source: Tutorials/MerohedralTwins/Merohedral twin refinement in GSAS.htm @ 2390

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414  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
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416  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
417  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
418  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
419  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
420  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
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424  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
425  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
426  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
427  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
428  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
429  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
430  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
431  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
432  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
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438  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
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440  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
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442  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
443  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
444  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
445  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
446  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
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452  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
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454  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
455  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
456  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
457  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
458  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
459  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
460  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
461  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
462  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
463  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
464  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
465  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
466  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
467  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
468  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
469  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
470  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
471  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
472  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
473  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
474  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
475  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
476  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
477  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
478  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
479  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
480  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
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485  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
486  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
487  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
488  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
489  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
490  <w:LsdException Locked="false" Priority="19" QFormat="true"
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492  <w:LsdException Locked="false" Priority="21" QFormat="true"
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494  <w:LsdException Locked="false" Priority="31" QFormat="true"
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498  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
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504  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
505  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
506  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
507  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
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510  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
511  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
512  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
513  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
514  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
515  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
516  <w:LsdException Locked="false" Priority="46"
517   Name="Grid Table 1 Light Accent 1"/>
518  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
519  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
520  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
521  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
522  <w:LsdException Locked="false" Priority="51"
523   Name="Grid Table 6 Colorful Accent 1"/>
524  <w:LsdException Locked="false" Priority="52"
525   Name="Grid Table 7 Colorful Accent 1"/>
526  <w:LsdException Locked="false" Priority="46"
527   Name="Grid Table 1 Light Accent 2"/>
528  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
529  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
530  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
531  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
532  <w:LsdException Locked="false" Priority="51"
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534  <w:LsdException Locked="false" Priority="52"
535   Name="Grid Table 7 Colorful Accent 2"/>
536  <w:LsdException Locked="false" Priority="46"
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538  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
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540  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
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558  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
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562  <w:LsdException Locked="false" Priority="51"
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564  <w:LsdException Locked="false" Priority="52"
565   Name="Grid Table 7 Colorful Accent 5"/>
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567   Name="Grid Table 1 Light Accent 6"/>
568  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
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570  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
571  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
572  <w:LsdException Locked="false" Priority="51"
573   Name="Grid Table 6 Colorful Accent 6"/>
574  <w:LsdException Locked="false" Priority="52"
575   Name="Grid Table 7 Colorful Accent 6"/>
576  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
577  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
578  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
579  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
580  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
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583  <w:LsdException Locked="false" Priority="46"
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585  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
586  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
587  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
