagnetic_files/image107.png" v:shapes="Picture_x0020_31"><![endif]></span></p>
2575
2576<p class=MsoNormal>The magnetic moment is clearly too small; to let the least
2577squares find a better value set the refine flag for <span class=SpellE>Mn</span>
2578to ‘<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2579mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2580minor-latin'>M</span></b>’ and repeat <b style='mso-bidi-font-weight:normal'><span
2581style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2582mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b>.
2583The residual will drop considerably to <span class=SpellE>Rwp</span> ~8.7% and
2584the low angle portion will show a much better fit.</p>
2585
2586<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2587 id="_x0000_i1068" type="#_x0000_t75" style='width:463.5pt;height:426pt;
2588 visibility:visible;mso-wrap-style:square'>
2589 <v:imagedata src="SimpleMagnetic_files/image059.png" o:title=""/>
2590</v:shape><![endif]--><![if !vml]><img border=0 width=618 height=568
2591src="SimpleMagnetic_files/image108.png" v:shapes="_x0000_i1068"><![endif]></span></p>
2592
2593<p class=MsoNormal>This appears to be a reasonable solution; a more complete
2594refinement still needs to be done, we’ll do that in the next step after we test
2595the <span class=SpellE>Pnma</span> model. Save the project (should be <b
2596style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2597mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2598minor-latin'>LaMnO3 try1</span></b>).</p>
2599
2600<h4 style='margin-left:.25in;text-indent:-.25in;mso-list:l5 level1 lfo8'><![if !supportLists]><span
2601style='mso-fareast-font-family:"Calibri Light";mso-fareast-theme-font:major-latin;
2602mso-bidi-font-family:"Calibri Light";mso-bidi-theme-font:major-latin'><span
2603style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
2604</span></span></span><![endif]>Test the <span class=SpellE>Pnma</span> model</h4>
2605
2606<p class=MsoNormal>Now reopen the original <b style='mso-bidi-font-weight:normal'><span
2607style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2608mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>LaMnO3.gpx</span></b>
2609file saved at the end of Step 6 above. Select <b style='mso-bidi-font-weight:
2610normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2611minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>La
2612<span class=SpellE>Mn</span> O3 mag</span></b> phase from the GSAS-II tree; the
2613General tab will be shown</p>
2614
2615<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2616 id="Picture_x0020_33" o:spid="_x0000_i1067" type="#_x0000_t75" style='width:465.75pt;
2617 height:263.25pt;visibility:visible;mso-wrap-style:square'>
2618 <v:imagedata src="SimpleMagnetic_files/image061.png" o:title=""/>
2619</v:shape><![endif]--><![if !vml]><img border=0 width=621 height=351
2620src="SimpleMagnetic_files/image109.png" v:shapes="Picture_x0020_33"><![endif]></span></p>
2621
2622<p class=MsoNormal>Now set the spin operators to all “<b style='mso-bidi-font-weight:
2623normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2624minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>black</span></b>”
2625for <span class=SpellE>Pnma</span> and then select the <b style='mso-bidi-font-weight:
2626normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2627minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Atoms</span></b>
2628tab</p>
2629
2630<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2631 id="Picture_x0020_18" o:spid="_x0000_i1066" type="#_x0000_t75" style='width:464.25pt;
2632 height:93pt;visibility:visible;mso-wrap-style:square'>
2633 <v:imagedata src="SimpleMagnetic_files/image063.png" o:title=""/>
2634</v:shape><![endif]--><![if !vml]><img border=0 width=619 height=124
2635src="SimpleMagnetic_files/image113.png" v:shapes="Picture_x0020_18"><![endif]></span></p>
2636
2637<p class=MsoNormal>Again, one can make the same argument that since the 010
2638reflection is large then <span class=GramE>My</span> should be zero. Set <span
2639class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
2640"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2641minor-latin;mso-bidi-theme-font:minor-latin'>Mx</span></b></span> &amp; <span
2642class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
2643"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2644minor-latin;mso-bidi-theme-font:minor-latin'>Mz</span></b></span> to 1.0 and
2645then go to <b style='mso-bidi-font-weight:normal'><span style='font-family:
2646"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2647minor-latin;mso-bidi-theme-font:minor-latin'>Constraints</span></b> and set the
2648hold on <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2649mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2650minor-latin'>1:<span class=GramE>:AMy:0</span></span></b>. Save the project as <b
2651style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2652mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2653minor-latin'>LaMnO3 try2</span></b>. Do <b style='mso-bidi-font-weight:normal'><span
2654style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2655mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b>
2656from the main menu to do a Rietveld refinement. It converges to <span
2657class=SpellE>Rwp</span> ~14%; about the same as the <span class=SpellE>Pn’ma</span>’
2658model at the same step. The low angle portion of the powder pattern shows</p>
2659
2660<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2661 id="Picture_x0020_19" o:spid="_x0000_i1065" type="#_x0000_t75" style='width:464.25pt;
2662 height:426pt;visibility:visible;mso-wrap-style:square'>
2663 <v:imagedata src="SimpleMagnetic_files/image065.png" o:title=""/>
2664</v:shape><![endif]--><![if !vml]><img border=0 width=619 height=568
2665src="SimpleMagnetic_files/image115.png" v:shapes="Picture_x0020_19"><![endif]></span></p>
2666
2667<p class=MsoNormal>There is intensity in the lowest angle reflection (the 010)
2668but not enough. Again we’ll try to refine the <span class=SpellE>Mx</span>
2669&amp; <span class=SpellE>Mz</span> components to see what happens. Set the
2670refine flag for <span class=SpellE>Mn</span> to ‘<b style='mso-bidi-font-weight:
2671normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2672minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>M</span></b>’
2673and repeat <b style='mso-bidi-font-weight:normal'><span style='font-family:
2674"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2675minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b>. The
2676residual will drop to <span class=SpellE>Rwp</span> ~10% and the low angle
2677portion will show a much better fit which is very similar, but slightly poorer
2678than the result from the <span class=SpellE>Pn’ma</span>’ model. To see how,
2679examine a slightly higher angle region (30-55°2&#920;) and compare it with the
2680same region for the plot for the <span class=SpellE>Pn’ma</span>’ model (you’ll
2681need2 instances of GSAS-II running to do this)</p>
2682
2683<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2684 id="Picture_x0020_20" o:spid="_x0000_i1064" type="#_x0000_t75" style='width:459pt;
2685 height:188.25pt;visibility:visible;mso-wrap-style:square'>
2686 <v:imagedata src="SimpleMagnetic_files/image104.png" o:title=""/>
2687</v:shape><![endif]--><![if !vml]><img border=0 width=612 height=251
2688src="SimpleMagnetic_files/image116.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
2689
2690<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2691 id="Picture_x0020_21" o:spid="_x0000_i1063" type="#_x0000_t75" style='width:457.5pt;
2692 height:176.25pt;visibility:visible;mso-wrap-style:square'>
2693 <v:imagedata src="SimpleMagnetic_files/image106.png" o:title=""/>
2694</v:shape><![endif]--><![if !vml]><img border=0 width=610 height=235
2695src="SimpleMagnetic_files/image117.png" v:shapes="Picture_x0020_21"><![endif]></span></p>
2696
2697<p class=MsoNormal>You can see in particular at the pair of peaks at 33.3 and
269834.4°2&#920; that are well fit by the <span class=SpellE>Pn’ma</span>’ model
2699and not by the <span class=SpellE>Pnma</span> one. On this basis the <span
2700class=SpellE>Pnma</span> model is rejected and the <span class=SpellE>Pn’ma</span>’
2701is selected as probably correct. NB: neither model produced any intensity for
2702the peak at ~15.69°2&#920;, so it is most likely to be from a minor
2703contaminating phase; we can either ignore it or exclude it in the final
2704refinements.</p>
2705
2706<h3>Step 8. Complete refinement of the <span class=SpellE>Pn’ma</span>’ model
2707for LaMnO<sub>3</sub></h3>
2708
2709<p class=MsoNormal>Reload the <b style='mso-bidi-font-weight:normal'><span
2710style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2711mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>LaMnO3
2712try1.gpx</span></b> project file which should have the <span class=SpellE>Pn’ma</span>’
2713model for the magnetic structure, and look at the powder pattern to decide how
2714to proceed to complete the refinement.</p>
2715
2716<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2717 id="Picture_x0020_38" o:spid="_x0000_i1062" type="#_x0000_t75" style='width:454.5pt;
2718 height:396pt;visibility:visible;mso-wrap-style:square'>
2719 <v:imagedata src="SimpleMagnetic_files/image110.png" o:title=""/>
2720</v:shape><![endif]--><![if !vml]><img border=0 width=606 height=528
2721src="SimpleMagnetic_files/image118.png" v:shapes="Picture_x0020_38"><![endif]></span></p>
2722
2723<p class=MsoNormal>Looking at the plot, it would seem that the lattice
2724parameters and sample position need to be refined. It is important to remember
2725that if a parameter in one phase is varied then the corresponding one in the
2726other phase must also be varied, otherwise GSAS-II will report the error and
2727refuse to attempt the refinement. To set refinement of the lattice parameters,
2728bring up the <b style='mso-bidi-font-weight:normal'><span style='font-family:
2729"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2730minor-latin;mso-bidi-theme-font:minor-latin'>General</span></b> tab for each
2731phase &amp; check the <b style='mso-bidi-font-weight:normal'><span
2732style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2733mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Refine unit
2734cell</span></b> box for the lattice parameters. Then select <b
2735style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2736mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2737minor-latin'>Sample Parameters</span></b> for the PWDR entry</p>
2738
2739<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2740 id="Picture_x0020_39" o:spid="_x0000_i1061" type="#_x0000_t75" style='width:359.25pt;
2741 height:237.75pt;visibility:visible;mso-wrap-style:square'>
2742 <v:imagedata src="SimpleMagnetic_files/image114.png" o:title=""/>
2743</v:shape><![endif]--><![if !vml]><img border=0 width=479 height=317
2744src="SimpleMagnetic_files/image122.png" v:shapes="Picture_x0020_39"><![endif]></span></p>
2745
2746<p class=MsoNormal>Since the scan covers a very wide range in 2<span
2747style='font-family:Symbol'>Q</span>, both sample displacements can be refined.
