source: Tutorials/MerohedralTwins/Merohedral twin refinement in GSAS.htm @ 2394

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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 twinning.
814There 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_i1057"
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; Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>,
912and you will see the General page for this phase</p>
913
914<p class=MsoNormal><span style='mso-no-proof:yes'><img width=403 height=310
915id="_x0000_i1056"
916src="Merohedral%20twin%20refinement%20in%20GSAS_files/image007.png"></span></p>
917
918<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
919Factor/from CIF file</span></b> (that is the format of a “<span class=SpellE>fcf</span>”
920file); a file selection dialog box will appear with the previously selected
921directory chosen. Select <b><span style='font-family:"Calibri",sans-serif'>1b.fcf</span></b>;
922a popup window will appear</p>
923
924<p class=MsoNormal><span style='mso-no-proof:yes'><img width=447 height=249
925id="_x0000_i1055"
926src="Merohedral%20twin%20refinement%20in%20GSAS_files/image008.png"></span></p>
927
928<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
929a new popup window allowing you to change the name</p>
930
931<p class=MsoNormal><span style='mso-no-proof:yes'><img width=336 height=137
932id="_x0000_i1054"
933src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"></span></p>
934
935<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
936after a pause and some activity a popup window will appear</p>
937
938<p class=MsoNormal><span style='mso-no-proof:yes'><img width=320 height=310
939id="_x0000_i1053"
940src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.png"></span></p>
941
942<p class=MsoNormal>This makes the connection between the data set and the
943previously imported phase. Select the entry and press <b><span
944style='font-family:"Calibri",sans-serif'>OK</span></b>. You now have loaded all
945that is needed for the first example. The structure had previously been solved
946and refined with <span class=SpellE>Shelx</span> so you need not trouble about
947those steps. You can try to solve the structure in GSAS-II via charge flipping
948but this is not part of this exercise; we will only explore the twin analysis
949features of GSAS-II.</p>
950
951<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
952of twinned structure<o:p></o:p></span></h2>
953
954<p class=MsoNormal>Before beginning the refinement, it usually the practice to
955eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
956&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
957style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
958GSAS-II data tree.</p>
959
960<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
961id="_x0000_i1052"
962src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
963
964<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
965<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
966"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
967style='font-family:"Calibri",sans-serif'>Phases/C8 H25 Al0.84 Ga1.16</span></b>
968<span class=GramE>entry</span> in the GSAS-II data tree and choose the <b><span
969style='font-family:"Calibri",sans-serif'>Data</span></b> tab</p>
970
971<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
972id="_x0000_i1051"
973src="Merohedral%20twin%20refinement%20in%20GSAS_files/image011.png"></span></p>
974
975<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
976factor</span></b> is selected for refinement by default. If you refine it, you
977will get an <span class=SpellE>R<sub>w</sub></span>= 2.85% which isn’t too bad.
