source: Tutorials/MerohedralTwins/Merohedral twin refinement in GSAS.htm @ 3739

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finish web tutorials for now

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409  <w:LsdException Locked="false" Priority="34" QFormat="true"
410   Name="List Paragraph"/>
411  <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
412  <w:LsdException Locked="false" Priority="30" QFormat="true"
413   Name="Intense Quote"/>
414  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
415  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
416  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
417  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
418  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
419  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
420  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
421  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
422  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
423  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
424  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
425  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
426  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
427  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
428  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
429  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
430  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
431  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
432  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
433  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
434  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
435  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
436  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
437  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
438  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
439  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
440  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
441  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
442  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
443  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
444  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
445  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
446  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
447  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
448  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
449  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
450  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
451  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
452  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
453  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
454  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
455  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
456  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
457  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
458  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
459  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
460  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
461  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
462  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
463  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
464  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
465  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
466  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
467  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
468  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
469  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
470  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
471  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
472  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
473  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
474  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
475  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
476  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
477  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
478  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
479  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
480  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
481  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
482  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
483  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
484  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
485  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
486  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
487  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
488  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
489  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
490  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
491  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
492  <w:LsdException Locked="false" Priority="19" QFormat="true"
493   Name="Subtle Emphasis"/>
494  <w:LsdException Locked="false" Priority="21" QFormat="true"
495   Name="Intense Emphasis"/>
496  <w:LsdException Locked="false" Priority="31" QFormat="true"
497   Name="Subtle Reference"/>
498  <w:LsdException Locked="false" Priority="32" QFormat="true"
499   Name="Intense Reference"/>
500  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
501  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
502   UnhideWhenUsed="true" Name="Bibliography"/>
503  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
504   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
505  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
506  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
507  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
508  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
509  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
510  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
511  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
512  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
513  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
514  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
515  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
516  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
517  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
518  <w:LsdException Locked="false" Priority="46"
519   Name="Grid Table 1 Light Accent 1"/>
520  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
521  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
522  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
523  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
524  <w:LsdException Locked="false" Priority="51"
525   Name="Grid Table 6 Colorful Accent 1"/>
526  <w:LsdException Locked="false" Priority="52"
527   Name="Grid Table 7 Colorful Accent 1"/>
528  <w:LsdException Locked="false" Priority="46"
529   Name="Grid Table 1 Light Accent 2"/>
530  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
531  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
532  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
533  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
534  <w:LsdException Locked="false" Priority="51"
535   Name="Grid Table 6 Colorful Accent 2"/>
536  <w:LsdException Locked="false" Priority="52"
537   Name="Grid Table 7 Colorful Accent 2"/>
538  <w:LsdException Locked="false" Priority="46"
539   Name="Grid Table 1 Light Accent 3"/>
540  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
541  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
542  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
543  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
544  <w:LsdException Locked="false" Priority="51"
545   Name="Grid Table 6 Colorful Accent 3"/>
546  <w:LsdException Locked="false" Priority="52"
547   Name="Grid Table 7 Colorful Accent 3"/>
548  <w:LsdException Locked="false" Priority="46"
549   Name="Grid Table 1 Light Accent 4"/>
550  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
551  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
552  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
553  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
554  <w:LsdException Locked="false" Priority="51"
555   Name="Grid Table 6 Colorful Accent 4"/>
556  <w:LsdException Locked="false" Priority="52"
557   Name="Grid Table 7 Colorful Accent 4"/>
558  <w:LsdException Locked="false" Priority="46"
