source: Tutorials/MerohedralTwins/Merohedral twin refinement in GSAS.htm @ 2293

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403  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
404  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
405  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
406  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
407  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
408  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
409  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
410  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
411  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
412  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
413  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
414  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
415  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
416  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
417  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
418  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
419  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
420  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
421  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
422  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
423  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
424  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
425  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
426  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
427  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
428  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
429  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
430  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
431  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
432  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
433  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
434  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
435  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
436  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
437  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
438  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
439  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
440  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
441  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
442  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
443  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
444  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
445  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
446  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
447  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
448  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
449  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
450  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
451  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
452  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
453  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
454  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
455  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
456  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
457  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
458  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
459  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
460  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
461  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
462  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
463  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
464  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
465  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
466  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
467  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
468  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
469  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
470  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
471  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
472  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
473  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
474  <w:LsdException Locked="false" Priority="19" QFormat="true"
475   Name="Subtle Emphasis"/>
476  <w:LsdException Locked="false" Priority="21" QFormat="true"
477   Name="Intense Emphasis"/>
478  <w:LsdException Locked="false" Priority="31" QFormat="true"
479   Name="Subtle Reference"/>
480  <w:LsdException Locked="false" Priority="32" QFormat="true"
481   Name="Intense Reference"/>
482  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
483  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
484   UnhideWhenUsed="true" Name="Bibliography"/>
485  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
486   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
487  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
488  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
489  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
490  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
491  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
492  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
493  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
494  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
495  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
496  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
497  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
498  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
499  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
500  <w:LsdException Locked="false" Priority="46"
501   Name="Grid Table 1 Light Accent 1"/>
502  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
503  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
504  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
505  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
506  <w:LsdException Locked="false" Priority="51"
507   Name="Grid Table 6 Colorful Accent 1"/>
508  <w:LsdException Locked="false" Priority="52"
509   Name="Grid Table 7 Colorful Accent 1"/>
510  <w:LsdException Locked="false" Priority="46"
511   Name="Grid Table 1 Light Accent 2"/>
512  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
513  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
514  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
515  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
516  <w:LsdException Locked="false" Priority="51"
517   Name="Grid Table 6 Colorful Accent 2"/>
518  <w:LsdException Locked="false" Priority="52"
519   Name="Grid Table 7 Colorful Accent 2"/>
520  <w:LsdException Locked="false" Priority="46"
521   Name="Grid Table 1 Light Accent 3"/>
522  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
523  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
524  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
525  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
526  <w:LsdException Locked="false" Priority="51"
527   Name="Grid Table 6 Colorful Accent 3"/>
528  <w:LsdException Locked="false" Priority="52"
529   Name="Grid Table 7 Colorful Accent 3"/>
530  <w:LsdException Locked="false" Priority="46"
531   Name="Grid Table 1 Light Accent 4"/>
532  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
533  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
534  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
535  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
536  <w:LsdException Locked="false" Priority="51"
537   Name="Grid Table 6 Colorful Accent 4"/>
538  <w:LsdException Locked="false" Priority="52"
539   Name="Grid Table 7 Colorful Accent 4"/>
540  <w:LsdException Locked="false" Priority="46"
541   Name="Grid Table 1 Light Accent 5"/>
542  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
543  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
544  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
545  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
546  <w:LsdException Locked="false" Priority="51"
547   Name="Grid Table 6 Colorful Accent 5"/>
548  <w:LsdException Locked="false" Priority="52"
549   Name="Grid Table 7 Colorful Accent 5"/>
550  <w:LsdException Locked="false" Priority="46"
551   Name="Grid Table 1 Light Accent 6"/>
552  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
553  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
554  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
555  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
556  <w:LsdException Locked="false" Priority="51"
557   Name="Grid Table 6 Colorful Accent 6"/>
558  <w:LsdException Locked="false" Priority="52"
559   Name="Grid Table 7 Colorful Accent 6"/>
560  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
561  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
562  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
563  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
564  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
565  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
566  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
567  <w:LsdException Locked="false" Priority="46"
568   Name="List Table 1 Light Accent 1"/>
