source: Tutorials/MerohedralTwins/Merohedral twin refinement in GSAS.htm @ 2353

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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_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 <b><span style='font-family:
895"Calibri",sans-serif'>/exercises/<span class=SpellE>MerohedralTwins</span>/1b.cif</span></b>
896and the data are in <b><span style='font-family:"Calibri",sans-serif'>/exercises/<span
897class=SpellE>MerohedralTwins</span>/1b.fcf</span></b>. This example is <span
898class=SpellE>noncentrosymmetric</span> and the data was collected with
899radiation (<span class=SpellE>MoK</span>&#945;) that gives significant resonant
900scattering from the Ga atoms. </p>
901
902<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
903refinement<o:p></o:p></span></h2>
904
905<p class=MsoNormal>To begin do <b><span style='font-family:"Calibri",sans-serif'>Import/Phase/from
906CIF file</span></b> from the main GSAS-II data tree menu. A file selection
907window will appear; find the above <span class=SpellE>cif</span> file (…<b><span
908style='font-family:"Calibri",sans-serif'>1b.cif</span></b>) and select it. A
909popup window will appear. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
910a new popup will appear</p>
911
912<p class=MsoNormal><span style='mso-no-proof:yes'><img width=336 height=137
913id="_x0000_i1057"
914src="Merohedral%20twin%20refinement%20in%20GSAS_files/image006.png"></span></p>
915
916<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>,
917and you will see the General page for this phase</p>
918
919<p class=MsoNormal><span style='mso-no-proof:yes'><img width=650 height=500
920id="_x0000_i1056"
921src="Merohedral%20twin%20refinement%20in%20GSAS_files/image007.png"></span></p>
922
923<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
924Factor/from CIF file</span></b> (that is the format of a “<span class=SpellE>fcf</span>”
925file); a file selection dialog box will appear with the previously selected directory
926chosen. Select <b><span style='font-family:"Calibri",sans-serif'>1b.fcf</span></b>;
927a popup window will appear</p>
928
929<p class=MsoNormal><span style='mso-no-proof:yes'><img width=447 height=249
930id="_x0000_i1055"
931src="Merohedral%20twin%20refinement%20in%20GSAS_files/image008.png"></span></p>
932
933<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
934a new popup window allowing you to change the name</p>
935
936<p class=MsoNormal><span style='mso-no-proof:yes'><img width=336 height=137
937id="_x0000_i1054"
938src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"></span></p>
939
940<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
941after a pause and some activity a popup window will appear</p>
942
943<p class=MsoNormal><span style='mso-no-proof:yes'><img width=320 height=310
944id="_x0000_i1053"
945src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.png"></span></p>
946
947<p class=MsoNormal>This makes the connection between the data set and the
948previously imported phase. Select the entry and press <b><span
949style='font-family:"Calibri",sans-serif'>OK</span></b>. You now have loaded all
950that is needed for the first example. The structure had previously been solved
951and refined with <span class=SpellE>Shelx</span> so you need not trouble about
952those steps. You can try to solve the structure in GSAS-II via charge flipping
953but this is not part of this exercise; we will only explore the twin analysis
954features of GSAS-II.</p>
955
956<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
957of twinned structure<o:p></o:p></span></h2>
958
959<p class=MsoNormal>Before beginning the refinement, it usually the practice to
960eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
961&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
962style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
963GSAS-II data tree.</p>
964
965<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
966id="_x0000_i1052"
967src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
968
969<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
970<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
971"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
972style='font-family:"Calibri",sans-serif'>Phases/C8 H25 Al0.84 Ga1.16</span></b>
973<span class=GramE>entry</span> in the GSAS-II data tree and choose the <b><span
974style='font-family:"Calibri",sans-serif'>Data</span></b> tab</p>
975
976<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
977id="_x0000_i1051"
978src="Merohedral%20twin%20refinement%20in%20GSAS_files/image011.png"></span></p>
979
980<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
981factor</span></b> is selected for refinement by default. If you refine it, you
982will get an <span class=SpellE>R<sub>w</sub></span>= 2.85% which isn’t too bad.