559   Name="Grid Table 1 Light Accent 5"/>
560  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
561  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
562  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
563  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
564  <w:LsdException Locked="false" Priority="51"
565   Name="Grid Table 6 Colorful Accent 5"/>
566  <w:LsdException Locked="false" Priority="52"
567   Name="Grid Table 7 Colorful Accent 5"/>
568  <w:LsdException Locked="false" Priority="46"
569   Name="Grid Table 1 Light Accent 6"/>
570  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
571  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
572  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
573  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
574  <w:LsdException Locked="false" Priority="51"
575   Name="Grid Table 6 Colorful Accent 6"/>
576  <w:LsdException Locked="false" Priority="52"
577   Name="Grid Table 7 Colorful Accent 6"/>
578  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
579  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
580  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
581  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
582  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
583  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
584  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
585  <w:LsdException Locked="false" Priority="46"
586   Name="List Table 1 Light Accent 1"/>
587  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
588  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
589  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
590  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
591  <w:LsdException Locked="false" Priority="51"
592   Name="List Table 6 Colorful Accent 1"/>
593  <w:LsdException Locked="false" Priority="52"
594   Name="List Table 7 Colorful Accent 1"/>
595  <w:LsdException Locked="false" Priority="46"
596   Name="List Table 1 Light Accent 2"/>
597  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
598  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
599  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
600  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
601  <w:LsdException Locked="false" Priority="51"
602   Name="List Table 6 Colorful Accent 2"/>
603  <w:LsdException Locked="false" Priority="52"
604   Name="List Table 7 Colorful Accent 2"/>
605  <w:LsdException Locked="false" Priority="46"
606   Name="List Table 1 Light Accent 3"/>
607  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
608  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
609  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
610  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
611  <w:LsdException Locked="false" Priority="51"
612   Name="List Table 6 Colorful Accent 3"/>
613  <w:LsdException Locked="false" Priority="52"
614   Name="List Table 7 Colorful Accent 3"/>
615  <w:LsdException Locked="false" Priority="46"
616   Name="List Table 1 Light Accent 4"/>
617  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
618  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
619  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
620  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
621  <w:LsdException Locked="false" Priority="51"
622   Name="List Table 6 Colorful Accent 4"/>
623  <w:LsdException Locked="false" Priority="52"
624   Name="List Table 7 Colorful Accent 4"/>
625  <w:LsdException Locked="false" Priority="46"
626   Name="List Table 1 Light Accent 5"/>
627  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
628  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
629  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
630  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
631  <w:LsdException Locked="false" Priority="51"
632   Name="List Table 6 Colorful Accent 5"/>
633  <w:LsdException Locked="false" Priority="52"
634   Name="List Table 7 Colorful Accent 5"/>
635  <w:LsdException Locked="false" Priority="46"
636   Name="List Table 1 Light Accent 6"/>
637  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
638  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
639  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
640  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
641  <w:LsdException Locked="false" Priority="51"
642   Name="List Table 6 Colorful Accent 6"/>
643  <w:LsdException Locked="false" Priority="52"
644   Name="List Table 7 Colorful Accent 6"/>
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804
805<body lang=EN-US style='tab-interval:.5in'>
806
807<div class=WordSection1>
808
809<h1><span style='mso-fareast-font-family:"Times New Roman"'>Merohedral twin
810refinement in GSAS-II<o:p></o:p></span></h1>
811
812<P><B>A video version of this tutorial is available at
813<A href="https://anl.box.com/v/MerohedraltwinrefinementinGSAS" target="_blank">
814https://anl.box.com/v/MerohedraltwinrefinementinGSAS</A></B></P>
815
816<h2><span style='mso-fareast-font-family:"Times New Roman"'>Introduction: <o:p></o:p></span></h2>
817
818<p class=MsoNormal>In these exercises you will use GSAS-II to refine the
819structure of a few single crystal structures where there is merohedral
820twinning. There is a general discussion of twinning in International Tables for
821Crystallography (2006), Vol. C, Chapter 1.3, pp 10-14. <span class=SpellE>Merohedral</span>
822twinning occurs when the twin operation (2, m <span class=GramE>or </span><span
823style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
824    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
825   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
826   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
827   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
828style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
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830top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
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857belongs to the point group of the vector lattice but not of the crystal
858structure. Of the 230 space groups only 159 of them may have merohedral
859twining. </p>
860
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875
876<p class=MsoNormal>&nbsp;</p>
877
878<p class=MsoNormal>The possible merohedral twin operators are shown in the
879above table (extracted from p 13 of Intl. Tables for <span class=SpellE>Cryst</span>.,
880Vol. C). Merohedral twins are of two types: Type 1 are inversion twins and have
881only 2 components and Type 2 are where the twin operation does not belong to
882the Laue class of the crystal (only for space groups marked with * in above
883table) and multiple twin components may be found. For Type 1 the twin lattice
884exactly superimpose so that if Friedel’s law is obeyed the twin <span
885class=GramE>components</span> have the same value of |F|<sup>2</sup> (the
886twinning is undetectable!). However, in the presence of resonant scattering the
887|F|<sup>2</sup> components differ and if the twin components have unequal
888volumes then the Bragg intensities will differ from that obtained from the <span
889class=SpellE>untwinned</span> structure and then the twinning effects must be
890considered for refinement.&nbsp; Obviously all Type 1 crystals are <span
891class=SpellE>noncentrosymmetric</span>. For Type 2 the space group may be
892centrosymmetric from within a choice of just 55 possible space groups. However,
893the diffraction pattern may display apparent higher symmetry especially if the
894twin components are all equally present in the crystal.&nbsp; Note that menu
895entries and user input are shown in bold face below as <b><span
896style='font-family:"Calibri",sans-serif'>Help/About GSAS-II</span></b>, which
897lists first the name of the menu (here <b><span style='font-family:"Calibri",sans-serif'>Help</span></b>)
898and second the name of the entry in the menu (here <b><span style='font-family:
899"Calibri",sans-serif'>About GSAS-II</span></b>). If you have not done so already,
900start GSAS-II.</p>
901
902<h2 style='margin-bottom:.25in'><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></h2>
903
904<p class=MsoNormal style='margin-bottom:8.0pt;line-height:105%'>.<br clear=all
905style='mso-special-character:line-break;page-break-before:always'>
906</p>
907
908<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 1. A Type 1
909inversion twin – C<sub>8</sub>H<sub>25</sub>Al<sub>0.84</sub>Ga<sub>1.16</sub>N<sub>3</sub>
910<o:p></o:p></span></h2>
911
912<p class=MsoNormal>This example was taken from Luo, et al., Dalton Trans.
