source: Tutorials/MerohedralTwins/Merohedral twin refinement in GSAS.htm @ 4948

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409  <w:LsdException Locked="false" Priority="34" QFormat="true"
410   Name="List Paragraph"/>
411  <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
412  <w:LsdException Locked="false" Priority="30" QFormat="true"
413   Name="Intense Quote"/>
414  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
415  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
416  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
417  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
418  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
419  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
420  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
421  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
422  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
423  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
424  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
425  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
426  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
427  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
428  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
429  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
430  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
431  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
432  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
433  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
434  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
435  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
436  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
437  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
438  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
439  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
440  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
441  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
442  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
443  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
444  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
445  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
446  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
447  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
448  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
449  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
450  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
451  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
452  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
453  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
454  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
455  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
456  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
457  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
458  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
459  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
460  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
461  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
462  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
463  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
464  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
465  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
466  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
467  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
468  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
469  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
470  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
471  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
472  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
473  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
474  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
475  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
476  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
477  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
478  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
479  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
480  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
481  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
482  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
483  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
484  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
485  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
486  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
487  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
488  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
489  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
490  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
491  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
492  <w:LsdException Locked="false" Priority="19" QFormat="true"
493   Name="Subtle Emphasis"/>
494  <w:LsdException Locked="false" Priority="21" QFormat="true"
495   Name="Intense Emphasis"/>
496  <w:LsdException Locked="false" Priority="31" QFormat="true"
497   Name="Subtle Reference"/>
498  <w:LsdException Locked="false" Priority="32" QFormat="true"
499   Name="Intense Reference"/>
500  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
501  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
502   UnhideWhenUsed="true" Name="Bibliography"/>
503  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
504   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
505  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
506  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
507  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
508  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
509  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
510  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
511  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
512  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
513  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
514  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
515  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
516  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
517  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
518  <w:LsdException Locked="false" Priority="46"
519   Name="Grid Table 1 Light Accent 1"/>
520  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
521  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
522  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
523  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
524  <w:LsdException Locked="false" Priority="51"
525   Name="Grid Table 6 Colorful Accent 1"/>
526  <w:LsdException Locked="false" Priority="52"
527   Name="Grid Table 7 Colorful Accent 1"/>
528  <w:LsdException Locked="false" Priority="46"
529   Name="Grid Table 1 Light Accent 2"/>
530  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
531  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
532  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
533  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
534  <w:LsdException Locked="false" Priority="51"
535   Name="Grid Table 6 Colorful Accent 2"/>
536  <w:LsdException Locked="false" Priority="52"
537   Name="Grid Table 7 Colorful Accent 2"/>
538  <w:LsdException Locked="false" Priority="46"
539   Name="Grid Table 1 Light Accent 3"/>
540  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
541  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
542  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
543  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
544  <w:LsdException Locked="false" Priority="51"
545   Name="Grid Table 6 Colorful Accent 3"/>
546  <w:LsdException Locked="false" Priority="52"
547   Name="Grid Table 7 Colorful Accent 3"/>
548  <w:LsdException Locked="false" Priority="46"
549   Name="Grid Table 1 Light Accent 4"/>
550  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
551  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
552  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
553  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
554  <w:LsdException Locked="false" Priority="51"
555   Name="Grid Table 6 Colorful Accent 4"/>
556  <w:LsdException Locked="false" Priority="52"
557   Name="Grid Table 7 Colorful Accent 4"/>
558  <w:LsdException Locked="false" Priority="46"
559   Name="Grid Table 1 Light Accent 5"/>
560  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
561  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
562  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
563  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