978However, you are unsure what the hand of the molecule is in this structure and
979the experiment with <span class=SpellE>MoKa</span> radiation should give
980sufficient resonant scattering to determine this. The <b><span
981style='font-family:"Calibri",sans-serif'>Flack parameter</span></b> gives you a
982way to evaluate which hand the molecule is. If upon refinement the value is ~0
983then you have correctly described the hand. Otherwise if the value is ~1 then
984the opposite hand is the correct and the structure needs to be inverted. So
985let’s test this; select the <b><span style='font-family:"Calibri",sans-serif'>Flack
986parameter</span></b> for refinement and do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>
987from the main GSAS-II data tree menu. The structure will quickly refine to give
988<span class=SpellE>R<sub>w</sub></span>=2.087% which is a considerable
989improvement on Scale factor alone. The Flack parameter is now 0.452, meaning
990that both hands somehow exist in the structure. This can happen if the crystal
991is <span class=SpellE>merohedrally</span> inversion twinned.</p>
992
993<p class=MsoNormal>To introduce this twin, press the <b><span style='font-family:
994"Calibri",sans-serif'>Add Twin Law</span></b> box; the window will be redrawn.</p>
995
996<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
997id="_x0000_i1050"
998src="Merohedral%20twin%20refinement%20in%20GSAS_files/image013.png"></span></p>
999
1000<p class=MsoNormal>Notice that two Twin Law matrices have been generated; one
1001is the identity for the reference structure and the other by default is the
1002merohedral inverse. If some other twin law is desired, then the matrix elements
1003need to be changed. Moreover, the Flack parameter has vanished as it is no
1004longer needed. Press the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1005button for the <b><span style='font-family:"Calibri",sans-serif'>Twin Law
1006fraction</span></b> and rerun the refinement. The Data window now has.</p>
1007
1008<p class=MsoNormal><span style='mso-no-proof:yes'><img width=449 height=500
1009id="_x0000_i1049"
1010src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.png"></span></p>
1011
1012<p class=MsoNormal>The refinement quickly converged to where it was before but
1013the twin fractions are now ~56/44 consistent with the ~45% Flack parameter
1014obtained earlier. It is likely that the crystal is macroscopically twinned thus
1015the twin fractions are not exactly 50/50. This completes this example; you can
1016save your project if you want to explore other features of GSAS-II with it.</p>
1017
1018<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 2. A Type 2
1019only merohedral twin – <br>
1020[Al(OC<sub>6</sub>H<sub>4</sub>(C<sub>3</sub>H<sub>7</sub>)<sub>2</sub>)]<sup>-</sup>
1021[NC<sub>7</sub>H<sub>8</sub>]<sup>+</sup><o:p></o:p></span></h2>
1022
1023<p class=MsoNormal>In this case the data collection Laue statistics (very
1024nearly <span style='position:relative;top:3pt'><span style='mso-no-proof:yes'>-3</span>m)
1025and systematic extinctions indicated that the space group was either one of the
1026<span class=SpellE>enantiomorphic</span> pair P3<sub>1</sub>21 or P3<sub>2</sub>21
1027or possibly one of the pair P3<sub>1</sub> or P3<sub>2</sub>. If the true
1028structure was of the lower symmetry P3<sub>1</sub> or P3<sub>2</sub> then there
1029must be Type 2 merohedral twinning to make the diffraction pattern appear to
1030have higher symmetry (<span style='position:relative;top:3pt'><span
1031style='mso-no-proof:yes'>-3</span>m instead of <span style='position:relative;
1032top:3pt'><span style='mso-no-proof:yes'>-3</span>); this exercise will explore
1033this possibility. The data were collected with <span class=SpellE>MoK</span><span
1034style='font-family:Symbol'>a</span> radiation so there is little resonant
1035scattering and thus the choice of hand is indeterminate.&nbsp; Solving the
1036structure in P3<sub>2</sub>21 yielded a poorly fitting structure with disorder
1037particularly in the cation. Resolving the structure in P3<sub>2</sub> gave a
1038structure with no disorder and a better fit to the data (but still not great).
1039As this work was done with <span class=SpellE>Shelx</span> this result is in
1040the form of a <span class=SpellE>Shelx</span> input file (2b.ins – thanks to V.