588  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
589  <w:LsdException Locked="false" Priority="51"
590   Name="List Table 6 Colorful Accent 1"/>
591  <w:LsdException Locked="false" Priority="52"
592   Name="List Table 7 Colorful Accent 1"/>
593  <w:LsdException Locked="false" Priority="46"
594   Name="List Table 1 Light Accent 2"/>
595  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
596  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
597  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
598  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
599  <w:LsdException Locked="false" Priority="51"
600   Name="List Table 6 Colorful Accent 2"/>
601  <w:LsdException Locked="false" Priority="52"
602   Name="List Table 7 Colorful Accent 2"/>
603  <w:LsdException Locked="false" Priority="46"
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605  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
606  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
607  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
608  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
609  <w:LsdException Locked="false" Priority="51"
610   Name="List Table 6 Colorful Accent 3"/>
611  <w:LsdException Locked="false" Priority="52"
612   Name="List Table 7 Colorful Accent 3"/>
613  <w:LsdException Locked="false" Priority="46"
614   Name="List Table 1 Light Accent 4"/>
615  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
616  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
617  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
618  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
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620   Name="List Table 6 Colorful Accent 4"/>
621  <w:LsdException Locked="false" Priority="52"
622   Name="List Table 7 Colorful Accent 4"/>
623  <w:LsdException Locked="false" Priority="46"
624   Name="List Table 1 Light Accent 5"/>
625  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
626  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
627  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
628  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
629  <w:LsdException Locked="false" Priority="51"
630   Name="List Table 6 Colorful Accent 5"/>
631  <w:LsdException Locked="false" Priority="52"
632   Name="List Table 7 Colorful Accent 5"/>
633  <w:LsdException Locked="false" Priority="46"
634   Name="List Table 1 Light Accent 6"/>
635  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
636  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
637  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
638  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
639  <w:LsdException Locked="false" Priority="51"
640   Name="List Table 6 Colorful Accent 6"/>
641  <w:LsdException Locked="false" Priority="52"
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802
803<body lang=EN-US style='tab-interval:.5in'>
804
805<div class=WordSection1>
806
807<h1><span style='mso-fareast-font-family:"Times New Roman"'>Merohedral twin
808refinement in GSAS-II<o:p></o:p></span></h1>
809
810<h2><span style='mso-fareast-font-family:"Times New Roman"'>Introduction: <o:p></o:p></span></h2>
811
812<p class=MsoNormal>In these exercises you will use GSAS-II to refine the
813structure of a few single crystal structures where there is merohedral
814twinning. There is a general discussion of twinning in International Tables for
815Crystallography (2006), Vol. C, Chapter 1.3, pp 10-14. Merohedral twinning
816occurs when the twin operation (2, m or <span style='position:relative;
817top:3pt'><span style='mso-no-proof:yes'><img width=9 height=19 id="_x0000_i1058"
818src="Merohedral%20twin%20refinement%20in%20GSAS_files/image015.png"></span>)
819belongs to the point group of the vector lattice but not of the crystal
820structure. Of the 230 space groups only 159 of them may have merohedral
821twining. </p>
822
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855src="Merohedral%20twin%20refinement%20in%20GSAS_files/image025.png" align=left
856hspace=12 v:shapes="Picture_x0020_2"><![endif]>&nbsp;</p>
857
858<p class=MsoNormal>&nbsp;</p>
859
860<p class=MsoNormal>The possible merohedral twin operators are shown in the
861above table (extracted from p 13 of Intl. Tables for <span class=SpellE>Cryst</span>.,
862Vol. C). Merohedral twins are of two types: Type 1 are inversion twins and have
863only 2 components and Type 2 are where the twin operation does not belong to
864the Laue class of the crystal (only for space groups marked with * in above
865table) and multiple twin components may be found. For Type 1 the twin lattice
866exactly <span class=GramE>superimpose</span> so that if Friedel’s law is obeyed
867the twin components have the same value of |F|<sup>2</sup> (the twinning is
868undetectable!). However, in the presence of resonant scattering the |F|<sup>2</sup>
869components differ and if the twin components have unequal volumes then the
870Bragg intensities will differ from that obtained from the <span class=SpellE>untwinned</span>
871structure and then the twinning effects must be considered for
872refinement.&nbsp; Obviously all Type 1 crystals are <span class=SpellE>noncentrosymmetric</span>.
873For Type 2 the space group may be centrosymmetric from within a choice of just
87455 possible space groups. However, the diffraction pattern may display apparent
875higher symmetry especially if the twin components are all equally present in
876the crystal.&nbsp; Note that menu entries and user input are shown in bold face
877below as <b><span style='font-family:"Calibri",sans-serif'>Help/About GSAS-II</span></b>,
878which lists first the name of the menu (here <b><span style='font-family:"Calibri",sans-serif'>Help</span></b>)
879and second the name of the entry in the menu (here <b><span style='font-family:
880"Calibri",sans-serif'>About GSAS-II</span></b>). If you have not done so
881already, start GSAS-II.</p>
882
883<h2 style='margin-bottom:.25in'><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></h2>
884
885<p class=MsoNormal style='margin-bottom:8.0pt;line-height:105%'>.<br clear=all
886style='mso-special-character:line-break;page-break-before:always'>
887</p>
888
889<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 1. A Type 1
890inversion twin – C<sub>8</sub>H<sub>25</sub>Al<sub>0.84</sub>Ga<sub>1.16</sub>N<sub>3</sub>
891<o:p></o:p></span></h2>
892
893<p class=MsoNormal>This example was taken from Luo, et al., Dalton Trans.
8944491(2006). The structure is given in the file <span class=SpellE><b><span
895style='font-family:"Calibri",sans-serif'>MerohedralTwins</span></b></span><b><span
896style='font-family:"Calibri",sans-serif'>/data/1b.cif</span></b> and the data
897are in <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>MerohedralTwins</span></b></span><b><span
898style='font-family:"Calibri",sans-serif'>/data/1b.fcf</span></b>. This example
899is <span class=SpellE>noncentrosymmetric</span> and the data was collected with
900radiation (<span class=SpellE>MoK</span>&#945;) that gives significant resonant
901scattering from the Ga atoms. </p>
902
903<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
904refinement<o:p></o:p></span></h2>
905
906<p class=MsoNormal>To begin do <b><span style='font-family:"Calibri",sans-serif'>Import/Phase/from
907CIF file</span></b> from the main GSAS-II data tree menu. A file selection
908window will appear; find the above <span class=SpellE>cif</span> file (…<b><span
909style='font-family:"Calibri",sans-serif'>1b.cif</span></b>) and select it. A
910popup window will appear. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
911a new popup will appear</p>
912
913<p class=MsoNormal><span style='mso-no-proof:yes'><img width=336 height=137