2748Check both <b style='mso-bidi-font-weight:normal'><span style='font-family:
2749"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2750minor-latin;mso-bidi-theme-font:minor-latin'>Sample X</span></b> and <b
2751style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2752mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2753minor-latin'>Y <span class=SpellE>displ</span></span></b> parameters. NB: if
2754the correct <b style='mso-bidi-font-weight:normal'><span style='font-family:
2755"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2756minor-latin;mso-bidi-theme-font:minor-latin'>Goniometer radius</span></b> (<b
2757style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2758mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2759minor-latin'>650</span></b>mm) is used, these displacements will be in microns.
2760Also, it would appear that the instrument parameters do not adequately describe
2761the anisotropic broadening of the lowest angle reflection so we will need to
2762include that. Select <b style='mso-bidi-font-weight:normal'><span
2763style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2764mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Instrument
2765Parameters</span></b> from the PWDR entry and check the <b style='mso-bidi-font-weight:
2766normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
2767minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>SH/L
2768Refine</span></b> box. Now do <b style='mso-bidi-font-weight:normal'><span
2769style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2770mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b>
2771until convergence is achieved (i.e. <span class=SpellE>Rwp</span> doesn’t
2772change). This will be 2-3 times. When done my <span class=SpellE>Rwp</span> was
2773~6.6% with a nice clean plot</p>
2774
2775<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2776 id="Picture_x0020_40" o:spid="_x0000_i1060" type="#_x0000_t75" style='width:465pt;
2777 height:404.25pt;visibility:visible;mso-wrap-style:square'>
2778 <v:imagedata src="SimpleMagnetic_files/image072.png" o:title=""/>
2779</v:shape><![endif]--><![if !vml]><img border=0 width=620 height=539
2780src="SimpleMagnetic_files/image123.png" v:shapes="Picture_x0020_40"><![endif]></span></p>
2781
2782<p class=MsoNormal>Now we can add refinement of the atom positions and thermal
2783parameters. For <b style='mso-bidi-font-weight:normal'><span style='font-family:
2784"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2785minor-latin;mso-bidi-theme-font:minor-latin'>Atoms</span></b> tab of the <b
2786style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2787mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2788minor-latin'>La <span class=SpellE>Mn</span> O3</span></b> </p>
2789
2790<p class=MsoNormal>Phase, double click the refine column heading and select <b
2791style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2792mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2793minor-latin'>X</span></b> &amp; <b style='mso-bidi-font-weight:normal'><span
2794style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2795mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>U.</span></b>
2796This will add these parameters as allowed by symmetry to the refinement. Now go
2797to the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2798mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2799minor-latin'>Atoms</span></b> tab for <b style='mso-bidi-font-weight:normal'><span
2800style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2801mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>La <span
2802class=SpellE>Mn</span> O3 mag</span></b> and double click the refine tab.
2803Select <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;mso-bidi-theme-font:
2805minor-latin'>U</span></b> &amp; <b style='mso-bidi-font-weight:normal'><span
2806style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2807mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>M</span></b>;
2808the <span class=SpellE>Uiso</span> for the <span class=SpellE>Mn</span> atom is
2809tied via a constraint to the <span class=SpellE>Mn</span> in the other phase.
2810Now select <b style='mso-bidi-font-weight:normal'><span style='font-family:
2811"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2812minor-latin;mso-bidi-theme-font:minor-latin'>Background</span></b> from the <b
2813style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2814mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2815minor-latin'>PWDR</span></b> entry and increase the number of terms to <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;mso-bidi-theme-font:
2818minor-latin'>6</span></b>. Finally do <b style='mso-bidi-font-weight:normal'><span
2819style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2820mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b>
2821until convergence (1-2 times). My <span class=SpellE>Rwp</span> was 6.29% with
2822a plot that is hardly different from the previous one. If you press the ‘<b
2823style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2824mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2825minor-latin'></span></b> key with the focus on the plot, GSAS-II will show
2826the weighted difference curve below the plot</p>
2827
2828<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2829 id="Picture_x0020_41" o:spid="_x0000_i1059" type="#_x0000_t75" style='width:461.25pt;
2830 height:395.25pt;visibility:visible;mso-wrap-style:square'>
2831 <v:imagedata src="SimpleMagnetic_files/image121.png" o:title=""/>
2832</v:shape><![endif]--><![if !vml]><img border=0 width=615 height=527
2833src="SimpleMagnetic_files/image124.png" v:shapes="Picture_x0020_41"><![endif]></span></p>
2834
2835<p class=MsoNormal>This curve shows a couple of peaks which are from some
2836contaminating phase, but otherwise the fluctuations are mostly within 2<span
2837style='font-family:Symbol'>s</span> of zero. Finally examine the magnetic
2838moment components of the <span class=SpellE>Mn</span> atom; <span class=SpellE><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;mso-bidi-theme-font:
2841minor-latin'>Mz</span></b></span> is close to zero. It is likely that it is
2842zero; set it to <b style='mso-bidi-font-weight:normal'><span style='font-family:
2843"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2844minor-latin;mso-bidi-theme-font:minor-latin'>zero</span></b> and then go to the
2845<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2846mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2847minor-latin'>Constraints</span></b> tree item and add a hold for the <b
2848style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2849mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2850minor-latin'>1::AMz:0</span></b> parameter so that it stays at zero. Repeat the
2851refinement; the residual is unchanged showing that setting <span class=SpellE>Mz</span>=0
2852was a valid assumption.</p>
2853
2854<h3>Step 9. Draw the magnetic structure of LaMnO<sub>3</sub></h3>
2855
2856<p class=MsoNormal>To draw the magnetic structure select the <b
2857style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2858mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2859minor-latin'>Draw Atoms</span></b> tab for the magnetic phase. The table will
2860have a single line matching that of the Atoms table with a few extra columns.</p>
2861
2862<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2863 id="Picture_x0020_42" o:spid="_x0000_i1058" type="#_x0000_t75" style='width:461.25pt;
2864 height:96.75pt;visibility:visible;mso-wrap-style:square'>
2865 <v:imagedata src="SimpleMagnetic_files/image111.png" o:title=""/>
2866</v:shape><![endif]--><![if !vml]><img border=0 width=615 height=129
2867src="SimpleMagnetic_files/image125.png" v:shapes="Picture_x0020_42"><![endif]></span></p>
2868
2869<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2870
2871<p class=MsoNormal>The plot will show one atom with magnetic moment. Select the
2872atom in the table and do <span class=GramE><b style='mso-bidi-font-weight:normal'><span
2873style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2874mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Edit</span></b></span><b
2875style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2876mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2877minor-latin'> Figure/Fill unit cell</span></b>. The table will show additional
2878entries</p>
2879
2880<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2881 id="Picture_x0020_44" o:spid="_x0000_i1057" type="#_x0000_t75" style='width:462pt;
2882 height:185.25pt;visibility:visible;mso-wrap-style:square'>
2883 <v:imagedata src="SimpleMagnetic_files/image119.png" o:title=""/>
2884</v:shape><![endif]--><![if !vml]><img border=0 width=616 height=247
2885src="SimpleMagnetic_files/image131.png" v:shapes="Picture_x0020_44"><![endif]></span></p>
2886
2887<p class=MsoNormal>The plot will show the unit cell contents of <span
2888class=SpellE>Mn</span> atoms each with its magnetic moment; they are arranged
2889in layers along the b-axis with the <span class=GramE>moments</span>
2890antiparallel from one layer to the next. Some are red indicating that a spin
2891inversion operation was applied for that atom moment.</p>
2892
2893<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2894 id="Picture_x0020_45" o:spid="_x0000_i1056" type="#_x0000_t75" style='width:457.5pt;
2895 height:384.75pt;visibility:visible;mso-wrap-style:square'>
2896 <v:imagedata src="SimpleMagnetic_files/image126.png" o:title=""/>
2897</v:shape><![endif]--><![if !vml]><img border=0 width=610 height=513
2898src="SimpleMagnetic_files/image132.png" v:shapes="Picture_x0020_45"><![endif]></span></p>
2899
2900<p class=MsoNormal>This completes this tutorial; you can save the project if
2901you wish &amp; close GSAS-II.</p>
2902
2903<h2>Simple Ferromagnet: La<sub>0.7</sub>Ca<sub>0.3</sub>MnO<sub>3.</sub></h2>
2904
2905<p class=MsoNormal>The magnetic structure of LaMnO<sub>3</sub> can be
2906profoundly changed by addition of Ca in place of some of the La; in this case
2907ferromagnetic ordering apparently was obtained. This tutorial will investigate
2908that from neutron powder data collected at 50K on the same instrument as the
2909first exercise (BT1 at NIST; thanks to Qingzhen Huang for providing the data).