1041Young for this example). If you have not done so already, start GSAS-II and
1042start with a fresh project.</p>
1043
1044<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1045refinement<o:p></o:p></span></h2>
1046
1047<p class=MsoNormal>To begin we need to import the phase information from the <span
1048class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1049style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1050ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1051and a res file is the output result after a <span class=SpellE>Shelx</span>
1052run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>2b.ins</span></b>
1053from the file selection window; a popup window will ask if this file is the one
1054you want.</p>
1055
1056<p class=MsoNormal><span style='mso-no-proof:yes'><img width=410 height=262
1057id="_x0000_i1048"
1058src="Merohedral%20twin%20refinement%20in%20GSAS_files/image012.png"></span></p>
1059
1060<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
1061a Read Warning will appear.</p>
1062
1063<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1064 id="Picture_x0020_39" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:371.25pt;
1065 height:176.25pt;visibility:visible;mso-wrap-style:square'>
1066 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image001.png"
1067  o:title=""/>
1068</v:shape><![endif]--><![if !vml]><img width=495 height=235
1069src="Merohedral%20twin%20refinement%20in%20GSAS_files/image002.gif" v:shapes="Picture_x0020_39"><![endif]></span></p>
1070
1071<p class=MsoNormal>There are two significant warnings concerning <span
1072class=SpellE>Shelx</span> files. One is that the file never contains the space
1073group symbol (<span class=SpellE>Shelx</span> requires just the operators), so
1074GSAS-II sets the space group to P 1 by default and you will need to change it
1075to P3<sub>2</sub> immediately (next window). The other warning is that hydrogen
1076atoms were found; these usually cannot be refined unconstrained with x-ray
1077data. The warning recommends replacing them with <span class=SpellE>stereochemically</span>
1078determined ones (this is illustrated in the 3<sup>rd</sup> Exercise of this
1079tutorial) and the last line of the Warning tells you what to do if they are to
1080be refined. Here we will only refine twin laws &amp; scale factors so this is
1081unnecessary. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1082you get the opportunity to change the Phase name (I know it is very long but
1083that doesn’t matter here). Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1084the General tab for this phase is shown. </p>
1085
1086<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=336
1087id="_x0000_i1046"
1088src="Merohedral%20twin%20refinement%20in%20GSAS_files/image027.png"></span></p>
1089
1090<p class=MsoNormal>Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
109132</span></b>; the window will be redrawn after a popup showing the operations.
1092You can see the structure by selecting <b><span style='font-family:"Calibri",sans-serif'>Draw
1093Atoms</span></b>.</p>
1094
1095<p class=MsoNormal><span style='mso-no-proof:yes'><img width=478 height=358
1096id="_x0000_i1045"
1097src="Merohedral%20twin%20refinement%20in%20GSAS_files/image028.jpg"></span></p>
1098
1099<p class=MsoNormal>&nbsp;</p>
1100
1101<p class=MsoNormal>The large anion containing the Al atom is to the left and
1102the smaller cation to the right.</p>
1103
1104<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1105Factor/from <span class=SpellE>Shelx</span> HKLF 4 F<sup>2</sup> file</span></b>
1106and select <b><span style='font-family:"Calibri",sans-serif'>2b.hkl</span></b>
1107from the file dialog box; a popup will appear showing a few lines.</p>
1108
1109<p class=MsoNormal><span style='mso-no-proof:yes'><img width=366 height=262
1110id="_x0000_i1044"
1111src="Merohedral%20twin%20refinement%20in%20GSAS_files/image022.png"></span></p>
1112
1113<p class=MsoNormal>This is the right file; a <span class=SpellE>Shelx</span>
1114HKLF 4 file consists of records with just <span class=SpellE><span class=GramE>h,k</span>,l</span>,
1115F<sup>2</sup> and <span style='font-family:Symbol'>s</span>(F<sup>2</sup>).