569  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
570  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
571  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
572  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
573  <w:LsdException Locked="false" Priority="51"
574   Name="List Table 6 Colorful Accent 1"/>
575  <w:LsdException Locked="false" Priority="52"
576   Name="List Table 7 Colorful Accent 1"/>
577  <w:LsdException Locked="false" Priority="46"
578   Name="List Table 1 Light Accent 2"/>
579  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
580  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
581  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
582  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
583  <w:LsdException Locked="false" Priority="51"
584   Name="List Table 6 Colorful Accent 2"/>
585  <w:LsdException Locked="false" Priority="52"
586   Name="List Table 7 Colorful Accent 2"/>
587  <w:LsdException Locked="false" Priority="46"
588   Name="List Table 1 Light Accent 3"/>
589  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
590  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
591  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
592  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
593  <w:LsdException Locked="false" Priority="51"
594   Name="List Table 6 Colorful Accent 3"/>
595  <w:LsdException Locked="false" Priority="52"
596   Name="List Table 7 Colorful Accent 3"/>
597  <w:LsdException Locked="false" Priority="46"
598   Name="List Table 1 Light Accent 4"/>
599  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
600  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
601  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
602  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
603  <w:LsdException Locked="false" Priority="51"
604   Name="List Table 6 Colorful Accent 4"/>
605  <w:LsdException Locked="false" Priority="52"
606   Name="List Table 7 Colorful Accent 4"/>
607  <w:LsdException Locked="false" Priority="46"
608   Name="List Table 1 Light Accent 5"/>
609  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
610  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
611  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
612  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
613  <w:LsdException Locked="false" Priority="51"
614   Name="List Table 6 Colorful Accent 5"/>
615  <w:LsdException Locked="false" Priority="52"
616   Name="List Table 7 Colorful Accent 5"/>
617  <w:LsdException Locked="false" Priority="46"
618   Name="List Table 1 Light Accent 6"/>
619  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
620  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
621  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
622  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
623  <w:LsdException Locked="false" Priority="51"
624   Name="List Table 6 Colorful Accent 6"/>
625  <w:LsdException Locked="false" Priority="52"
626   Name="List Table 7 Colorful Accent 6"/>
627 </w:LatentStyles>
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632 @font-face
633        {font-family:"Cambria Math";
634        panose-1:2 4 5 3 5 4 6 3 2 4;
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636        mso-generic-font-family:roman;
637        mso-font-pitch:variable;
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644        mso-font-pitch:variable;
645        mso-font-signature:-536870145 1073786111 1 0 415 0;}
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649        mso-style-qformat:yes;
650        mso-style-parent:"";
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652        margin-bottom:.0001pt;
653        mso-pagination:widow-orphan;
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656        mso-fareast-font-family:"Times New Roman";
657        mso-fareast-theme-font:minor-fareast;}
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660        mso-style-unhide:no;
661        mso-style-qformat:yes;
662        mso-style-link:"Heading 1 Char";
663        mso-margin-top-alt:auto;
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673h2
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680        mso-margin-bottom-alt:auto;
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682        mso-pagination:widow-orphan;
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684        font-size:18.0pt;
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687        mso-fareast-theme-font:minor-fareast;}
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691        mso-style-unhide:no;
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696        mso-style-unhide:no;
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698        mso-style-link:"Heading 1";
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700        mso-ascii-font-family:"Times New Roman";
701        mso-hansi-font-family:"Times New Roman";
702        mso-bidi-font-family:"Times New Roman";
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712        mso-ascii-font-family:"Times New Roman";
713        mso-hansi-font-family:"Times New Roman";
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725        font-family:"Times New Roman",serif;
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727        mso-fareast-theme-font:minor-fareast;}
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730        mso-style-unhide:no;
731        mso-margin-top-alt:auto;
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737        font-family:"Times New Roman",serif;
738        mso-fareast-font-family:"Times New Roman";
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740span.SpellE
741        {mso-style-name:"";
742        mso-spl-e:yes;}
743span.GramE
744        {mso-style-name:"";
745        mso-gram-e:yes;}
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748        mso-default-props:yes;
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750        mso-ansi-font-size:10.0pt;
751        mso-bidi-font-size:10.0pt;}
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755        mso-header-margin:.5in;
756        mso-footer-margin:.5in;
757        mso-paper-source:0;}
758div.WordSection1
759        {page:WordSection1;}
760-->
761</style>
762<!--[if gte mso 10]>
763<style>
764 /* Style Definitions */
765 table.MsoNormalTable
766        {mso-style-name:"Table Normal";
767        mso-tstyle-rowband-size:0;
768        mso-tstyle-colband-size:0;
769        mso-style-noshow:yes;
770        mso-style-priority:99;
771        mso-style-parent:"";
772        mso-padding-alt:0in 5.4pt 0in 5.4pt;
773        mso-para-margin:0in;
774        mso-para-margin-bottom:.0001pt;
775        mso-pagination:widow-orphan;
776        font-size:10.0pt;
777        font-family:"Times New Roman",serif;}
778</style>
779<![endif]--><!--[if gte mso 9]><xml>
780 <o:shapedefaults v:ext="edit" spidmax="1027"/>
781</xml><![endif]--><!--[if gte mso 9]><xml>
782 <o:shapelayout v:ext="edit">
783  <o:idmap v:ext="edit" data="1"/>
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785</head>
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787<body lang=EN-US style='tab-interval:.5in'>
788
789<div class=WordSection1>
790
791<h1><span style='mso-fareast-font-family:"Times New Roman"'>Merohedral twin
792refinement in GSAS-II<o:p></o:p></span></h1>
793
794<h2><span style='mso-fareast-font-family:"Times New Roman"'>Introduction: <o:p></o:p></span></h2>
795
796<p class=MsoNormal>In these exercises you will use GSAS-II to refine the
797structure of a few single crystal structures where there is merohedral
798twinning. There is a general discussion of twinning in International Tables for
799Crystallography (2006), Vol. C, Chapter 1.3, pp 10-14. Merohedral twinning
800occurs when the twin operation (2, m or <span style='position:relative;
801top:3pt'><span style='mso-no-proof:yes'><img width=9 height=19 id="_x0000_i1064"
802src="Merohedral%20twin%20refinement%20in%20GSAS_files/image015.png"></span>)
803belongs to the point group of the vector lattice but not of the crystal
804structure. Of the 230 space groups only 159 of them may have merohedral
805twining. </p>
806
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841
842<p class=MsoNormal>&nbsp;</p>
843
844<p class=MsoNormal>The possible merohedral twin operators are shown in the
845above table (extracted from p 13 of Intl. Tables for <span class=SpellE>Cryst</span>.,
846Vol. C). Merohedral twins are of two types: Type 1 are inversion twins and have
847only 2 components and Type 2 are where the twin operation does not belong to
848the Laue class of the crystal (only for space groups marked with * in above
849table) and multiple twin components may be found. For Type 1 the twin lattice
850exactly <span class=GramE>superimpose</span> so that if Friedel’s law is obeyed
851the twin components have the same value of |F|<sup>2</sup> (the twinning is
852undetectable!). However, in the presence of resonant scattering the |F|<sup>2</sup>
853components differ and if the twin components have unequal volumes then the
854Bragg intensities will differ from that obtained from the <span class=SpellE>untwinned</span>
855structure and then the twinning effects must be considered for
856refinement.&nbsp; Obviously all Type 1 crystals are <span class=SpellE>noncentrosymmetric</span>.