564  <w:LsdException Locked="false" Priority="51"
565   Name="Grid Table 6 Colorful Accent 5"/>
566  <w:LsdException Locked="false" Priority="52"
567   Name="Grid Table 7 Colorful Accent 5"/>
568  <w:LsdException Locked="false" Priority="46"
569   Name="Grid Table 1 Light Accent 6"/>
570  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
571  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
572  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
573  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
574  <w:LsdException Locked="false" Priority="51"
575   Name="Grid Table 6 Colorful Accent 6"/>
576  <w:LsdException Locked="false" Priority="52"
577   Name="Grid Table 7 Colorful Accent 6"/>
578  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
579  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
580  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
581  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
582  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
583  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
584  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
585  <w:LsdException Locked="false" Priority="46"
586   Name="List Table 1 Light Accent 1"/>
587  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
588  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
589  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
590  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
591  <w:LsdException Locked="false" Priority="51"
592   Name="List Table 6 Colorful Accent 1"/>
593  <w:LsdException Locked="false" Priority="52"
594   Name="List Table 7 Colorful Accent 1"/>
595  <w:LsdException Locked="false" Priority="46"
596   Name="List Table 1 Light Accent 2"/>
597  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
598  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
599  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
600  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
601  <w:LsdException Locked="false" Priority="51"
602   Name="List Table 6 Colorful Accent 2"/>
603  <w:LsdException Locked="false" Priority="52"
604   Name="List Table 7 Colorful Accent 2"/>
605  <w:LsdException Locked="false" Priority="46"
606   Name="List Table 1 Light Accent 3"/>
607  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
608  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
609  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
610  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
611  <w:LsdException Locked="false" Priority="51"
612   Name="List Table 6 Colorful Accent 3"/>
613  <w:LsdException Locked="false" Priority="52"
614   Name="List Table 7 Colorful Accent 3"/>
615  <w:LsdException Locked="false" Priority="46"
616   Name="List Table 1 Light Accent 4"/>
617  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
618  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
619  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
620  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
621  <w:LsdException Locked="false" Priority="51"
622   Name="List Table 6 Colorful Accent 4"/>
623  <w:LsdException Locked="false" Priority="52"
624   Name="List Table 7 Colorful Accent 4"/>
625  <w:LsdException Locked="false" Priority="46"
626   Name="List Table 1 Light Accent 5"/>
627  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
628  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
629  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
630  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
631  <w:LsdException Locked="false" Priority="51"
632   Name="List Table 6 Colorful Accent 5"/>
633  <w:LsdException Locked="false" Priority="52"
634   Name="List Table 7 Colorful Accent 5"/>
635  <w:LsdException Locked="false" Priority="46"
636   Name="List Table 1 Light Accent 6"/>
637  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
638  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
639  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
640  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
641  <w:LsdException Locked="false" Priority="51"
642   Name="List Table 6 Colorful Accent 6"/>
643  <w:LsdException Locked="false" Priority="52"
644   Name="List Table 7 Colorful Accent 6"/>
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804
805<body lang=EN-US style='tab-interval:.5in'>
806
807<div class=WordSection1>
808
809<h1><span style='mso-fareast-font-family:"Times New Roman"'>Merohedral twin
810refinement in GSAS-II<o:p></o:p></span></h1>
811
812<P><BL>
813  <LI><B>A video version of this tutorial is available at
814<A href="https://anl.box.com/v/MerohedraltwinrefinementinGSAS" target="_blank">
815https://anl.box.com/v/MerohedraltwinrefinementinGSAS</A></B>
816  <LI>Exercise files are found <A href="./data/" target="_blank">here</a>
817</BL></P><P></P>
818
819<h2><span style='mso-fareast-font-family:"Times New Roman"'>Introduction: <o:p></o:p></span></h2>
820
821<p class=MsoNormal>In these exercises you will use GSAS-II to refine the
822structure of a few single crystal structures where there is merohedral
823twinning. There is a general discussion of twinning in International Tables for
824Crystallography (2006), Vol. C, Chapter 1.3, pp 10-14. <span class=SpellE>Merohedral</span>
825twinning occurs when the twin operation (2, m <span class=GramE>or </span><span
826style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
827    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
828   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
829   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
830   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:bar></m:oMath><![endif]--><![if !msEquation]><span
831style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
832"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
833top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
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860belongs to the point group of the vector lattice but not of the crystal
861structure. Of the 230 space groups only 159 of them may have merohedral
862twining. </p>
863
864<p class=MsoNormal><!--[if gte vml 1]><v:shape id="Picture_x0020_2" o:spid="_x0000_s1026"
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876src="Merohedral%20twin%20refinement%20in%20GSAS_files/image025.png" align=left
877hspace=12 v:shapes="Picture_x0020_2"><![endif]>&nbsp;</p>
878
879<p class=MsoNormal>&nbsp;</p>
880
881<p class=MsoNormal>The possible merohedral twin operators are shown in the
882above table (extracted from p 13 of Intl. Tables for <span class=SpellE>Cryst</span>.,
883Vol. C). Merohedral twins are of two types: Type 1 are inversion twins and have
884only 2 components and Type 2 are where the twin operation does not belong to
885the Laue class of the crystal (only for space groups marked with * in above
886table) and multiple twin components may be found. For Type 1 the twin lattice
887exactly superimpose so that if Friedel’s law is obeyed the twin <span
888class=GramE>components</span> have the same value of |F|<sup>2</sup> (the
889twinning is undetectable!). However, in the presence of resonant scattering the
890|F|<sup>2</sup> components differ and if the twin components have unequal
891volumes then the Bragg intensities will differ from that obtained from the <span
892class=SpellE>untwinned</span> structure and then the twinning effects must be
893considered for refinement.&nbsp; Obviously all Type 1 crystals are <span
894class=SpellE>noncentrosymmetric</span>. For Type 2 the space group may be
895centrosymmetric from within a choice of just 55 possible space groups. However,
896the diffraction pattern may display apparent higher symmetry especially if the
897twin components are all equally present in the crystal.&nbsp; Note that menu
898entries and user input are shown in bold face below as <b><span
899style='font-family:"Calibri",sans-serif'>Help/About GSAS-II</span></b>, which
900lists first the name of the menu (here <b><span style='font-family:"Calibri",sans-serif'>Help</span></b>)
901and second the name of the entry in the menu (here <b><span style='font-family:
902"Calibri",sans-serif'>About GSAS-II</span></b>). If you have not done so already,
903start GSAS-II.</p>
904
905<h2 style='margin-bottom:.25in'><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></h2>
906
907<p class=MsoNormal style='margin-bottom:8.0pt;line-height:105%'>.<br clear=all
908style='mso-special-character:line-break;page-break-before:always'>
909</p>
910
911<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 1. A Type 1
912inversion twin – C<sub>8</sub>H<sub>25</sub>Al<sub>0.84</sub>Ga<sub>1.16</sub>N<sub>3</sub>
913<o:p></o:p></span></h2>
914
915<p class=MsoNormal>This example was taken from Luo, et al., Dalton Trans.
