source: Tutorials/MerohedralTwins/Merohedral twin refinement in GSAS.htm @ 3059

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408  <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
409  <w:LsdException Locked="false" Priority="34" QFormat="true"
410   Name="List Paragraph"/>
411  <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
412  <w:LsdException Locked="false" Priority="30" QFormat="true"
413   Name="Intense Quote"/>
414  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
415  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
416  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
417  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
418  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
419  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
420  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
421  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
422  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
423  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
424  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
425  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
426  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
427  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
428  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
429  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
430  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
431  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
432  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
433  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
434  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
435  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
436  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
437  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
438  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
439  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
440  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
441  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
442  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
443  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
444  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
445  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
446  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
447  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
448  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
449  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
450  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
451  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
452  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
453  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
454  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
455  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
456  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
457  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
458  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
459  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
460  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
461  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
462  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
463  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
464  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
465  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
466  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
467  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
468  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
469  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
470  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
471  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
472  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
473  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
474  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
475  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
476  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
477  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
478  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
479  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
480  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
481  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
482  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
483  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
484  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
485  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
486  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
487  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
488  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
489  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
490  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
491  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
492  <w:LsdException Locked="false" Priority="19" QFormat="true"
493   Name="Subtle Emphasis"/>
494  <w:LsdException Locked="false" Priority="21" QFormat="true"
495   Name="Intense Emphasis"/>
496  <w:LsdException Locked="false" Priority="31" QFormat="true"
497   Name="Subtle Reference"/>
498  <w:LsdException Locked="false" Priority="32" QFormat="true"
499   Name="Intense Reference"/>
500  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
501  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
502   UnhideWhenUsed="true" Name="Bibliography"/>
503  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
504   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
505  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
506  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
507  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
508  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
509  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
510  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
511  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
512  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
513  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
514  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
515  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
516  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
517  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
518  <w:LsdException Locked="false" Priority="46"
519   Name="Grid Table 1 Light Accent 1"/>
520  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
521  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
522  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
523  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
524  <w:LsdException Locked="false" Priority="51"
525   Name="Grid Table 6 Colorful Accent 1"/>
526  <w:LsdException Locked="false" Priority="52"
527   Name="Grid Table 7 Colorful Accent 1"/>
528  <w:LsdException Locked="false" Priority="46"
529   Name="Grid Table 1 Light Accent 2"/>
530  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
531  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
532  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
533  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
534  <w:LsdException Locked="false" Priority="51"
535   Name="Grid Table 6 Colorful Accent 2"/>
536  <w:LsdException Locked="false" Priority="52"
537   Name="Grid Table 7 Colorful Accent 2"/>
538  <w:LsdException Locked="false" Priority="46"
539   Name="Grid Table 1 Light Accent 3"/>
540  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
541  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
542  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
543  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
544  <w:LsdException Locked="false" Priority="51"
545   Name="Grid Table 6 Colorful Accent 3"/>
546  <w:LsdException Locked="false" Priority="52"
547   Name="Grid Table 7 Colorful Accent 3"/>
548  <w:LsdException Locked="false" Priority="46"
549   Name="Grid Table 1 Light Accent 4"/>
550  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
551  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
552  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
553  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
554  <w:LsdException Locked="false" Priority="51"
555   Name="Grid Table 6 Colorful Accent 4"/>
556  <w:LsdException Locked="false" Priority="52"
557   Name="Grid Table 7 Colorful Accent 4"/>
558  <w:LsdException Locked="false" Priority="46"
559   Name="Grid Table 1 Light Accent 5"/>
560  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
561  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
562  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
563  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
564  <w:LsdException Locked="false" Priority="51"
565   Name="Grid Table 6 Colorful Accent 5"/>
566  <w:LsdException Locked="false" Priority="52"
567   Name="Grid Table 7 Colorful Accent 5"/>
568  <w:LsdException Locked="false" Priority="46"
569   Name="Grid Table 1 Light Accent 6"/>
570  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
571  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