1116Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b> and <b><span
1117style='font-family:"Calibri",sans-serif'>OK</span></b> on the next one (we’ll
1118keep the name as it is). Choose the phase with the long name on the next popup
1119and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; a 2D
1120display of the hk0 zone is plotted.</p>
1121
1122<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=535
1123id="_x0000_i1043"
1124src="Merohedral%20twin%20refinement%20in%20GSAS_files/image029.png"></span></p>
1125
1126<p class=MsoNormal>The size of the green circles <span class=GramE>are</span>
1127proportional to <span class=SpellE>Fo</span> (after a structure factor
1128calculation blue rings will appear for Fc).</p>
1129
1130<p class=MsoNormal>You now have loaded all that is needed for the second
1131example. The structure had previously been solved and refined with <span
1132class=SpellE>Shelx</span> so you need not trouble about those steps. You can
1133try to solve the structure in GSAS-II via charge flipping but this is not part
1134of this exercise (it isn’t easy because of the twinning); we will only explore
1135the twin analysis features of GSAS-II.</p>
1136
1137<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1138of twinned structure<o:p></o:p></span></h2>
1139
1140<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1141eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1142&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1143style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1144GSAS-II data tree.</p>
1145
1146<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
1147id="_x0000_i1042"
1148src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
1149
1150<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1151<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1152"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1153style='font-family:"Calibri",sans-serif'>Phases/MEROHEDRAL…</span></b> entry in
1154the GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1155tab.</p>
1156
1157<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=444
1158id="_x0000_i1041"
1159src="Merohedral%20twin%20refinement%20in%20GSAS_files/image030.png"></span></p>
1160
1161<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1162factor</span></b> is selected for refinement by default. If you refine it, you
1163will get an <span class=SpellE>R<sub>w</sub></span>~ 25% which is terrible. If
1164you try refining atom positions &amp; thermal parameters you could possibly <span
1165class=GramE>lower</span> it to ~15% (still terrible) and the resulting
1166structure would not be very satisfactory. However, we have suspected from the
1167equivalence of <span style='position:relative;top:3pt'><span style='mso-no-proof:
1168yes'><img width=9 height=19 id="_x0000_i1040"
1169src="Merohedral%20twin%20refinement%20in%20GSAS_files/image031.png"></span>&nbsp;and
1170<span style='position:relative;top:3pt'><span style='mso-no-proof:yes'><img
1171width=9 height=19 id="_x0000_i1039"
1172src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m1
1173Laue data symmetries that there is twinning so don’t bother trying to make it
1174better by refining the structure. To determine the possible twin law we refer
1175to Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
1176that indeed Laue <span style='position:relative;top:3pt'><span
1177style='mso-no-proof:yes'><img width=9 height=19 id="_x0000_i1038"
1178src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m1
1179as P3<sub>2</sub>21 can be simulated by twinned Laue <span style='position:
1180relative;top:3pt'><span style='mso-no-proof:yes'><img width=9 height=19
1181id="_x0000_i1037"
1182src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>&nbsp;crystals
1183in P3<sub>2</sub>; the possible operator is shown in Table 1.3.4.1 (reproduced
1184above) as either a mirror or a 2-fold. The detailed symbolism in the table (‘m.<span
1185class=GramE>., ..</span>2/.2.’) indicates (perhaps obscurely) the operator
1186specifics. See P3m1 and P3<sub>2</sub>21 space groups in International Tables
1187for Crystallography, Vol A for the operations m as <span style='position:relative;
1188top:3pt'><span style='mso-no-proof:yes'>-y-xz</span>&nbsp;or 2 as <span
1189style='position:relative;top:3pt'><span style='mso-no-proof:yes'>yx-z</span>;
1190we will use the 2-fold since the m inverts the structure which we are not
1191sensitive to in this experiment.</p>
1192
1193<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Add
1194Twin Law</span></b>; the Data tab will be redrawn with the inversion for the
1195second law. Replace this with the 2-fold (<b><span style='font-family:"Calibri",sans-serif'>0
11961 0, 1 0 0, 0 0 -1</span></b>) and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1197box. It should look like.</p>
1198
1199<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=500
1200id="_x0000_i1036"
1201src="Merohedral%20twin%20refinement%20in%20GSAS_files/image034.png"></span></p>
1202
1203<p class=MsoNormal>Now do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>;
1204there will be an immediate improvement in the fit to <span class=SpellE>Rw</span>=5.05%
1205and the twin fractions will be ~50/50. Clearly this crystal is Type 2 <span
1206class=SpellE>merohedrally</span> twinned; we cannot determine if there is any
1207Type 1 twinning because we lack sufficient resonant scattering to see it. This
1208ends the second example; you can save the project file.</p>
1209
1210<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 3. A Type 1
1211&amp; 2 merohedral twin – <span class=SpellE>Cp</span>*Cs(NC<sub>5</sub>H<sub>5</sub>)<o:p></o:p></span></h2>
1212
1213<p class=MsoNormal>This <span class=SpellE>ecample</span> is very similar to
1214the previous one except that the Cs atom has significant resonant scattering
1215for <span class=SpellE>MoKa</span> radiation allowing detection of Type 1 <span
1216class=SpellE>merohedry</span>. The data set has apparent 6/m Laue symmetry but
1217may 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.