9134491(2006). The structure is given in the file <span class=SpellE><b><span
914style='font-family:"Calibri",sans-serif'>MerohedralTwins</span></b></span><b><span
915style='font-family:"Calibri",sans-serif'>/data/1b.cif</span></b> and the data
916are in <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>MerohedralTwins</span></b></span><b><span
917style='font-family:"Calibri",sans-serif'>/data/1b.fcf</span></b>. This example
918is <span class=SpellE>noncentrosymmetric</span> and the data was collected with
919radiation (<span class=SpellE>MoK</span>&#945;) that gives significant resonant
920scattering from the Ga atoms. </p>
921
922<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
923refinement<o:p></o:p></span></h2>
924
925<p class=MsoNormal>To begin do <b><span style='font-family:"Calibri",sans-serif'>Import/Phase/from
926CIF file</span></b> from the main GSAS-II data tree menu. A file selection
927window will appear; find the above <span class=SpellE>cif</span> file (…<b><span
928style='font-family:"Calibri",sans-serif'>1b.cif</span></b>) and select it. A
929popup window will appear. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
930a new popup will appear; Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>,
931and you will see the General page for this phase</p>
932
933<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
934 id="Picture_x0020_1" o:spid="_x0000_i1052" type="#_x0000_t75" style='width:468pt;
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936 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image005.png"
937  o:title=""/>
938</v:shape><![endif]--><![if !vml]><img width=624 height=498
939src="Merohedral%20twin%20refinement%20in%20GSAS_files/image002.gif" v:shapes="Picture_x0020_1"><![endif]></span></p>
940
941<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
942Factor/from CIF file</span></b> (that is the format of <span class=GramE>a</span>
943“<span class=SpellE>fcf</span>” file); a file selection dialog box will appear
944with the previously selected directory chosen. Select <b><span
945style='font-family:"Calibri",sans-serif'>1b.fcf</span></b>; a popup window will
946appear</p>
947
948<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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954src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.gif" v:shapes="Picture_x0020_3"><![endif]></span></p>
955
956<p class=MsoNormal>Select <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Yes</span></b></span>;
957a new popup window allowing you to change the name</p>
958
959<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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963  o:title=""/>
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966
967<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
968after a pause and some activity a popup window will appear</p>
969
970<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
971 id="Picture_x0020_5" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:233.25pt;
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973 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image023.png"
974  o:title=""/>
975</v:shape><![endif]--><![if !vml]><img width=311 height=305
976src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.gif" v:shapes="Picture_x0020_5"><![endif]></span></p>
977
978<p class=MsoNormal>This makes the connection between the data set and the
979previously imported phase. Select the entry and press <b><span
980style='font-family:"Calibri",sans-serif'>OK</span></b>. You now have loaded all
981that is needed for the first example. The structure had previously been solved
982and refined with <span class=SpellE>Shelx</span> so you need not trouble about
983those steps. You can try to solve the structure in GSAS-II via charge flipping
984but this is not part of this exercise; we will only explore the twin analysis
985features of GSAS-II.</p>
986
987<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
988of twinned structure<o:p></o:p></span></h2>
989
990<p class=MsoNormal>Before beginning the refinement, it usually the practice to
991eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
992&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
993style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
994GSAS-II data tree.</p>
995
996<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
997 id="Picture_x0020_6" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:468pt;
998 height:209.25pt;visibility:visible;mso-wrap-style:square'>
999 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"
1000  o:title=""/>
1001</v:shape><![endif]--><![if !vml]><img width=624 height=279
1002src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.gif" v:shapes="Picture_x0020_6"><![endif]></span></p>
1003
1004<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1005<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1006"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1007style='font-family:"Calibri",sans-serif'>Phases/C8 H25 Al0.84 Ga1.16</span></b>
1008entry in the GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1009tab</p>
1010
1011<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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1014 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image028.png"
1015  o:title=""/>
1016</v:shape><![endif]--><![if !vml]><img width=624 height=349
1017src="Merohedral%20twin%20refinement%20in%20GSAS_files/image018.gif" v:shapes="Picture_x0020_23"><![endif]></span></p>
1018
1019<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1020factor</span></b> is selected for refinement by default. If you refine it, you
1021will get an <span class=SpellE>R<sub>w</sub></span>= 2.85% which isn’t too bad.
1022However, you are unsure what the hand of the molecule is in this structure and
1023the experiment with <span class=SpellE>MoKa</span> radiation should give
1024sufficient resonant scattering to determine this. The <b><span
1025style='font-family:"Calibri",sans-serif'>Flack parameter</span></b> gives you a
1026way to evaluate which hand the molecule is. If upon refinement the value is ~0
1027then you have correctly described the hand. Otherwise if the value is ~1 then
1028the opposite hand is the correct and the structure needs to be inverted. So
1029let’s test this; select the <b><span style='font-family:"Calibri",sans-serif'>Flack
1030parameter</span></b> for refinement and do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>
1031from the main GSAS-II data tree menu. You’ll be asked to save the project; pick
1032a directory &amp; a name – I chose <b style='mso-bidi-font-weight:normal'><span
1033style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1034mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>1b</span></b>.