572  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
573  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
574  <w:LsdException Locked="false" Priority="51"
575   Name="Grid Table 6 Colorful Accent 6"/>
576  <w:LsdException Locked="false" Priority="52"
577   Name="Grid Table 7 Colorful Accent 6"/>
578  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
579  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
580  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
581  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
582  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
583  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
584  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
585  <w:LsdException Locked="false" Priority="46"
586   Name="List Table 1 Light Accent 1"/>
587  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
588  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
589  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
590  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
591  <w:LsdException Locked="false" Priority="51"
592   Name="List Table 6 Colorful Accent 1"/>
593  <w:LsdException Locked="false" Priority="52"
594   Name="List Table 7 Colorful Accent 1"/>
595  <w:LsdException Locked="false" Priority="46"
596   Name="List Table 1 Light Accent 2"/>
597  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
598  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
599  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
600  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
601  <w:LsdException Locked="false" Priority="51"
602   Name="List Table 6 Colorful Accent 2"/>
603  <w:LsdException Locked="false" Priority="52"
604   Name="List Table 7 Colorful Accent 2"/>
605  <w:LsdException Locked="false" Priority="46"
606   Name="List Table 1 Light Accent 3"/>
607  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
608  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
609  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
610  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
611  <w:LsdException Locked="false" Priority="51"
612   Name="List Table 6 Colorful Accent 3"/>
613  <w:LsdException Locked="false" Priority="52"
614   Name="List Table 7 Colorful Accent 3"/>
615  <w:LsdException Locked="false" Priority="46"
616   Name="List Table 1 Light Accent 4"/>
617  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
618  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
619  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
620  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
621  <w:LsdException Locked="false" Priority="51"
622   Name="List Table 6 Colorful Accent 4"/>
623  <w:LsdException Locked="false" Priority="52"
624   Name="List Table 7 Colorful Accent 4"/>
625  <w:LsdException Locked="false" Priority="46"
626   Name="List Table 1 Light Accent 5"/>
627  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
628  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
629  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
630  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
631  <w:LsdException Locked="false" Priority="51"
632   Name="List Table 6 Colorful Accent 5"/>
633  <w:LsdException Locked="false" Priority="52"
634   Name="List Table 7 Colorful Accent 5"/>
635  <w:LsdException Locked="false" Priority="46"
636   Name="List Table 1 Light Accent 6"/>
637  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
638  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
639  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
640  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
641  <w:LsdException Locked="false" Priority="51"
642   Name="List Table 6 Colorful Accent 6"/>
643  <w:LsdException Locked="false" Priority="52"
644   Name="List Table 7 Colorful Accent 6"/>
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804
805<body lang=EN-US style='tab-interval:.5in'>
806
807<div class=WordSection1>
808
809<h1><span style='mso-fareast-font-family:"Times New Roman"'>Merohedral twin
810refinement in GSAS-II<o:p></o:p></span></h1>
811
812<h2><span style='mso-fareast-font-family:"Times New Roman"'>Introduction: <o:p></o:p></span></h2>
813
814<p class=MsoNormal>In these exercises you will use GSAS-II to refine the
815structure of a few single crystal structures where there is merohedral
816twinning. There is a general discussion of twinning in International Tables for
817Crystallography (2006), Vol. C, Chapter 1.3, pp 10-14. <span class=SpellE>Merohedral</span>
818twinning occurs when the twin operation (2, m <span class=GramE>or </span><span
819style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
820    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
821   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
822   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
823   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:bar></m:oMath><![endif]--><![if !msEquation]><span
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853belongs to the point group of the vector lattice but not of the crystal
854structure. Of the 230 space groups only 159 of them may have merohedral
855twining. </p>
856
857<p class=MsoNormal><!--[if gte vml 1]><v:shape id="Picture_x0020_2" o:spid="_x0000_s1026"
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870hspace=12 v:shapes="Picture_x0020_2"><![endif]>&nbsp;</p>
871
872<p class=MsoNormal>&nbsp;</p>
873
874<p class=MsoNormal>The possible merohedral twin operators are shown in the
875above table (extracted from p 13 of Intl. Tables for <span class=SpellE>Cryst</span>.,
876Vol. C). Merohedral twins are of two types: Type 1 are inversion twins and have
877only 2 components and Type 2 are where the twin operation does not belong to
878the Laue class of the crystal (only for space groups marked with * in above
879table) and multiple twin components may be found. For Type 1 the twin lattice
880exactly superimpose so that if Friedel’s law is obeyed the twin <span
881class=GramE>components</span> have the same value of |F|<sup>2</sup> (the
882twinning is undetectable!). However, in the presence of resonant scattering the
883|F|<sup>2</sup> components differ and if the twin components have unequal
884volumes then the Bragg intensities will differ from that obtained from the <span
885class=SpellE>untwinned</span> structure and then the twinning effects must be
886considered for refinement.&nbsp; Obviously all Type 1 crystals are <span
887class=SpellE>noncentrosymmetric</span>. For Type 2 the space group may be
888centrosymmetric from within a choice of just 55 possible space groups. However,
889the diffraction pattern may display apparent higher symmetry especially if the
890twin components are all equally present in the crystal.&nbsp; Note that menu
891entries and user input are shown in bold face below as <b><span
892style='font-family:"Calibri",sans-serif'>Help/About GSAS-II</span></b>, which
893lists first the name of the menu (here <b><span style='font-family:"Calibri",sans-serif'>Help</span></b>)
894and second the name of the entry in the menu (here <b><span style='font-family:
895"Calibri",sans-serif'>About GSAS-II</span></b>). If you have not done so already,
896start GSAS-II.</p>
897
898<h2 style='margin-bottom:.25in'><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></h2>
899
900<p class=MsoNormal style='margin-bottom:8.0pt;line-height:105%'>.<br clear=all
901style='mso-special-character:line-break;page-break-before:always'>
902</p>
903
904<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 1. A Type 1
905inversion twin – C<sub>8</sub>H<sub>25</sub>Al<sub>0.84</sub>Ga<sub>1.16</sub>N<sub>3</sub>
906<o:p></o:p></span></h2>
907
908<p class=MsoNormal>This example was taken from Luo, et al., Dalton Trans.
9094491(2006). The structure is given in the file <span class=SpellE><b><span
910style='font-family:"Calibri",sans-serif'>MerohedralTwins</span></b></span><b><span
911style='font-family:"Calibri",sans-serif'>/data/1b.cif</span></b> and the data
912are in <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>MerohedralTwins</span></b></span><b><span
913style='font-family:"Calibri",sans-serif'>/data/1b.fcf</span></b>. This example
914is <span class=SpellE>noncentrosymmetric</span> and the data was collected with
915radiation (<span class=SpellE>MoK</span>&#945;) that gives significant resonant
916scattering from the Ga atoms. </p>
917
918<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
919refinement<o:p></o:p></span></h2>
920
921<p class=MsoNormal>To begin do <b><span style='font-family:"Calibri",sans-serif'>Import/Phase/from
922CIF file</span></b> from the main GSAS-II data tree menu. A file selection
923window will appear; find the above <span class=SpellE>cif</span> file (…<b><span
924style='font-family:"Calibri",sans-serif'>1b.cif</span></b>) and select it. A
925popup window will appear. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
926a new popup will appear; Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>,
927and you will see the General page for this phase</p>
928
929<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
930 id="Picture_x0020_1" o:spid="_x0000_i1052" type="#_x0000_t75" style='width:468pt;