1218The combination of Type 1 and Type 2 twins requires 4 twin laws to be explored
1219for this <span class=SpellE>pentamethylcyclopentadienyl</span> Cs complex. As
1220this work was done with <span class=SpellE>Shelx</span> this result is in the
1221form of a <span class=SpellE>Shelx</span> input file (3a.ins – thanks to V.
1222Young for this example). If you have not done so already, start GSAS-II and
1223start with a fresh project.</p>
1224
1225<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1226refinement<o:p></o:p></span></h2>
1227
1228<p class=MsoNormal>To begin we need to import the phase information from the <span
1229class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1230style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1231ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1232and a res file is the output result after a <span class=SpellE>Shelx</span>
1233run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>3a.ins</span></b>
1234from the file selection window; a popup window will ask if this file is the one
1235you want.</p>
1236
1237<p class=MsoNormal><span style='mso-no-proof:yes'><img width=366 height=262
1238id="_x0000_i1035"
1239src="Merohedral%20twin%20refinement%20in%20GSAS_files/image035.png"></span></p>
1240
1241<p class=MsoNormal>It is; press the <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1242button. You will then see the SHELX Read Warning; you will have to change the
1243space group to P6<sub>1</sub> in a bit. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1244and leave the name alone (press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1245again). Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
124661</span></b>; the General tab will be redrawn after showing you the operators.</p>
1247
1248<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=467
1249id="_x0000_i1034"
1250src="Merohedral%20twin%20refinement%20in%20GSAS_files/image036.png"></span></p>
1251
1252<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1253Factor/from CIF file</span></b> and select <b><span style='font-family:"Calibri",sans-serif'>3a.fcf</span></b>
1254from the file dialog. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1255in the next popup and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1256on the name change popup. Select the file name in the Add to phases popup and
1257press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; the hk0
1258zone of the structure factors will be displayed. Note that this plot shows both
1259green (<span class=SpellE>Fo</span>) and blue (Fc) circles with a small solid
1260red or green circle in the centers. These are for the +/- <span
1261style='font-family:Symbol'>D</span>F values. Fc is here because this <span
1262class=SpellE>fcf</span> file was obtained after refinement via <span
1263class=SpellE>Shelx</span>.</p>
1264
1265<p class=MsoNormal>You now have loaded all that is needed for the third
1266example. The structure had previously been solved and refined with <span
1267class=SpellE>Shelx</span> so you need not trouble about those steps. You can
1268try to solve the structure in GSAS-II via charge flipping but this is not part
1269of this exercise (it isn’t easy because of the twinning; charge flipping will
1270readily give the Cs position &amp; most of the rest. It can be completed via
1271difference Fourier techniques); we will only explore the twin analysis features
1272of GSAS-II.</p>
1273
1274<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1275of twinned structure<o:p></o:p></span></h2>
1276
1277<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1278eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub> &lt;
12792<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1280style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1281GSAS-II data tree.</p>
1282
1283<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
1284id="_x0000_i1033"
1285src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
1286
1287<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1288<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1289"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1290style='font-family:"Calibri",sans-serif'>Phases/Cs…</span></b> entry in the
1291GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1292tab.</p>
1293
1294<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
1295id="_x0000_i1032"
1296src="Merohedral%20twin%20refinement%20in%20GSAS_files/image037.png"></span></p>
1297
1298<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1299factor</span></b> is selected for refinement by default. If you refine it, you
1300will get an <span class=SpellE>R<sub>w</sub></span>~ 17% which is terrible. It
1301doesn’t change much if you add the Flack parameter (~0.36). If you try refining
1302atom positions &amp; thermal parameters you could possibly <span class=GramE>lower</span>
1303it but the resulting structure would not be very satisfactory. However, we have
1304suspected from the equivalence of 6/m and 6/mmm Laue data symmetries that there
1305is twinning so don’t bother trying to make it better by refining the structure.