1035The structure will quickly refine to give <span class=SpellE>R<sub>w</sub></span>=2.155%
1036which is a considerable improvement on Scale factor alone. The Flack parameter
1037is now 0.433, meaning that both hands somehow exist in the structure. This can
1038happen if the crystal is <span class=SpellE>merohedrally</span> inversion twinned.</p>
1039
1040<p class=MsoNormal>To introduce this twin, press the <b><span style='font-family:
1041"Calibri",sans-serif'>Add Twin Law</span></b> box; the window will be redrawn.</p>
1042
1043<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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1046 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image030.png"
1047  o:title=""/>
1048</v:shape><![endif]--><![if !vml]><img width=624 height=446
1049src="Merohedral%20twin%20refinement%20in%20GSAS_files/image019.gif" v:shapes="_x0000_i1046"><![endif]></span></p>
1050
1051<p class=MsoNormal>Notice that two Twin Law matrices have been generated; one is
1052the identity for the reference structure and the other by default is the
1053merohedral inverse. If some other twin law is desired, then the matrix elements
1054need to be changed. Moreover, the Flack parameter has vanished as it is no
1055longer needed. Press the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1056button for the <b><span style='font-family:"Calibri",sans-serif'>Twin Law
1057fraction</span></b> and rerun the refinement. The Data window now has.</p>
1058
1059<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1060 id="Picture_x0020_42" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:468pt;
1061 height:337.5pt;visibility:visible;mso-wrap-style:square'>
1062 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image032.png"
1063  o:title=""/>
1064</v:shape><![endif]--><![if !vml]><img width=624 height=450
1065src="Merohedral%20twin%20refinement%20in%20GSAS_files/image062.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
1066
1067<p class=MsoNormal>The refinement quickly converged to where it was before but
1068the twin fractions are now ~56/44 consistent with the ~45% Flack parameter
1069obtained earlier. It is likely that the crystal is macroscopically twinned thus
1070the twin fractions are not exactly 50/50. This completes this example; you can
1071save your project if you want to explore other features of GSAS-II with it.</p>
1072
1073<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 2. A Type 2
1074only merohedral twin – <br>
1075[Al(OC<sub>6</sub>H<sub>4</sub>(C<sub>3</sub>H<sub>7</sub>)<sub>2</sub>)]<sup>-</sup>
1076[NC<sub>7</sub>H<sub>8</sub>]<sup>+</sup><o:p></o:p></span></h2>
1077
1078<p class=MsoNormal>In this case the data collection Laue statistics (very
1079nearly <span style='position:relative;top:3pt'><span style='mso-no-proof:yes'>-3</span>m)
1080and systematic extinctions indicated that the space group was either one of the
1081<span class=SpellE>enantiomorphic</span> pair P3<sub>1</sub>21 or P3<sub>2</sub>21
1082or possibly one of the pair P3<sub>1</sub> or P3<sub>2</sub>. If the true
1083structure was of the lower symmetry P3<sub>1</sub> or P3<sub>2</sub> then there
1084must be Type 2 merohedral twinning to make the diffraction pattern appear to
1085have higher symmetry (<span style='position:relative;top:3pt'><span
1086style='mso-no-proof:yes'>-3</span>m instead of <span style='position:relative;
1087top:3pt'><span style='mso-no-proof:yes'>-3</span>); this exercise will explore
1088this possibility. The data were collected with <span class=SpellE>MoK</span><span
1089style='font-family:Symbol'>a</span> radiation so there is little resonant
1090scattering and thus the choice of hand is indeterminate.&nbsp; Solving the
1091structure in P3<sub>2</sub>21 yielded a poorly fitting structure with disorder
1092particularly in the cation. Resolving the structure in P3<sub>2</sub> gave a
1093structure with no disorder and a better fit to the data (but still not great).
1094As this work was done with <span class=SpellE>Shelx</span> this result is in
1095the form of a <span class=SpellE>Shelx</span> input file (2b.ins – thanks to V.
1096Young for this example). If you have not done so already, start GSAS-II and
1097start with a fresh project.</p>
1098
1099<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1100refinement<o:p></o:p></span></h2>
1101
1102<p class=MsoNormal>To begin we need to import the phase information from the <span
1103class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1104style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1105ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1106and a res file is the output result after a <span class=SpellE>Shelx</span>
1107run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>2b.ins</span></b>
1108from the file selection window; a popup window will ask if this file is the one
1109you want.</p>
1110
1111<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1112 id="Picture_x0020_43" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:314.25pt;
1113 height:159pt;visibility:visible;mso-wrap-style:square'>
1114 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image034.png"
1115  o:title=""/>
1116</v:shape><![endif]--><![if !vml]><img width=419 height=212
1117src="Merohedral%20twin%20refinement%20in%20GSAS_files/image063.gif" v:shapes="Picture_x0020_43"><![endif]></span></p>
1118
1119<p class=MsoNormal>Press <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Yes</span></b></span>;
1120a Read Warning will appear.</p>
1121
1122<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1123 id="Picture_x0020_44" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:378.75pt;
1124 height:177pt;visibility:visible;mso-wrap-style:square'>
1125 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image036.png"
1126  o:title=""/>
1127</v:shape><![endif]--><![if !vml]><img width=505 height=236
1128src="Merohedral%20twin%20refinement%20in%20GSAS_files/image064.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
1129
1130<p class=MsoNormal>There are two significant warnings concerning <span
1131class=SpellE>Shelx</span> files. One is that the file never contains the space
1132group symbol (<span class=SpellE>Shelx</span> requires just the operators), so
1133GSAS-II sets the space group to P 1 by default and you will need to change it
1134to P3<sub>2</sub> immediately (next window). The other warning is that hydrogen
1135atoms were found; these usually cannot be refined unconstrained with x-ray
1136data. The warning recommends replacing them with <span class=SpellE>stereochemically</span>
1137determined ones (this is illustrated in the 3<sup>rd</sup> Exercise of this
1138tutorial) and the last line of the Warning tells you what to do if they are to
1139be refined. Here we will only refine twin laws &amp; scale factors so this is
1140unnecessary. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1141you get the opportunity to change the Phase name (I know it is very long but
1142that doesn’t matter here). Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1143the General tab for this phase is shown. </p>
1144
1145<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1146 id="Picture_x0020_45" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:468pt;
1147 height:206.25pt;visibility:visible;mso-wrap-style:square'>
1148 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image038.png"
1149  o:title=""/>
1150</v:shape><![endif]--><![if !vml]><img width=624 height=275
1151src="Merohedral%20twin%20refinement%20in%20GSAS_files/image065.gif" v:shapes="Picture_x0020_45"><![endif]></span></p>
1152
1153<p class=MsoNormal>Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
115432</span></b>; the window will be redrawn after a popup showing the operations.