931 height:373.5pt;visibility:visible;mso-wrap-style:square'>
932 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image005.png"
933  o:title=""/>
934</v:shape><![endif]--><![if !vml]><img width=624 height=498
935src="Merohedral%20twin%20refinement%20in%20GSAS_files/image002.gif" v:shapes="Picture_x0020_1"><![endif]></span></p>
936
937<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
938Factor/from CIF file</span></b> (that is the format of <span class=GramE>a</span>
939“<span class=SpellE>fcf</span>” file); a file selection dialog box will appear
940with the previously selected directory chosen. Select <b><span
941style='font-family:"Calibri",sans-serif'>1b.fcf</span></b>; a popup window will
942appear</p>
943
944<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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950src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.gif" v:shapes="Picture_x0020_3"><![endif]></span></p>
951
952<p class=MsoNormal>Select <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Yes</span></b></span>;
953a new popup window allowing you to change the name</p>
954
955<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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960</v:shape><![endif]--><![if !vml]><img width=346 height=156
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962
963<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
964after a pause and some activity a popup window will appear</p>
965
966<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
967 id="Picture_x0020_5" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:233.25pt;
968 height:228.75pt;visibility:visible;mso-wrap-style:square'>
969 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image023.png"
970  o:title=""/>
971</v:shape><![endif]--><![if !vml]><img width=311 height=305
972src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.gif" v:shapes="Picture_x0020_5"><![endif]></span></p>
973
974<p class=MsoNormal>This makes the connection between the data set and the
975previously imported phase. Select the entry and press <b><span
976style='font-family:"Calibri",sans-serif'>OK</span></b>. You now have loaded all
977that is needed for the first example. The structure had previously been solved
978and refined with <span class=SpellE>Shelx</span> so you need not trouble about
979those steps. You can try to solve the structure in GSAS-II via charge flipping
980but this is not part of this exercise; we will only explore the twin analysis
981features of GSAS-II.</p>
982
983<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
984of twinned structure<o:p></o:p></span></h2>
985
986<p class=MsoNormal>Before beginning the refinement, it usually the practice to
987eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
988&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
989style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
990GSAS-II data tree.</p>
991
992<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
993 id="Picture_x0020_6" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:468pt;
994 height:209.25pt;visibility:visible;mso-wrap-style:square'>
995 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"
996  o:title=""/>
997</v:shape><![endif]--><![if !vml]><img width=624 height=279
998src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.gif" v:shapes="Picture_x0020_6"><![endif]></span></p>
999
1000<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1001<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1002"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1003style='font-family:"Calibri",sans-serif'>Phases/C8 H25 Al0.84 Ga1.16</span></b>
1004entry in the GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1005tab</p>
1006
1007<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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1011  o:title=""/>
1012</v:shape><![endif]--><![if !vml]><img width=624 height=349
1013src="Merohedral%20twin%20refinement%20in%20GSAS_files/image018.gif" v:shapes="Picture_x0020_23"><![endif]></span></p>
1014
1015<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1016factor</span></b> is selected for refinement by default. If you refine it, you
1017will get an <span class=SpellE>R<sub>w</sub></span>= 2.85% which isn’t too bad.
1018However, you are unsure what the hand of the molecule is in this structure and
1019the experiment with <span class=SpellE>MoKa</span> radiation should give
1020sufficient resonant scattering to determine this. The <b><span
1021style='font-family:"Calibri",sans-serif'>Flack parameter</span></b> gives you a
1022way to evaluate which hand the molecule is. If upon refinement the value is ~0
1023then you have correctly described the hand. Otherwise if the value is ~1 then
1024the opposite hand is the correct and the structure needs to be inverted. So
1025let’s test this; select the <b><span style='font-family:"Calibri",sans-serif'>Flack
1026parameter</span></b> for refinement and do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>
1027from the main GSAS-II data tree menu. You’ll be asked to save the project; pick
1028a directory &amp; a name – I chose <b style='mso-bidi-font-weight:normal'><span
1029style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1030mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>1b</span></b>.
1031The structure will quickly refine to give <span class=SpellE>R<sub>w</sub></span>=2.155%
1032which is a considerable improvement on Scale factor alone. The Flack parameter
1033is now 0.433, meaning that both hands somehow exist in the structure. This can
1034happen if the crystal is <span class=SpellE>merohedrally</span> inversion twinned.</p>
1035
1036<p class=MsoNormal>To introduce this twin, press the <b><span style='font-family:
1037"Calibri",sans-serif'>Add Twin Law</span></b> box; the window will be redrawn.</p>
1038
1039<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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1042 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image030.png"
1043  o:title=""/>
1044</v:shape><![endif]--><![if !vml]><img width=624 height=446
1045src="Merohedral%20twin%20refinement%20in%20GSAS_files/image019.gif" v:shapes="_x0000_i1046"><![endif]></span></p>
1046
1047<p class=MsoNormal>Notice that two Twin Law matrices have been generated; one is
1048the identity for the reference structure and the other by default is the
1049merohedral inverse. If some other twin law is desired, then the matrix elements
1050need to be changed. Moreover, the Flack parameter has vanished as it is no
1051longer needed. Press the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1052button for the <b><span style='font-family:"Calibri",sans-serif'>Twin Law
1053fraction</span></b> and rerun the refinement. The Data window now has.</p>
1054
1055<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1056 id="Picture_x0020_42" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:468pt;
1057 height:337.5pt;visibility:visible;mso-wrap-style:square'>
1058 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image032.png"
1059  o:title=""/>
1060</v:shape><![endif]--><![if !vml]><img width=624 height=450
1061src="Merohedral%20twin%20refinement%20in%20GSAS_files/image062.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
1062
1063<p class=MsoNormal>The refinement quickly converged to where it was before but
1064the twin fractions are now ~56/44 consistent with the ~45% Flack parameter
1065obtained earlier. It is likely that the crystal is macroscopically twinned thus
1066the twin fractions are not exactly 50/50. This completes this example; you can
1067save your project if you want to explore other features of GSAS-II with it.</p>
1068
1069<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 2. A Type 2
1070only merohedral twin – <br>
1071[Al(OC<sub>6</sub>H<sub>4</sub>(C<sub>3</sub>H<sub>7</sub>)<sub>2</sub>)]<sup>-</sup>
1072[NC<sub>7</sub>H<sub>8</sub>]<sup>+</sup><o:p></o:p></span></h2>
1073
1074<p class=MsoNormal>In this case the data collection Laue statistics (very
1075nearly <span style='position:relative;top:3pt'><span style='mso-no-proof:yes'>-3</span>m)
1076and systematic extinctions indicated that the space group was either one of the
1077<span class=SpellE>enantiomorphic</span> pair P3<sub>1</sub>21 or P3<sub>2</sub>21
1078or possibly one of the pair P3<sub>1</sub> or P3<sub>2</sub>. If the true
1079structure was of the lower symmetry P3<sub>1</sub> or P3<sub>2</sub> then there
1080must be Type 2 merohedral twinning to make the diffraction pattern appear to
1081have higher symmetry (<span style='position:relative;top:3pt'><span
1082style='mso-no-proof:yes'>-3</span>m instead of <span style='position:relative;
1083top:3pt'><span style='mso-no-proof:yes'>-3</span>); this exercise will explore
1084this possibility. The data were collected with <span class=SpellE>MoK</span><span
1085style='font-family:Symbol'>a</span> radiation so there is little resonant
1086scattering and thus the choice of hand is indeterminate.&nbsp; Solving the
1087structure in P3<sub>2</sub>21 yielded a poorly fitting structure with disorder
1088particularly in the cation. Resolving the structure in P3<sub>2</sub> gave a
1089structure with no disorder and a better fit to the data (but still not great).