914id="_x0000_i1057"
915src="Merohedral%20twin%20refinement%20in%20GSAS_files/image006.png"></span></p>
916
917<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>,
918and you will see the General page for this phase</p>
919
920<p class=MsoNormal><span style='mso-no-proof:yes'><img width=403 height=310
921id="_x0000_i1056"
922src="Merohedral%20twin%20refinement%20in%20GSAS_files/image007.png"></span></p>
923
924<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
925Factor/from CIF file</span></b> (that is the format of a “<span class=SpellE>fcf</span>”
926file); a file selection dialog box will appear with the previously selected
927directory chosen. Select <b><span style='font-family:"Calibri",sans-serif'>1b.fcf</span></b>;
928a popup window will appear</p>
929
930<p class=MsoNormal><span style='mso-no-proof:yes'><img width=447 height=249
931id="_x0000_i1055"
932src="Merohedral%20twin%20refinement%20in%20GSAS_files/image008.png"></span></p>
933
934<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
935a new popup window allowing you to change the name</p>
936
937<p class=MsoNormal><span style='mso-no-proof:yes'><img width=336 height=137
938id="_x0000_i1054"
939src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"></span></p>
940
941<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
942after a pause and some activity a popup window will appear</p>
943
944<p class=MsoNormal><span style='mso-no-proof:yes'><img width=320 height=310
945id="_x0000_i1053"
946src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.png"></span></p>
947
948<p class=MsoNormal>This makes the connection between the data set and the
949previously imported phase. Select the entry and press <b><span
950style='font-family:"Calibri",sans-serif'>OK</span></b>. You now have loaded all
951that is needed for the first example. The structure had previously been solved
952and refined with <span class=SpellE>Shelx</span> so you need not trouble about
953those steps. You can try to solve the structure in GSAS-II via charge flipping
954but this is not part of this exercise; we will only explore the twin analysis
955features of GSAS-II.</p>
956
957<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
958of twinned structure<o:p></o:p></span></h2>
959
960<p class=MsoNormal>Before beginning the refinement, it usually the practice to
961eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
962&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
963style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
964GSAS-II data tree.</p>
965
966<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
967id="_x0000_i1052"
968src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
969
970<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
971<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
972"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
973style='font-family:"Calibri",sans-serif'>Phases/C8 H25 Al0.84 Ga1.16</span></b>
974<span class=GramE>entry</span> in the GSAS-II data tree and choose the <b><span
975style='font-family:"Calibri",sans-serif'>Data</span></b> tab</p>
976
977<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
978id="_x0000_i1051"
979src="Merohedral%20twin%20refinement%20in%20GSAS_files/image011.png"></span></p>
980
981<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
982factor</span></b> is selected for refinement by default. If you refine it, you
983will get an <span class=SpellE>R<sub>w</sub></span>= 2.85% which isn’t too bad.
984However, you are unsure what the hand of the molecule is in this structure and
985the experiment with <span class=SpellE>MoKa</span> radiation should give
986sufficient resonant scattering to determine this. The <b><span
987style='font-family:"Calibri",sans-serif'>Flack parameter</span></b> gives you a
988way to evaluate which hand the molecule is. If upon refinement the value is ~0
989then you have correctly described the hand. Otherwise if the value is ~1 then
990the opposite hand is the correct and the structure needs to be inverted. So
991let’s test this; select the <b><span style='font-family:"Calibri",sans-serif'>Flack
992parameter</span></b> for refinement and do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>
993from the main GSAS-II data tree menu. The structure will quickly refine to give
994<span class=SpellE>R<sub>w</sub></span>=2.087% which is a considerable improvement
995on Scale factor alone. The Flack parameter is now 0.452, meaning that both
996hands somehow exist in the structure. This can happen if the crystal is <span
997class=SpellE>merohedrally</span> inversion twinned.</p>
998
999<p class=MsoNormal>To introduce this twin, press the <b><span style='font-family:
1000"Calibri",sans-serif'>Add Twin Law</span></b> box; the window will be redrawn.</p>
1001
1002<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
1003id="_x0000_i1050"
1004src="Merohedral%20twin%20refinement%20in%20GSAS_files/image013.png"></span></p>
1005
1006<p class=MsoNormal>Notice that two Twin Law matrices have been generated; one
1007is the identity for the reference structure and the other by default is the
1008merohedral inverse. If some other twin law is desired, then the matrix elements
1009need to be changed. Moreover, the Flack parameter has vanished as it is no
1010longer needed. Press the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1011button for the <b><span style='font-family:"Calibri",sans-serif'>Twin Law
1012fraction</span></b> and rerun the refinement. The Data window now has.</p>
1013
1014<p class=MsoNormal><span style='mso-no-proof:yes'><img width=449 height=500
1015id="_x0000_i1049"
1016src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.png"></span></p>
1017
1018<p class=MsoNormal>The refinement quickly converged to where it was before but
1019the twin fractions are now ~56/44 consistent with the ~45% Flack parameter
1020obtained earlier. It is likely that the crystal is macroscopically twinned thus
1021the twin fractions are not exactly 50/50. This completes this example; you can
1022save your project if you want to explore other features of GSAS-II with it.</p>
1023
1024<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 2. A Type 2
1025only merohedral twin – <br>
1026[Al(OC<sub>6</sub>H<sub>4</sub>(C<sub>3</sub>H<sub>7</sub>)<sub>2</sub>)]<sup>-</sup>
1027[NC<sub>7</sub>H<sub>8</sub>]<sup>+</sup><o:p></o:p></span></h2>
1028
1029<p class=MsoNormal>In this case the data collection Laue statistics (very nearly
1030<span style='position:relative;top:3pt'><span style='mso-no-proof:yes'>-3</span>m)
1031and systematic extinctions indicated that the space group was either one of the
1032<span class=SpellE>enantiomorphic</span> pair P3<sub>1</sub>21 or P3<sub>2</sub>21
1033or possibly one of the pair P3<sub>1</sub> or P3<sub>2</sub>. If the true
1034structure was of the lower symmetry P3<sub>1</sub> or P3<sub>2</sub> then there
1035must be Type 2 merohedral twinning to make the diffraction pattern appear to
1036have higher symmetry (<span style='position:relative;top:3pt'><span
1037style='mso-no-proof:yes'>-3</span>m instead of <span style='position:relative;
1038top:3pt'><span style='mso-no-proof:yes'>-3</span>); this exercise will explore
1039this possibility. The data were collected with <span class=SpellE>MoK</span><span
1040style='font-family:Symbol'>a</span> radiation so there is little resonant
1041scattering and thus the choice of hand is indeterminate.&nbsp; Solving the
1042structure in P3<sub>2</sub>21 yielded a poorly fitting structure with disorder
1043particularly in the cation. Resolving the structure in P3<sub>2</sub> gave a
1044structure with no disorder and a better fit to the data (but still not great).