9164491(2006). The structure is given in the file <span class=SpellE><b><span
917style='font-family:"Calibri",sans-serif'>MerohedralTwins</span></b></span><b><span
918style='font-family:"Calibri",sans-serif'>/data/1b.cif</span></b> and the data
919are in <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>MerohedralTwins</span></b></span><b><span
920style='font-family:"Calibri",sans-serif'>/data/1b.fcf</span></b>. This example
921is <span class=SpellE>noncentrosymmetric</span> and the data was collected with
922radiation (<span class=SpellE>MoK</span>&#945;) that gives significant resonant
923scattering from the Ga atoms. </p>
924
925<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
926refinement<o:p></o:p></span></h2>
927
928<p class=MsoNormal>To begin do <b><span style='font-family:"Calibri",sans-serif'>Import/Phase/from
929CIF file</span></b> from the main GSAS-II data tree menu. A file selection
930window will appear; find the above <span class=SpellE>cif</span> file (…<b><span
931style='font-family:"Calibri",sans-serif'>1b.cif</span></b>) and select it. A
932popup window will appear. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
933a new popup will appear; Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>,
934and you will see the General page for this phase</p>
935
936<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
937 id="Picture_x0020_1" o:spid="_x0000_i1052" type="#_x0000_t75" style='width:468pt;
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939 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image005.png"
940  o:title=""/>
941</v:shape><![endif]--><![if !vml]><img width=624 height=498
942src="Merohedral%20twin%20refinement%20in%20GSAS_files/image002.gif" v:shapes="Picture_x0020_1"><![endif]></span></p>
943
944<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
945Factor/from CIF file</span></b> (that is the format of <span class=GramE>a</span>
946“<span class=SpellE>fcf</span>” file); a file selection dialog box will appear
947with the previously selected directory chosen. Select <b><span
948style='font-family:"Calibri",sans-serif'>1b.fcf</span></b>; a popup window will
949appear</p>
950
951<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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958
959<p class=MsoNormal>Select <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Yes</span></b></span>;
960a new popup window allowing you to change the name</p>
961
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967</v:shape><![endif]--><![if !vml]><img width=346 height=156
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969
970<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
971after a pause and some activity a popup window will appear</p>
972
973<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
974 id="Picture_x0020_5" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:233.25pt;
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976 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image023.png"
977  o:title=""/>
978</v:shape><![endif]--><![if !vml]><img width=311 height=305
979src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.gif" v:shapes="Picture_x0020_5"><![endif]></span></p>
980
981<p class=MsoNormal>This makes the connection between the data set and the
982previously imported phase. Select the entry and press <b><span
983style='font-family:"Calibri",sans-serif'>OK</span></b>. You now have loaded all
984that is needed for the first example. The structure had previously been solved
985and refined with <span class=SpellE>Shelx</span> so you need not trouble about
986those steps. You can try to solve the structure in GSAS-II via charge flipping
987but this is not part of this exercise; we will only explore the twin analysis
988features of GSAS-II.</p>
989
990<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
991of twinned structure<o:p></o:p></span></h2>
992
993<p class=MsoNormal>Before beginning the refinement, it usually the practice to
994eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
995&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
996style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
997GSAS-II data tree.</p>
998
999<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1000 id="Picture_x0020_6" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:468pt;
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1002 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"
1003  o:title=""/>
1004</v:shape><![endif]--><![if !vml]><img width=624 height=279
1005src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.gif" v:shapes="Picture_x0020_6"><![endif]></span></p>
1006
1007<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1008<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1009"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1010style='font-family:"Calibri",sans-serif'>Phases/C8 H25 Al0.84 Ga1.16</span></b>
1011entry in the GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1012tab</p>
1013
1014<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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1017 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image028.png"
1018  o:title=""/>
1019</v:shape><![endif]--><![if !vml]><img width=624 height=349
1020src="Merohedral%20twin%20refinement%20in%20GSAS_files/image018.gif" v:shapes="Picture_x0020_23"><![endif]></span></p>
1021
1022<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1023factor</span></b> is selected for refinement by default. If you refine it, you
1024will get an <span class=SpellE>R<sub>w</sub></span>= 2.85% which isn’t too bad.
1025However, you are unsure what the hand of the molecule is in this structure and
1026the experiment with <span class=SpellE>MoKa</span> radiation should give
1027sufficient resonant scattering to determine this. The <b><span
1028style='font-family:"Calibri",sans-serif'>Flack parameter</span></b> gives you a
1029way to evaluate which hand the molecule is. If upon refinement the value is ~0
1030then you have correctly described the hand. Otherwise if the value is ~1 then
1031the opposite hand is the correct and the structure needs to be inverted. So
1032let’s test this; select the <b><span style='font-family:"Calibri",sans-serif'>Flack
1033parameter</span></b> for refinement and do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>
1034from the main GSAS-II data tree menu. You’ll be asked to save the project; pick
1035a directory &amp; a name – I chose <b style='mso-bidi-font-weight:normal'><span
1036style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1037mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>1b</span></b>.
1038The structure will quickly refine to give <span class=SpellE>R<sub>w</sub></span>=2.155%
1039which is a considerable improvement on Scale factor alone. The Flack parameter
1040is now 0.433, meaning that both hands somehow exist in the structure. This can
1041happen if the crystal is <span class=SpellE>merohedrally</span> inversion twinned.</p>
1042
1043<p class=MsoNormal>To introduce this twin, press the <b><span style='font-family:
1044"Calibri",sans-serif'>Add Twin Law</span></b> box; the window will be redrawn.</p>
1045
1046<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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1050  o:title=""/>
1051</v:shape><![endif]--><![if !vml]><img width=624 height=446
1052src="Merohedral%20twin%20refinement%20in%20GSAS_files/image019.gif" v:shapes="_x0000_i1046"><![endif]></span></p>
1053
1054<p class=MsoNormal>Notice that two Twin Law matrices have been generated; one is
1055the identity for the reference structure and the other by default is the
1056merohedral inverse. If some other twin law is desired, then the matrix elements
1057need to be changed. Moreover, the Flack parameter has vanished as it is no
1058longer needed. Press the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1059button for the <b><span style='font-family:"Calibri",sans-serif'>Twin Law
1060fraction</span></b> and rerun the refinement. The Data window now has.</p>
1061
1062<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1063 id="Picture_x0020_42" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:468pt;
1064 height:337.5pt;visibility:visible;mso-wrap-style:square'>
1065 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image032.png"
1066  o:title=""/>
1067</v:shape><![endif]--><![if !vml]><img width=624 height=450
1068src="Merohedral%20twin%20refinement%20in%20GSAS_files/image062.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
1069
1070<p class=MsoNormal>The refinement quickly converged to where it was before but
1071the twin fractions are now ~56/44 consistent with the ~45% Flack parameter
1072obtained earlier. It is likely that the crystal is macroscopically twinned thus
1073the twin fractions are not exactly 50/50. This completes this example; you can
1074save your project if you want to explore other features of GSAS-II with it.</p>
1075
1076<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 2. A Type 2
1077only merohedral twin – <br>
1078[Al(OC<sub>6</sub>H<sub>4</sub>(C<sub>3</sub>H<sub>7</sub>)<sub>2</sub>)]<sup>-</sup>
1079[NC<sub>7</sub>H<sub>8</sub>]<sup>+</sup><o:p></o:p></span></h2>
1080
1081<p class=MsoNormal>In this case the data collection Laue statistics (very
1082nearly <span style='position:relative;top:3pt'><span style='mso-no-proof:yes'>-3</span>m)
1083and systematic extinctions indicated that the space group was either one of the
1084<span class=SpellE>enantiomorphic</span> pair P3<sub>1</sub>21 or P3<sub>2</sub>21
1085or possibly one of the pair P3<sub>1</sub> or P3<sub>2</sub>. If the true
1086structure was of the lower symmetry P3<sub>1</sub> or P3<sub>2</sub> then there
1087must be Type 2 merohedral twinning to make the diffraction pattern appear to
1088have higher symmetry (<span style='position:relative;top:3pt'><span
1089style='mso-no-proof:yes'>-3</span>m instead of <span style='position:relative;
1090top:3pt'><span style='mso-no-proof:yes'>-3</span>); this exercise will explore
1091this possibility. The data were collected with <span class=SpellE>MoK</span><span
1092style='font-family:Symbol'>a</span> radiation so there is little resonant
1093scattering and thus the choice of hand is indeterminate.&nbsp; Solving the
1094structure in P3<sub>2</sub>21 yielded a poorly fitting structure with disorder
1095particularly in the cation. Resolving the structure in P3<sub>2</sub> gave a
1096structure with no disorder and a better fit to the data (but still not great).