1155You can see the structure by selecting <b><span style='font-family:"Calibri",sans-serif'>Draw
1156Atoms</span></b>.</p>
1157
1158<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1159 id="Picture_x0020_47" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:468pt;
1160 height:405pt;visibility:visible;mso-wrap-style:square'>
1161 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image040.png"
1162  o:title=""/>
1163</v:shape><![endif]--><![if !vml]><img width=624 height=540
1164src="Merohedral%20twin%20refinement%20in%20GSAS_files/image066.gif" v:shapes="Picture_x0020_47"><![endif]></span></p>
1165
1166<p class=MsoNormal>&nbsp;</p>
1167
1168<p class=MsoNormal>The large anion containing the Al atom is to the left and
1169the smaller cation to the right.</p>
1170
1171<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1172Factor/from <span class=SpellE>Shelx</span> HKLF 4 F<sup>2</sup> file</span></b>
1173and select <b><span style='font-family:"Calibri",sans-serif'>2b.hkl</span></b>
1174from the file dialog box; a popup will appear showing a few lines.</p>
1175
1176<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1177 id="Picture_x0020_48" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:274.5pt;
1178 height:186pt;visibility:visible;mso-wrap-style:square'>
1179 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image042.png"
1180  o:title=""/>
1181</v:shape><![endif]--><![if !vml]><img width=366 height=248
1182src="Merohedral%20twin%20refinement%20in%20GSAS_files/image067.gif" v:shapes="Picture_x0020_48"><![endif]></span></p>
1183
1184<p class=MsoNormal>This is the right file; a <span class=SpellE>Shelx</span>
1185HKLF 4 file consists of records with just <span class=SpellE>h<span
1186class=GramE>,k,l</span></span>, F<sup>2</sup> and <span style='font-family:
1187Symbol'>s</span>(F<sup>2</sup>). Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1188and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b> on the next
1189one (we’ll keep the name as it is). Choose the phase with the long name on the
1190next popup and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
1191select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
1192"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1193minor-latin;mso-bidi-theme-font:minor-latin'>Structure factors</span></b> tab, a
11942D display of the hk0 zone is plotted.</p>
1195
1196<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1197 id="Picture_x0020_49" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:468pt;
1198 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1199 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image044.png"
1200  o:title=""/>
1201</v:shape><![endif]--><![if !vml]><img width=624 height=535
1202src="Merohedral%20twin%20refinement%20in%20GSAS_files/image068.gif" v:shapes="Picture_x0020_49"><![endif]></span></p>
1203
1204<p class=MsoNormal>The size of the green circles are proportional to <span
1205class=SpellE><span class=GramE>Fo</span></span> (after a structure factor
1206calculation blue rings will appear for Fc).</p>
1207
1208<p class=MsoNormal>You now have loaded all that is needed for the second
1209example. The structure had previously been solved and refined with <span
1210class=SpellE>Shelx</span> so you need not trouble about those steps. You can
1211try to solve the structure in GSAS-II via charge flipping but this is not part
1212of this exercise (it isn’t easy because of the twinning); we will only explore
1213the twin analysis features of GSAS-II.</p>
1214
1215<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1216of twinned structure<o:p></o:p></span></h2>
1217
1218<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1219eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1220&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1221style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1222GSAS-II data tree.</p>
1223
1224<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1225 id="Picture_x0020_50" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:468pt;
1226 height:215.25pt;visibility:visible;mso-wrap-style:square'>
1227 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image046.png"
1228  o:title=""/>
1229</v:shape><![endif]--><![if !vml]><img width=624 height=287
1230src="Merohedral%20twin%20refinement%20in%20GSAS_files/image069.gif" v:shapes="Picture_x0020_50"><![endif]></span></p>
1231
1232<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1233<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1234"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1235style='font-family:"Calibri",sans-serif'>Phases/MEROHEDRAL…</span></b> entry in
1236the GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1237tab.</p>
1238
1239<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=444
1240id="_x0000_i1037"
1241src="Merohedral%20twin%20refinement%20in%20GSAS_files/image030.png"></span></p>
1242
1243<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1244factor</span></b> is selected for refinement by default. If you refine it, you
1245will get an <span class=SpellE>R<sub>w</sub></span>~ 25% which is terrible. If
1246you try refining atom positions &amp; thermal parameters you could possibly
1247lower it to ~15% (still terrible) and the resulting structure would not be very
1248satisfactory. However, we have suspected from the equivalence of <span
1249style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1250    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1251   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1252   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1253   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
1254style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1255"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1256top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1257EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1258 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1259 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1260  o:title="" chromakey="white"/>