983However, you are unsure what the hand of the molecule is in this structure and
984the experiment with <span class=SpellE>MoKa</span> radiation should give
985sufficient resonant scattering to determine this. The <b><span
986style='font-family:"Calibri",sans-serif'>Flack parameter</span></b> gives you a
987way to evaluate which hand the molecule is. If upon refinement the value is ~0
988then you have correctly described the hand. Otherwise if the value is ~1 then
989the opposite hand is the correct and the structure needs to be inverted. So
990let’s test this; select the <b><span style='font-family:"Calibri",sans-serif'>Flack
991parameter</span></b> for refinement and do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>
992from the main GSAS-II data tree menu. The structure will quickly refine to give
993<span class=SpellE>R<sub>w</sub></span>=2.087% which is a considerable
994improvement on Scale factor alone. The Flack parameter is now 0.452, meaning
995that both hands somehow exist in the structure. This can happen if the crystal
996is <span class=SpellE>merohedrally</span> inversion twinned.</p>
997
998<p class=MsoNormal>To introduce this twin, press the <b><span style='font-family:
999"Calibri",sans-serif'>Add Twin Law</span></b> box; the window will be redrawn.</p>
1000
1001<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
1002id="_x0000_i1050"
1003src="Merohedral%20twin%20refinement%20in%20GSAS_files/image013.png"></span></p>
1004
1005<p class=MsoNormal>Notice that two Twin Law matrices have been generated; one
1006is the identity for the reference structure and the other by default is the
1007merohedral inverse. If some other twin law is desired, then the matrix elements
1008need to be changed. Moreover, the Flack parameter has vanished as it is no
1009longer needed. Press the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1010button for the <b><span style='font-family:"Calibri",sans-serif'>Twin Law
1011fraction</span></b> and rerun the refinement. The Data window now has.</p>
1012
1013<p class=MsoNormal><span style='mso-no-proof:yes'><img width=449 height=500
1014id="_x0000_i1049"
1015src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.png"></span></p>
1016
1017<p class=MsoNormal>The refinement quickly converged to where it was before but
1018the twin fractions are now ~56/44 consistent with the ~45% Flack parameter
1019obtained earlier. It is likely that the crystal is macroscopically twinned thus
1020the twin fractions are not exactly 50/50. This completes this example; you can
1021save your project if you want to explore other features of GSAS-II with it.</p>
1022
1023<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 2. A Type 2
1024only merohedral twin – <br>
1025[Al(OC<sub>6</sub>H<sub>4</sub>(C<sub>3</sub>H<sub>7</sub>)<sub>2</sub>)]<sup>-</sup>
1026[NC<sub>7</sub>H<sub>8</sub>]<sup>+</sup><o:p></o:p></span></h2>
1027
1028<p class=MsoNormal>In this case the data collection Laue statistics (very
1029nearly <span style='position:relative;top:3pt'><span style='mso-no-proof:yes'>-3</span>m)
1030and systematic extinctions indicated that the space group was either one of the
1031<span class=SpellE>enantiomorphic</span> pair P3<sub>1</sub>21 or P3<sub>2</sub>21
1032or possibly one of the pair P3<sub>1</sub> or P3<sub>2</sub>. If the true
1033structure was of the lower symmetry P3<sub>1</sub> or P3<sub>2</sub> then there
1034must be Type 2 merohedral twinning to make the diffraction pattern appear to
1035have higher symmetry (<span style='position:relative;top:3pt'><span
1036style='mso-no-proof:yes'>-3</span>m instead of <span style='position:relative;
1037top:3pt'><span style='mso-no-proof:yes'>-3</span>); this exercise will explore
1038this possibility. The data were collected with <span class=SpellE>MoK</span><span
1039style='font-family:Symbol'>a</span> radiation so there is little resonant
1040scattering and thus the choice of hand is indeterminate.&nbsp; Solving the
1041structure in P3<sub>2</sub>21 yielded a poorly fitting structure with disorder
1042particularly in the cation. Resolving the structure in P3<sub>2</sub> gave a
1043structure with no disorder and a better fit to the data (but still not great).