1097As this work was done with <span class=SpellE>Shelx</span> this result is in
1098the form of a <span class=SpellE>Shelx</span> input file (2b.ins – thanks to V.
1099Young for this example). If you have not done so already, start GSAS-II and
1100start with a fresh project.</p>
1101
1102<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1103refinement<o:p></o:p></span></h2>
1104
1105<p class=MsoNormal>To begin we need to import the phase information from the <span
1106class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1107style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1108ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1109and a res file is the output result after a <span class=SpellE>Shelx</span>
1110run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>2b.ins</span></b>
1111from the file selection window; a popup window will ask if this file is the one
1112you want.</p>
1113
1114<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1115 id="Picture_x0020_43" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:314.25pt;
1116 height:159pt;visibility:visible;mso-wrap-style:square'>
1117 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image034.png"
1118  o:title=""/>
1119</v:shape><![endif]--><![if !vml]><img width=419 height=212
1120src="Merohedral%20twin%20refinement%20in%20GSAS_files/image063.gif" v:shapes="Picture_x0020_43"><![endif]></span></p>
1121
1122<p class=MsoNormal>Press <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Yes</span></b></span>;
1123a Read Warning will appear.</p>
1124
1125<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1126 id="Picture_x0020_44" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:378.75pt;
1127 height:177pt;visibility:visible;mso-wrap-style:square'>
1128 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image036.png"
1129  o:title=""/>
1130</v:shape><![endif]--><![if !vml]><img width=505 height=236
1131src="Merohedral%20twin%20refinement%20in%20GSAS_files/image064.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
1132
1133<p class=MsoNormal>There are two significant warnings concerning <span
1134class=SpellE>Shelx</span> files. One is that the file never contains the space
1135group symbol (<span class=SpellE>Shelx</span> requires just the operators), so
1136GSAS-II sets the space group to P 1 by default and you will need to change it
1137to P3<sub>2</sub> immediately (next window). The other warning is that hydrogen
1138atoms were found; these usually cannot be refined unconstrained with x-ray
1139data. The warning recommends replacing them with <span class=SpellE>stereochemically</span>
1140determined ones (this is illustrated in the 3<sup>rd</sup> Exercise of this
1141tutorial) and the last line of the Warning tells you what to do if they are to
1142be refined. Here we will only refine twin laws &amp; scale factors so this is
1143unnecessary. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1144you get the opportunity to change the Phase name (I know it is very long but
1145that doesn’t matter here). Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1146the General tab for this phase is shown. </p>
1147
1148<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1149 id="Picture_x0020_45" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:468pt;
1150 height:206.25pt;visibility:visible;mso-wrap-style:square'>
1151 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image038.png"
1152  o:title=""/>
1153</v:shape><![endif]--><![if !vml]><img width=624 height=275
1154src="Merohedral%20twin%20refinement%20in%20GSAS_files/image065.gif" v:shapes="Picture_x0020_45"><![endif]></span></p>
1155
1156<p class=MsoNormal>Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
115732</span></b>; the window will be redrawn after a popup showing the operations.