1306To determine the possible twin <span class=GramE>laws</span> we again refer to
1307Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
1308that indeed Laue 6/mmm as P6<sub>1</sub>22 can be simulated by twinned Laue 6/m
1309crystals in P6<sub>1</sub>; the possible operator is shown in Table 1.3.4.1
1310(reproduced above) as either a mirror or a 2-fold. The detailed symbolism in the
1311table (‘m.., ..2/.2.’) indicates (perhaps obscurely) the operator specifics;
1312they are m as <span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:acc><m:accPr><m:chr
1313    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1314   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1315   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1316   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
1317    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1318   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1319   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1320   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e></m:acc><i
1321 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
1322style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1323"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1324top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1325EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1326 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1327 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image004.png"
1328  o:title="" chromakey="white"/>
1329</v:shape><![endif]--><![if !vml]><img width=26 height=19
1330src="Merohedral%20twin%20refinement%20in%20GSAS_files/image005.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;or
13312 as <!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span
1332 style='font-family:"Cambria Math",serif'><span style='position:relative;
1333 top:3pt'><m:r>y</m:r><m:r>x</span></m:r></span></i><m:acc><m:accPr><m:chr
1334    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1335   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1336   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1337   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
1338style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1339"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1340top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1341EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1342 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1343 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image006.png"
1344  o:title="" chromakey="white"/>
1345</v:shape><![endif]--><![if !vml]><img width=26 height=19
1346src="Merohedral%20twin%20refinement%20in%20GSAS_files/image008.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1347style='font-family:"Cambria Math",serif'>; we will use the 2-fold, m and
1348inversion operators to fully test for presence of the 4 possible twin laws.
1349Press the </span><b><span style='font-family:"Calibri",sans-serif'>Add Twin Law</span></b><span
1350style='font-family:"Cambria Math",serif'> button </span><b><span
1351style='font-family:"Calibri",sans-serif'>3 times</span></b><span
1352style='font-family:"Cambria Math",serif'>; each time the window will be
1353redrawn. When done you should see.<o:p></o:p></span></p>
1354
1355<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
1356id="_x0000_i1031"
1357src="Merohedral%20twin%20refinement%20in%20GSAS_files/image038.png"></span>&nbsp;</p>
1358
1359<p class=MsoNormal>For the third and fourth matrix enter <b><span
1360style='font-family:"Calibri",sans-serif'>0 1 0 1 0 0 0 0 -1</span></b> and <b><span
1361style='font-family:"Calibri",sans-serif'>0 -1 0 -1 0 0 0 0</span></b> <b><span
1362style='font-family:"Calibri",sans-serif'>1</span></b> as the 2-fold and mirror
1363operators (the 2<sup>nd</sup> matrix is the inversion by default). Select the <b><span
1364style='font-family:"Calibri",sans-serif'>Refine</span></b> button and do <b><span
1365style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
1366main menu. The <span class=SpellE>Rw</span> will immediately drop to ~2.26%
1367(RF~2.05%). The four twin element fractions will show various values.</p>
1368
1369<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1370 id="Picture_x0020_40" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:336.75pt;
1371 height:375pt;visibility:visible;mso-wrap-style:square'>
1372 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image007.png"
1373  o:title=""/>
1374</v:shape><![endif]--><![if !vml]><img width=449 height=500
1375src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.gif" v:shapes="Picture_x0020_40"><![endif]></span></p>
1376
1377<p class=MsoNormal>The negative one for the 3<sup>rd</sup> twin fraction is
1378nonphysical and the 1<sup>st</sup> twin fraction is small. It is likely that
1379the true space group is P6<sub>5</sub> and Type 2 <span class=SpellE>merohedrally</span>
1380twinned (twin fractions 2 &amp; 4). We can improve it by refining the atom
1381positions and thermal parameters, but first we need to replace the hydrogen
1382atoms as suggested by the <span class=SpellE>Shelx</span> warning. Select the <b
1383style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1384mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms </span></b>tab
1385for the phase.</p>
1386
1387<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1388 id="Picture_x0020_41" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:525pt;
1389 height:225pt;visibility:visible;mso-wrap-style:square'>
1390 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"
1391  o:title=""/>
1392</v:shape><![endif]--><![if !vml]><img width=700 height=300
1393src="Merohedral%20twin%20refinement%20in%20GSAS_files/image012.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
1394