1044As this work was done with <span class=SpellE>Shelx</span> this result is in
1045the form of a <span class=SpellE>Shelx</span> input file (2b.ins – thanks to V.
1046Young for this example). If you have not done so already, start GSAS-II and
1047start with a fresh project.</p>
1048
1049<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1050refinement<o:p></o:p></span></h2>
1051
1052<p class=MsoNormal>To begin we need to import the phase information from the <span
1053class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1054style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1055ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1056and a res file is the output result after a <span class=SpellE>Shelx</span>
1057run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>2b.ins</span></b>
1058from the file selection window; a popup window will ask if this file is the one
1059you want.</p>
1060
1061<p class=MsoNormal><span style='mso-no-proof:yes'><img width=410 height=262
1062id="_x0000_i1048"
1063src="Merohedral%20twin%20refinement%20in%20GSAS_files/image012.png"></span></p>
1064
1065<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
1066a Read Warning will appear.</p>
1067
1068<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1069 id="Picture_x0020_39" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:371.25pt;
1070 height:176.25pt;visibility:visible;mso-wrap-style:square'>
1071 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image001.png"
1072  o:title=""/>
1073</v:shape><![endif]--><![if !vml]><img width=495 height=235
1074src="Merohedral%20twin%20refinement%20in%20GSAS_files/image002.gif" v:shapes="Picture_x0020_39"><![endif]></span></p>
1075
1076<p class=MsoNormal>There are two significant warnings concerning <span
1077class=SpellE>Shelx</span> files. One is that the file never contains the space
1078group symbol (<span class=SpellE>Shelx</span> requires just the operators), so
1079GSAS-II sets the space group to P 1 by default and you will need to change it
1080to P3<sub>2</sub> immediately (next window). The other warning is that hydrogen
1081atoms were found; these usually cannot be refined unconstrained with x-ray
1082data. The warning recommends replacing them with <span class=SpellE>stereochemically</span>
1083determined ones (this is illustrated in the 3<sup>rd</sup> Exercise of this
1084tutorial) and the last line of the Warning tells you what to do if they are to
1085be refined. Here we will only refine twin laws &amp; scale factors so this is
1086unnecessary. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1087you get the opportunity to change the Phase name (I know it is very long but
1088that doesn’t matter here). Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1089the General tab for this phase is shown. </p>
1090
1091<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=336
1092id="_x0000_i1046"
1093src="Merohedral%20twin%20refinement%20in%20GSAS_files/image027.png"></span></p>
1094
1095<p class=MsoNormal>Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
109632</span></b>; the window will be redrawn after a popup showing the operations.
1097You can see the structure by selecting <b><span style='font-family:"Calibri",sans-serif'>Draw
1098Atoms</span></b>.</p>
1099
1100<p class=MsoNormal><span style='mso-no-proof:yes'><img width=478 height=358
1101id="_x0000_i1045"
1102src="Merohedral%20twin%20refinement%20in%20GSAS_files/image028.jpg"></span></p>
1103
1104<p class=MsoNormal>&nbsp;</p>
1105
1106<p class=MsoNormal>The large anion containing the Al atom is to the left and
1107the smaller cation to the right.</p>
1108
1109<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1110Factor/from <span class=SpellE>Shelx</span> HKLF 4 F<sup>2</sup> file</span></b>
1111and select <b><span style='font-family:"Calibri",sans-serif'>2b.hkl</span></b>
1112from the file dialog box; a popup will appear showing a few lines.</p>
1113
1114<p class=MsoNormal><span style='mso-no-proof:yes'><img width=366 height=262
1115id="_x0000_i1044"
1116src="Merohedral%20twin%20refinement%20in%20GSAS_files/image022.png"></span></p>
1117
1118<p class=MsoNormal>This is the right file; a <span class=SpellE>Shelx</span>
1119HKLF 4 file consists of records with just <span class=SpellE><span class=GramE>h,k</span>,l</span>,
1120F<sup>2</sup> and <span style='font-family:Symbol'>s</span>(F<sup>2</sup>).