1158You can see the structure by selecting <b><span style='font-family:"Calibri",sans-serif'>Draw
1159Atoms</span></b>.</p>
1160
1161<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1162 id="Picture_x0020_47" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:468pt;
1163 height:405pt;visibility:visible;mso-wrap-style:square'>
1164 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image040.png"
1165  o:title=""/>
1166</v:shape><![endif]--><![if !vml]><img width=624 height=540
1167src="Merohedral%20twin%20refinement%20in%20GSAS_files/image066.gif" v:shapes="Picture_x0020_47"><![endif]></span></p>
1168
1169<p class=MsoNormal>&nbsp;</p>
1170
1171<p class=MsoNormal>The large anion containing the Al atom is to the left and
1172the smaller cation to the right.</p>
1173
1174<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1175Factor/from <span class=SpellE>Shelx</span> HKLF 4 F<sup>2</sup> file</span></b>
1176and select <b><span style='font-family:"Calibri",sans-serif'>2b.hkl</span></b>
1177from the file dialog box; a popup will appear showing a few lines.</p>
1178
1179<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1180 id="Picture_x0020_48" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:274.5pt;
1181 height:186pt;visibility:visible;mso-wrap-style:square'>
1182 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image042.png"
1183  o:title=""/>
1184</v:shape><![endif]--><![if !vml]><img width=366 height=248
1185src="Merohedral%20twin%20refinement%20in%20GSAS_files/image067.gif" v:shapes="Picture_x0020_48"><![endif]></span></p>
1186
1187<p class=MsoNormal>This is the right file; a <span class=SpellE>Shelx</span>
1188HKLF 4 file consists of records with just <span class=SpellE>h<span
1189class=GramE>,k,l</span></span>, F<sup>2</sup> and <span style='font-family:
1190Symbol'>s</span>(F<sup>2</sup>). Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1191and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b> on the next
1192one (we’ll keep the name as it is). Choose the phase with the long name on the
1193next popup and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1194select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
1195"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1196minor-latin;mso-bidi-theme-font:minor-latin'>Structure factors</span></b> tab, a
11972D display of the hk0 zone is plotted.</p>
1198
1199<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1200 id="Picture_x0020_49" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:468pt;
1201 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1202 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image044.png"
1203  o:title=""/>
1204</v:shape><![endif]--><![if !vml]><img width=624 height=535
1205src="Merohedral%20twin%20refinement%20in%20GSAS_files/image068.gif" v:shapes="Picture_x0020_49"><![endif]></span></p>
1206
1207<p class=MsoNormal>The size of the green circles are proportional to <span
1208class=SpellE><span class=GramE>Fo</span></span> (after a structure factor
1209calculation blue rings will appear for Fc).</p>
1210
1211<p class=MsoNormal>You now have loaded all that is needed for the second
1212example. The structure had previously been solved and refined with <span
1213class=SpellE>Shelx</span> so you need not trouble about those steps. You can
1214try to solve the structure in GSAS-II via charge flipping but this is not part
1215of this exercise (it isn’t easy because of the twinning); we will only explore
1216the twin analysis features of GSAS-II.</p>
1217
1218<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1219of twinned structure<o:p></o:p></span></h2>
1220
1221<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1222eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1223&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1224style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1225GSAS-II data tree.</p>
1226
1227<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1228 id="Picture_x0020_50" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:468pt;
1229 height:215.25pt;visibility:visible;mso-wrap-style:square'>
1230 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image046.png"
1231  o:title=""/>
1232</v:shape><![endif]--><![if !vml]><img width=624 height=287
1233src="Merohedral%20twin%20refinement%20in%20GSAS_files/image069.gif" v:shapes="Picture_x0020_50"><![endif]></span></p>
1234
1235<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1236<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1237"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1238style='font-family:"Calibri",sans-serif'>Phases/MEROHEDRAL…</span></b> entry in
1239the GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1240tab.</p>
1241
1242<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=444
1243id="_x0000_i1037"
1244src="Merohedral%20twin%20refinement%20in%20GSAS_files/image030.png"></span></p>
1245
1246<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1247factor</span></b> is selected for refinement by default. If you refine it, you
1248will get an <span class=SpellE>R<sub>w</sub></span>~ 25% which is terrible. If
1249you try refining atom positions &amp; thermal parameters you could possibly
1250lower it to ~15% (still terrible) and the resulting structure would not be very
1251satisfactory. However, we have suspected from the equivalence of <span
1252style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1253    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1254   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1255   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1256   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:e></m:bar></m:oMath><![endif]--><![if !msEquation]><span
1257style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1258"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1259top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1260EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1261 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1262 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1263  o:title="" chromakey="white"/>
1264</v:shape><![endif]--><![if !vml]><img width=9 height=21
1265src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;and
1266<span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1267    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1268   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1269   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1270   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:e></m:bar></m:oMath><![endif]--><![if !msEquation]><span
1271style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1272"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1273top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1274EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1275 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1276 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1277  o:title="" chromakey="white"/>
1278</v:shape><![endif]--><![if !vml]><img width=9 height=21
1279src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>m1
1280Laue data symmetries that there is twinning so don’t bother trying to make it
1281better by refining the structure. To determine the possible twin law we refer
1282to Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
1283that indeed Laue <span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1284    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1285   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1286   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1287   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:e></m:bar></m:oMath><![endif]--><![if !msEquation]><span
1288style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1289"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1290top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1291EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1292 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1293 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1294  o:title="" chromakey="white"/>
1295</v:shape><![endif]--><![if !vml]><img width=9 height=21
1296src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>m1
1297as P3<sub>2</sub>21 can be simulated by twinned Laue <span style='position:
1298relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1299    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1300   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1301   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1302   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:e></m:bar></m:oMath><![endif]--><![if !msEquation]><span
1303style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1304"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1305top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1306EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1307 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1308 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1309  o:title="" chromakey="white"/>
1310</v:shape><![endif]--><![if !vml]><img width=9 height=21
1311src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;crystals
1312in P3<sub>2</sub>; the possible operator is shown in Table 1.3.4.1 (reproduced
1313above) as either a mirror or a 2-fold. The detailed symbolism in the table
1314(‘m.., ..2/.2.’) indicates (perhaps obscurely) the operator specifics. See P3m1
1315and P3<sub>2</sub>21 space groups in International Tables for Crystallography,
1316Vol A for the operations m as <span style='position:relative;top:3pt'><span
1317style='mso-no-proof:yes'>-y-xz</span>&nbsp;or 2 as <span style='position:relative;
1318top:3pt'><span style='mso-no-proof:yes'>yx-z</span>; we will use the 2-fold
1319since the m inverts the structure which we are not sensitive to in this
1320experiment.</p>
1321
1322<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Add
1323Twin Law</span></b>; the Data tab will be redrawn with the inversion for the
1324second law. Replace this with the 2-fold (<b><span style='font-family:"Calibri",sans-serif'>0
13251 0, 1 0 0, 0 0 -1</span></b>) and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1326box. It should look like.</p>
1327
1328<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1329 id="Picture_x0020_51" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt;
1330 height:352.5pt;visibility:visible;mso-wrap-style:square'>
1331 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image050.png"
1332  o:title=""/>
1333</v:shape><![endif]--><![if !vml]><img width=624 height=470
1334src="Merohedral%20twin%20refinement%20in%20GSAS_files/image071.gif" v:shapes="Picture_x0020_51"><![endif]></span></p>
1335
1336<p class=MsoNormal>Now do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>;
1337you’ll have to save the project. Pick a directory &amp; file name - I used <b
1338style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1339mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1340minor-latin'>2b</span></b>. <span class=GramE>there</span> will be an immediate
1341improvement in the fit to <span class=SpellE>Rw</span>=5.05% and the twin
1342fractions will be ~50/50. Clearly this crystal is Type 2 <span class=SpellE>merohedrally</span>
1343twinned; we cannot determine if there is any Type 1 twinning because we lack
1344sufficient resonant scattering to see it. This ends the second example; you can
1345save the project file.</p>
1346
1347<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 3. A Type 1
1348&amp; 2 <span class=SpellE>merohedral</span> twin – <span class=SpellE>Cp</span>*Cs(NC<sub>5</sub>H<sub>5</sub>)<o:p></o:p></span></h2>
1349
1350<p class=MsoNormal>This <span class=SpellE>ecample</span> is very similar to
1351the previous one except that the Cs atom has significant resonant scattering
1352for <span class=SpellE>MoKa</span> radiation allowing detection of Type 1 <span
1353class=SpellE>merohedry</span>. The data set has apparent 6/m Laue symmetry but
1354may be 6/mmm for the space groups P6<sub>1</sub>/P6<sub>5</sub> or P6<sub>1</sub>22/P6<sub>5</sub>22.