1395<p class=MsoNormal>If you scroll down the page, you’ll see H-atoms with default
1396<span class=SpellE>Uiso</span> (=0.025) values. To replace them, the old ones
1397need to be deleted; double click the <b style='mso-bidi-font-weight:normal'><span
1398style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1399mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1400style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1401mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>H</span></b>
1402and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1403mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
1404The H-atoms will be highlighted (and plotted in green). Do <b style='mso-bidi-font-weight:
1405normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1406minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Delete atom</span></b> from
1407the menu; the H-atoms will be deleted and the structure will be redrawn. Next
1408double <span class=GramE>click</span> the <b style='mso-bidi-font-weight:normal'><span
1409style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1410mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1411style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1412mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>C</span></b>;
1413all the C-atoms will be selected (and shown in green on the plot). Do <b
1414style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1415mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Insert
1416H atoms</span></b>; a Distance Angle Controls will appear. Occasionally these
1417values may need to be changed but not this time; press <b style='mso-bidi-font-weight:
1418normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1419minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>. The next popup is
1420for the H atoms add controls.</p>
1421
1422<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1423 id="Picture_x0020_42" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:300pt;
1424 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1425 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image011.png"
1426  o:title=""/>
1427</v:shape><![endif]--><![if !vml]><img width=400 height=485
1428src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
1429
1430<p class=MsoNormal>It specifies the expected geometry around each C-atom for
1431H-atom placement. As expected we want 3 H-atoms on the terminal CH<sub>3</sub>
1432groups on the <span class=SpellE>Cp</span>* ring and one for each C-atom for
1433the NC<sub>5</sub>H<sub>5</sub> molecule. Press <b style='mso-bidi-font-weight:
1434normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1435minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; you will see the
1436H-atoms added in turn to the structure and they will be inserted immediately
1437after their respective C-atom. Their positions and thermal parameters are tied
1438to the C-atoms so that after refinement of the structure they can be shifted to
1439the <span class=SpellE>stereochemically</span> best positions. For the refinement,
1440double click the <b style='mso-bidi-font-weight:normal'><span style='font-family:
1441"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1442minor-latin'>Refine</span></b> column heading and select <b style='mso-bidi-font-weight:
1443normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1444minor-latin;mso-hansi-theme-font:minor-latin'>X</span></b> and <b
1445style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1446mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>U</span></b>
1447from the popup; press <b style='mso-bidi-font-weight:normal'><span
1448style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1449mso-hansi-theme-font:minor-latin'>OK</span></b>. The Atom table will be redrawn
1450with XU in every entry under Refine. Now do <b style='mso-bidi-font-weight:
1451normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1452minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from
1453the main GSASII data tree window; the <span class=SpellE>Rw</span> will drop to
1454~1.92%. If you look at the <b style='mso-bidi-font-weight:normal'><span
1455style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1456mso-hansi-theme-font:minor-latin'>Data</span></b> tab the Twin element
1457fractions are much clearer.</p>
1458
1459<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1460 id="Picture_x0020_43" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:336.75pt;
1461 height:375pt;visibility:visible;mso-wrap-style:square'>
1462 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image013.png"
1463  o:title=""/>
1464</v:shape><![endif]--><![if !vml]><img width=449 height=500
1465src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.gif" v:shapes="Picture_x0020_43"><![endif]></span><span
1466style='mso-spacerun:yes'> </span></p>
1467
1468<p class=MsoNormal>The identity Twin Law has virtually vanished along with the
14692-fold one leaving just the inverse and mirror Twin Laws.</p>
1470
1471<p class=MsoNormal>This means the structure is the inverse in space group P6<sub>5</sub>
1472but still Type 2 <span class=SpellE>merohedrally</span> twinned. </p>
1473
1474<p class=MsoNormal>To test this, we need to both change the space group and
1475invert the structure. First select the <b style='mso-bidi-font-weight:normal'><span
1476style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1477mso-hansi-theme-font:minor-latin'>General</span></b> tab and change the space
1478group to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1479mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P 65</span></b>;
1480you’ll see the Operators popup (press <b style='mso-bidi-font-weight:normal'><span
1481style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1482mso-hansi-theme-font:minor-latin'>Ok</span></b>) and the General tab will be redrawn.