1261</v:shape><![endif]--><![if !vml]><img width=9 height=21
1262src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;and
1263<span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1264    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1265   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1266   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1267   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
1268style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1269"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1270top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1271EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1272 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1273 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1274  o:title="" chromakey="white"/>
1275</v:shape><![endif]--><![if !vml]><img width=9 height=21
1276src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>m1
1277Laue data symmetries that there is twinning so don’t bother trying to make it
1278better by refining the structure. To determine the possible twin law we refer
1279to Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
1280that indeed Laue <span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1281    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1282   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1283   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1284   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
1285style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1286"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1287top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1288EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1289 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1290 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1291  o:title="" chromakey="white"/>
1292</v:shape><![endif]--><![if !vml]><img width=9 height=21
1293src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>m1
1294as P3<sub>2</sub>21 can be simulated by twinned Laue <span style='position:
1295relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
1296    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1297   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1298   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
1299   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
1300style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1301"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1302top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1303EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1304 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
1305 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
1306  o:title="" chromakey="white"/>
1307</v:shape><![endif]--><![if !vml]><img width=9 height=21
1308src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;crystals
1309in P3<sub>2</sub>; the possible operator is shown in Table 1.3.4.1 (reproduced
1310above) as either a mirror or a 2-fold. The detailed symbolism in the table
1311(‘m.., ..2/.2.’) indicates (perhaps obscurely) the operator specifics. See P3m1
1312and P3<sub>2</sub>21 space groups in International Tables for Crystallography,
1313Vol A for the operations m as <span style='position:relative;top:3pt'><span
1314style='mso-no-proof:yes'>-y-xz</span>&nbsp;or 2 as <span style='position:relative;
1315top:3pt'><span style='mso-no-proof:yes'>yx-z</span>; we will use the 2-fold
1316since the m inverts the structure which we are not sensitive to in this
1317experiment.</p>
1318
1319<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Add
1320Twin Law</span></b>; the Data tab will be redrawn with the inversion for the
1321second law. Replace this with the 2-fold (<b><span style='font-family:"Calibri",sans-serif'>0
13221 0, 1 0 0, 0 0 -1</span></b>) and check the <b><span style='font-family:"Calibri",sans-serif'>Refine</span></b>
1323box. It should look like.</p>
1324
1325<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1326 id="Picture_x0020_51" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt;
1327 height:352.5pt;visibility:visible;mso-wrap-style:square'>
1328 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image050.png"
1329  o:title=""/>
1330</v:shape><![endif]--><![if !vml]><img width=624 height=470
1331src="Merohedral%20twin%20refinement%20in%20GSAS_files/image071.gif" v:shapes="Picture_x0020_51"><![endif]></span></p>
1332
1333<p class=MsoNormal>Now do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>;
1334you’ll have to save the project. Pick a directory &amp; file name - I used <b
1335style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1336mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1337minor-latin'>2b</span></b>. <span class=GramE>there</span> will be an immediate
1338improvement in the fit to <span class=SpellE>Rw</span>=5.05% and the twin
1339fractions will be ~50/50. Clearly this crystal is Type 2 <span class=SpellE>merohedrally</span>
1340twinned; we cannot determine if there is any Type 1 twinning because we lack
1341sufficient resonant scattering to see it. This ends the second example; you can
1342save the project file.</p>
1343
1344<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 3. A Type 1
1345&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>
1346
1347<p class=MsoNormal>This <span class=SpellE>ecample</span> is very similar to
1348the previous one except that the Cs atom has significant resonant scattering
1349for <span class=SpellE>MoKa</span> radiation allowing detection of Type 1 <span
1350class=SpellE>merohedry</span>. The data set has apparent 6/m Laue symmetry but
1351may 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.
1352The combination of Type 1 and Type 2 twins requires 4 twin laws to be explored
1353for this <span class=SpellE>pentamethylcyclopentadienyl</span> Cs complex. As
1354this work was done with <span class=SpellE>Shelx</span> this result is in the
1355form of a <span class=SpellE>Shelx</span> input file (3a.ins – thanks to V.