1045As this work was done with <span class=SpellE>Shelx</span> this result is in
1046the form of a <span class=SpellE>Shelx</span> input file (2b.ins – thanks to V.
1047Young for this example). If you have not done so already, start GSAS-II and
1048start with a fresh project.</p>
1049
1050<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1051refinement<o:p></o:p></span></h2>
1052
1053<p class=MsoNormal>To begin we need to import the phase information from the <span
1054class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1055style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1056ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1057and a res file is the output result after a <span class=SpellE>Shelx</span>
1058run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>2b.ins</span></b>
1059from the file selection window; a popup window will ask if this file is the one
1060you want.</p>
1061
1062<p class=MsoNormal><span style='mso-no-proof:yes'><img width=410 height=262
1063id="_x0000_i1048"
1064src="Merohedral%20twin%20refinement%20in%20GSAS_files/image012.png"></span></p>
1065
1066<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
1067a Read Warning will appear.</p>
1068
1069<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1070 id="Picture_x0020_39" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:371.25pt;
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1072 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image001.png"
1073  o:title=""/>
1074</v:shape><![endif]--><![if !vml]><img width=495 height=235
1075src="Merohedral%20twin%20refinement%20in%20GSAS_files/image003.gif" v:shapes="Picture_x0020_39"><![endif]></span></p>
1076
1077<p class=MsoNormal>There are two significant warnings concerning <span
1078class=SpellE>Shelx</span> files. One is that the file never contains the space
1079group symbol (<span class=SpellE>Shelx</span> requires just the operators), so
1080GSAS-II sets the space group to P 1 by default and you will need to change it
1081to P3<sub>2</sub> immediately (next window). The other warning is that hydrogen
1082atoms were found; these usually cannot be refined unconstrained with x-ray
1083data. The warning recommends replacing them with <span class=SpellE>stereochemically</span>
1084determined ones (this is illustrated in the 3<sup>rd</sup> Exercise of this
1085tutorial) and the last line of the Warning tells you what to do if they are to
1086be refined. Here we will only refine twin laws &amp; scale factors so this is
1087unnecessary. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1088you get the opportunity to change the Phase name (I know it is very long but
1089that doesn’t matter here). Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1090the General tab for this phase is shown. </p>
1091
1092<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=336
1093id="_x0000_i1046"
1094src="Merohedral%20twin%20refinement%20in%20GSAS_files/image027.png"></span></p>
1095
1096<p class=MsoNormal>Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
109732</span></b>; the window will be redrawn after a popup showing the operations.
1098You can see the structure by selecting <b><span style='font-family:"Calibri",sans-serif'>Draw
1099Atoms</span></b>.</p>
1100
1101<p class=MsoNormal><span style='mso-no-proof:yes'><img width=478 height=358
1102id="_x0000_i1045"
1103src="Merohedral%20twin%20refinement%20in%20GSAS_files/image028.jpg"></span></p>
1104
1105<p class=MsoNormal>&nbsp;</p>
1106
1107<p class=MsoNormal>The large anion containing the Al atom is to the left and
1108the smaller cation to the right.</p>
1109
1110<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1111Factor/from <span class=SpellE>Shelx</span> HKLF 4 F<sup>2</sup> file</span></b>
1112and select <b><span style='font-family:"Calibri",sans-serif'>2b.hkl</span></b>
1113from the file dialog box; a popup will appear showing a few lines.</p>
1114
1115<p class=MsoNormal><span style='mso-no-proof:yes'><img width=366 height=262
1116id="_x0000_i1044"
1117src="Merohedral%20twin%20refinement%20in%20GSAS_files/image022.png"></span></p>
1118
1119<p class=MsoNormal>This is the right file; a <span class=SpellE>Shelx</span>
1120HKLF 4 file consists of records with just <span class=SpellE><span class=GramE>h,k</span>,l</span>,
1121F<sup>2</sup> and <span style='font-family:Symbol'>s</span>(F<sup>2</sup>).