1090As this work was done with <span class=SpellE>Shelx</span> this result is in
1091the form of a <span class=SpellE>Shelx</span> input file (2b.ins – thanks to V.
1092Young for this example). If you have not done so already, start GSAS-II and
1093start with a fresh project.</p>
1094
1095<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1096refinement<o:p></o:p></span></h2>
1097
1098<p class=MsoNormal>To begin we need to import the phase information from the <span
1099class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1100style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1101ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1102and a res file is the output result after a <span class=SpellE>Shelx</span>
1103run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>2b.ins</span></b>
1104from the file selection window; a popup window will ask if this file is the one
1105you want.</p>
1106
1107<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1108 id="Picture_x0020_43" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:314.25pt;
1109 height:159pt;visibility:visible;mso-wrap-style:square'>
1110 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image034.png"
1111  o:title=""/>
1112</v:shape><![endif]--><![if !vml]><img width=419 height=212
1113src="Merohedral%20twin%20refinement%20in%20GSAS_files/image063.gif" v:shapes="Picture_x0020_43"><![endif]></span></p>
1114
1115<p class=MsoNormal>Press <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Yes</span></b></span>;
1116a Read Warning will appear.</p>
1117
1118<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1119 id="Picture_x0020_44" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:378.75pt;
1120 height:177pt;visibility:visible;mso-wrap-style:square'>
1121 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image036.png"
1122  o:title=""/>
1123</v:shape><![endif]--><![if !vml]><img width=505 height=236
1124src="Merohedral%20twin%20refinement%20in%20GSAS_files/image064.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
1125
1126<p class=MsoNormal>There are two significant warnings concerning <span
1127class=SpellE>Shelx</span> files. One is that the file never contains the space
1128group symbol (<span class=SpellE>Shelx</span> requires just the operators), so
1129GSAS-II sets the space group to P 1 by default and you will need to change it
1130to P3<sub>2</sub> immediately (next window). The other warning is that hydrogen
1131atoms were found; these usually cannot be refined unconstrained with x-ray
1132data. The warning recommends replacing them with <span class=SpellE>stereochemically</span>
1133determined ones (this is illustrated in the 3<sup>rd</sup> Exercise of this
1134tutorial) and the last line of the Warning tells you what to do if they are to
1135be refined. Here we will only refine twin laws &amp; scale factors so this is
1136unnecessary. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1137you get the opportunity to change the Phase name (I know it is very long but
1138that doesn’t matter here). Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1139the General tab for this phase is shown. </p>
1140
1141<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1142 id="Picture_x0020_45" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:468pt;
1143 height:206.25pt;visibility:visible;mso-wrap-style:square'>
1144 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image038.png"
1145  o:title=""/>
1146</v:shape><![endif]--><![if !vml]><img width=624 height=275
1147src="Merohedral%20twin%20refinement%20in%20GSAS_files/image065.gif" v:shapes="Picture_x0020_45"><![endif]></span></p>
1148
1149<p class=MsoNormal>Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
115032</span></b>; the window will be redrawn after a popup showing the operations.