857For Type 2 the space group may be centrosymmetric from within a choice of just
85855 possible space groups. However, the diffraction pattern may display apparent
859higher symmetry especially if the twin components are all equally present in
860the crystal.&nbsp; Note that menu entries and user input are shown in bold face
861below as <b><span style='font-family:"Calibri",sans-serif'>Help/About GSAS-II</span></b>,
862which lists first the name of the menu (here <b><span style='font-family:"Calibri",sans-serif'>Help</span></b>)
863and second the name of the entry in the menu (here <b><span style='font-family:
864"Calibri",sans-serif'>About GSAS-II</span></b>). If you have not done so
865already, start GSAS-II.</p>
866
867<h2 style='margin-bottom:.25in'><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></h2>
868
869<p class=MsoNormal style='margin-bottom:8.0pt;line-height:105%'>.<br clear=all
870style='mso-special-character:line-break;page-break-before:always'>
871</p>
872
873<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 1. A Type 1
874inversion twin – C<sub>8</sub>H<sub>25</sub>Al<sub>0.84</sub>Ga<sub>1.16</sub>N<sub>3</sub>
875<o:p></o:p></span></h2>
876
877<p class=MsoNormal>This example was taken from Luo, et al., Dalton Trans.
8784491(2006). The structure is given in the file <b><span style='font-family:
879"Calibri",sans-serif'>/exercises/<span class=SpellE>MerohedralTwins</span>/1b.cif</span></b>
880and the data are in <b><span style='font-family:"Calibri",sans-serif'>/exercises/<span
881class=SpellE>MerohedralTwins</span>/1b.fcf</span></b>. This example is <span
882class=SpellE>noncentrosymmetric</span> and the data was collected with
883radiation (<span class=SpellE>MoK</span>&#945;) that gives significant resonant
884scattering from the Ga atoms. </p>
885
886<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
887refinement<o:p></o:p></span></h2>
888
889<p class=MsoNormal>To begin do <b><span style='font-family:"Calibri",sans-serif'>Import/Phase/from
890CIF file</span></b> from the main GSAS-II data tree menu. A file selection
891window will appear; find the above <span class=SpellE>cif</span> file (…<b><span
892style='font-family:"Calibri",sans-serif'>1b.cif</span></b>) and select it. A
893popup window will appear</p>
894
895<p class=MsoNormal><span style='mso-no-proof:yes'><img width=445 height=249
896id="_x0000_i1063"
897src="Merohedral%20twin%20refinement%20in%20GSAS_files/image005.png"></span></p>
898
899<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
900a new popup will appear</p>
901
902<p class=MsoNormal><span style='mso-no-proof:yes'><img width=336 height=137
903id="_x0000_i1062"
904src="Merohedral%20twin%20refinement%20in%20GSAS_files/image006.png"></span></p>
905
906<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>,
907and you will see the General page for this phase</p>
908
909<p class=MsoNormal><span style='mso-no-proof:yes'><img width=650 height=500
910id="_x0000_i1061"
911src="Merohedral%20twin%20refinement%20in%20GSAS_files/image007.png"></span></p>
912
913<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
914Factor/from CIF file</span></b> (that is the format of a “<span class=SpellE>fcf</span>”
915file); a file selection dialog box will appear with the previously selected
916directory chosen. Select <b><span style='font-family:"Calibri",sans-serif'>1b.fcf</span></b>;
917a popup window will appear</p>
918
919<p class=MsoNormal><span style='mso-no-proof:yes'><img width=447 height=249
920id="_x0000_i1060"
921src="Merohedral%20twin%20refinement%20in%20GSAS_files/image008.png"></span></p>
922
923<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
924a new popup window allowing you to change the name</p>
925
926<p class=MsoNormal><span style='mso-no-proof:yes'><img width=336 height=137
927id="_x0000_i1059"
928src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"></span></p>
929
930<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
931after a pause and some activity a popup window will appear</p>
932
933<p class=MsoNormal><span style='mso-no-proof:yes'><img width=320 height=310
934id="_x0000_i1058"
935src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.png"></span></p>
936
937<p class=MsoNormal>This makes the connection between the data set and the
938previously imported phase. Select the entry and press <b><span
939style='font-family:"Calibri",sans-serif'>OK</span></b>. You now have loaded all
940that is needed for the first example. The structure had previously been solved
941and refined with <span class=SpellE>Shelx</span> so you need not trouble about
942those steps. You can try to solve the structure in GSAS-II via charge flipping
943but this is not part of this exercise; we will only explore the twin analysis
944features of GSAS-II.</p>
945
946<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
947of twinned structure<o:p></o:p></span></h2>
948
949<p class=MsoNormal>Before beginning the refinement, it usually the practice to
950eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
951&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
952style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
953GSAS-II data tree.</p>
954
955<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
956id="_x0000_i1057"
957src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
958
959<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
960<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
961"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
962style='font-family:"Calibri",sans-serif'>Phases/C8 H25 Al0.84 Ga1.16</span></b>
963<span class=GramE>entry</span> in the GSAS-II data tree and choose the <b><span
964style='font-family:"Calibri",sans-serif'>Data</span></b> tab</p>
965
966<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
967id="_x0000_i1056"
968src="Merohedral%20twin%20refinement%20in%20GSAS_files/image011.png"></span></p>
969
970<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
971factor</span></b> is selected for refinement by default. If you refine it, you
972will get an <span class=SpellE>R<sub>w</sub></span>= 2.85% which isn’t too bad.