2910Start GSAS-II if you have not done so already.</p>
2911
2912<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2913
2914<h3>Step 1: Read in the data file</h3>
2915
2916<p class=MsoListParagraphCxSpFirst style='margin-left:.25in;mso-add-space:auto;
2917text-indent:-.25in;mso-list:l2 level1 lfo10'><![if !supportLists]><span
2918style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
2919style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
2920the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2921mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2922minor-latin'>Import/Powder Data/from GSAS powder data file</span></b> menu item
2923to read the data file into the current GSAS-II project. This read option is set
2924to read any of the powder data formats defined for GSAS (angles in <span
2925class=SpellE>centidegrees</span>, TOF in µsec). Other submenu items will read
2926the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
2927style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2928mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>cif</span></b></span>
2929format or the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
2930style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2931mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>xye</span></b></span>
2932format (angles in degrees) used by <span class=SpellE>Topas</span>, etc.<span
2933style='mso-spacerun:yes'>  </span>In those cases, you would change the file
2934directory to <b style='mso-bidi-font-weight:normal'><span style='font-family:
2935"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2936minor-latin;mso-bidi-theme-font:minor-latin'>cif</span></b> format or the <span
2937class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
2938"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
2939minor-latin;mso-bidi-theme-font:minor-latin'>xye</span></b></span> format
2940(angles in degrees) used by <span class=SpellE>Topas</span>, etc. to see them.
2941Because you used <span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
2942minor-latin'>the </span><b style='mso-bidi-font-weight:normal'><span
2943style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2944mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font:
2945minor-latin'>Help/Download tutorial</span></b><span style='mso-fareast-font-family:
2946Calibri;mso-fareast-theme-font:minor-latin'> menu entry to open this page and
2947downloaded the exercise files (recommended), then the </span><span
2948class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
2949"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
2950Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SimpleMagnetic</span></b></span><b
2951style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2952mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
2953minor-latin;mso-hansi-theme-font:minor-latin'>/data/...</span></b><span
2954style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>
2955entry will bring you to the location where the files have been downloaded. (It
2956is also possible to download them manually from <a
2957href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimpleMagnetic/data/">https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimpleMagnetic/data/</a>.
2958In this case you will need to navigate to the download location manually.)<br>
2959For this tutorial you should see the data file in the file browser, but if
2960extensions on data files are not the expected ones, you may need to change the
2961file type to <b style='mso-bidi-font-weight:normal'>All files (*.*)</b> to find
2962the desired file.</span></p>
2963
2964<p class=MsoListParagraphCxSpMiddle style='margin-left:.25in;mso-add-space:
2965auto;text-indent:-.25in;mso-list:l2 level1 lfo10'><![if !supportLists]><span
2966style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
2967style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
2968the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2969mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2970minor-latin'>La7Ca3MnO3_50K.gsas</span></b><span style='font-family:"Calibri",sans-serif;
2971mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2972minor-latin'> data</span> file in the first dialog and press <b
2973style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2974mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2975minor-latin'>Open</span></b>. There will be a Dialog box asking <span
2976class=GramE><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;mso-bidi-theme-font:minor-latin'>Is</span></b></span><b
2979style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2980mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2981minor-latin'> this the file you want?</span></b> Press <span class=GramE><b
2982style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2983mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2984minor-latin'>Yes</span></b></span> button to proceed.</p>
2985
2986<p class=MsoListParagraphCxSpLast style='margin-left:.25in;mso-add-space:auto;
2987text-indent:-.25in;mso-list:l2 level1 lfo10'><![if !supportLists]><span
2988style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3.<span
2989style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Since
2990this data file does not define an instrument parameter file, a file dialog will
2991appear for you to select the correct instrument parameter file. Select <b
2992style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2993mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
2994minor-latin'>BT1_Cu300.inst</span></b>; you may have to change the file type in
2995the file selection Dialog box to <b style='mso-bidi-font-weight:normal'><span
2996style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2997mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>GSAS <span
2998class=SpellE>iparm</span> file</span></b> to see it. At this point the <b
2999style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3000mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3001minor-latin'>GSAS-II data tree</span></b> window will have several entries </p>
3002
3003<p class=MsoNormal style='margin-left:.25in'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3004 id="Picture_x0020_27" o:spid="_x0000_i1055" type="#_x0000_t75" style='width:195.75pt;
3005 height:207pt;visibility:visible;mso-wrap-style:square'>
3006 <v:imagedata src="SimpleMagnetic_files/image067.png" o:title=""/>
3007</v:shape><![endif]--><![if !vml]><img border=0 width=261 height=276
3008src="SimpleMagnetic_files/image133.png" v:shapes="Picture_x0020_27"><![endif]></span></p>
3009
3010<p class=MsoNormal style='margin-left:.25in'><span class=GramE>and</span> the
3011plot window will show the powder pattern</p>
3012
3013<p class=MsoNormal style='margin-left:.25in'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3014 id="Picture_x0020_28" o:spid="_x0000_i1054" type="#_x0000_t75" style='width:447pt;
3015 height:407.25pt;visibility:visible;mso-wrap-style:square'>
3016 <v:imagedata src="SimpleMagnetic_files/image069.png" o:title=""/>
3017</v:shape><![endif]--><![if !vml]><img border=0 width=596 height=543
3018src="SimpleMagnetic_files/image135.png" v:shapes="Picture_x0020_28"><![endif]></span></p>
3019
3020<h3>Step 2: Select Limits </h3>
3021
3022<p class=MsoNormal><span style='mso-spacerun:yes'> </span>This pattern has more
3023data than we need, so it is helpful to cut down the range. Click on the <b
3024style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3025mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3026minor-latin'>Limits</span></b> item in the <b style='mso-bidi-font-weight:normal'><span
3027style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3028mso-bidi-theme-font:minor-latin'>GSAS-II data tree</span></b>. Use the <b
3029style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3030mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3031minor-latin'>New:</span></b> row of entry boxes to set <span class=SpellE><b
3032style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3033mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3034minor-latin'>Tmin</span></b></span> and <span class=SpellE><b style='mso-bidi-font-weight:
3035normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3036minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Tmax</span></b></span>
3037to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3038mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>18</span></b>
3039and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3040mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3041minor-latin'>157.5</span></b>. Notice on the plot that the limit lines have
3042moved to these positions; the green lower limit is just below the small 1<sup>st</sup>
3043peak and the red upper limit is just below that last broad hump. You may also
3044drag the limit lines to the desired location or place them by a left mouse
3045click on a data point for the lower limit or a right click on a data point for
3046the upper limit.</p>
3047
3048<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3049 id="Picture_x0020_29" o:spid="_x0000_i1053" type="#_x0000_t75" style='width:468pt;
3050 height:426pt;visibility:visible;mso-wrap-style:square'>
3051 <v:imagedata src="SimpleMagnetic_files/image071.png" o:title=""/>
3052</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=568
3053src="SimpleMagnetic_files/image137.png" v:shapes="Picture_x0020_29"><![endif]></span></p>
3054
3055<h3><a name="sucrose_peak_fit"></a>Step 3: Read in the chemical structure for
3056La<sub>0.7</sub>Ca<sub>0.3</sub>MnO<sub>3</sub></h3>
3057
3058<p class=MsoListParagraphCxSpFirst style='margin-left:.25in;mso-add-space:auto;
3059text-indent:-.25in;mso-list:l4 level1 lfo12'><![if !supportLists]><span
3060style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
3061style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
3062the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3063mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3064minor-latin'>Import/Phase/from CIF file</span></b> menu item to read the phase
3065information for LaMnO<sub>3</sub> into the current GSAS-II project. This read
3066option is set to read Crystallographic Information Files (CIF). Other submenu
3067items will read phase information in other formats.<span
3068style='mso-spacerun:yes'>  </span>Because you used <span style='mso-fareast-font-family:
3069Calibri;mso-fareast-theme-font:minor-latin'>the </span><b style='mso-bidi-font-weight:
3070normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3071minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;
3072mso-hansi-theme-font:minor-latin'>Help/Download tutorial</span></b><span
3073style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin'>
3074menu entry to open this page and downloaded the exercise files (recommended),
3075then the </span><span class=SpellE><b style='mso-bidi-font-weight:normal'><span
3076style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3077mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-hansi-theme-font:
3078minor-latin'>SimpleMagnetic</span></b></span><b style='mso-bidi-font-weight:
3079normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3080minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;
3081mso-hansi-theme-font:minor-latin'>/data/...</span></b><span style='mso-fareast-font-family:
3082Calibri;mso-fareast-theme-font:minor-latin'> entry will bring you to the
3083location where the files have been downloaded. (It is also possible to download
3084them manually from <a
3085href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimpleMagnetic/data/">https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimpleMagnetic/data/</a>.