1151You can see the structure by selecting <b><span style='font-family:"Calibri",sans-serif'>Draw
1152Atoms</span></b>.</p>
1153
1154<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1155 id="Picture_x0020_47" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:468pt;
1156 height:405pt;visibility:visible;mso-wrap-style:square'>
1157 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image040.png"
1158  o:title=""/>
1159</v:shape><![endif]--><![if !vml]><img width=624 height=540
1160src="Merohedral%20twin%20refinement%20in%20GSAS_files/image066.gif" v:shapes="Picture_x0020_47"><![endif]></span></p>
1161
1162<p class=MsoNormal>&nbsp;</p>
1163
1164<p class=MsoNormal>The large anion containing the Al atom is to the left and
1165the smaller cation to the right.</p>
1166
1167<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1168Factor/from <span class=SpellE>Shelx</span> HKLF 4 F<sup>2</sup> file</span></b>
1169and select <b><span style='font-family:"Calibri",sans-serif'>2b.hkl</span></b>
1170from the file dialog box; a popup will appear showing a few lines.</p>
1171
1172<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1173 id="Picture_x0020_48" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:274.5pt;
1174 height:186pt;visibility:visible;mso-wrap-style:square'>
1175 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image042.png"
1176  o:title=""/>
1177</v:shape><![endif]--><![if !vml]><img width=366 height=248
1178src="Merohedral%20twin%20refinement%20in%20GSAS_files/image067.gif" v:shapes="Picture_x0020_48"><![endif]></span></p>
1179
1180<p class=MsoNormal>This is the right file; a <span class=SpellE>Shelx</span>
1181HKLF 4 file consists of records with just <span class=SpellE>h<span
1182class=GramE>,k,l</span></span>, F<sup>2</sup> and <span style='font-family:
1183Symbol'>s</span>(F<sup>2</sup>). Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1184and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b> on the next
1185one (we’ll keep the name as it is). Choose the phase with the long name on the
1186next popup and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1187select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
1188"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1189minor-latin;mso-bidi-theme-font:minor-latin'>Structure factors</span></b> tab, a
11902D display of the hk0 zone is plotted.</p>
1191
1192<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1193 id="Picture_x0020_49" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:468pt;
1194 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1195 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image044.png"
1196  o:title=""/>
1197</v:shape><![endif]--><![if !vml]><img width=624 height=535
1198src="Merohedral%20twin%20refinement%20in%20GSAS_files/image068.gif" v:shapes="Picture_x0020_49"><![endif]></span></p>
1199
1200<p class=MsoNormal>The size of the green circles are proportional to <span
1201class=SpellE><span class=GramE>Fo</span></span> (after a structure factor
1202calculation blue rings will appear for Fc).</p>
1203
1204<p class=MsoNormal>You now have loaded all that is needed for the second
1205example. The structure had previously been solved and refined with <span
1206class=SpellE>Shelx</span> so you need not trouble about those steps. You can
1207try to solve the structure in GSAS-II via charge flipping but this is not part
1208of this exercise (it isn’t easy because of the twinning); we will only explore
1209the twin analysis features of GSAS-II.</p>
1210
1211<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1212of twinned structure<o:p></o:p></span></h2>
1213
1214<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1215eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1216&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1217style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1218GSAS-II data tree.</p>
1219
1220<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1221 id="Picture_x0020_50" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:468pt;
1222 height:215.25pt;visibility:visible;mso-wrap-style:square'>
1223 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image046.png"
1224  o:title=""/>
1225</v:shape><![endif]--><![if !vml]><img width=624 height=287
1226src="Merohedral%20twin%20refinement%20in%20GSAS_files/image069.gif" v:shapes="Picture_x0020_50"><![endif]></span></p>
1227
1228<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1229<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1230"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1231style='font-family:"Calibri",sans-serif'>Phases/MEROHEDRAL…</span></b> entry in
1232the GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1233tab.</p>
1234
1235<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=444
1236id="_x0000_i1037"
1237src="Merohedral%20twin%20refinement%20in%20GSAS_files/image030.png"></span></p>
1238
1239<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1240factor</span></b> is selected for refinement by default. If you refine it, you
1241will get an <span class=SpellE>R<sub>w</sub></span>~ 25% which is terrible. If
1242you try refining atom positions &amp; thermal parameters you could possibly
1243lower it to ~15% (still terrible) and the resulting structure would not be very
1244satisfactory. However, we have suspected from the equivalence of <span
1245style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1246    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1247   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1248   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1249   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:e></m:bar></m:oMath><![endif]--><![if !msEquation]><span
1250style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1251"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1252top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1253EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1254 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1255 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1256  o:title="" chromakey="white"/>
1257</v:shape><![endif]--><![if !vml]><img width=9 height=21
1258src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;and
1259<span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1260    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1261   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1262   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1263   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:e></m:bar></m:oMath><![endif]--><![if !msEquation]><span
1264style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1265"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1266top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1267EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1268 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1269 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1270  o:title="" chromakey="white"/>
1271</v:shape><![endif]--><![if !vml]><img width=9 height=21
1272src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>m1
1273Laue data symmetries that there is twinning so don’t bother trying to make it
1274better by refining the structure. To determine the possible twin law we refer
1275to Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
1276that indeed Laue <span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1277    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1278   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1279   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1280   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:e></m:bar></m:oMath><![endif]--><![if !msEquation]><span
1281style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1282"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1283top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1284EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1285 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1286 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1287  o:title="" chromakey="white"/>
1288</v:shape><![endif]--><![if !vml]><img width=9 height=21
1289src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>m1
1290as P3<sub>2</sub>21 can be simulated by twinned Laue <span style='position:
1291relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1292    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1293   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1294   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1295   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:e></m:bar></m:oMath><![endif]--><![if !msEquation]><span
1296style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1297"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1298top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1299EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1300 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1301 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1302  o:title="" chromakey="white"/>
1303</v:shape><![endif]--><![if !vml]><img width=9 height=21
1304src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;crystals
1305in P3<sub>2</sub>; the possible operator is shown in Table 1.3.4.1 (reproduced
1306above) as either a mirror or a 2-fold. The detailed symbolism in the table
1307(‘m.., ..2/.2.’) indicates (perhaps obscurely) the operator specifics. See P3m1
1308and P3<sub>2</sub>21 space groups in International Tables for Crystallography,
1309Vol A for the operations m as <span style='position:relative;top:3pt'><span
1310style='mso-no-proof:yes'>-y-xz</span>&nbsp;or 2 as <span style='position:relative;
1311top:3pt'><span style='mso-no-proof:yes'>yx-z</span>; we will use the 2-fold
1312since the m inverts the structure which we are not sensitive to in this
1313experiment.</p>
1314
1315<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Add
1316Twin Law</span></b>; the Data tab will be redrawn with the inversion for the
1317second law. Replace this with the 2-fold (<b><span style='font-family:"Calibri",sans-serif'>0
13181 0, 1 0 0, 0 0 -1</span></b>) and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1319box. It should look like.</p>
1320
1321<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1322 id="Picture_x0020_51" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt;
1323 height:352.5pt;visibility:visible;mso-wrap-style:square'>
1324 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image050.png"
1325  o:title=""/>
1326</v:shape><![endif]--><![if !vml]><img width=624 height=470
1327src="Merohedral%20twin%20refinement%20in%20GSAS_files/image071.gif" v:shapes="Picture_x0020_51"><![endif]></span></p>
1328
1329<p class=MsoNormal>Now do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>;
1330you’ll have to save the project. Pick a directory &amp; file name - I used <b
1331style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1332mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1333minor-latin'>2b</span></b>. <span class=GramE>there</span> will be an immediate
1334improvement in the fit to <span class=SpellE>Rw</span>=5.05% and the twin
1335fractions will be ~50/50. Clearly this crystal is Type 2 <span class=SpellE>merohedrally</span>
1336twinned; we cannot determine if there is any Type 1 twinning because we lack
1337sufficient resonant scattering to see it. This ends the second example; you can
1338save the project file.</p>
1339
1340<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 3. A Type 1
1341&amp; 2 <span class=SpellE>merohedral</span> twin – <span class=SpellE>Cp</span>*Cs(NC<sub>5</sub>H<sub>5</sub>)<o:p></o:p></span></h2>
1342
1343<p class=MsoNormal>This <span class=SpellE>ecample</span> is very similar to
1344the previous one except that the Cs atom has significant resonant scattering
1345for <span class=SpellE>MoKa</span> radiation allowing detection of Type 1 <span
1346class=SpellE>merohedry</span>. The data set has apparent 6/m Laue symmetry but
1347may 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.