973However, you are unsure what the hand of the molecule is in this structure and
974the experiment with <span class=SpellE>MoKa</span> radiation should give
975sufficient resonant scattering to determine this. The <b><span
976style='font-family:"Calibri",sans-serif'>Flack parameter</span></b> gives you a
977way to evaluate which hand the molecule is. If upon refinement the value is ~0
978then you have correctly described the hand. Otherwise if the value is ~1 then
979the opposite hand is the correct and the structure needs to be inverted. So
980let’s test this; select the <b><span style='font-family:"Calibri",sans-serif'>Flack
981parameter</span></b> for refinement and do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>
982from the main GSAS-II data tree menu. The structure will quickly refine to give
983<span class=SpellE>R<sub>w</sub></span>=2.087% which is a considerable
984improvement on Scale factor alone. The Flack parameter is now 0.452, meaning
985that both hands somehow exist in the structure. This can happen if the crystal
986is <span class=SpellE>merohedrally</span> inversion twinned.</p>
987
988<p class=MsoNormal>To introduce this twin, press the <b><span style='font-family:
989"Calibri",sans-serif'>Add Twin Law</span></b> box; the window will be redrawn.</p>
990
991<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
992id="_x0000_i1055"
993src="Merohedral%20twin%20refinement%20in%20GSAS_files/image013.png"></span></p>
994
995<p class=MsoNormal>Notice that two Twin Law matrices have been generated; one
996is the identity for the reference structure and the other by default is the
997merohedral inverse. If some other twin law is desired, then the matrix elements
998need to be changed. Moreover, the Flack parameter has vanished as it is no
999longer needed. Press the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1000button for the <b><span style='font-family:"Calibri",sans-serif'>Twin Law
1001fraction</span></b> and rerun the refinement. The Data window now has.</p>
1002
1003<p class=MsoNormal><span style='mso-no-proof:yes'><img width=449 height=500
1004id="_x0000_i1054"
1005src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.png"></span></p>
1006
1007<p class=MsoNormal>The refinement quickly converged to where it was before but
1008the twin fractions are now ~56/44 consistent with the ~45% Flack parameter
1009obtained earlier. It is likely that the crystal is macroscopically twinned thus
1010the twin fractions are not exactly 50/50. This completes this example; you can
1011save your project if you want to explore other features of GSAS-II with it.</p>
1012
1013<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 2. A Type 2
1014only merohedral twin – <br>
1015[Al(OC<sub>6</sub>H<sub>4</sub>(C<sub>3</sub>H<sub>7</sub>)<sub>2</sub>)]<sup>-</sup>
1016[NC<sub>7</sub>H<sub>8</sub>]<sup>+</sup><o:p></o:p></span></h2>
1017
1018<p class=MsoNormal>In this case the data collection Laue statistics (very
1019nearly <span style='position:relative;top:3pt'><span style='mso-no-proof:yes'><img
1020width=9 height=19 id="_x0000_i1053"
1021src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m)
1022and systematic extinctions indicated that the space group was either one of the
1023<span class=SpellE>enantiomorphic</span> pair P3<sub>1</sub>21 or P3<sub>2</sub>21
1024or possibly one of the pair P3<sub>1</sub> or P3<sub>2</sub>. If the true structure
1025was of the lower symmetry P3<sub>1</sub> or P3<sub>2</sub> then there must be
1026Type 2 merohedral twinning to make the diffraction pattern appear to have
1027higher symmetry (<span style='position:relative;top:3pt'><span
1028style='mso-no-proof:yes'><img width=9 height=19 id="_x0000_i1052"
1029src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m
1030instead of <span style='position:relative;top:3pt'><span style='mso-no-proof:
1031yes'><img width=9 height=19 id="_x0000_i1051"
1032src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>);
1033this exercise will explore this possibility. The data were collected with <span
1034class=SpellE>MoK</span><span style='font-family:Symbol'>a</span> radiation so
1035there is little resonant scattering and thus the choice of hand is
1036indeterminate.&nbsp; Solving the structure in P3<sub>2</sub>21 yielded a poorly
1037fitting structure with disorder particularly in the cation. Resolving the
1038structure in P3<sub>2</sub> gave a structure with no disorder and a better fit
1039to the data (but still not great). As this work was done with <span
1040class=SpellE>Shelx</span> this result is in the form of a <span class=SpellE>Shelx</span>
1041input file (2b.ins – thanks to V. Young for this example). If you have not done
1042so already, start GSAS-II and start with a fresh project.</p>
1043
1044<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1045refinement<o:p></o:p></span></h2>
1046
1047<p class=MsoNormal>To begin we need to import the phase information from the <span
1048class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1049style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1050ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1051and a res file is the output result after a <span class=SpellE>Shelx</span>
1052run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>2b.ins</span></b>
1053from the file selection window; a popup window will ask if this file is the one
1054you want.</p>
1055
1056<p class=MsoNormal><span style='mso-no-proof:yes'><img width=410 height=262
1057id="_x0000_i1050"
1058src="Merohedral%20twin%20refinement%20in%20GSAS_files/image012.png"></span></p>
1059
1060<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
1061a Read Warning will appear.</p>
1062
1063<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1064 id="Picture_x0020_39" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:371.25pt;
1065 height:176.25pt;visibility:visible;mso-wrap-style:square'>
1066 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image001.png"
1067  o:title=""/>
1068</v:shape><![endif]--><![if !vml]><img width=495 height=235
1069src="Merohedral%20twin%20refinement%20in%20GSAS_files/image002.gif" v:shapes="Picture_x0020_39"><![endif]></span></p>
1070
1071<p class=MsoNormal>There are two significant warnings concerning <span
1072class=SpellE>Shelx</span> files. One is that the file never contains the space
1073group symbol (<span class=SpellE>Shelx</span> requires just the operators), so
1074GSAS-II sets the space group to P 1 by default and you will need to change it
1075to P3<sub>2</sub> immediately (next window). The other warning is that hydrogen
1076atoms were found; these usually cannot be refined unconstrained with x-ray
1077data. The warning recommends replacing them with <span class=SpellE>stereochemically</span>
1078determined ones (this is illustrated in the 3<sup>rd</sup> Exercise of this
1079tutorial) and the last line of the Warning tells you what to do if they are to
1080be refined. Here we will only refine twin laws &amp; scale factors so this is
1081unnecessary. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1082you get the opportunity to change the Phase name (I know it is very long but
1083that doesn’t matter here). Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1084the General tab for this phase is shown. </p>
1085
1086<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=336
1087id="_x0000_i1048"
1088src="Merohedral%20twin%20refinement%20in%20GSAS_files/image027.png"></span></p>
1089
1090<p class=MsoNormal>Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
109132</span></b>; the window will be redrawn after a popup showing the operations.