3086In this case you will need to navigate to the download location manually.)</span></p>
3087
3088<p class=MsoListParagraphCxSpLast style='margin-left:.25in;mso-add-space:auto;
3089text-indent:-.25in;mso-list:l4 level1 lfo12'><![if !supportLists]><span
3090style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
3091style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
3092the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3093mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3094minor-latin'>LaCaMnO3.cif</span></b><span style='font-family:"Calibri",sans-serif;
3095mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3096minor-latin'> data</span> file in the first dialog and press <b
3097style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3098mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3099minor-latin'>Open</span></b>. There will be a Dialog box asking <span
3100class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3101"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3102minor-latin;mso-bidi-theme-font:minor-latin'>Is</span></b></span><b
3103style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3104mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3105minor-latin'> this the file you want?</span></b> Press <span class=GramE><b
3106style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3107mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3108minor-latin'>Yes</span></b></span> button to proceed. You will get the
3109opportunity to change the phase name next; press <b style='mso-bidi-font-weight:
3110normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3111minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>OK</span></b>
3112to continue.</p>
3113
3114<p class=MsoNormal style='margin-left:.25in'>Next is the histogram selection
3115window; this connects the phase to the data so it can be used in subsequent</p>
3116
3117<p class=MsoNormal style='margin-left:.25in'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3118 id="Picture_x0020_46" o:spid="_x0000_i1052" type="#_x0000_t75" style='width:210pt;
3119 height:168pt;visibility:visible;mso-wrap-style:square'>
3120 <v:imagedata src="SimpleMagnetic_files/image134.png" o:title=""/>
3121</v:shape><![endif]--><![if !vml]><img border=0 width=280 height=224
3122src="SimpleMagnetic_files/image139.png" v:shapes="Picture_x0020_46"><![endif]></span></p>
3123
3124<p class=MsoNormal style='margin-left:.25in'>Select the histogram (or press <b
3125style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3126mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3127minor-latin'>Set All</span></b>) and press <b style='mso-bidi-font-weight:normal'><span
3128style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3129mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>OK</span></b>.
3130The General tab for the phase is shown next<br>
3131<span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_47"
3132 o:spid="_x0000_i1051" type="#_x0000_t75" style='width:448.5pt;height:228pt;
3133 visibility:visible;mso-wrap-style:square'>
3134 <v:imagedata src="SimpleMagnetic_files/image136.png" o:title=""/>
3135</v:shape><![endif]--><![if !vml]><img border=0 width=598 height=304
3136src="SimpleMagnetic_files/image161.png" v:shapes="Picture_x0020_47"><![endif]></span></p>
3137
3138<p class=MsoNormal style='margin-left:.25in'>Notice that the space group from
3139the <span class=SpellE>cif</span> file is <span class=SpellE>Pbnm</span>; this
3140is a nonstandard setting of <span class=SpellE>Pnma</span>. GSAS-II can treat
3141this case just as well as the standard setting so we can proceed without any
3142concern.</p>
3143
3144<h3>Step 4. Check powder pattern indexing</h3>
3145
3146<p class=MsoNormal>Here the objective is to determine how the reflection
3147positions generated from the chemical (“nuclear”) crystal structure lattice
3148match up with the peaks observed for this antiferromagnet. </p>
3149
3150<p class=MsoNormal>Select <b style='mso-bidi-font-weight:normal'><span
3151style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3152mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Unit Cells
3153List</span></b> from the tree entries under the histogram (begins with PWDR);
3154the Indexing controls will be shown<br>
3155<span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48"
3156 o:spid="_x0000_i1050" type="#_x0000_t75" style='width:466.5pt;height:165.75pt;
3157 visibility:visible;mso-wrap-style:square'>
3158 <v:imagedata src="SimpleMagnetic_files/image138.png" o:title=""/>
3159</v:shape><![endif]--><![if !vml]><img border=0 width=622 height=221
3160src="SimpleMagnetic_files/image162.png" v:shapes="Picture_x0020_48"><![endif]></span></p>
3161
3162<p class=MsoListParagraphCxSpFirst style='margin-left:0in;mso-add-space:auto'>This
3163can be use lattice parameters &amp; space groups to generate expected
3164reflection positions to check against the peaks in the powder pattern. Do <b
3165style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3166mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3167minor-latin'>Cell Index/Refine/Load Cell</span></b> from the menu; a Phase
3168selection box will appear with only one choice. This was taken from the Phases
3169present in this project; there could be more than one depending on what you
3170loaded/created earlier. The <b style='mso-bidi-font-weight:normal'><span
3171style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3172mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Import</span></b>
3173menu item allows you to get lattice information from any one of the other phase
3174containing files known to GSAS-II. Press <b style='mso-bidi-font-weight:normal'><span
3175style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3176mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>OK</span></b>
3177and the Indexing controls will be change</p>
3178
3179<p class=MsoListParagraphCxSpLast style='margin-left:0in;mso-add-space:auto'><span
3180style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_49"
3181 o:spid="_x0000_i1049" type="#_x0000_t75" style='width:466.5pt;height:165.75pt;
3182 visibility:visible;mso-wrap-style:square'>
3183 <v:imagedata src="SimpleMagnetic_files/image143.png" o:title=""/>
3184</v:shape><![endif]--><![if !vml]><img border=0 width=622 height=221
3185src="SimpleMagnetic_files/image163.png" v:shapes="Picture_x0020_49"><![endif]></span><br
3186style='mso-special-character:line-break'>
3187<![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'>
3188<![endif]></p>
3189
3190<p class=MsoNormal><span class=GramE>showing</span> the lattice constants for
3191LaCaMnO<sub>3</sub> you had obtained from the <span class=SpellE>cif</span>
3192file. Note that the space group is set to that of the <span class=SpellE>Bravais</span>
3193lattice (P m <span class=SpellE>m</span> m) and not the space group for LaCaMnO<sub>3</sub>
3194(P b n m).</p>
3195
3196<p class=MsoListParagraphCxSpFirst style='margin-left:0in;mso-add-space:auto'>Press
3197the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3198mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3199minor-latin'>Show <span class=SpellE>hkl</span> positions</span></b> button;
3200after a short pause (while reflections are generated), the plot will show the
3201calculated reflection line positions. Zoom in on the lowest part of the pattern
3202to see details of the indexing<span style='mso-no-proof:yes'> <!--[if gte vml 1]><v:shape
3203 id="Picture_x0020_50" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:465.75pt;
3204 height:327pt;visibility:visible;mso-wrap-style:square'>
3205 <v:imagedata src="SimpleMagnetic_files/image145.png" o:title=""/>
3206</v:shape><![endif]--><![if !vml]><img border=0 width=621 height=436
3207src="SimpleMagnetic_files/image164.png" v:shapes="Picture_x0020_50"><![endif]></span></p>
3208
3209<p class=MsoListParagraphCxSpLast style='margin-left:0in;mso-add-space:auto'>Note
3210that almost every observed peak is indexed; even the two weak peaks that are on
3211either side of the 1<sup>st</sup> strong peak. More about those later. There is
3212also a few seemingly misplaced unindexed lines (at 37.4, 53.9 &amp;
321367.4°2&#920;); probably some contaminating minor phase. We’ll have to ignore
3214them. Change the space group to <span class=SpellE>Pbnm</span>; the indexing
3215will change.</p>
3216
3217<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3218 id="Picture_x0020_51" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:468.75pt;
3219 height:329.25pt;visibility:visible;mso-wrap-style:square'>
3220 <v:imagedata src="SimpleMagnetic_files/image147.png" o:title=""/>
3221</v:shape><![endif]--><![if !vml]><img border=0 width=625 height=439
3222src="SimpleMagnetic_files/image165.png" v:shapes="Picture_x0020_51"><![endif]></span><br>
3223Then check the box <b style='mso-bidi-font-weight:normal'><span
3224style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3225mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Magnetic<span
3226class=GramE>?<span style='font-family:"Times New Roman",serif;font-weight:normal'>;</span></span></span></b>
3227the tab will be changed showing some more options</p>
3228
3229<p class=MsoListParagraphCxSpFirst style='margin-left:0in;mso-add-space:auto'><span
3230style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_52"
3231 o:spid="_x0000_i1046" type="#_x0000_t75" style='width:467.25pt;height:149.25pt;
3232 visibility:visible;mso-wrap-style:square'>
3233 <v:imagedata src="SimpleMagnetic_files/image149.png" o:title=""/>
3234</v:shape><![endif]--><![if !vml]><img border=0 width=623 height=199
3235src="SimpleMagnetic_files/image166.png" v:shapes="Picture_x0020_52"><![endif]></span></p>
3236
3237<p class=MsoListParagraphCxSpLast style='margin-left:0in;mso-add-space:auto'>Because
3238the sample is ferromagnetic, all the magnetic scattering could be expected to
3239coincide with the scattering from the chemical cell. There are no extra
3240reflections; making it difficult to discern which spin configuration is
3241appropriate without knowing the scattering from the chemical cell. Changing the