1122Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b> and <b><span
1123style='font-family:"Calibri",sans-serif'>OK</span></b> on the next one (we’ll
1124keep the name as it is). Choose the phase with the long name on the next popup
1125and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; a 2D
1126display of the hk0 zone is plotted.</p>
1127
1128<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=535
1129id="_x0000_i1043"
1130src="Merohedral%20twin%20refinement%20in%20GSAS_files/image029.png"></span></p>
1131
1132<p class=MsoNormal>The size of the green circles <span class=GramE>are</span>
1133proportional to <span class=SpellE>Fo</span> (after a structure factor
1134calculation blue rings will appear for Fc).</p>
1135
1136<p class=MsoNormal>You now have loaded all that is needed for the second
1137example. The structure had previously been solved and refined with <span
1138class=SpellE>Shelx</span> so you need not trouble about those steps. You can
1139try to solve the structure in GSAS-II via charge flipping but this is not part
1140of this exercise (it isn’t easy because of the twinning); we will only explore
1141the twin analysis features of GSAS-II.</p>
1142
1143<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1144of twinned structure<o:p></o:p></span></h2>
1145
1146<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1147eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1148&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1149style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1150GSAS-II data tree.</p>
1151
1152<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
1153id="_x0000_i1042"
1154src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
1155
1156<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1157<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1158"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1159style='font-family:"Calibri",sans-serif'>Phases/MEROHEDRAL…</span></b> entry in
1160the GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1161tab.</p>
1162
1163<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=444
1164id="_x0000_i1041"
1165src="Merohedral%20twin%20refinement%20in%20GSAS_files/image030.png"></span></p>
1166
1167<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1168factor</span></b> is selected for refinement by default. If you refine it, you
1169will get an <span class=SpellE>R<sub>w</sub></span>~ 25% which is terrible. If
1170you try refining atom positions &amp; thermal parameters you could possibly <span
1171class=GramE>lower</span> it to ~15% (still terrible) and the resulting
1172structure would not be very satisfactory. However, we have suspected from the
1173equivalence of <span style='position:relative;top:3pt'><span style='mso-no-proof:
1174yes'><img width=9 height=19 id="_x0000_i1040"
1175src="Merohedral%20twin%20refinement%20in%20GSAS_files/image031.png"></span>&nbsp;and
1176<span style='position:relative;top:3pt'><span style='mso-no-proof:yes'><img
1177width=9 height=19 id="_x0000_i1039"
1178src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m1
1179Laue data symmetries that there is twinning so don’t bother trying to make it
1180better by refining the structure. To determine the possible twin law we refer
1181to Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
1182that indeed Laue <span style='position:relative;top:3pt'><span
1183style='mso-no-proof:yes'><img width=9 height=19 id="_x0000_i1038"
1184src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m1
1185as P3<sub>2</sub>21 can be simulated by twinned Laue <span style='position:
1186relative;top:3pt'><span style='mso-no-proof:yes'><img width=9 height=19
1187id="_x0000_i1037"
1188src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>&nbsp;crystals
1189in P3<sub>2</sub>; the possible operator is shown in Table 1.3.4.1 (reproduced
1190above) as either a mirror or a 2-fold. The detailed symbolism in the table (‘m.<span
1191class=GramE>., ..</span>2/.2.’) indicates (perhaps obscurely) the operator
1192specifics. See P3m1 and P3<sub>2</sub>21 space groups in International Tables
1193for Crystallography, Vol A for the operations m as <span style='position:relative;
1194top:3pt'><span style='mso-no-proof:yes'>-y-xz</span>&nbsp;or 2 as <span
1195style='position:relative;top:3pt'><span style='mso-no-proof:yes'>yx-z</span>;
1196we will use the 2-fold since the m inverts the structure which we are not
1197sensitive to in this experiment.</p>
1198
1199<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Add
1200Twin Law</span></b>; the Data tab will be redrawn with the inversion for the
1201second law. Replace this with the 2-fold (<b><span style='font-family:"Calibri",sans-serif'>0
12021 0, 1 0 0, 0 0 -1</span></b>) and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1203box. It should look like.</p>
1204
1205<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=500
1206id="_x0000_i1036"
1207src="Merohedral%20twin%20refinement%20in%20GSAS_files/image034.png"></span></p>
1208
1209<p class=MsoNormal>Now do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>;
1210there will be an immediate improvement in the fit to <span class=SpellE>Rw</span>=5.05%
1211and the twin fractions will be ~50/50. Clearly this crystal is Type 2 <span
1212class=SpellE>merohedrally</span> twinned; we cannot determine if there is any
1213Type 1 twinning because we lack sufficient resonant scattering to see it. This
1214ends the second example; you can save the project file.</p>
1215
1216<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 3. A Type 1
1217&amp; 2 merohedral twin – <span class=SpellE>Cp</span>*Cs(NC<sub>5</sub>H<sub>5</sub>)<o:p></o:p></span></h2>
1218
1219<p class=MsoNormal>This <span class=SpellE>ecample</span> is very similar to
1220the previous one except that the Cs atom has significant resonant scattering
1221for <span class=SpellE>MoKa</span> radiation allowing detection of Type 1 <span
1222class=SpellE>merohedry</span>. The data set has apparent 6/m Laue symmetry but
1223may 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.