1348The combination of Type 1 and Type 2 twins requires 4 twin laws to be explored
1349for this <span class=SpellE>pentamethylcyclopentadienyl</span> Cs complex. As
1350this work was done with <span class=SpellE>Shelx</span> this result is in the
1351form of a <span class=SpellE>Shelx</span> input file (3a.ins – thanks to V.
1352Young for this example). If you have not done so already, start GSAS-II and
1353start with a fresh project.</p>
1354
1355<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1356refinement<o:p></o:p></span></h2>
1357
1358<p class=MsoNormal>To begin we need to import the phase information from the <span
1359class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1360style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1361ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1362and a res file is the output result after a <span class=SpellE>Shelx</span>
1363run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>3a.ins</span></b>
1364from the file selection window; a popup window will ask if this file is the one
1365you want.</p>
1366
1367<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1368 id="Picture_x0020_52" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:274.5pt;
1369 height:174.75pt;visibility:visible;mso-wrap-style:square'>
1370 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image072.png"
1371  o:title=""/>
1372</v:shape><![endif]--><![if !vml]><img width=366 height=233
1373src="Merohedral%20twin%20refinement%20in%20GSAS_files/image073.gif" v:shapes="Picture_x0020_52"><![endif]></span></p>
1374
1375<p class=MsoNormal>It is; press the <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1376button. You will then see the SHELX Read Warning; you will have to change the
1377space group to P6<sub>1</sub> in a bit. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1378and leave the name alone (press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1379again). Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
138061</span></b>; the General tab will be redrawn after showing you the operators.</p>
1381
1382<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1383 id="Picture_x0020_53" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:468pt;
1384 height:234.75pt;visibility:visible;mso-wrap-style:square'>
1385 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image074.png"
1386  o:title=""/>
1387</v:shape><![endif]--><![if !vml]><img width=624 height=313
1388src="Merohedral%20twin%20refinement%20in%20GSAS_files/image075.gif" v:shapes="Picture_x0020_53"><![endif]></span></p>
1389
1390<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1391Factor/from CIF file</span></b> and select <b><span style='font-family:"Calibri",sans-serif'>3a.fcf</span></b>
1392from the file dialog. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1393in the next popup and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1394on the name change popup. Select the file name in the Add to phases popup and
1395press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; the hk0
1396zone of the structure factors will be displayed. Note that this plot shows both
1397green (<span class=SpellE>Fo</span>) and blue (Fc) circles with a small solid
1398red or green circle in the centers. These are for the +/- <span
1399style='font-family:Symbol'>D</span>F values. Fc is here because this <span
1400class=SpellE>fcf</span> file was obtained after refinement via <span
1401class=SpellE>Shelx</span>.</p>
1402
1403<p class=MsoNormal>You now have loaded all that is needed for the third example.
1404The structure had previously been solved and refined with <span class=SpellE>Shelx</span>
1405so you need not trouble about those steps. You can try to solve the structure
1406in GSAS-II via charge flipping but this is not part of this exercise (it isn’t
1407easy because of the twinning; charge flipping will readily give the Cs position
1408&amp; most of the rest. It can be completed via difference Fourier techniques);
1409we will only explore the twin analysis features of GSAS-II.</p>
1410
1411<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1412of twinned structure<o:p></o:p></span></h2>
1413
1414<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1415eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1416&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1417style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1418GSAS-II data tree.</p>
1419
1420<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1421 id="Picture_x0020_54" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt;
1422 height:205.5pt;visibility:visible;mso-wrap-style:square'>
1423 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image076.png"
1424  o:title=""/>
1425</v:shape><![endif]--><![if !vml]><img width=624 height=274
1426src="Merohedral%20twin%20refinement%20in%20GSAS_files/image077.gif" v:shapes="Picture_x0020_54"><![endif]></span></p>
1427
1428<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1429<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1430"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1431style='font-family:"Calibri",sans-serif'>Phases/Cs…</span></b> entry in the
1432GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1433tab.</p>
1434
1435<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1436 id="Picture_x0020_55" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:468pt;
1437 height:303.75pt;visibility:visible;mso-wrap-style:square'>
1438 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image078.png"
1439  o:title=""/>
1440</v:shape><![endif]--><![if !vml]><img width=624 height=405
1441src="Merohedral%20twin%20refinement%20in%20GSAS_files/image079.gif" v:shapes="Picture_x0020_55"><![endif]></span></p>
1442
1443<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1444factor</span></b> is selected for refinement by default. If you refine it, you
1445will get an <span class=SpellE>R<sub>w</sub></span>~ 17% which is terrible. It
1446doesn’t change much if you add the Flack parameter (~0.36). If you try refining
1447atom positions &amp; thermal parameters you could possibly lower it but the
1448resulting structure would not be very satisfactory. However, we have suspected
1449from the equivalence of 6/m and 6/mmm Laue data symmetries that there is
1450twinning so don’t bother trying to make it better by refining the structure. To
1451determine the possible twin laws we again refer to Table 1.3.4.2 of the
1452International Tables for Crystallography Vol C. and see that indeed Laue 6/mmm
1453as P6<sub>1</sub>22 can be simulated by twinned Laue 6/m crystals in P6<sub>1</sub>;
1454the possible operator is shown in Table 1.3.4.1 (reproduced above) as either a
1455mirror or a 2-fold. The detailed symbolism in the table (‘m.., ..2/.2.’)