3242spins will cause the lowest index lines to be extinct (as antiferromagnetic
3243selections are made); these can be seen by moving the lower limit to below
324410°2&#920;. The problem is that they may have no intensity because of the
3245moment directions, e.g. if only <span class=SpellE>M<sub>x</sub></span> &#8800;
32460, then all F<sub>h00</sub> (parallel to the moment) will be zero even if
3247allowed by the magnetic symmetry. Thus, we will have to defer this testing
3248until after we have a computed pattern from the chemical cell and can compute
3249some trial patterns from the magnetic cell.</p>
3250
3251<h3>Step 5. Make the magnetic phase</h3>
3252
3253<p class=MsoNormal>In the previous step we did not have to resort to any
3254doubling of a cell axis to explain the suite of magnetic reflections, so the
3255propagation vector is zero (in case anyone asks!). To make the magnetic cell
3256from the chemical cell we will use the transform tool that is in GSAS-II in the
3257General tab for the chemical structure. That tab is</p>
3258
3259<p class=MsoListParagraph style='margin-left:0in;mso-add-space:auto'><span
3260style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_53"
3261 o:spid="_x0000_i1045" type="#_x0000_t75" style='width:467.25pt;height:206.25pt;
3262 visibility:visible;mso-wrap-style:square'>
3263 <v:imagedata src="SimpleMagnetic_files/image151.png" o:title=""/>
3264</v:shape><![endif]--><![if !vml]><img border=0 width=623 height=275
3265src="SimpleMagnetic_files/image167.png" v:shapes="Picture_x0020_53"><![endif]></span></p>
3266
3267<p class=MsoNormal>Under the <b style='mso-bidi-font-weight:normal'><span
3268style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3269mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Compute</span></b>
3270menu item do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3271"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3272minor-latin;mso-bidi-theme-font:minor-latin'>Transform</span></b>; a new popup
3273dialog box will appear with stuff needed to effect a cell transformation.</p>
3274
3275<p class=MsoListParagraph style='margin-left:0in;mso-add-space:auto'><span
3276style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_78"
3277 o:spid="_x0000_i1044" type="#_x0000_t75" style='width:274.5pt;height:327pt;
3278 visibility:visible;mso-wrap-style:square'>
3279 <v:imagedata src="SimpleMagnetic_files/image142.png" o:title=""/>
3280</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=436
3281src="SimpleMagnetic_files/image142.png" v:shapes="Picture_x0020_78"><![endif]></span></p>
3282
3283<p class=MsoNormal>The order of operations for the transformation is given at
3284the top of the window; this was described in the 1<sup>st</sup> part of this
3285tutorial. We do want the new phase to be magnetic so press the <b
3286style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3287mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3288minor-latin'>Make new phase magnetic</span></b> button; the dialog will be
3289redrawn</p>
3290
3291<p class=MsoListParagraph style='margin-left:0in;mso-add-space:auto'><span
3292style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_79"
3293 o:spid="_x0000_i1043" type="#_x0000_t75" style='width:212.25pt;height:252.75pt;
3294 visibility:visible;mso-wrap-style:square'>
3295 <v:imagedata src="SimpleMagnetic_files/image144.png" o:title=""/>
3296</v:shape><![endif]--><![if !vml]><img border=0 width=283 height=337
3297src="SimpleMagnetic_files/image144.png" v:shapes="Picture_x0020_79"><![endif]></span></p>
3298
3299<p class=MsoNormal>This allows one to select possible magnetic lattice
3300centering operations as given by the BNS nomenclature. This can be needed if
3301one had discovered a requirement of doubling a cell axis in the previous step
3302(e.g. a nonzero propagation vector). This is not required in this case and we
3303are using the same nonstandard space group (<span class=SpellE>Pnma</span>) for
3304the magnetic cell that is used for the chemical cell. Leave the box at the
3305bottom about constraints checked as we want them to tie the two phases
3306together.<span style='mso-spacerun:yes'>  </span>Press <b style='mso-bidi-font-weight:
3307normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3308minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Ok</span></b>
3309to continue; a new popup will appear</p>
3310
3311<p class=MsoListParagraph style='margin-left:0in;mso-add-space:auto'><span
3312style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_56"
3313 o:spid="_x0000_i1042" type="#_x0000_t75" style='width:147pt;height:65.25pt;
3314 visibility:visible;mso-wrap-style:square'>
3315 <v:imagedata src="SimpleMagnetic_files/image157.png" o:title=""/>
3316</v:shape><![endif]--><![if !vml]><img border=0 width=196 height=87
3317src="SimpleMagnetic_files/image168.png" v:shapes="Picture_x0020_56"><![endif]></span></p>
3318
3319<p class=MsoNormal>This allows one to reject certain atoms that are known to
3320not be magnetic; press <b style='mso-bidi-font-weight:normal'><span
3321style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3322mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Ok</span></b>
3323to continue. A new phase will be created and the General tab for it will be
3324shown.</p>
3325
3326<p class=MsoListParagraph style='margin-left:0in;mso-add-space:auto'><span
3327style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_57"
3328 o:spid="_x0000_i1041" type="#_x0000_t75" style='width:464.25pt;height:273.75pt;
3329 visibility:visible;mso-wrap-style:square'>
3330 <v:imagedata src="SimpleMagnetic_files/image159.png" o:title=""/>
3331</v:shape><![endif]--><![if !vml]><img border=0 width=619 height=365
3332src="SimpleMagnetic_files/image169.png" v:shapes="Picture_x0020_57"><![endif]></span></p>
3333
3334<p class=MsoNormal>The phase is named with “mag” appended to the end, the phase
3335type is magnetic and there are magnetic spin operator selections part way down
3336the page; they are all “black”. You also can see the <span class=SpellE>Lande</span>’
3337g factor can be changed if needed and the phase only contains the <span
3338class=SpellE>Mn</span> atom. As before the appropriate constraints have been
3339built linking the two phases together. Look at Constraints if you wish to see
3340them.</p>
3341
3342<h3>Step 6. Select spin configuration</h3>
3343
3344<p class=MsoListParagraphCxSpFirst style='margin-left:0in;mso-add-space:auto'>Select
3345the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3346mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3347minor-latin'>Atoms</span></b> tab, the parameters for <span class=SpellE>Mn</span>
3348are shown</p>
3349
3350<p class=MsoListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'><span
3351style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_58"
3352 o:spid="_x0000_i1040" type="#_x0000_t75" style='width:468.75pt;height:107.25pt;
3353 visibility:visible;mso-wrap-style:square'>
3354 <v:imagedata src="SimpleMagnetic_files/image170.png" o:title=""/>
3355</v:shape><![endif]--><![if !vml]><img border=0 width=625 height=143
3356src="SimpleMagnetic_files/image171.png" v:shapes="Picture_x0020_58"><![endif]></span></p>
3357
3358<p class=MsoListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'>Notice
3359that <span class=SpellE>Mx</span>, My &amp; <span class=SpellE>Mz</span> are
3360shown with 0.0 for each and the site symmetry is “-1”; an inversion with no
3361spin flip allows the site to have a magnetic moment. So the all “black”
3362configuration is possible on the basis of the <span class=SpellE>Mn</span> site
3363symmetry. If you make one of the spin operators “<b style='mso-bidi-font-weight:
3364normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3365minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>red</span></b>”
3366(say <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3367mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3368minor-latin'>mx</span></b>) and then press <b style='mso-bidi-font-weight:normal'><span
3369style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3370mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Show spins<span
3371class=GramE>?<span style='font-family:"Times New Roman",serif;font-weight:normal'>,</span></span></span></b>
3372the popup will show a red <span style='color:red'>(-1)</span> symbol indicating
3373that the inversion operation (#5) also has a spin inversion. This spin
3374arrangement wouldn’t allow the <span class=SpellE>Mn</span> to have a moment so
3375it must be rejected.</p>
3376
3377<p class=MsoListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'><span
3378style='mso-spacerun:yes'> </span><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3379 id="Picture_x0020_60" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:240pt;
3380 height:199.5pt;visibility:visible;mso-wrap-style:square'>
3381 <v:imagedata src="SimpleMagnetic_files/image172.png" o:title=""/>
3382</v:shape><![endif]--><![if !vml]><img border=0 width=320 height=266
3383src="SimpleMagnetic_files/image173.png" v:shapes="Picture_x0020_60"><![endif]></span></p>
3384
3385<p class=MsoListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'>The
3386<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3387mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3388minor-latin'>Atoms</span></b> tab would show <span class=SpellE>Mx</span>, My
3389&amp; <span class=SpellE>Mz</span> as gray indicating that they cannot have a
3390nonzero value.</p>
3391
3392<p class=MsoListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'><span
3393style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_61"
3394 o:spid="_x0000_i1038" type="#_x0000_t75" style='width:475.5pt;height:99.75pt;
3395 visibility:visible;mso-wrap-style:square'>
3396 <v:imagedata src="SimpleMagnetic_files/image174.png" o:title=""/>
3397</v:shape><![endif]--><![if !vml]><img border=0 width=634 height=133
3398src="SimpleMagnetic_files/image177.png" v:shapes="Picture_x0020_61"><![endif]></span></p>
3399
3400<p class=MsoListParagraphCxSpLast style='margin-left:0in;mso-add-space:auto'>If