1092You can see the structure by selecting <b><span style='font-family:"Calibri",sans-serif'>Draw
1093Atoms</span></b>.</p>
1094
1095<p class=MsoNormal><span style='mso-no-proof:yes'><img width=478 height=358
1096id="_x0000_i1047"
1097src="Merohedral%20twin%20refinement%20in%20GSAS_files/image028.jpg"></span></p>
1098
1099<p class=MsoNormal>&nbsp;</p>
1100
1101<p class=MsoNormal>The large anion containing the Al atom is to the left and
1102the smaller cation to the right.</p>
1103
1104<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1105Factor/from <span class=SpellE>Shelx</span> HKLF 4 F<sup>2</sup> file</span></b>
1106and select <b><span style='font-family:"Calibri",sans-serif'>2b.hkl</span></b>
1107from the file dialog box; a popup will appear showing a few lines.</p>
1108
1109<p class=MsoNormal><span style='mso-no-proof:yes'><img width=366 height=262
1110id="_x0000_i1046"
1111src="Merohedral%20twin%20refinement%20in%20GSAS_files/image022.png"></span></p>
1112
1113<p class=MsoNormal>This is the right file; a <span class=SpellE>Shelx</span>
1114HKLF 4 file consists of records with just <span class=SpellE><span class=GramE>h,k</span>,l</span>,
1115F<sup>2</sup> and <span style='font-family:Symbol'>s</span>(F<sup>2</sup>).
1116Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b> and <b><span
1117style='font-family:"Calibri",sans-serif'>OK</span></b> on the next one (we’ll
1118keep the name as it is). Choose the phase with the long name on the next popup
1119and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; a 2D
1120display of the hk0 zone is plotted.</p>
1121
1122<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=535
1123id="_x0000_i1045"
1124src="Merohedral%20twin%20refinement%20in%20GSAS_files/image029.png"></span></p>
1125
1126<p class=MsoNormal>The size of the green circles <span class=GramE>are</span>
1127proportional to <span class=SpellE>Fo</span> (after a structure factor
1128calculation blue rings will appear for Fc).</p>
1129
1130<p class=MsoNormal>You now have loaded all that is needed for the second
1131example. The structure had previously been solved and refined with <span
1132class=SpellE>Shelx</span> so you need not trouble about those steps. You can
1133try to solve the structure in GSAS-II via charge flipping but this is not part
1134of this exercise (it isn’t easy because of the twinning); we will only explore
1135the twin analysis features of GSAS-II.</p>
1136
1137<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1138of twinned structure<o:p></o:p></span></h2>
1139
1140<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1141eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1142&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1143style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1144GSAS-II data tree.</p>
1145
1146<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
1147id="_x0000_i1044"
1148src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
1149
1150<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1151<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1152"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1153style='font-family:"Calibri",sans-serif'>Phases/MEROHEDRAL…</span></b> entry in
1154the GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1155tab.</p>
1156
1157<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=444
1158id="_x0000_i1043"
1159src="Merohedral%20twin%20refinement%20in%20GSAS_files/image030.png"></span></p>
1160
1161<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1162factor</span></b> is selected for refinement by default. If you refine it, you
1163will get an <span class=SpellE>R<sub>w</sub></span>~ 25% which is terrible. If
1164you try refining atom positions &amp; thermal parameters you could possibly <span
1165class=GramE>lower</span> it to ~15% (still terrible) and the resulting
1166structure would not be very satisfactory. However, we have suspected from the
1167equivalence of <span style='position:relative;top:3pt'><span style='mso-no-proof:
1168yes'><img width=9 height=19 id="_x0000_i1042"
1169src="Merohedral%20twin%20refinement%20in%20GSAS_files/image031.png"></span>&nbsp;and
1170<span style='position:relative;top:3pt'><span style='mso-no-proof:yes'><img
1171width=9 height=19 id="_x0000_i1041"
1172src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m1
1173Laue data symmetries that there is twinning so don’t bother trying to make it
1174better by refining the structure. To determine the possible twin law we refer
1175to Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
1176that indeed Laue <span style='position:relative;top:3pt'><span
1177style='mso-no-proof:yes'><img width=9 height=19 id="_x0000_i1040"
1178src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m1
1179as P3<sub>2</sub>21 can be simulated by twinned Laue <span style='position:
1180relative;top:3pt'><span style='mso-no-proof:yes'><img width=9 height=19
1181id="_x0000_i1039"
1182src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>&nbsp;crystals
1183in P3<sub>2</sub>; the possible operator is shown in Table 1.3.4.1 (reproduced
1184above) as either a mirror or a 2-fold. The detailed symbolism in the table (‘m.<span
1185class=GramE>., ..</span>2/.2.’) indicates (perhaps obscurely) the operator
1186specifics. See P3m1 and P3<sub>2</sub>21 space groups in International Tables
1187for Crystallography, Vol A for the operations m as <span style='position:relative;
1188top:3pt'><span style='mso-no-proof:yes'><img width=26 height=19
1189id="_x0000_i1038"
1190src="Merohedral%20twin%20refinement%20in%20GSAS_files/image032.png"></span>&nbsp;or
11912 as <span style='position:relative;top:3pt'><span style='mso-no-proof:yes'><img
1192width=26 height=19 id="_x0000_i1037"
1193src="Merohedral%20twin%20refinement%20in%20GSAS_files/image033.png"></span>; we
1194will use the 2-fold since the m inverts the structure which we are not
1195sensitive to in this experiment.</p>
1196
1197<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Add
1198Twin Law</span></b>; the Data tab will be redrawn with the inversion for the
1199second law. Replace this with the 2-fold (<b><span style='font-family:"Calibri",sans-serif'>0
12001 0, 1 0 0, 0 0 -1</span></b>) and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1201box. It should look like.</p>
1202