1355The combination of Type 1 and Type 2 twins requires 4 twin laws to be explored
1356for this <span class=SpellE>pentamethylcyclopentadienyl</span> Cs complex. As
1357this work was done with <span class=SpellE>Shelx</span> this result is in the
1358form of a <span class=SpellE>Shelx</span> input file (3a.ins – thanks to V.
1359Young for this example). If you have not done so already, start GSAS-II and
1360start with a fresh project.</p>
1361
1362<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1363refinement<o:p></o:p></span></h2>
1364
1365<p class=MsoNormal>To begin we need to import the phase information from the <span
1366class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1367style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1368ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1369and a res file is the output result after a <span class=SpellE>Shelx</span>
1370run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>3a.ins</span></b>
1371from the file selection window; a popup window will ask if this file is the one
1372you want.</p>
1373
1374<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1375 id="Picture_x0020_52" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:274.5pt;
1376 height:174.75pt;visibility:visible;mso-wrap-style:square'>
1377 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image072.png"
1378  o:title=""/>
1379</v:shape><![endif]--><![if !vml]><img width=366 height=233
1380src="Merohedral%20twin%20refinement%20in%20GSAS_files/image073.gif" v:shapes="Picture_x0020_52"><![endif]></span></p>
1381
1382<p class=MsoNormal>It is; press the <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1383button. You will then see the SHELX Read Warning; you will have to change the
1384space group to P6<sub>1</sub> in a bit. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1385and leave the name alone (press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1386again). Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
138761</span></b>; the General tab will be redrawn after showing you the operators.</p>
1388
1389<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1390 id="Picture_x0020_53" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:468pt;
1391 height:234.75pt;visibility:visible;mso-wrap-style:square'>
1392 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image074.png"
1393  o:title=""/>
1394</v:shape><![endif]--><![if !vml]><img width=624 height=313
1395src="Merohedral%20twin%20refinement%20in%20GSAS_files/image075.gif" v:shapes="Picture_x0020_53"><![endif]></span></p>
1396
1397<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1398Factor/from CIF file</span></b> and select <b><span style='font-family:"Calibri",sans-serif'>3a.fcf</span></b>
1399from the file dialog. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1400in the next popup and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1401on the name change popup. Select the file name in the Add to phases popup and
1402press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; the hk0
1403zone of the structure factors will be displayed. Note that this plot shows both
1404green (<span class=SpellE>Fo</span>) and blue (Fc) circles with a small solid
1405red or green circle in the centers. These are for the +/- <span
1406style='font-family:Symbol'>D</span>F values. Fc is here because this <span
1407class=SpellE>fcf</span> file was obtained after refinement via <span
1408class=SpellE>Shelx</span>.</p>
1409
1410<p class=MsoNormal>You now have loaded all that is needed for the third example.
1411The structure had previously been solved and refined with <span class=SpellE>Shelx</span>
1412so you need not trouble about those steps. You can try to solve the structure
1413in GSAS-II via charge flipping but this is not part of this exercise (it isn’t
1414easy because of the twinning; charge flipping will readily give the Cs position
1415&amp; most of the rest. It can be completed via difference Fourier techniques);
1416we will only explore the twin analysis features of GSAS-II.</p>
1417
1418<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1419of twinned structure<o:p></o:p></span></h2>
1420
1421<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1422eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1423&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1424style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1425GSAS-II data tree.</p>
1426
1427<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1428 id="Picture_x0020_54" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt;
1429 height:205.5pt;visibility:visible;mso-wrap-style:square'>
1430 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image076.png"
1431  o:title=""/>
1432</v:shape><![endif]--><![if !vml]><img width=624 height=274
1433src="Merohedral%20twin%20refinement%20in%20GSAS_files/image077.gif" v:shapes="Picture_x0020_54"><![endif]></span></p>
1434
1435<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1436<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1437"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1438style='font-family:"Calibri",sans-serif'>Phases/Cs…</span></b> entry in the
1439GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1440tab.</p>
1441
1442<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1443 id="Picture_x0020_55" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:468pt;
1444 height:303.75pt;visibility:visible;mso-wrap-style:square'>
1445 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image078.png"
1446  o:title=""/>
1447</v:shape><![endif]--><![if !vml]><img width=624 height=405
1448src="Merohedral%20twin%20refinement%20in%20GSAS_files/image079.gif" v:shapes="Picture_x0020_55"><![endif]></span></p>
1449
1450<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1451factor</span></b> is selected for refinement by default. If you refine it, you
1452will get an <span class=SpellE>R<sub>w</sub></span>~ 17% which is terrible. It
1453doesn’t change much if you add the Flack parameter (~0.36). If you try refining
1454atom positions &amp; thermal parameters you could possibly lower it but the
1455resulting structure would not be very satisfactory. However, we have suspected
1456from the equivalence of 6/m and 6/mmm Laue data symmetries that there is
1457twinning so don’t bother trying to make it better by refining the structure. To
1458determine the possible twin laws we again refer to Table 1.3.4.2 of the
1459International Tables for Crystallography Vol C. and see that indeed Laue 6/mmm
1460as P6<sub>1</sub>22 can be simulated by twinned Laue 6/m crystals in P6<sub>1</sub>;
1461the possible operator is shown in Table 1.3.4.1 (reproduced above) as either a
1462mirror or a 2-fold. The detailed symbolism in the table (‘m.., ..2/.2.’)