1121Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b> and <b><span
1122style='font-family:"Calibri",sans-serif'>OK</span></b> on the next one (we’ll
1123keep the name as it is). Choose the phase with the long name on the next popup
1124and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; a 2D
1125display of the hk0 zone is plotted.</p>
1126
1127<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=535
1128id="_x0000_i1043"
1129src="Merohedral%20twin%20refinement%20in%20GSAS_files/image029.png"></span></p>
1130
1131<p class=MsoNormal>The size of the green circles <span class=GramE>are</span>
1132proportional to <span class=SpellE>Fo</span> (after a structure factor
1133calculation blue rings will appear for Fc).</p>
1134
1135<p class=MsoNormal>You now have loaded all that is needed for the second
1136example. The structure had previously been solved and refined with <span
1137class=SpellE>Shelx</span> so you need not trouble about those steps. You can
1138try to solve the structure in GSAS-II via charge flipping but this is not part
1139of this exercise (it isn’t easy because of the twinning); we will only explore
1140the twin analysis features of GSAS-II.</p>
1141
1142<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1143of twinned structure<o:p></o:p></span></h2>
1144
1145<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1146eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1147&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1148style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1149GSAS-II data tree.</p>
1150
1151<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
1152id="_x0000_i1042"
1153src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
1154
1155<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1156<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1157"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1158style='font-family:"Calibri",sans-serif'>Phases/MEROHEDRAL…</span></b> entry in
1159the GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1160tab.</p>
1161
1162<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=444
1163id="_x0000_i1041"
1164src="Merohedral%20twin%20refinement%20in%20GSAS_files/image030.png"></span></p>
1165
1166<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1167factor</span></b> is selected for refinement by default. If you refine it, you
1168will get an <span class=SpellE>R<sub>w</sub></span>~ 25% which is terrible. If
1169you try refining atom positions &amp; thermal parameters you could possibly <span
1170class=GramE>lower</span> it to ~15% (still terrible) and the resulting
1171structure would not be very satisfactory. However, we have suspected from the
1172equivalence of <span style='position:relative;top:3pt'><span style='mso-no-proof:
1173yes'><img width=9 height=19 id="_x0000_i1040"
1174src="Merohedral%20twin%20refinement%20in%20GSAS_files/image031.png"></span>&nbsp;and
1175<span style='position:relative;top:3pt'><span style='mso-no-proof:yes'><img
1176width=9 height=19 id="_x0000_i1039"
1177src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m1
1178Laue data symmetries that there is twinning so don’t bother trying to make it better
1179by refining the structure. To determine the possible twin law we refer to Table
11801.3.4.2 of the International Tables for Crystallography Vol C. and see that
1181indeed Laue <span style='position:relative;top:3pt'><span style='mso-no-proof:
1182yes'><img width=9 height=19 id="_x0000_i1038"
1183src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m1
1184as P3<sub>2</sub>21 can be simulated by twinned Laue <span style='position:
1185relative;top:3pt'><span style='mso-no-proof:yes'><img width=9 height=19
1186id="_x0000_i1037"
1187src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>&nbsp;crystals
1188in P3<sub>2</sub>; the possible operator is shown in Table 1.3.4.1 (reproduced
1189above) as either a mirror or a 2-fold. The detailed symbolism in the table (‘m.<span
1190class=GramE>., ..</span>2/.2.’) indicates (perhaps obscurely) the operator
1191specifics. See P3m1 and P3<sub>2</sub>21 space groups in International Tables
1192for Crystallography, Vol A for the operations m as <span style='position:relative;
1193top:3pt'><span style='mso-no-proof:yes'>-y-xz</span>&nbsp;or 2 as <span
1194style='position:relative;top:3pt'><span style='mso-no-proof:yes'>yx-z</span>;
1195we will use the 2-fold since the m inverts the structure which we are not
1196sensitive to in this experiment.</p>
1197
1198<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Add
1199Twin Law</span></b>; the Data tab will be redrawn with the inversion for the
1200second law. Replace this with the 2-fold (<b><span style='font-family:"Calibri",sans-serif'>0
12011 0, 1 0 0, 0 0 -1</span></b>) and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1202box. It should look like.</p>
1203
1204<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=500
1205id="_x0000_i1036"
1206src="Merohedral%20twin%20refinement%20in%20GSAS_files/image034.png"></span></p>
1207
1208<p class=MsoNormal>Now do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>;
1209there will be an immediate improvement in the fit to <span class=SpellE>Rw</span>=5.05%
1210and the twin fractions will be ~50/50. Clearly this crystal is Type 2 <span
1211class=SpellE>merohedrally</span> twinned; we cannot determine if there is any
1212Type 1 twinning because we lack sufficient resonant scattering to see it. This
1213ends the second example; you can save the project file.</p>
1214
1215<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 3. A Type 1
1216&amp; 2 merohedral twin – <span class=SpellE>Cp</span>*Cs(NC<sub>5</sub>H<sub>5</sub>)<o:p></o:p></span></h2>
1217
1218<p class=MsoNormal>This <span class=SpellE>ecample</span> is very similar to
1219the previous one except that the Cs atom has significant resonant scattering
1220for <span class=SpellE>MoKa</span> radiation allowing detection of Type 1 <span
1221class=SpellE>merohedry</span>. The data set has apparent 6/m Laue symmetry but
1222may 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.