1456indicates (perhaps obscurely) the operator specifics; they are m as <span
1457style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:acc><m:accPr><m:chr
1458    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1459   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1460   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1461   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
1462    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1463   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1464   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1465   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
1466 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
1467style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1468"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1469top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1470EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1471 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1472 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image052.png"
1473  o:title="" chromakey="white"/>
1474</v:shape><![endif]--><![if !vml]><img width=26 height=19
1475src="Merohedral%20twin%20refinement%20in%20GSAS_files/image080.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;or
14762 as <!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span
1477 style='font-family:"Cambria Math",serif'><span style='position:relative;
1478 top:3pt'><m:r>y</m:r><m:r>x</span></m:r></span></i><m:acc><m:accPr><m:chr
1479    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1480   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1481   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1482   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
1483style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1484"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1485top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1486EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1487 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1488 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image054.png"
1489  o:title="" chromakey="white"/>
1490</v:shape><![endif]--><![if !vml]><img width=26 height=19
1491src="Merohedral%20twin%20refinement%20in%20GSAS_files/image081.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1492style='font-family:"Cambria Math",serif'>; we will use the 2-fold, m and
1493inversion operators to fully test for presence of the 4 possible twin laws.
1494Press the </span><b><span style='font-family:"Calibri",sans-serif'>Add Twin Law</span></b><span
1495style='font-family:"Cambria Math",serif'> button </span><b><span
1496style='font-family:"Calibri",sans-serif'>3 times</span></b><span
1497style='font-family:"Cambria Math",serif'>; each time the window will be
1498redrawn. When done you should see.<o:p></o:p></span></p>
1499
1500<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1501 id="Picture_x0020_56" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
1502 height:405.75pt;visibility:visible;mso-wrap-style:square'>
1503 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image082.png"
1504  o:title=""/>
1505</v:shape><![endif]--><![if !vml]><img width=624 height=541
1506src="Merohedral%20twin%20refinement%20in%20GSAS_files/image083.gif" v:shapes="Picture_x0020_56"><![endif]></span>&nbsp;</p>
1507
1508<p class=MsoNormal>For the third and fourth matrix enter <b><span
1509style='font-family:"Calibri",sans-serif'>0 1 0 1 0 0 0 0 -1</span></b> and <b><span
1510style='font-family:"Calibri",sans-serif'>0 -1 0 -1 0 0 0 0</span></b> <b><span
1511style='font-family:"Calibri",sans-serif'>1</span></b> as the 2-fold and mirror
1512operators (the 2<sup>nd</sup> matrix is the inversion by default). Select the <b><span
1513style='font-family:"Calibri",sans-serif'>Refine</span></b> button and do <b><span
1514style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
1515main menu; again you’ll have to save the project file – I called it 3a. The <span
1516class=SpellE>Rw</span> will immediately drop to ~2.26% (RF~2.05%). The four
1517twin element fractions will show various values</p>
1518
1519<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1520 id="Picture_x0020_57" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;
1521 height:405.75pt;visibility:visible;mso-wrap-style:square'>
1522 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image084.png"
1523  o:title=""/>
1524</v:shape><![endif]--><![if !vml]><img width=624 height=541
1525src="Merohedral%20twin%20refinement%20in%20GSAS_files/image085.gif" v:shapes="Picture_x0020_57"><![endif]></span></p>
1526
1527<p class=MsoNormal>The negative one for the 3<sup>rd</sup> twin fraction is nonphysical
1528and the 1<sup>st</sup> twin fraction is small. It is likely that the true space
1529group is P6<sub>5</sub> and Type 2 <span class=SpellE>merohedrally</span>
1530twinned (twin fractions 2 &amp; 4). We can improve it by refining the atom
1531positions and thermal parameters, but first we need to replace the hydrogen
1532atoms as suggested by the <span class=SpellE>Shelx</span> warning. Select the <b
1533style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1534mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms </span></b>tab
1535for the phase.</p>
1536
1537<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1538 id="Picture_x0020_41" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:525pt;
1539 height:225pt;visibility:visible;mso-wrap-style:square'>
1540 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"
1541  o:title=""/>
1542</v:shape><![endif]--><![if !vml]><img width=700 height=300
1543src="Merohedral%20twin%20refinement%20in%20GSAS_files/image086.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
1544
1545<p class=MsoNormal>If you scroll down the page, you’ll see H-atoms with default
1546<span class=SpellE>Uiso</span> (=0.025) values. To replace them, the old ones
1547need to be deleted; double click the <b style='mso-bidi-font-weight:normal'><span
1548style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1549mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1550style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1551mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>H</span></b>
1552and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1553mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
1554The H-atoms will be highlighted (and plotted in green). Do <b style='mso-bidi-font-weight:
1555normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1556minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/On selected atoms…/Delete
1557atom</span></b> from the menu; the H-atoms will be deleted and the structure
1558will be redrawn. Next double click the <b style='mso-bidi-font-weight:normal'><span
1559style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1560mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1561style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1562mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>C</span></b>;
1563all the C-atoms will be selected (and shown in green on the plot). Do <b
1564style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1565mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/On
1566selected atoms…/<span class=SpellE>Calc</span> H atoms</span></b>; a Distance
1567Angle Controls will appear. Occasionally these values may need to be changed
1568but not this time; press <b style='mso-bidi-font-weight:normal'><span
1569style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1570mso-hansi-theme-font:minor-latin'>Ok</span></b>. The next popup is for the H
1571atoms add controls.</p>
1572