1224The combination of Type 1 and Type 2 twins requires 4 twin laws to be explored
1225for this <span class=SpellE>pentamethylcyclopentadienyl</span> Cs complex. As
1226this work was done with <span class=SpellE>Shelx</span> this result is in the
1227form of a <span class=SpellE>Shelx</span> input file (3a.ins – thanks to V.
1228Young for this example). If you have not done so already, start GSAS-II and
1229start with a fresh project.</p>
1230
1231<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1232refinement<o:p></o:p></span></h2>
1233
1234<p class=MsoNormal>To begin we need to import the phase information from the <span
1235class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1236style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1237ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1238and a res file is the output result after a <span class=SpellE>Shelx</span>
1239run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>3a.ins</span></b>
1240from the file selection window; a popup window will ask if this file is the one
1241you want.</p>
1242
1243<p class=MsoNormal><span style='mso-no-proof:yes'><img width=366 height=262
1244id="_x0000_i1035"
1245src="Merohedral%20twin%20refinement%20in%20GSAS_files/image035.png"></span></p>
1246
1247<p class=MsoNormal>It is; press the <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1248button. You will then see the SHELX Read Warning; you will have to change the
1249space group to P6<sub>1</sub> in a bit. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1250and leave the name alone (press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1251again). Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
125261</span></b>; the General tab will be redrawn after showing you the operators.</p>
1253
1254<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=467
1255id="_x0000_i1034"
1256src="Merohedral%20twin%20refinement%20in%20GSAS_files/image036.png"></span></p>
1257
1258<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1259Factor/from CIF file</span></b> and select <b><span style='font-family:"Calibri",sans-serif'>3a.fcf</span></b>
1260from the file dialog. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1261in the next popup and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1262on the name change popup. Select the file name in the Add to phases popup and
1263press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; the hk0
1264zone of the structure factors will be displayed. Note that this plot shows both
1265green (<span class=SpellE>Fo</span>) and blue (Fc) circles with a small solid
1266red or green circle in the centers. These are for the +/- <span
1267style='font-family:Symbol'>D</span>F values. Fc is here because this <span
1268class=SpellE>fcf</span> file was obtained after refinement via <span
1269class=SpellE>Shelx</span>.</p>
1270
1271<p class=MsoNormal>You now have loaded all that is needed for the third
1272example. The structure had previously been solved and refined with <span
1273class=SpellE>Shelx</span> so you need not trouble about those steps. You can
1274try to solve the structure in GSAS-II via charge flipping but this is not part
1275of this exercise (it isn’t easy because of the twinning; charge flipping will
1276readily give the Cs position &amp; most of the rest. It can be completed via
1277difference Fourier techniques); we will only explore the twin analysis features
1278of GSAS-II.</p>
1279
1280<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1281of twinned structure<o:p></o:p></span></h2>
1282
1283<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1284eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub> &lt;
12852<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1286style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1287GSAS-II data tree.</p>
1288
1289<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
1290id="_x0000_i1033"
1291src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
1292
1293<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1294<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1295"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1296style='font-family:"Calibri",sans-serif'>Phases/Cs…</span></b> entry in the
1297GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1298tab.</p>
1299
1300<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
1301id="_x0000_i1032"
1302src="Merohedral%20twin%20refinement%20in%20GSAS_files/image037.png"></span></p>
1303
1304<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1305factor</span></b> is selected for refinement by default. If you refine it, you
1306will get an <span class=SpellE>R<sub>w</sub></span>~ 17% which is terrible. It
1307doesn’t change much if you add the Flack parameter (~0.36). If you try refining
1308atom positions &amp; thermal parameters you could possibly <span class=GramE>lower</span>
1309it but the resulting structure would not be very satisfactory. However, we have
1310suspected from the equivalence of 6/m and 6/mmm Laue data symmetries that there
1311is twinning so don’t bother trying to make it better by refining the structure.
1312To determine the possible twin <span class=GramE>laws</span> we again refer to
1313Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
1314that indeed Laue 6/mmm as P6<sub>1</sub>22 can be simulated by twinned Laue 6/m
1315crystals in P6<sub>1</sub>; the possible operator is shown in Table 1.3.4.1
1316(reproduced above) as either a mirror or a 2-fold. The detailed symbolism in the
1317table (‘m.., ..2/.2.’) indicates (perhaps obscurely) the operator specifics;
1318they are m as <span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:acc><m:accPr><m:chr
1319    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1320   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1321   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1322   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
1323    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1324   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1325   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1326   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
1327 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
1328style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1329"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1330top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1331EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1332 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1333 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image004.png"
1334  o:title="" chromakey="white"/>
1335</v:shape><![endif]--><![if !vml]><img width=26 height=19
1336src="Merohedral%20twin%20refinement%20in%20GSAS_files/image005.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;or
13372 as <!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span
1338 style='font-family:"Cambria Math",serif'><span style='position:relative;
1339 top:3pt'><m:r>y</m:r><m:r>x</span></m:r></span></i><m:acc><m:accPr><m:chr
1340    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1341   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1342   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1343   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
1344style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1345"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1346top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1347EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1348 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1349 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image006.png"
1350  o:title="" chromakey="white"/>
1351</v:shape><![endif]--><![if !vml]><img width=26 height=19
1352src="Merohedral%20twin%20refinement%20in%20GSAS_files/image019.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1353style='font-family:"Cambria Math",serif'>; we will use the 2-fold, m and
1354inversion operators to fully test for presence of the 4 possible twin laws.