1223The combination of Type 1 and Type 2 twins requires 4 twin laws to be explored
1224for this <span class=SpellE>pentamethylcyclopentadienyl</span> Cs complex. As
1225this work was done with <span class=SpellE>Shelx</span> this result is in the
1226form of a <span class=SpellE>Shelx</span> input file (3a.ins – thanks to V.
1227Young for this example). If you have not done so already, start GSAS-II and
1228start with a fresh project.</p>
1229
1230<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1231refinement<o:p></o:p></span></h2>
1232
1233<p class=MsoNormal>To begin we need to import the phase information from the <span
1234class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1235style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1236ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1237and a res file is the output result after a <span class=SpellE>Shelx</span>
1238run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>3a.ins</span></b>
1239from the file selection window; a popup window will ask if this file is the one
1240you want.</p>
1241
1242<p class=MsoNormal><span style='mso-no-proof:yes'><img width=366 height=262
1243id="_x0000_i1035"
1244src="Merohedral%20twin%20refinement%20in%20GSAS_files/image035.png"></span></p>
1245
1246<p class=MsoNormal>It is; press the <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1247button. You will then see the SHELX Read Warning; you will have to change the
1248space group to P6<sub>1</sub> in a bit. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1249and leave the name alone (press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1250again). Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
125161</span></b>; the General tab will be redrawn after showing you the operators.</p>
1252
1253<p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=467
1254id="_x0000_i1034"
1255src="Merohedral%20twin%20refinement%20in%20GSAS_files/image036.png"></span></p>
1256
1257<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1258Factor/from CIF file</span></b> and select <b><span style='font-family:"Calibri",sans-serif'>3a.fcf</span></b>
1259from the file dialog. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1260in the next popup and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1261on the name change popup. Select the file name in the Add to phases popup and
1262press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; the hk0
1263zone of the structure factors will be displayed. Note that this plot shows both
1264green (<span class=SpellE>Fo</span>) and blue (Fc) circles with a small solid
1265red or green circle in the centers. These are for the +/- <span
1266style='font-family:Symbol'>D</span>F values. Fc is here because this <span
1267class=SpellE>fcf</span> file was obtained after refinement via <span
1268class=SpellE>Shelx</span>.</p>
1269
1270<p class=MsoNormal>You now have loaded all that is needed for the third
1271example. The structure had previously been solved and refined with <span
1272class=SpellE>Shelx</span> so you need not trouble about those steps. You can
1273try to solve the structure in GSAS-II via charge flipping but this is not part
1274of this exercise (it isn’t easy because of the twinning; charge flipping will
1275readily give the Cs position &amp; most of the rest. It can be completed via
1276difference Fourier techniques); we will only explore the twin analysis features
1277of GSAS-II.</p>
1278
1279<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1280of twinned structure<o:p></o:p></span></h2>
1281
1282<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1283eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1284&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1285style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1286GSAS-II data tree.</p>
1287
1288<p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
1289id="_x0000_i1033"
1290src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
1291
1292<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1293<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1294"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1295style='font-family:"Calibri",sans-serif'>Phases/Cs…</span></b> entry in the
1296GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1297tab.</p>
1298
1299<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
1300id="_x0000_i1032"
1301src="Merohedral%20twin%20refinement%20in%20GSAS_files/image037.png"></span></p>
1302
1303<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1304factor</span></b> is selected for refinement by default. If you refine it, you
1305will get an <span class=SpellE>R<sub>w</sub></span>~ 17% which is terrible. It
1306doesn’t change much if you add the Flack parameter (~0.36). If you try refining
1307atom positions &amp; thermal parameters you could possibly <span class=GramE>lower</span>
1308it but the resulting structure would not be very satisfactory. However, we have
1309suspected from the equivalence of 6/m and 6/mmm Laue data symmetries that there
1310is twinning so don’t bother trying to make it better by refining the structure.