3401you try other spin configurations this way, you will quickly see that an odd
3402number of spin flips will yield for <span class=SpellE>Pbnm</span> inversions
3403centers with spin flips and all must be rejected on that basis leaving only
3404configurations with an even number of spin flips (e.g. “<span class=SpellE>bbb</span>”,
3405“<span class=SpellE>rrb</span>”, “<span class=SpellE>rbr</span>” and “<span
3406class=SpellE>brr</span>”) for which the inversion center does not have a spin
3407flip and thus can carry a magnetic moment. We will have to test each in turn,
3408moreover the moment direction also needs to be established (e.g. values of <span
3409class=SpellE>Mx</span>, My &amp; <span class=SpellE>Mz</span>).</p>
3410
3411<h3>Step 7. Solving the magnetic structure - Trial and Error</h3>
3412
3413<p class=MsoListParagraphCxSpFirst style='margin-left:0in;mso-add-space:auto'>Because
3414of the equivalence of ± <span class=SpellE>Mx</span>, ± <span class=GramE>My</span>
3415and ± <span class=SpellE>Mz</span>, the least squares will show singular matrix
3416behavior if any are started at zero. So we must begin any test refinement with
3417nonzero moment components. We may discover later that some moment component is
3418nearly zero; it can then be set to zero and a hold placed on that value to
3419avoid the singularity. We will need to test each spin configuration in turn
3420&amp; then compare them to find the best one. To proceed select the <span
3421class=SpellE>the</span> magnetic phase and set the spins to “<span
3422class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
3423"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3424minor-latin;mso-bidi-theme-font:minor-latin'>bbb</span></b></span>” (i.e. all “<b
3425style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3426mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3427minor-latin'>black</span></b>”). Then select the <b style='mso-bidi-font-weight:
3428normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3429minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Atoms</span></b>
3430tab and enter <b style='mso-bidi-font-weight:normal'><span style='font-family:
3431"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3432minor-latin;mso-bidi-theme-font:minor-latin'>1.0</span></b> for each of <span
3433class=SpellE><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;mso-bidi-theme-font:minor-latin'>Mx</span></b></span>, <b
3436style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3437mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3438minor-latin'>My</span></b> &amp; <span class=SpellE><b style='mso-bidi-font-weight:
3439normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3440minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Mz</span></b></span>;
3441this provides a suitable starting point. The default refinement is just scale
3442factor &amp; background; do <b style='mso-bidi-font-weight:normal'><span
3443style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3444mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b>.
3445It will quickly converge to <span class=SpellE>Rwp</span> ~15.5% and the plot
3446will look like</p>
3447
3448<p class=MsoListParagraphCxSpMiddle style='margin-left:0in;mso-add-space:auto'><span
3449style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_64"
3450 o:spid="_x0000_i1037" type="#_x0000_t75" style='width:519pt;height:364.5pt;
3451 visibility:visible;mso-wrap-style:square'>
3452 <v:imagedata src="SimpleMagnetic_files/image176.png" o:title=""/>
3453</v:shape><![endif]--><![if !vml]><img border=0 width=692 height=486
3454src="SimpleMagnetic_files/image181.png" v:shapes="Picture_x0020_64"><![endif]></span></p>
3455
3456<p class=MsoListParagraphCxSpLast style='margin-left:0in;mso-add-space:auto'>Clearly
3457there is intensity mismatches at low angles because the magnetic structure is
3458incorrect, but there is also misfits due to peak position errors. We can refine
3459lattice parameters and sample position to address this. Select each phase in
3460turn and select <b style='mso-bidi-font-weight:normal'><span style='font-family:
3461"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3462minor-latin;mso-bidi-theme-font:minor-latin'>Refine unit cell</span></b> on the
3463<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3464mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3465minor-latin'>General</span></b> tab for each; the constraints connecting them
3466were built earlier by the Transform operation in GSAS-II. Next select <b
3467style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3468mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3469minor-latin'>Sample Parameters</span></b> under the <b style='mso-bidi-font-weight:
3470normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3471minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>PWDR</span></b>
3472entry and select <b style='mso-bidi-font-weight:normal'><span style='font-family:
3473"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3474minor-latin;mso-bidi-theme-font:minor-latin'>Sample X <span class=SpellE>displ</span></span></b>
3475and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3476mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3477minor-latin'>Sample Y <span class=SpellE>displ</span></span></b> for
3478refinement; change <b style='mso-bidi-font-weight:normal'><span
3479style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3480mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Goniometer
3481radius</span></b> to <b style='mso-bidi-font-weight:normal'><span
3482style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3483mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>650</span></b>
3484so the result is in microns. Now do <b style='mso-bidi-font-weight:normal'><span
3485style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3486mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b>
3487again; <span class=SpellE>Rwp</span> will drop slightly (mine was ~13.6%). <b
3488style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3489mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3490minor-latin'>Save</span></b> the project, and do a <b style='mso-bidi-font-weight:
3491normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3492minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Save
3493Project as<span class=GramE>..</span></span></b> <span class=GramE>and</span>
3494name it <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3495mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3496minor-latin'>LaCaMnO3 <span class=SpellE>bbb.gpx</span></span></b> (the <span
3497class=SpellE>gpx</span> is assumed &amp; the ‘<span class=SpellE>bbb</span>’
3498refers to the <span class=SpellE>all black</span> configuration which we will
3499test next. The saved LaCaMnO3.gpx will then be our starting point for testing
3500the spin configurations.</p>
3501
3502<h4 style='margin-left:.5in;text-indent:-.25in;mso-list:l6 level1 lfo14'><![if !supportLists]><span
3503style='mso-fareast-font-family:"Calibri Light";mso-fareast-theme-font:major-latin;
3504mso-bidi-font-family:"Calibri Light";mso-bidi-theme-font:major-latin'><span
3505style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
3506</span></span></span><![endif]>Test the <span class=SpellE>bbb</span>
3507configuration – <span class=SpellE>Pbnm</span></h4>
3508
3509<p class=MsoNormal>To test the magnetic configuration, we need to refine the
3510magnetic moment components to obtain the optimal values for the spin
3511configuration and thus the best fit. Select the magnetic phase and go to the <b
3512style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3513mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3514minor-latin'>Atoms</span></b> tab. Then double click the refine column heading
3515and select ‘<b style='mso-bidi-font-weight:normal'><span style='font-family:
3516"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3517minor-latin;mso-bidi-theme-font:minor-latin'>M</span></b>’ from the popup
3518dialog. It should look like</p>
3519
3520<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3521 id="Picture_x0020_63" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt;
3522 height:89.25pt;visibility:visible;mso-wrap-style:square'>
3523 <v:imagedata src="SimpleMagnetic_files/image178.png" o:title=""/>
3524</v:shape><![endif]--><![if !vml]><img border=0 width=624 height=119
3525src="SimpleMagnetic_files/image183.png" v:shapes="Picture_x0020_63"><![endif]></span></p>
3526
3527<p class=MsoNormal>Then do <b style='mso-bidi-font-weight:normal'><span
3528style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3529mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b>
3530from the main menu, it converges quickly (<span class=SpellE>Rwp</span> ~11.8%)
3531and still a poor fit for the low angle reflections</p>
3532
3533<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3534 id="Picture_x0020_65" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:468.75pt;
3535 height:329.25pt;visibility:visible;mso-wrap-style:square'>
3536 <v:imagedata src="SimpleMagnetic_files/image180.png" o:title=""/>
3537</v:shape><![endif]--><![if !vml]><img border=0 width=625 height=439
3538src="SimpleMagnetic_files/image185.png" v:shapes="Picture_x0020_65"><![endif]></span></p>
3539
3540<p class=MsoNormal><span class=GramE>and</span> the magnetic moment components
3541are</p>
3542
3543<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3544 id="Picture_x0020_66" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:471pt;
3545 height:92.25pt;visibility:visible;mso-wrap-style:square'>
3546 <v:imagedata src="SimpleMagnetic_files/image182.png" o:title=""/>
3547</v:shape><![endif]--><![if !vml]><img border=0 width=628 height=123
3548src="SimpleMagnetic_files/image187.png" v:shapes="Picture_x0020_66"><![endif]></span></p>
3549
3550<p class=MsoNormal>So we test the next possibility.</p>
3551
3552<h4 style='margin-left:.5in;text-indent:-.25in;mso-list:l6 level1 lfo14'><![if !supportLists]><span
3553style='mso-fareast-font-family:"Calibri Light";mso-fareast-theme-font:major-latin;