1203<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=500
1204id="_x0000_i1036"
1205src="Merohedral%20twin%20refinement%20in%20GSAS_files/image034.png"></span></p>
1206
1207<p class=MsoNormal>Now do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>;
1208there will be an immediate improvement in the fit to <span class=SpellE>Rw</span>=5.05%
1209and the twin fractions will be ~50/50. Clearly this crystal is Type 2 <span
1210class=SpellE>merohedrally</span> twinned; we cannot determine if there is any
1211Type 1 twinning because we lack sufficient resonant scattering to see it. This
1212ends the second example; you can save the project file.</p>
1213
1214<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 3. A Type 1
1215&amp; 2 merohedral twin – <span class=SpellE>Cp</span>*Cs(NC<sub>5</sub>H<sub>5</sub>)<o:p></o:p></span></h2>
1216
1217<p class=MsoNormal>This <span class=SpellE>ecample</span> is very similar to
1218the previous one except that the Cs atom has significant resonant scattering
1219for <span class=SpellE>MoKa</span> radiation allowing detection of Type 1 <span
1220class=SpellE>merohedry</span>. The data set has apparent 6/m Laue symmetry but
1221may be 6/mmm for the space groups P61/P65 or P6122/P6522. The combination of
1222Type 1 and Type 2 twins requires 4 twin laws to be explored for this <span
1223class=SpellE>pentamethylcyclopentadienyl</span> Cs complex. As this work was
1224done with <span class=SpellE>Shelx</span> this result is in the form of a <span
1225class=SpellE>Shelx</span> input file (3a.ins – thanks to V. Young for this
1226example). If you have not done so already, start GSAS-II and start with a fresh
1227project.</p>
1228
1229<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1230refinement<o:p></o:p></span></h2>
1231
1232<p class=MsoNormal>To begin we need to import the phase information from the <span
1233class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1234style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1235ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1236and a res file is the output result after a <span class=SpellE>Shelx</span>
1237run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>3a.ins</span></b>
1238from the file selection window; a popup window will ask if this file is the one
1239you want.</p>
1240
1241<p class=MsoNormal><span style='mso-no-proof:yes'><img width=366 height=262
1242id="_x0000_i1035"
1243src="Merohedral%20twin%20refinement%20in%20GSAS_files/image035.png"></span></p>
1244
1245<p class=MsoNormal>It is; press the <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1246button. You will then see the SHELX Read Warning; you will have to change the
1247space group to P61 in a bit. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1248and leave the name alone (press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1249again). Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
125061</span></b>; the General tab will be redrawn after showing you the operators.</p>
1251
1252<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=467
1253id="_x0000_i1034"
1254src="Merohedral%20twin%20refinement%20in%20GSAS_files/image036.png"></span></p>
1255
1256<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1257Factor/from CIF file</span></b> and select <b><span style='font-family:"Calibri",sans-serif'>3a.fcf</span></b>
1258from the file dialog. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1259in the next popup and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1260on the name change popup. Select the file name in the Add to phases popup and
1261press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; the hk0
1262zone of the structure factors will be displayed. Note that this plot shows both
1263green (<span class=SpellE>Fo</span>) and blue (Fc) circles with a small solid
1264red or green circle in the centers. These are for the +/- <span
1265style='font-family:Symbol'>D</span>F values. Fc is here because this <span
1266class=SpellE>fcf</span> file was obtained after refinement via <span
1267class=SpellE>Shelx</span>.</p>
1268
1269<p class=MsoNormal>You now have loaded all that is needed for the third
1270example. The structure had previously been solved and refined with <span
1271class=SpellE>Shelx</span> so you need not trouble about those steps. You can
1272try to solve the structure in GSAS-II via charge flipping but this is not part
1273of this exercise (it isn’t easy because of the twinning; charge flipping will
1274readily give the Cs position &amp; most of the rest. It can be completed via
1275difference Fourier techniques); we will only explore the twin analysis features
1276of GSAS-II.</p>
1277
1278<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1279of twinned structure<o:p></o:p></span></h2>
1280
1281<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1282eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1283&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1284style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1285GSAS-II data tree.</p>
1286
1287<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
1288id="_x0000_i1033"
1289src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
1290
1291<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1292<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1293"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1294style='font-family:"Calibri",sans-serif'>Phases/Cs…</span></b> entry in the
1295GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1296tab.</p>
1297
1298<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
1299id="_x0000_i1032"
1300src="Merohedral%20twin%20refinement%20in%20GSAS_files/image037.png"></span></p>
1301
1302<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1303factor</span></b> is selected for refinement by default. If you refine it, you
1304will get an <span class=SpellE>R<sub>w</sub></span>~ 17% which is terrible. It
1305doesn’t change much if you add the Flack parameter (~0.36). If you try refining
1306atom positions &amp; thermal parameters you could possibly <span class=GramE>lower</span>
1307it but the resulting structure would not be very satisfactory. However, we have
1308suspected from the equivalence of 6/m and 6/mmm Laue data symmetries that there
1309is twinning so don’t bother trying to make it better by refining the structure.