1483Next select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
1484"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1485minor-latin'>Atoms</span></b> tab; do <b style='mso-bidi-font-weight:normal'><span
1486style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1487mso-hansi-theme-font:minor-latin'>Edit/Update H atoms</span></b> to put them in
1488their best positions.<span style='mso-spacerun:yes'>  </span>Next select all
1489the atoms by double clicking the empty box in upper left corner of the table;
1490all atoms will be highlighted &amp; plotted green. Do <b style='mso-bidi-font-weight:
1491normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1492minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Transform atoms</span></b>;
1493a popup will appear.</p>
1494
1495<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1496 id="Picture_x0020_44" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:270pt;
1497 height:263.25pt;visibility:visible;mso-wrap-style:square'>
1498 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image015.png"
1499  o:title=""/>
1500</v:shape><![endif]--><![if !vml]><img width=360 height=351
1501src="Merohedral%20twin%20refinement%20in%20GSAS_files/image018.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
1502
1503<p class=MsoNormal>Check the <b style='mso-bidi-font-weight:normal'><span
1504style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1505mso-hansi-theme-font:minor-latin'>Choose inversion</span></b> box and
1506(important) set <b style='mso-bidi-font-weight:normal'><span style='font-family:
1507"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1508minor-latin'>Choose unit cell</span></b> to <b style='mso-bidi-font-weight:
1509normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1510minor-latin;mso-hansi-theme-font:minor-latin'>1 1 1</span></b>; this will put
1511the inverted structure back inside the unit cell. Press <b style='mso-bidi-font-weight:
1512normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1513minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; the table and plot
1514will both be redrawn. Now do <b style='mso-bidi-font-weight:normal'><span
1515style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1516mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>; the <span
1517class=SpellE>Rw</span> will drop back to where it was before and the <b
1518style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1519mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
1520tab will show new Twin fractions.</p>
1521
1522<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1523 id="Picture_x0020_46" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:336.75pt;
1524 height:375pt;visibility:visible;mso-wrap-style:square'>
1525 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image017.png"
1526  o:title=""/>
1527</v:shape><![endif]--><![if !vml]><img width=449 height=500
1528src="Merohedral%20twin%20refinement%20in%20GSAS_files/image019.gif" v:shapes="Picture_x0020_46"><![endif]></span></p>
1529
1530<p class=MsoNormal>Now the identity Twin Law is ~2/3 and the 2-fold Twin Law is
1531the other ~1/3 while the other two are ~zero. You can delete them and repeat
1532the refinement; <span class=SpellE>Rw</span> ~1.7%. This completed the
1533merohedral twin exercises. You can save this project if desired.</p>
1534
1535<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1536
1537</span></div>
1538
1539</span></span></span></span></span></span></span></span></span></span>
1540</body>
1541
1542</html>
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