1356Young for this example). If you have not done so already, start GSAS-II and
1357start with a fresh project.</p>
1358
1359<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 1. Setup for
1360refinement<o:p></o:p></span></h2>
1361
1362<p class=MsoNormal>To begin we need to import the phase information from the <span
1363class=SpellE>Shelx</span> ins file. From the main GSAS-II data tree menu, do <b><span
1364style='font-family:"Calibri",sans-serif'>Import/Phase/from <span class=SpellE>Shelx</span>
1365ins, res file</span></b> (the ins file is input to <span class=SpellE>Shelx</span>
1366and a res file is the output result after a <span class=SpellE>Shelx</span>
1367run; either can be used here). Select <b><span style='font-family:"Calibri",sans-serif'>3a.ins</span></b>
1368from the file selection window; a popup window will ask if this file is the one
1369you want.</p>
1370
1371<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1372 id="Picture_x0020_52" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:274.5pt;
1373 height:174.75pt;visibility:visible;mso-wrap-style:square'>
1374 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image072.png"
1375  o:title=""/>
1376</v:shape><![endif]--><![if !vml]><img width=366 height=233
1377src="Merohedral%20twin%20refinement%20in%20GSAS_files/image073.gif" v:shapes="Picture_x0020_52"><![endif]></span></p>
1378
1379<p class=MsoNormal>It is; press the <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1380button. You will then see the SHELX Read Warning; you will have to change the
1381space group to P6<sub>1</sub> in a bit. Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1382and leave the name alone (press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1383again). Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
138461</span></b>; the General tab will be redrawn after showing you the operators.</p>
1385
1386<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1387 id="Picture_x0020_53" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:468pt;
1388 height:234.75pt;visibility:visible;mso-wrap-style:square'>
1389 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image074.png"
1390  o:title=""/>
1391</v:shape><![endif]--><![if !vml]><img width=624 height=313
1392src="Merohedral%20twin%20refinement%20in%20GSAS_files/image075.gif" v:shapes="Picture_x0020_53"><![endif]></span></p>
1393
1394<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
1395Factor/from CIF file</span></b> and select <b><span style='font-family:"Calibri",sans-serif'>3a.fcf</span></b>
1396from the file dialog. Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
1397in the next popup and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>
1398on the name change popup. Select the file name in the Add to phases popup and
1399press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; the hk0
1400zone of the structure factors will be displayed. Note that this plot shows both
1401green (<span class=SpellE>Fo</span>) and blue (Fc) circles with a small solid
1402red or green circle in the centers. These are for the +/- <span
1403style='font-family:Symbol'>D</span>F values. Fc is here because this <span
1404class=SpellE>fcf</span> file was obtained after refinement via <span
1405class=SpellE>Shelx</span>.</p>
1406
1407<p class=MsoNormal>You now have loaded all that is needed for the third example.
1408The structure had previously been solved and refined with <span class=SpellE>Shelx</span>
1409so you need not trouble about those steps. You can try to solve the structure
1410in GSAS-II via charge flipping but this is not part of this exercise (it isn’t
1411easy because of the twinning; charge flipping will readily give the Cs position
1412&amp; most of the rest. It can be completed via difference Fourier techniques);
1413we will only explore the twin analysis features of GSAS-II.</p>
1414
1415<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
1416of twinned structure<o:p></o:p></span></h2>
1417
1418<p class=MsoNormal>Before beginning the refinement, it usually the practice to
1419eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
1420&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
1421style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
1422GSAS-II data tree.</p>
1423
1424<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1425 id="Picture_x0020_54" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt;
1426 height:205.5pt;visibility:visible;mso-wrap-style:square'>
1427 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image076.png"
1428  o:title=""/>
1429</v:shape><![endif]--><![if !vml]><img width=624 height=274
1430src="Merohedral%20twin%20refinement%20in%20GSAS_files/image077.gif" v:shapes="Picture_x0020_54"><![endif]></span></p>
1431
1432<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
1433<span class=SpellE>obs</span>/sig</span></b> to <b><span style='font-family:
1434"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
1435style='font-family:"Calibri",sans-serif'>Phases/Cs…</span></b> entry in the
1436GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
1437tab.</p>
1438
1439<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1440 id="Picture_x0020_55" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:468pt;
1441 height:303.75pt;visibility:visible;mso-wrap-style:square'>
1442 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image078.png"
1443  o:title=""/>
1444</v:shape><![endif]--><![if !vml]><img width=624 height=405
1445src="Merohedral%20twin%20refinement%20in%20GSAS_files/image079.gif" v:shapes="Picture_x0020_55"><![endif]></span></p>
1446
1447<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
1448factor</span></b> is selected for refinement by default. If you refine it, you
1449will get an <span class=SpellE>R<sub>w</sub></span>~ 17% which is terrible. It
1450doesn’t change much if you add the Flack parameter (~0.36). If you try refining
1451atom positions &amp; thermal parameters you could possibly lower it but the
1452resulting structure would not be very satisfactory. However, we have suspected
1453from the equivalence of 6/m and 6/mmm Laue data symmetries that there is
1454twinning so don’t bother trying to make it better by refining the structure. To
1455determine the possible twin laws we again refer to Table 1.3.4.2 of the
1456International Tables for Crystallography Vol C. and see that indeed Laue 6/mmm
1457as P6<sub>1</sub>22 can be simulated by twinned Laue 6/m crystals in P6<sub>1</sub>;
1458the possible operator is shown in Table 1.3.4.1 (reproduced above) as either a
1459mirror or a 2-fold. The detailed symbolism in the table (‘m.., ..2/.2.’)
1460indicates (perhaps obscurely) the operator specifics; they are m as <span
1461style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><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>y</m:r></span></i></m:e></m:acc><m:acc><m:accPr><m:chr
1466    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1467   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1468   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1469   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
1470 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
1471style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1472"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1473top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1474EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1475 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1476 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image052.png"
1477  o:title="" chromakey="white"/>
1478</v:shape><![endif]--><![if !vml]><img width=26 height=19
1479src="Merohedral%20twin%20refinement%20in%20GSAS_files/image080.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;or
14802 as <!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span
1481 style='font-family:"Cambria Math",serif'><span style='position:relative;
1482 top:3pt'><m:r>y</m:r><m:r>x</span></m:r></span></i><m:acc><m:accPr><m:chr
1483    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1484   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1485   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i
1486   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
1487style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1488"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1489top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1490EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1491 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
1492 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image054.png"
1493  o:title="" chromakey="white"/>
1494</v:shape><![endif]--><![if !vml]><img width=26 height=19
1495src="Merohedral%20twin%20refinement%20in%20GSAS_files/image081.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
1496style='font-family:"Cambria Math",serif'>; we will use the 2-fold, m and
1497inversion operators to fully test for presence of the 4 possible twin laws.