1310To determine the possible twin <span class=GramE>laws</span> we again refer to
1311Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
1312that indeed Laue 6/mmm as P6122 can be simulated by twinned Laue 6/m crystals
1313in P61; the possible operator is shown in Table 1.3.4.1 (reproduced above) as
1314either a mirror or a 2-fold. The detailed symbolism in the table (‘m..,
1315..2/.2.’) indicates (perhaps obscurely) the operator specifics; they are m as <span
1316style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:acc><m:accPr><m:chr
1317    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1318   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1319   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1320   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>y</m:r></span></i></m:e></m:acc><m:acc><m:accPr><m:chr
1321    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1322   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1323   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1324   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e></m:acc><i
1325 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>z</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
1326style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1327"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1328top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1329EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1330 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1331 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image003.png"
1332  o:title="" chromakey="white"/>
1333</v:shape><![endif]--><![if !vml]><img width=26 height=19
1334src="Merohedral%20twin%20refinement%20in%20GSAS_files/image004.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;or
13352 as <!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span
1336 style='font-family:"Cambria Math",serif'><m:r><span style='position:relative;
1337  top:3pt'>yx</m:r></span></i><m:acc><m:accPr><m:chr m:val="&#773;"/><span
1338   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1339   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1340   normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i style='mso-bidi-font-style:
1341   normal'><span style='font-family:"Cambria Math",serif'><m:r>z</m:r></span></i></m:e></m:acc></m:oMath><![endif]--><![if !msEquation]><span
1342style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1343"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1344top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1345EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1346 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1347 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image005.png"
1348  o:title="" chromakey="white"/>
1349</v:shape><![endif]--><![if !vml]><img width=26 height=19
1350src="Merohedral%20twin%20refinement%20in%20GSAS_files/image006.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>;
1351we will use the 2-fold, m and inversion operators to fully test for presence of
1352the 4 possible twin laws. Press the <b><span style='font-family:"Calibri",sans-serif'>Add
1353Twin Law</span></b> button <b><span style='font-family:"Calibri",sans-serif'>3
1354times</span></b>; each time the window will be redrawn. When done you should
1355see.</p>
1356
1357<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
1358id="_x0000_i1031"
1359src="Merohedral%20twin%20refinement%20in%20GSAS_files/image038.png"></span>&nbsp;</p>
1360
1361<p class=MsoNormal>For the third and fourth matrix enter <b><span
1362style='font-family:"Calibri",sans-serif'>0 1 0 1 0 0 0 0 -1</span></b> and <b><span
1363style='font-family:"Calibri",sans-serif'>0 -1 0 -1 0 0 0 0</span></b> <b><span
1364style='font-family:"Calibri",sans-serif'>1</span></b> as the 2-fold and mirror
1365operators (the 2<sup>nd</sup> matrix is the inversion by default). Select the <b><span
1366style='font-family:"Calibri",sans-serif'>Refine</span></b> button and do <b><span
1367style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
1368main menu. The <span class=SpellE>Rw</span> will immediately drop to ~2.26%
1369(RF~2.05%). The four twin element fractions will show various values.</p>
1370
1371<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1372 id="Picture_x0020_40" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:336.75pt;
1373 height:375pt;visibility:visible;mso-wrap-style:square'>
1374 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image007.png"
1375  o:title=""/>
1376</v:shape><![endif]--><![if !vml]><img width=449 height=500
1377src="Merohedral%20twin%20refinement%20in%20GSAS_files/image008.gif" v:shapes="Picture_x0020_40"><![endif]></span></p>
1378
1379<p class=MsoNormal>The negative one for the 3<sup>rd</sup> twin fraction is
1380nonphysical and the 1<sup>st</sup> twin fraction is small. It is likely that
1381the true space group is P6<sub>5</sub> and Type 2 <span class=SpellE>merohedrally</span>
1382twinned (twin fractions 2 &amp; 4). We can improve it by refining the atom
1383positions and thermal parameters, but first we need to replace the hydrogen
1384atoms as suggested by the <span class=SpellE>Shelx</span> warning. Select the <b
1385style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1386mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms </span></b>tab
1387for the phase.</p>
1388
1389<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1390 id="Picture_x0020_41" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:525pt;
1391 height:225pt;visibility:visible;mso-wrap-style:square'>
1392 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"
1393  o:title=""/>
1394</v:shape><![endif]--><![if !vml]><img width=700 height=300
1395src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
1396
1397<p class=MsoNormal>If you scroll down the page, you’ll see H-atoms with default
1398<span class=SpellE>Uiso</span> (=0.025) values. To replace them, the old ones
1399need to be deleted; double click the <b style='mso-bidi-font-weight:normal'><span
1400style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1401mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1402style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1403mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>H</span></b>
1404and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1405mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
1406The H-atoms will be highlighted (and plotted in green). Do <b style='mso-bidi-font-weight:
1407normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1408minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Delete atom</span></b> from
1409the menu; the H-atoms will be deleted and the structure will be redrawn. Next
1410double <span class=GramE>click</span> the <b style='mso-bidi-font-weight:normal'><span
1411style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1412mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1413style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1414mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>C</span></b>;
1415all the C-atoms will be selected (and shown in green on the plot). Do <b
1416style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1417mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Insert
1418H atoms</span></b>; a Distance Angle Controls will appear. Occasionally these values
1419may need to be changed but not this time; press <b style='mso-bidi-font-weight:
1420normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1421minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>. The next popup is