1463indicates (perhaps obscurely) the operator specifics; they are m as <span
1464style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:acc><m:accPr><m:chr
1465    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1466   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1467   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1468   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
1469    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1470   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1471   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1472   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
1473 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
1474style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1475"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1476top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1477EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1478 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1479 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image052.png"
1480  o:title="" chromakey="white"/>
1481</v:shape><![endif]--><![if !vml]><img width=26 height=19
1482src="Merohedral%20twin%20refinement%20in%20GSAS_files/image080.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;or
14832 as <!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span
1484 style='font-family:"Cambria Math",serif'><span style='position:relative;
1485 top:3pt'><m:r>y</m:r><m:r>x</span></m:r></span></i><m:acc><m:accPr><m:chr
1486    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1487   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1488   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1489   style='mso-bidi-font-style: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
1490style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1491"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1492top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1493EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1494 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1495 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image054.png"
1496  o:title="" chromakey="white"/>
1497</v:shape><![endif]--><![if !vml]><img width=26 height=19
1498src="Merohedral%20twin%20refinement%20in%20GSAS_files/image081.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1499style='font-family:"Cambria Math",serif'>; we will use the 2-fold, m and
1500inversion operators to fully test for presence of the 4 possible twin laws.
1501Press the </span><b><span style='font-family:"Calibri",sans-serif'>Add Twin Law</span></b><span
1502style='font-family:"Cambria Math",serif'> button </span><b><span
1503style='font-family:"Calibri",sans-serif'>3 times</span></b><span
1504style='font-family:"Cambria Math",serif'>; each time the window will be
1505redrawn. When done you should see.<o:p></o:p></span></p>
1506
1507<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1508 id="Picture_x0020_56" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
1509 height:405.75pt;visibility:visible;mso-wrap-style:square'>
1510 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image082.png"
1511  o:title=""/>
1512</v:shape><![endif]--><![if !vml]><img width=624 height=541
1513src="Merohedral%20twin%20refinement%20in%20GSAS_files/image083.gif" v:shapes="Picture_x0020_56"><![endif]></span>&nbsp;</p>
1514
1515<p class=MsoNormal>For the third and fourth matrix enter <b><span
1516style='font-family:"Calibri",sans-serif'>0 1 0 1 0 0 0 0 -1</span></b> and <b><span
1517style='font-family:"Calibri",sans-serif'>0 -1 0 -1 0 0 0 0</span></b> <b><span
1518style='font-family:"Calibri",sans-serif'>1</span></b> as the 2-fold and mirror
1519operators (the 2<sup>nd</sup> matrix is the inversion by default). Select the <b><span
1520style='font-family:"Calibri",sans-serif'>Refine</span></b> button and do <b><span
1521style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
1522main menu; again you’ll have to save the project file – I called it 3a. The <span
1523class=SpellE>Rw</span> will immediately drop to ~2.26% (RF~2.05%). The four
1524twin element fractions will show various values</p>
1525
1526<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1527 id="Picture_x0020_57" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;
1528 height:405.75pt;visibility:visible;mso-wrap-style:square'>
1529 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image084.png"
1530  o:title=""/>
1531</v:shape><![endif]--><![if !vml]><img width=624 height=541
1532src="Merohedral%20twin%20refinement%20in%20GSAS_files/image085.gif" v:shapes="Picture_x0020_57"><![endif]></span></p>
1533
1534<p class=MsoNormal>The negative one for the 3<sup>rd</sup> twin fraction is nonphysical
1535and the 1<sup>st</sup> twin fraction is small. It is likely that the true space
1536group is P6<sub>5</sub> and Type 2 <span class=SpellE>merohedrally</span>
1537twinned (twin fractions 2 &amp; 4). We can improve it by refining the atom
1538positions and thermal parameters, but first we need to replace the hydrogen
1539atoms as suggested by the <span class=SpellE>Shelx</span> warning. Select the <b
1540style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1541mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms </span></b>tab
1542for the phase.</p>
1543
1544<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1545 id="Picture_x0020_41" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:525pt;
1546 height:225pt;visibility:visible;mso-wrap-style:square'>
1547 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"
1548  o:title=""/>
1549</v:shape><![endif]--><![if !vml]><img width=700 height=300
1550src="Merohedral%20twin%20refinement%20in%20GSAS_files/image086.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
1551
1552<p class=MsoNormal>If you scroll down the page, you’ll see H-atoms with default
1553<span class=SpellE>Uiso</span> (=0.025) values. To replace them, the old ones
1554need to be deleted; double click the <b style='mso-bidi-font-weight:normal'><span
1555style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1556mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1557style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1558mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>H</span></b>
1559and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1560mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
1561The H-atoms will be highlighted (and plotted in green). Do <b style='mso-bidi-font-weight:
1562normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1563minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/On selected atoms…/Delete
1564atom</span></b> from the menu; the H-atoms will be deleted and the structure
1565will be redrawn. Next double click the <b style='mso-bidi-font-weight:normal'><span
1566style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1567mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1568style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1569mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>C</span></b>;
1570all the C-atoms will be selected (and shown in green on the plot). Do <b
1571style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1572mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/On
1573selected atoms…/<span class=SpellE>Calc</span> H atoms</span></b>; a Distance
1574Angle Controls will appear. Occasionally these values may need to be changed
1575but not this time; press <b style='mso-bidi-font-weight:normal'><span
1576style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1577mso-hansi-theme-font:minor-latin'>Ok</span></b>. The next popup is for the H
1578atoms add controls.</p>
1579