1311To determine the possible twin <span class=GramE>laws</span> we again refer to
1312Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
1313that indeed Laue 6/mmm as P6<sub>1</sub>22 can be simulated by twinned Laue 6/m
1314crystals in P6<sub>1</sub>; the possible operator is shown in Table 1.3.4.1
1315(reproduced above) as either a mirror or a 2-fold. The detailed symbolism in
1316the table (‘m.., ..2/.2.’) indicates (perhaps obscurely) the operator
1317specifics; they are m as <span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:acc><m:accPr><m:chr
1318    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1319   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1320   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1321   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
1322    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1323   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1324   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1325   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
1326 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
1327style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1328"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1329top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1330EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1331 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1332 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image003.png"
1333  o:title="" chromakey="white"/>
1334</v:shape><![endif]--><![if !vml]><img width=26 height=19
1335src="Merohedral%20twin%20refinement%20in%20GSAS_files/image004.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;or
13362 as <!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span
1337 style='font-family:"Cambria Math",serif'><span style='position:relative;
1338 top:3pt'><m:r>y</m:r><m:r>x</span></m:r></span></i><m:acc><m:accPr><m:chr
1339    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1340   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1341   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1342   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
1343style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1344"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1345top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1346EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1347 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1348 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image005.png"
1349  o:title="" chromakey="white"/>
1350</v:shape><![endif]--><![if !vml]><img width=26 height=19
1351src="Merohedral%20twin%20refinement%20in%20GSAS_files/image006.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1352style='font-family:"Cambria Math",serif'>; we will use the 2-fold, m and
1353inversion operators to fully test for presence of the 4 possible twin laws.
1354Press the </span><b><span style='font-family:"Calibri",sans-serif'>Add Twin Law</span></b><span
1355style='font-family:"Cambria Math",serif'> button </span><b><span
1356style='font-family:"Calibri",sans-serif'>3 times</span></b><span
1357style='font-family:"Cambria Math",serif'>; each time the window will be
1358redrawn. When done you should see.<o:p></o:p></span></p>
1359
1360<p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
1361id="_x0000_i1031"
1362src="Merohedral%20twin%20refinement%20in%20GSAS_files/image038.png"></span>&nbsp;</p>
1363
1364<p class=MsoNormal>For the third and fourth matrix enter <b><span
1365style='font-family:"Calibri",sans-serif'>0 1 0 1 0 0 0 0 -1</span></b> and <b><span
1366style='font-family:"Calibri",sans-serif'>0 -1 0 -1 0 0 0 0</span></b> <b><span
1367style='font-family:"Calibri",sans-serif'>1</span></b> as the 2-fold and mirror
1368operators (the 2<sup>nd</sup> matrix is the inversion by default). Select the <b><span
1369style='font-family:"Calibri",sans-serif'>Refine</span></b> button and do <b><span
1370style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
1371main menu. The <span class=SpellE>Rw</span> will immediately drop to ~2.26%
1372(RF~2.05%). The four twin element fractions will show various values.</p>
1373
1374<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1375 id="Picture_x0020_40" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:336.75pt;