1422for the H atoms add controls.</p>
1423
1424<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1425 id="Picture_x0020_42" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:300pt;
1426 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1427 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image011.png"
1428  o:title=""/>
1429</v:shape><![endif]--><![if !vml]><img width=400 height=485
1430src="Merohedral%20twin%20refinement%20in%20GSAS_files/image012.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
1431
1432<p class=MsoNormal>It specifies the expected geometry around each C-atom for
1433H-atom placement. As expected we want 3 H-atoms on the terminal CH<sub>3</sub>
1434groups on the <span class=SpellE>Cp</span>* ring and one for each C-atom for
1435the NC<sub>5</sub>H<sub>5</sub> molecule. Press <b style='mso-bidi-font-weight:
1436normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1437minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; you will see the
1438H-atoms added in turn to the structure and they will be inserted immediately
1439after their respective C-atom. Their positions and thermal parameters are tied
1440to the C-atoms so that after refinement of the structure they can be shifted to
1441the <span class=SpellE>stereochemically</span> best positions. For the
1442refinement, double click the <b style='mso-bidi-font-weight:normal'><span
1443style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1444mso-hansi-theme-font:minor-latin'>Refine</span></b> column heading and select <b
1445style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1446mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>X</span></b>
1447and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1448mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>U</span></b>
1449from the popup; press <b style='mso-bidi-font-weight:normal'><span
1450style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1451mso-hansi-theme-font:minor-latin'>OK</span></b>. The Atom table will be redrawn
1452with XU in every entry under Refine. Now do <b style='mso-bidi-font-weight:
1453normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1454minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from the
1455main GSASII data tree window; the <span class=SpellE>Rw</span> will drop to
1456~1.92%. If you look at the <b style='mso-bidi-font-weight:normal'><span
1457style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1458mso-hansi-theme-font:minor-latin'>Data</span></b> tab the Twin element fractions
1459are much clearer.</p>
1460
1461<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1462 id="Picture_x0020_43" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:336.75pt;
1463 height:375pt;visibility:visible;mso-wrap-style:square'>
1464 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image013.png"
1465  o:title=""/>
1466</v:shape><![endif]--><![if !vml]><img width=449 height=500
1467src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.gif" v:shapes="Picture_x0020_43"><![endif]></span><span
1468style='mso-spacerun:yes'> </span></p>
1469
1470<p class=MsoNormal>The identity Twin Law has virtually vanished along with the
14712-fold one leaving just the inverse and mirror Twin Laws.</p>
1472
1473<p class=MsoNormal>This means the structure is the inverse in space group P6<sub>5</sub>
1474but still Type 2 <span class=SpellE>merohedrally</span> twinned. </p>
1475
1476<p class=MsoNormal>To test this, we need to both change the space group and
1477invert the structure. First select the <b style='mso-bidi-font-weight:normal'><span
1478style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1479mso-hansi-theme-font:minor-latin'>General</span></b> tab and change the space
1480group to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1481mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P 65</span></b>;
1482you’ll see the Operators popup (press <b style='mso-bidi-font-weight:normal'><span
1483style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1484mso-hansi-theme-font:minor-latin'>Ok</span></b>) and the General tab will be
1485redrawn. Next select the <b style='mso-bidi-font-weight:normal'><span
1486style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1487mso-hansi-theme-font:minor-latin'>Atoms</span></b> tab; do <b style='mso-bidi-font-weight:
1488normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1489minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Update H atoms</span></b> to
1490put them in their best positions. <span style='mso-spacerun:yes'> </span>Next
1491select all the atoms by double clicking the empty box in upper left corner of
1492the table; all atoms will be highlighted &amp; plotted green. Do <b
1493style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1494mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Transform
1495atoms</span></b>; a popup will appear.</p>
1496
1497<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1498 id="Picture_x0020_44" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:270pt;
1499 height:263.25pt;visibility:visible;mso-wrap-style:square'>
1500 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image015.png"
1501  o:title=""/>
1502</v:shape><![endif]--><![if !vml]><img width=360 height=351
1503src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
1504
1505<p class=MsoNormal>Check the <b style='mso-bidi-font-weight:normal'><span
1506style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1507mso-hansi-theme-font:minor-latin'>Choose inversion</span></b> box and
1508(important) set <b style='mso-bidi-font-weight:normal'><span style='font-family:
1509"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1510minor-latin'>Choose unit cell</span></b> to <b style='mso-bidi-font-weight:
1511normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1512minor-latin;mso-hansi-theme-font:minor-latin'>1 1 1</span></b>; this will put
1513the inverted structure back inside the unit cell. Press <b style='mso-bidi-font-weight:
1514normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1515minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; the table and plot
1516will both be redrawn. Now do <b style='mso-bidi-font-weight:normal'><span
1517style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1518mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>; the <span
1519class=SpellE>Rw</span> will drop back to where it was before and the <b
1520style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1521mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
1522tab will show new Twin fractions.</p>
1523
1524<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1525 id="Picture_x0020_46" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:336.75pt;
1526 height:375pt;visibility:visible;mso-wrap-style:square'>
1527 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image017.png"
1528  o:title=""/>
1529</v:shape><![endif]--><![if !vml]><img width=449 height=500
1530src="Merohedral%20twin%20refinement%20in%20GSAS_files/image018.gif" v:shapes="Picture_x0020_46"><![endif]></span></p>
1531
1532<p class=MsoNormal>Now the identity Twin Law is ~2/3 and the 2-fold Twin Law is
1533the other ~1/3 while the other two are ~zero. You can delete them and repeat
1534the refinement; <span class=SpellE>Rw</span> ~1.7%. This completed the
1535merohedral twin exercises. You can save this project if desired.<o:p></o:p></p>
1536
1537<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1538
1539</div>
1540
1541</body>
1542
1543</html>
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