1573<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1574 id="Picture_x0020_58" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:300pt;
1575 height:187.5pt;visibility:visible;mso-wrap-style:square'>
1576 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image087.png"
1577  o:title=""/>
1578</v:shape><![endif]--><![if !vml]><img width=400 height=250
1579src="Merohedral%20twin%20refinement%20in%20GSAS_files/image088.gif" v:shapes="Picture_x0020_58"><![endif]></span></p>
1580
1581<p class=MsoNormal>It specifies the expected geometry around each C-atom for
1582H-atom placement. As expected we want 3 H-atoms on the terminal CH<sub>3</sub>
1583groups on the <span class=SpellE>Cp</span>* ring and one for each C-atom for
1584the NC<sub>5</sub>H<sub>5</sub> molecule. Press <b style='mso-bidi-font-weight:
1585normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1586minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; you will see the
1587H-atoms added in turn to the structure and they will be inserted immediately
1588after their respective C-atom. Their positions and thermal parameters are tied
1589to the C-atoms so that after refinement of the structure they can be shifted to
1590the <span class=SpellE>stereochemically</span> best positions. For the
1591refinement, double click the <b style='mso-bidi-font-weight:normal'><span
1592style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1593mso-hansi-theme-font:minor-latin'>Refine</span></b> column heading and select <b
1594style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1595mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>X</span></b>
1596and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1597mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>U</span></b>
1598from the popup; press <b style='mso-bidi-font-weight:normal'><span
1599style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1600mso-hansi-theme-font:minor-latin'>OK</span></b>. The Atom table will be redrawn
1601with XU in every entry under Refine. Now do <b style='mso-bidi-font-weight:
1602normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1603minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> (2-3
1604times until convergence<span class=GramE>)from</span> the main GSASII data tree
1605window; the <span class=SpellE>Rw</span> will drop to ~1.80%. If you look at
1606the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1607mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
1608tab the Twin element fractions are much clearer.</p>
1609
1610<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1611 id="Picture_x0020_59" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;
1612 height:342.75pt;visibility:visible;mso-wrap-style:square'>
1613 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image089.png"
1614  o:title=""/>
1615</v:shape><![endif]--><![if !vml]><img width=624 height=457
1616src="Merohedral%20twin%20refinement%20in%20GSAS_files/image090.gif" v:shapes="Picture_x0020_59"><![endif]></span><span
1617style='mso-spacerun:yes'> </span></p>
1618
1619<p class=MsoNormal>The identity Twin Law has virtually vanished along with the
16202-fold one leaving just the inverse and mirror Twin Laws.</p>
1621
1622<p class=MsoNormal>This means the structure is the inverse in space group P6<sub>5</sub>
1623but still Type 2 <span class=SpellE>merohedrally</span> twinned. </p>
1624
1625<p class=MsoNormal>To test this, we need to both change the space group and
1626invert the structure. First select the <b style='mso-bidi-font-weight:normal'><span
1627style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1628mso-hansi-theme-font:minor-latin'>General</span></b> tab and change the space
1629group to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1630mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P 65</span></b>;
1631you’ll see the Operators popup (press <b style='mso-bidi-font-weight:normal'><span
1632style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1633mso-hansi-theme-font:minor-latin'>Ok</span></b>) and the General tab will be
1634redrawn. Next select the <b style='mso-bidi-font-weight:normal'><span
1635style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1636mso-hansi-theme-font:minor-latin'>Atoms</span></b> tab; do <b style='mso-bidi-font-weight:
1637normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1638minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/Update H atoms</span></b>
1639to put them in their best positions.<span style='mso-spacerun:yes'> 
1640</span>Next select all the atoms by double clicking the empty box in upper left
1641corner of the table; all atoms will be highlighted &amp; plotted green. Do <b
1642style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1643mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
1644Atoms/On selected atoms…/Transform atoms</span></b>; a popup will appear.</p>
1645
1646<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1647 id="Picture_x0020_60" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:270pt;
1648 height:264pt;visibility:visible;mso-wrap-style:square'>
1649 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image091.png"
1650  o:title=""/>
1651</v:shape><![endif]--><![if !vml]><img width=360 height=352
1652src="Merohedral%20twin%20refinement%20in%20GSAS_files/image092.gif" v:shapes="Picture_x0020_60"><![endif]></span></p>
1653
1654<p class=MsoNormal>Check the <b style='mso-bidi-font-weight:normal'><span
1655style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1656mso-hansi-theme-font:minor-latin'>Choose inversion</span></b> box and
1657(important) set <b style='mso-bidi-font-weight:normal'><span style='font-family:
1658"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1659minor-latin'>Choose unit cell</span></b> to <b style='mso-bidi-font-weight:
1660normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1661minor-latin;mso-hansi-theme-font:minor-latin'>1 1 1</span></b>; this will put
1662the inverted structure back inside the unit cell. Press <b style='mso-bidi-font-weight:
1663normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1664minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; the table and plot
1665will both be redrawn. Now do <b style='mso-bidi-font-weight:normal'><span
1666style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1667mso-hansi-theme-font:minor-latin'>Calculate/Refine </span></b>2-3 times; the <span
1668class=SpellE>Rw</span> will drop back to where it was before and the <b
1669style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1670mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
1671tab will show new Twin fractions.</p>
1672
1673<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1674 id="Picture_x0020_61" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt;
1675 height:400.5pt;visibility:visible;mso-wrap-style:square'>
1676 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image093.png"
1677  o:title=""/>
1678</v:shape><![endif]--><![if !vml]><img width=624 height=534
1679src="Merohedral%20twin%20refinement%20in%20GSAS_files/image094.gif" v:shapes="Picture_x0020_61"><![endif]></span></p>
1680
1681<p class=MsoNormal>Now the identity Twin Law is ~2/3 and the 2-fold Twin Law is
1682the other ~1/3 while the other two are ~zero. You can delete them and repeat
1683the refinement; <span class=SpellE>Rw</span> ~1.7%. This completed the
1684merohedral twin exercises. You can save this project if desired.</p>
1685
1686<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1687
1688</span></div>
1689
1690</span></span></span></span></span></span></span></span></span></span>
1691</body>
1692
1693</html>
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