1376 height:375pt;visibility:visible;mso-wrap-style:square'>
1377 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image007.png"
1378  o:title=""/>
1379</v:shape><![endif]--><![if !vml]><img width=449 height=500
1380src="Merohedral%20twin%20refinement%20in%20GSAS_files/image008.gif" v:shapes="Picture_x0020_40"><![endif]></span></p>
1381
1382<p class=MsoNormal>The negative one for the 3<sup>rd</sup> twin fraction is
1383nonphysical and the 1<sup>st</sup> twin fraction is small. It is likely that
1384the true space group is P6<sub>5</sub> and Type 2 <span class=SpellE>merohedrally</span>
1385twinned (twin fractions 2 &amp; 4). We can improve it by refining the atom
1386positions and thermal parameters, but first we need to replace the hydrogen
1387atoms as suggested by the <span class=SpellE>Shelx</span> warning. Select the <b
1388style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1389mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms </span></b>tab
1390for the phase.</p>
1391
1392<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1393 id="Picture_x0020_41" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:525pt;
1394 height:225pt;visibility:visible;mso-wrap-style:square'>
1395 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"
1396  o:title=""/>
1397</v:shape><![endif]--><![if !vml]><img width=700 height=300
1398src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
1399
1400<p class=MsoNormal>If you scroll down the page, you’ll see H-atoms with default
1401<span class=SpellE>Uiso</span> (=0.025) values. To replace them, the old ones
1402need to be deleted; double click the <b style='mso-bidi-font-weight:normal'><span
1403style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1404mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1405style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1406mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>H</span></b>
1407and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1408mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
1409The H-atoms will be highlighted (and plotted in green). Do <b style='mso-bidi-font-weight:
1410normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1411minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Delete atom</span></b> from
1412the menu; the H-atoms will be deleted and the structure will be redrawn. Next
1413double <span class=GramE>click</span> the <b style='mso-bidi-font-weight:normal'><span
1414style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1415mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1416style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1417mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>C</span></b>;
1418all the C-atoms will be selected (and shown in green on the plot). Do <b
1419style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1420mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Insert
1421H atoms</span></b>; a Distance Angle Controls will appear. Occasionally these
1422values may need to be changed but not this time; press <b style='mso-bidi-font-weight:
1423normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1424minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>. The next popup is
1425for the H atoms add controls.</p>
1426
1427<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1428 id="Picture_x0020_42" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:300pt;
1429 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1430 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image011.png"
1431  o:title=""/>
1432</v:shape><![endif]--><![if !vml]><img width=400 height=485
1433src="Merohedral%20twin%20refinement%20in%20GSAS_files/image012.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
1434
1435<p class=MsoNormal>It specifies the expected geometry around each C-atom for H-atom
1436placement. As expected we want 3 H-atoms on the terminal CH<sub>3</sub> groups
1437on the <span class=SpellE>Cp</span>* ring and one for each C-atom for the NC<sub>5</sub>H<sub>5</sub>
1438molecule. Press <b style='mso-bidi-font-weight:normal'><span style='font-family:
1439"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1440minor-latin'>Ok</span></b>; you will see the H-atoms added in turn to the
1441structure and they will be inserted immediately after their respective C-atom.