1580<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1581 id="Picture_x0020_58" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:300pt;
1582 height:187.5pt;visibility:visible;mso-wrap-style:square'>
1583 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image087.png"
1584  o:title=""/>
1585</v:shape><![endif]--><![if !vml]><img width=400 height=250
1586src="Merohedral%20twin%20refinement%20in%20GSAS_files/image088.gif" v:shapes="Picture_x0020_58"><![endif]></span></p>
1587
1588<p class=MsoNormal>It specifies the expected geometry around each C-atom for
1589H-atom placement. As expected we want 3 H-atoms on the terminal CH<sub>3</sub>
1590groups on the <span class=SpellE>Cp</span>* ring and one for each C-atom for
1591the NC<sub>5</sub>H<sub>5</sub> molecule. Press <b style='mso-bidi-font-weight:
1592normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1593minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; you will see the
1594H-atoms added in turn to the structure and they will be inserted immediately
1595after their respective C-atom. Their positions and thermal parameters are tied
1596to the C-atoms so that after refinement of the structure they can be shifted to
1597the <span class=SpellE>stereochemically</span> best positions. For the
1598refinement, double click the <b style='mso-bidi-font-weight:normal'><span
1599style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1600mso-hansi-theme-font:minor-latin'>Refine</span></b> column heading and select <b
1601style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1602mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>X</span></b>
1603and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1604mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>U</span></b>
1605from the popup; press <b style='mso-bidi-font-weight:normal'><span
1606style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1607mso-hansi-theme-font:minor-latin'>OK</span></b>. The Atom table will be redrawn
1608with XU in every entry under Refine. Now do <b style='mso-bidi-font-weight:
1609normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1610minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> (2-3
1611times until convergence<span class=GramE>)from</span> the main GSASII data tree
1612window; the <span class=SpellE>Rw</span> will drop to ~1.80%. If you look at
1613the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1614mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
1615tab the Twin element fractions are much clearer.</p>
1616
1617<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1618 id="Picture_x0020_59" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;
1619 height:342.75pt;visibility:visible;mso-wrap-style:square'>
1620 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image089.png"
1621  o:title=""/>
1622</v:shape><![endif]--><![if !vml]><img width=624 height=457
1623src="Merohedral%20twin%20refinement%20in%20GSAS_files/image090.gif" v:shapes="Picture_x0020_59"><![endif]></span><span
1624style='mso-spacerun:yes'> </span></p>
1625
1626<p class=MsoNormal>The identity Twin Law has virtually vanished along with the
16272-fold one leaving just the inverse and mirror Twin Laws.</p>
1628
1629<p class=MsoNormal>This means the structure is the inverse in space group P6<sub>5</sub>
1630but still Type 2 <span class=SpellE>merohedrally</span> twinned. </p>
1631
1632<p class=MsoNormal>To test this, we need to both change the space group and
1633invert the structure. First select the <b style='mso-bidi-font-weight:normal'><span
1634style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1635mso-hansi-theme-font:minor-latin'>General</span></b> tab and change the space
1636group to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1637mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P 65</span></b>;
1638you’ll see the Operators popup (press <b style='mso-bidi-font-weight:normal'><span
1639style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1640mso-hansi-theme-font:minor-latin'>Ok</span></b>) and the General tab will be
1641redrawn. Next select the <b style='mso-bidi-font-weight:normal'><span
1642style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1643mso-hansi-theme-font:minor-latin'>Atoms</span></b> tab; do <b style='mso-bidi-font-weight:
1644normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1645minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/Update H atoms</span></b>
1646to put them in their best positions.<span style='mso-spacerun:yes'> 
1647</span>Next select all the atoms by double clicking the empty box in upper left
1648corner of the table; all atoms will be highlighted &amp; plotted green. Do <b
1649style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1650mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
1651Atoms/On selected atoms…/Transform atoms</span></b>; a popup will appear.</p>
1652
1653<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1654 id="Picture_x0020_60" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:270pt;
1655 height:264pt;visibility:visible;mso-wrap-style:square'>
1656 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image091.png"
1657  o:title=""/>
1658</v:shape><![endif]--><![if !vml]><img width=360 height=352
1659src="Merohedral%20twin%20refinement%20in%20GSAS_files/image092.gif" v:shapes="Picture_x0020_60"><![endif]></span></p>
1660
1661<p class=MsoNormal>Check the <b style='mso-bidi-font-weight:normal'><span
1662style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1663mso-hansi-theme-font:minor-latin'>Choose inversion</span></b> box and
1664(important) set <b style='mso-bidi-font-weight:normal'><span style='font-family:
1665"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1666minor-latin'>Choose unit cell</span></b> to <b style='mso-bidi-font-weight:
1667normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1668minor-latin;mso-hansi-theme-font:minor-latin'>1 1 1</span></b>; this will put
1669the inverted structure back inside the unit cell. Press <b style='mso-bidi-font-weight:
1670normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1671minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; the table and plot
1672will both be redrawn. Now do <b style='mso-bidi-font-weight:normal'><span
1673style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1674mso-hansi-theme-font:minor-latin'>Calculate/Refine </span></b>2-3 times; the <span
1675class=SpellE>Rw</span> will drop back to where it was before and the <b
1676style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1677mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
1678tab will show new Twin fractions.</p>
1679
1680<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1681 id="Picture_x0020_61" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt;
1682 height:400.5pt;visibility:visible;mso-wrap-style:square'>
1683 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image093.png"
1684  o:title=""/>
1685</v:shape><![endif]--><![if !vml]><img width=624 height=534
1686src="Merohedral%20twin%20refinement%20in%20GSAS_files/image094.gif" v:shapes="Picture_x0020_61"><![endif]></span></p>
1687
1688<p class=MsoNormal>Now the identity Twin Law is ~2/3 and the 2-fold Twin Law is
1689the other ~1/3 while the other two are ~zero. You can delete them and repeat
1690the refinement; <span class=SpellE>Rw</span> ~1.7%. This completed the
1691merohedral twin exercises. You can save this project if desired.</p>
1692
1693<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1694
1695</span></div>
1696
1697</span></span></span></span></span></span></span></span></span></span>
1698</body>
1699
1700</html>
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