3554mso-bidi-font-family:"Calibri Light";mso-bidi-theme-font:major-latin'><span
3555style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
3556</span></span></span><![endif]>Test the <span class=SpellE><span class=GramE>rrb</span></span>
3557configuration – <span class=SpellE>Pb’n’m</span></h4>
3558
3559<p class=MsoNormal>Since we want to be able to compare results, start a new
3560GSAS-II and open the <b style='mso-bidi-font-weight:normal'><span
3561style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3562mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>LaCaMnO3.gpx</span></b>
3563project. Immediately do a <b style='mso-bidi-font-weight:normal'><span
3564style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3565mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Save Project
3566as…</span></b> and name it <b style='mso-bidi-font-weight:normal'><span
3567style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3568mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>LaCaMnO3 <span
3569class=SpellE>rrb.gpx</span></span></b> (this step might easily be forgotten and
3570then your reference starting structure will be lost!). Then select the magnetic
3571phase and the General tab is displayed. Set the spin configuration to “<b
3572style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3573mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3574minor-latin'>red</span></b>”, “<b style='mso-bidi-font-weight:normal'><span
3575style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3576mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>red</span></b>”
3577<span class=GramE>&amp; ”</span><b style='mso-bidi-font-weight:normal'><span
3578style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3579mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>black</span></b>”.
3580Then go to the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3581"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3582minor-latin;mso-bidi-theme-font:minor-latin'>Atoms</span></b> tab and set the <b
3583style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3584mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3585minor-latin'>refine</span></b> flag to ‘<b style='mso-bidi-font-weight:normal'><span
3586style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3587mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>M</span></b>’;
3588then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3589mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3590minor-latin'>Calculate/Refine</span></b>. The residual will immediately drop to
3591<span class=SpellE>Rwp</span> ~8.0% which is much better than the “<span
3592class=SpellE>bbb</span>” spin configuration and the plot gives a far better fit
3593to the low angle peaks</p>
3594
3595<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3596 id="Picture_x0020_67" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:472.5pt;
3597 height:331.5pt;visibility:visible;mso-wrap-style:square'>
3598 <v:imagedata src="SimpleMagnetic_files/image184.png" o:title=""/>
3599</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=442
3600src="SimpleMagnetic_files/image189.png" v:shapes="Picture_x0020_67"><![endif]></span></p>
3601
3602<p class=MsoNormal>The <b style='mso-bidi-font-weight:normal'><span
3603style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3604mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Atoms</span></b>
3605tab shows a very strong <span class=SpellE>Mz</span> component <span
3606class=SpellE><span class=GramE>ot</span></span> the magnetic moment on <span
3607class=SpellE>Mn</span> with the other two components near zero.</p>
3608
3609<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3610 id="Picture_x0020_68" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:472.5pt;
3611 height:88.5pt;visibility:visible;mso-wrap-style:square'>
3612 <v:imagedata src="SimpleMagnetic_files/image186.png" o:title=""/>
3613</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=118
3614src="SimpleMagnetic_files/image191.png" v:shapes="Picture_x0020_68"><![endif]></span></p>
3615
3616<p class=MsoNormal>Let’s test the next one.</p>
3617
3618<h4 style='margin-left:.25in;text-indent:-.25in;mso-list:l4 level1 lfo12'><![if !supportLists]><span
3619style='mso-fareast-font-family:"Calibri Light";mso-fareast-theme-font:major-latin;
3620mso-bidi-font-family:"Calibri Light";mso-bidi-theme-font:major-latin'><span
3621style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
3622</span></span></span><![endif]>Test the <span class=SpellE>rbr</span>
3623configuration – <span class=SpellE>Pb’nm</span>’</h4>
3624
3625<p class=MsoNormal><o:p>&nbsp;</o:p></p>
3626
3627<p class=MsoNormal>Again start a new GSAS-II with the reference project <b
3628style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3629mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3630minor-latin'>LaCaMnO3.gpx</span></b> and immediately <b style='mso-bidi-font-weight:
3631normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3632minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Save
3633project as<span class=GramE>..</span></span></b> <span class=GramE>with</span>
3634the name <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3635mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3636minor-latin'>LaCaMnO3 <span class=SpellE>rbr.gpx</span></span></b>. Then select
3637the magnetic phase and the General tab is displayed. Set the spin configuration
3638to “<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3639mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3640minor-latin'>red</span></b>”, “<b style='mso-bidi-font-weight:normal'><span
3641style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3642mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>black</span></b>”
3643<span class=GramE>&amp; ”</span><b style='mso-bidi-font-weight:normal'><span
3644style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3645mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>red</span></b>”.
3646Then go to the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3647"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3648minor-latin;mso-bidi-theme-font:minor-latin'>Atoms</span></b> tab and set the <b
3649style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3650mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3651minor-latin'>refine</span></b> flag to ‘<b style='mso-bidi-font-weight:normal'><span
3652style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3653mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>M</span></b>’;
3654then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3655mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3656minor-latin'>Calculate/Refine</span></b>. The residual will be just a bit
3657poorer (<span class=SpellE>Rwp</span> ~8.2%) than the “<span class=SpellE>rrb</span>”
3658model. The plot is very similar</p>
3659
3660<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3661 id="Picture_x0020_69" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:471.75pt;
3662 height:330.75pt;visibility:visible;mso-wrap-style:square'>
3663 <v:imagedata src="SimpleMagnetic_files/image188.png" o:title=""/>
3664</v:shape><![endif]--><![if !vml]><img border=0 width=629 height=441
3665src="SimpleMagnetic_files/image193.png" v:shapes="Picture_x0020_69"><![endif]></span></p>
3666
3667<p class=MsoNormal>The <b style='mso-bidi-font-weight:normal'><span
3668style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3669mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Atoms</span></b>
3670display shows a strong <span class=GramE>My</span> moment component with <span
3671class=SpellE>Mx</span> &amp; <span class=SpellE>Mz</span> small</p>
3672
3673<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3674 id="Picture_x0020_70" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:472.5pt;
3675 height:94.5pt;visibility:visible;mso-wrap-style:square'>
3676 <v:imagedata src="SimpleMagnetic_files/image190.png" o:title=""/>
3677</v:shape><![endif]--><![if !vml]><img border=0 width=630 height=126
3678src="SimpleMagnetic_files/image200.png" v:shapes="Picture_x0020_70"><![endif]></span></p>
3679
3680<p class=MsoNormal>We should now check the last spin configuration.</p>
3681
3682<h4 style='margin-left:.25in;text-indent:-.25in;mso-list:l4 level1 lfo12'><![if !supportLists]><span
3683style='mso-fareast-font-family:"Calibri Light";mso-fareast-theme-font:major-latin;
3684mso-bidi-font-family:"Calibri Light";mso-bidi-theme-font:major-latin'><span
3685style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;
3686</span></span></span><![endif]>Test the <span class=SpellE>brr</span>
3687configuration – <span class=SpellE>Pbn’m</span>’</h4>
3688
3689<p class=MsoNormal>As before, start a new GSAS-II with the reference project <b
3690style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3691mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3692minor-latin'>LaCaMnO3.gpx</span></b> and immediately <b style='mso-bidi-font-weight:
3693normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3694minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Save
3695project as<span class=GramE>..</span></span></b> <span class=GramE>with</span>
3696the name <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3697mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3698minor-latin'>LaCaMnO3 <span class=SpellE>brr.gpx</span></span></b>. Then select
3699the magnetic phase and the General tab is displayed. Set the spin configuration
3700to “<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3701mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3702minor-latin'>black</span></b>”, “<b style='mso-bidi-font-weight:normal'><span
3703style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3704mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>red</span></b>”
3705<span class=GramE>&amp; ”</span><b style='mso-bidi-font-weight:normal'><span
3706style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3707mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>red</span></b>”.