1355Press the </span><b><span style='font-family:"Calibri",sans-serif'>Add Twin Law</span></b><span
1356style='font-family:"Cambria Math",serif'> button </span><b><span
1357style='font-family:"Calibri",sans-serif'>3 times</span></b><span
1358style='font-family:"Cambria Math",serif'>; each time the window will be
1359redrawn. When done you should see.<o:p></o:p></span></p>
1360
1361<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
1362id="_x0000_i1031"
1363src="Merohedral%20twin%20refinement%20in%20GSAS_files/image038.png"></span>&nbsp;</p>
1364
1365<p class=MsoNormal>For the third and fourth matrix enter <b><span
1366style='font-family:"Calibri",sans-serif'>0 1 0 1 0 0 0 0 -1</span></b> and <b><span
1367style='font-family:"Calibri",sans-serif'>0 -1 0 -1 0 0 0 0</span></b> <b><span
1368style='font-family:"Calibri",sans-serif'>1</span></b> as the 2-fold and mirror
1369operators (the 2<sup>nd</sup> matrix is the inversion by default). Select the <b><span
1370style='font-family:"Calibri",sans-serif'>Refine</span></b> button and do <b><span
1371style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
1372main menu. The <span class=SpellE>Rw</span> will immediately drop to ~2.26%
1373(RF~2.05%). The four twin element fractions will show various values.</p>
1374
1375<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1376 id="Picture_x0020_40" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:336.75pt;
1377 height:375pt;visibility:visible;mso-wrap-style:square'>
1378 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image007.png"
1379  o:title=""/>
1380</v:shape><![endif]--><![if !vml]><img width=449 height=500
1381src="Merohedral%20twin%20refinement%20in%20GSAS_files/image020.gif" v:shapes="Picture_x0020_40"><![endif]></span></p>
1382
1383<p class=MsoNormal>The negative one for the 3<sup>rd</sup> twin fraction is nonphysical
1384and the 1<sup>st</sup> twin fraction is small. It is likely that the true space
1385group is P6<sub>5</sub> and Type 2 <span class=SpellE>merohedrally</span>
1386twinned (twin fractions 2 &amp; 4). We can improve it by refining the atom
1387positions and thermal parameters, but first we need to replace the hydrogen
1388atoms as suggested by the <span class=SpellE>Shelx</span> warning. Select the <b
1389style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1390mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms </span></b>tab
1391for the phase.</p>
1392
1393<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1394 id="Picture_x0020_41" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:525pt;
1395 height:225pt;visibility:visible;mso-wrap-style:square'>
1396 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"
1397  o:title=""/>
1398</v:shape><![endif]--><![if !vml]><img width=700 height=300
1399src="Merohedral%20twin%20refinement%20in%20GSAS_files/image021.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
1400
1401<p class=MsoNormal>If you scroll down the page, you’ll see H-atoms with default
1402<span class=SpellE>Uiso</span> (=0.025) values. To replace them, the old ones
1403need to be deleted; double click the <b style='mso-bidi-font-weight:normal'><span
1404style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1405mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1406style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1407mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>H</span></b>
1408and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1409mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
1410The H-atoms will be highlighted (and plotted in green). Do <b style='mso-bidi-font-weight:
1411normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1412minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Delete atom</span></b> from
1413the menu; the H-atoms will be deleted and the structure will be redrawn. Next
1414double <span class=GramE>click</span> the <b style='mso-bidi-font-weight:normal'><span
1415style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1416mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1417style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1418mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>C</span></b>;
1419all the C-atoms will be selected (and shown in green on the plot). Do <b
1420style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1421mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Insert
1422H atoms</span></b>; a Distance Angle Controls will appear. Occasionally these
1423values may need to be changed but not this time; press <b style='mso-bidi-font-weight:
1424normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1425minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>. The next popup is
1426for the H atoms add controls.</p>
1427
1428<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1429 id="Picture_x0020_42" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:300pt;
1430 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1431 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image011.png"
1432  o:title=""/>
1433</v:shape><![endif]--><![if !vml]><img width=400 height=485
1434src="Merohedral%20twin%20refinement%20in%20GSAS_files/image022.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
1435
1436<p class=MsoNormal>It specifies the expected geometry around each C-atom for
1437H-atom placement. As expected we want 3 H-atoms on the terminal CH<sub>3</sub>
1438groups on the <span class=SpellE>Cp</span>* ring and one for each C-atom for
1439the NC<sub>5</sub>H<sub>5</sub> molecule. Press <b style='mso-bidi-font-weight:
1440normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1441minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; you will see the
1442H-atoms added in turn to the structure and they will be inserted immediately
1443after their respective C-atom. Their positions and thermal parameters are tied
1444to the C-atoms so that after refinement of the structure they can be shifted to
1445the <span class=SpellE>stereochemically</span> best positions. For the
1446refinement, double click the <b style='mso-bidi-font-weight:normal'><span
1447style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1448mso-hansi-theme-font:minor-latin'>Refine</span></b> column heading and select <b