1442Their positions and thermal parameters are tied to the C-atoms so that after
1443refinement of the structure they can be shifted to the <span class=SpellE>stereochemically</span>
1444best positions. For the refinement, double click the <b style='mso-bidi-font-weight:
1445normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1446minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b> column heading
1447and select <b style='mso-bidi-font-weight:normal'><span style='font-family:
1448"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1449minor-latin'>X</span></b> and <b style='mso-bidi-font-weight:normal'><span
1450style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1451mso-hansi-theme-font:minor-latin'>U</span></b> from the popup; press <b
1452style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1453mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
1454The Atom table will be redrawn with XU in every entry under Refine. Now do <b
1455style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1456mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>
1457from the main GSASII data tree window; the <span class=SpellE>Rw</span> will
1458drop to ~1.92%. If you look at the <b style='mso-bidi-font-weight:normal'><span
1459style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1460mso-hansi-theme-font:minor-latin'>Data</span></b> tab the Twin element
1461fractions are much clearer.</p>
1462
1463<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1464 id="Picture_x0020_43" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:336.75pt;
1465 height:375pt;visibility:visible;mso-wrap-style:square'>
1466 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image013.png"
1467  o:title=""/>
1468</v:shape><![endif]--><![if !vml]><img width=449 height=500
1469src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.gif" v:shapes="Picture_x0020_43"><![endif]></span><span
1470style='mso-spacerun:yes'> </span></p>
1471
1472<p class=MsoNormal>The identity Twin Law has virtually vanished along with the
14732-fold one leaving just the inverse and mirror Twin Laws.</p>
1474
1475<p class=MsoNormal>This means the structure is the inverse in space group P6<sub>5</sub>
1476but still Type 2 <span class=SpellE>merohedrally</span> twinned. </p>
1477
1478<p class=MsoNormal>To test this, we need to both change the space group and
1479invert the structure. First select the <b style='mso-bidi-font-weight:normal'><span
1480style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1481mso-hansi-theme-font:minor-latin'>General</span></b> tab and change the space
1482group to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1483mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P 65</span></b>;
1484you’ll see the Operators popup (press <b style='mso-bidi-font-weight:normal'><span
1485style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1486mso-hansi-theme-font:minor-latin'>Ok</span></b>) and the General tab will be
1487redrawn. Next select the <b style='mso-bidi-font-weight:normal'><span
1488style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1489mso-hansi-theme-font:minor-latin'>Atoms</span></b> tab; do <b style='mso-bidi-font-weight:
1490normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1491minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Update H atoms</span></b> to
1492put them in their best positions.<span style='mso-spacerun:yes'>  </span>Next
1493select all the atoms by double clicking the empty box in upper left corner of
1494the table; all atoms will be highlighted &amp; plotted green. Do <b
1495style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1496mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Transform
1497atoms</span></b>; a popup will appear.</p>
1498
1499<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1500 id="Picture_x0020_44" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:270pt;
1501 height:263.25pt;visibility:visible;mso-wrap-style:square'>
1502 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image015.png"
1503  o:title=""/>
1504</v:shape><![endif]--><![if !vml]><img width=360 height=351
1505src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
1506
1507<p class=MsoNormal>Check the <b style='mso-bidi-font-weight:normal'><span
1508style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1509mso-hansi-theme-font:minor-latin'>Choose inversion</span></b> box and (important)
1510set <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1511mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Choose unit
1512cell</span></b> to <b style='mso-bidi-font-weight:normal'><span
1513style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1514mso-hansi-theme-font:minor-latin'>1 1 1</span></b>; this will put the inverted
1515structure back inside the unit cell. Press <b style='mso-bidi-font-weight:normal'><span
1516style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1517mso-hansi-theme-font:minor-latin'>Ok</span></b>; the table and plot will both
1518be redrawn. Now do <b style='mso-bidi-font-weight:normal'><span
1519style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1520mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>; the <span
1521class=SpellE>Rw</span> will drop back to where it was before and the <b
1522style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1523mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
1524tab will show new Twin fractions.</p>
1525
1526<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1527 id="Picture_x0020_46" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:336.75pt;
1528 height:375pt;visibility:visible;mso-wrap-style:square'>
1529 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image017.png"
1530  o:title=""/>
1531</v:shape><![endif]--><![if !vml]><img width=449 height=500
1532src="Merohedral%20twin%20refinement%20in%20GSAS_files/image018.gif" v:shapes="Picture_x0020_46"><![endif]></span></p>
1533
1534<p class=MsoNormal>Now the identity Twin Law is ~2/3 and the 2-fold Twin Law is
1535the other ~1/3 while the other two are ~zero. You can delete them and repeat
1536the refinement; <span class=SpellE>Rw</span> ~1.7%. This completed the
1537merohedral twin exercises. You can save this project if desired.</p>
1538
1539<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1540
1541</span></span></span></span></span></span></span></span></span></span></span></div>
1542
1543</body>
1544
1545</html>
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