3708Then go to the <b style='mso-bidi-font-weight:normal'><span style='font-family:
3709"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3710minor-latin;mso-bidi-theme-font:minor-latin'>Atoms</span></b> tab and set the <b
3711style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3712mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3713minor-latin'>refine</span></b> flag to ‘<b style='mso-bidi-font-weight:normal'><span
3714style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3715mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>M</span></b>’;
3716then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3717mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3718minor-latin'>Calculate/Refine</span></b>. The residual virtually the same as
3719the “<span class=SpellE>rrb</span>” model (Rwp~8.0%) but better than the “<span
3720class=SpellE>rbr</span>” one. The plot is very similar</p>
3721
3722<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3723 id="Picture_x0020_71" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:474.75pt;
3724 height:333pt;visibility:visible;mso-wrap-style:square'>
3725 <v:imagedata src="SimpleMagnetic_files/image192.png" o:title=""/>
3726</v:shape><![endif]--><![if !vml]><img border=0 width=633 height=444
3727src="SimpleMagnetic_files/image201.png" v:shapes="Picture_x0020_71"><![endif]></span></p>
3728
3729<p class=MsoNormal><span class=GramE>and</span> with the strong <span
3730class=SpellE>Mx</span> moment component with My &amp; <span class=SpellE>Mz</span>
3731small.</p>
3732
3733<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3734 id="Picture_x0020_72" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:477pt;
3735 height:81pt;visibility:visible;mso-wrap-style:square'>
3736 <v:imagedata src="SimpleMagnetic_files/image206.png" o:title=""/>
3737</v:shape><![endif]--><![if !vml]><img border=0 width=636 height=108
3738src="SimpleMagnetic_files/image202.png" v:shapes="Picture_x0020_72"><![endif]></span></p>
3739
3740<p class=MsoNormal><o:p>&nbsp;</o:p></p>
3741
3742<p class=MsoNormal>Clearly the “<span class=SpellE>bbb</span>” configuration is
3743not correct, but which one of the other three is difficult to choose at
3744present. Let’s complete the refinement on each one and see where that leads.
3745All that is required is to add the remaining atom parameters (<b
3746style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3747mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3748minor-latin'>X</span></b> &amp; <b style='mso-bidi-font-weight:normal'><span
3749style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
3750mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>U</span></b>).
3751For each of the “<span class=SpellE>rrb</span>”, “<span class=SpellE>rbr</span>”
3752and “<span class=SpellE>brr</span>” models go to each phase <b
3753style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3754mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3755minor-latin'>Atoms</span></b> tab and change the refinement flags to <b
3756style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3757mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3758minor-latin'>XU</span></b> for the chemical ones and <b style='mso-bidi-font-weight:
3759normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3760minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>UM</span></b>
3761for the magnetic ones. Also make the number of <b style='mso-bidi-font-weight:
3762normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
3763minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Background</span></b>
3764terms <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3765mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3766minor-latin'>6</span></b> for each; that will provide slight improvement as
3767well. The do <b style='mso-bidi-font-weight:normal'><span style='font-family:
3768"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
3769minor-latin;mso-bidi-theme-font:minor-latin'>Calculate/Refine</span></b> for each
3770one. After several cycles of refinement I find the “<span class=SpellE>rrb</span>”
3771model <span class=SpellE>Rwp</span>=7.615%, the “<span class=SpellE>rbr</span>”
3772model <span class=SpellE>Rwp</span>=7.716% and the “<span class=SpellE>brr</span>”
3773model <span class=SpellE>Rwp</span>=7.591%.</p>
3774
3775<p class=MsoNormal>Finally, if one examines the Atom tabs for the “<span
3776class=SpellE>rrb</span>” and “<span class=SpellE>brr</span>’ models, the <span
3777class=GramE>My</span> component of the magnetic moment is quite close to zero
3778(My ~0.2) for both. Set it to zero in both cases and add the hold on <b
3779style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3780mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3781minor-latin'>1:<span class=GramE>:AMy:0</span></span></b> in the <b
3782style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3783mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3784minor-latin'>Constraints</span></b> for each as well to keep them at zero.
3785Repeat <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
3786mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
3787minor-latin'>Calculate/Refine</span></b>. I got <span class=SpellE>Rwp</span>=7.616%
3788for the “<span class=SpellE>rrb</span>” model and <span class=SpellE>Rwp</span>=7.558%
3789for the “<span class=SpellE>brr</span>” model indicating a slight preference
3790for the latter. A very close look at the peak at 32.7°2&#920; gives some
3791indication of where this small difference in residual comes from (“<span
3792class=SpellE>rrb</span>” on left &amp; “<span class=SpellE>brr</span>” on
3793right).The plots are the square root of intensity and the weighted difference
3794is shown below. </p>
3795
3796<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3797 id="Picture_x0020_73" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:237.75pt;
3798 height:510.75pt;visibility:visible;mso-wrap-style:square'>
3799 <v:imagedata src="SimpleMagnetic_files/image209.png" o:title=""/>
3800</v:shape><![endif]--><![if !vml]><img border=0 width=317 height=681
3801src="SimpleMagnetic_files/image203.png" v:shapes="Picture_x0020_73"><![endif]><!--[if gte vml 1]><v:shape
3802 id="Picture_x0020_74" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:239.25pt;
3803 height:510pt;visibility:visible;mso-wrap-style:square'>
3804 <v:imagedata src="SimpleMagnetic_files/image211.png" o:title=""/>
3805</v:shape><![endif]--><![if !vml]><img border=0 width=319 height=680
3806src="SimpleMagnetic_files/image204.png" v:shapes="Picture_x0020_74"><![endif]></span></p>
3807
3808<p class=MsoNormal>The magnetic peaks contributing to this peak are the 200,221
3809&amp; 020 for the “<span class=SpellE>rrb</span>” model; for the “<span
3810class=SpellE>brr</span>” model the 200 is absent. This extra reflection makes a
3811contribution to the profile for “<span class=SpellE>rrb</span>” that makes the
3812fit slightly worse than for the “<span class=SpellE>brr</span>” model. Thus,
3813the correct magnetic structure can be assigned for La<sub>0.7</sub>Ca<sub>0.3</sub>MnO3
3814as <span class=SpellE>Pbn’m</span>’ (not <span class=SpellE>Pb’n’m</span>). The
3815structure looks like</p>
3816
3817<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
3818 id="Picture_x0020_75" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:474pt;
3819 height:501.75pt;visibility:visible;mso-wrap-style:square'>
3820 <v:imagedata src="SimpleMagnetic_files/image213.png" o:title=""/>
3821</v:shape><![endif]--><![if !vml]><img border=0 width=632 height=669
3822src="SimpleMagnetic_files/image205.png" v:shapes="Picture_x0020_75"><![endif]></span></p>
3823
3824<p class=MsoNormal><span class=GramE>which</span> shows that the ferromagnetic
3825arrangement is slightly canted in the z-direction (<span class=SpellE>Mz</span>
3826=0.50) with the major component (<span class=SpellE>Mx</span> =3.25) along the
3827x-axis. A test refinement with <span class=SpellE>Mz</span> = 0 gives a
3828slightly poorer fit <span class=SpellE>Rwp</span>=7.596% vs 7.591% and fails to
3829put any calculated intensity into the 1<sup>st</sup> weak peak (101 &amp; 011)
3830at 19.82°2&#920; thus confirming that the canting is apparently real.</p>
3831
3832<p class=MsoNormal>This completes the “simple magnetic structure” tutorials.</p>
3833
3834<p class=MsoNormal><o:p>&nbsp;</o:p></p>
3835
3836<p class=MsoNormal><o:p>&nbsp;</o:p></p>
3837
3838</div>
3839
3840</body>
3841
3842</html>
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