1449style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1450mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>X</span></b>
1451and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1452mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>U</span></b>
1453from the popup; press <b style='mso-bidi-font-weight:normal'><span
1454style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1455mso-hansi-theme-font:minor-latin'>OK</span></b>. The Atom table will be redrawn
1456with XU in every entry under Refine. Now do <b style='mso-bidi-font-weight:
1457normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1458minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from
1459the main GSASII data tree window; the <span class=SpellE>Rw</span> will drop to
1460~1.92%. If you look at the <b style='mso-bidi-font-weight:normal'><span
1461style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1462mso-hansi-theme-font:minor-latin'>Data</span></b> tab the Twin element
1463fractions are much clearer.</p>
1464
1465<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1466 id="Picture_x0020_43" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:336.75pt;
1467 height:375pt;visibility:visible;mso-wrap-style:square'>
1468 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image013.png"
1469  o:title=""/>
1470</v:shape><![endif]--><![if !vml]><img width=449 height=500
1471src="Merohedral%20twin%20refinement%20in%20GSAS_files/image023.gif" v:shapes="Picture_x0020_43"><![endif]></span><span
1472style='mso-spacerun:yes'> </span></p>
1473
1474<p class=MsoNormal>The identity Twin Law has virtually vanished along with the
14752-fold one leaving just the inverse and mirror Twin Laws.</p>
1476
1477<p class=MsoNormal>This means the structure is the inverse in space group P6<sub>5</sub>
1478but still Type 2 <span class=SpellE>merohedrally</span> twinned. </p>
1479
1480<p class=MsoNormal>To test this, we need to both change the space group and
1481invert the structure. First select the <b style='mso-bidi-font-weight:normal'><span
1482style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1483mso-hansi-theme-font:minor-latin'>General</span></b> tab and change the space
1484group to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1485mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P 65</span></b>;
1486you’ll see the Operators popup (press <b style='mso-bidi-font-weight:normal'><span
1487style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1488mso-hansi-theme-font:minor-latin'>Ok</span></b>) and the General tab will be
1489redrawn. Next select the <b style='mso-bidi-font-weight:normal'><span
1490style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1491mso-hansi-theme-font:minor-latin'>Atoms</span></b> tab; do <b style='mso-bidi-font-weight:
1492normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1493minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Update H atoms</span></b> to
1494put them in their best positions.<span style='mso-spacerun:yes'>  </span>Next
1495select all the atoms by double clicking the empty box in upper left corner of
1496the table; all atoms will be highlighted &amp; plotted green. Do <b
1497style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1498mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Transform
1499atoms</span></b>; a popup will appear.</p>
1500
1501<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1502 id="Picture_x0020_44" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:270pt;
1503 height:263.25pt;visibility:visible;mso-wrap-style:square'>
1504 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image015.png"
1505  o:title=""/>
1506</v:shape><![endif]--><![if !vml]><img width=360 height=351
1507src="Merohedral%20twin%20refinement%20in%20GSAS_files/image024.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
1508
1509<p class=MsoNormal>Check the <b style='mso-bidi-font-weight:normal'><span
1510style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1511mso-hansi-theme-font:minor-latin'>Choose inversion</span></b> box and
1512(important) set <b style='mso-bidi-font-weight:normal'><span style='font-family:
1513"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1514minor-latin'>Choose unit cell</span></b> to <b style='mso-bidi-font-weight:
1515normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1516minor-latin;mso-hansi-theme-font:minor-latin'>1 1 1</span></b>; this will put
1517the inverted structure back inside the unit cell. Press <b style='mso-bidi-font-weight:
1518normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1519minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; the table and plot
1520will both be redrawn. Now do <b style='mso-bidi-font-weight:normal'><span
1521style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1522mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>; the <span
1523class=SpellE>Rw</span> will drop back to where it was before and the <b
1524style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1525mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
1526tab will show new Twin fractions.</p>
1527
1528<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1529 id="Picture_x0020_46" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:336.75pt;
1530 height:375pt;visibility:visible;mso-wrap-style:square'>
1531 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image017.png"
1532  o:title=""/>
1533</v:shape><![endif]--><![if !vml]><img width=449 height=500
1534src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.gif" v:shapes="Picture_x0020_46"><![endif]></span></p>
1535
1536<p class=MsoNormal>Now the identity Twin Law is ~2/3 and the 2-fold Twin Law is
1537the other ~1/3 while the other two are ~zero. You can delete them and repeat
1538the refinement; <span class=SpellE>Rw</span> ~1.7%. This completed the merohedral
1539twin exercises. You can save this project if desired.</p>
1540
1541<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1542
1543</span></div>
1544
1545</span></span></span></span></span></span></span></span></span></span>
1546</body>
1547
1548</html>
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