1498Press the </span><b><span style='font-family:"Calibri",sans-serif'>Add Twin Law</span></b><span
1499style='font-family:"Cambria Math",serif'> button </span><b><span
1500style='font-family:"Calibri",sans-serif'>3 times</span></b><span
1501style='font-family:"Cambria Math",serif'>; each time the window will be
1502redrawn. When done you should see.<o:p></o:p></span></p>
1503
1504<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1505 id="Picture_x0020_56" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
1506 height:405.75pt;visibility:visible;mso-wrap-style:square'>
1507 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image082.png"
1508  o:title=""/>
1509</v:shape><![endif]--><![if !vml]><img width=624 height=541
1510src="Merohedral%20twin%20refinement%20in%20GSAS_files/image083.gif" v:shapes="Picture_x0020_56"><![endif]></span>&nbsp;</p>
1511
1512<p class=MsoNormal>For the third and fourth matrix enter <b><span
1513style='font-family:"Calibri",sans-serif'>0 1 0 1 0 0 0 0 -1</span></b> and <b><span
1514style='font-family:"Calibri",sans-serif'>0 -1 0 -1 0 0 0 0</span></b> <b><span
1515style='font-family:"Calibri",sans-serif'>1</span></b> as the 2-fold and mirror
1516operators (the 2<sup>nd</sup> matrix is the inversion by default). Select the <b><span
1517style='font-family:"Calibri",sans-serif'>Refine</span></b> button and do <b><span
1518style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
1519main menu; again you’ll have to save the project file – I called it 3a. The <span
1520class=SpellE>Rw</span> will immediately drop to ~2.26% (RF~2.05%). The four
1521twin element fractions will show various values</p>
1522
1523<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1524 id="Picture_x0020_57" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;
1525 height:405.75pt;visibility:visible;mso-wrap-style:square'>
1526 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image084.png"
1527  o:title=""/>
1528</v:shape><![endif]--><![if !vml]><img width=624 height=541
1529src="Merohedral%20twin%20refinement%20in%20GSAS_files/image085.gif" v:shapes="Picture_x0020_57"><![endif]></span></p>
1530
1531<p class=MsoNormal>The negative one for the 3<sup>rd</sup> twin fraction is nonphysical
1532and the 1<sup>st</sup> twin fraction is small. It is likely that the true space
1533group is P6<sub>5</sub> and Type 2 <span class=SpellE>merohedrally</span>
1534twinned (twin fractions 2 &amp; 4). We can improve it by refining the atom
1535positions and thermal parameters, but first we need to replace the hydrogen
1536atoms as suggested by the <span class=SpellE>Shelx</span> warning. Select the <b
1537style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1538mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms </span></b>tab
1539for the phase.</p>
1540
1541<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1542 id="Picture_x0020_41" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:525pt;
1543 height:225pt;visibility:visible;mso-wrap-style:square'>
1544 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"
1545  o:title=""/>
1546</v:shape><![endif]--><![if !vml]><img width=700 height=300
1547src="Merohedral%20twin%20refinement%20in%20GSAS_files/image086.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
1548
1549<p class=MsoNormal>If you scroll down the page, you’ll see H-atoms with default
1550<span class=SpellE>Uiso</span> (=0.025) values. To replace them, the old ones
1551need to be deleted; double click the <b style='mso-bidi-font-weight:normal'><span
1552style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1553mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1554style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1555mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>H</span></b>
1556and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1557mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>.
1558The H-atoms will be highlighted (and plotted in green). Do <b style='mso-bidi-font-weight:
1559normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1560minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/On selected atoms…/Delete
1561atom</span></b> from the menu; the H-atoms will be deleted and the structure
1562will be redrawn. Next double click the <b style='mso-bidi-font-weight:normal'><span
1563style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1564mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
1565style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1566mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>C</span></b>;
1567all the C-atoms will be selected (and shown in green on the plot). Do <b
1568style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1569mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/On
1570selected atoms…/<span class=SpellE>Calc</span> H atoms</span></b>; a Distance
1571Angle Controls will appear. Occasionally these values may need to be changed
1572but not this time; press <b style='mso-bidi-font-weight:normal'><span
1573style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1574mso-hansi-theme-font:minor-latin'>Ok</span></b>. The next popup is for the H
1575atoms add controls.</p>
1576
1577<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1578 id="Picture_x0020_58" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:300pt;
1579 height:187.5pt;visibility:visible;mso-wrap-style:square'>
1580 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image087.png"
1581  o:title=""/>
1582</v:shape><![endif]--><![if !vml]><img width=400 height=250
1583src="Merohedral%20twin%20refinement%20in%20GSAS_files/image088.gif" v:shapes="Picture_x0020_58"><![endif]></span></p>
1584
1585<p class=MsoNormal>It specifies the expected geometry around each C-atom for
1586H-atom placement. As expected we want 3 H-atoms on the terminal CH<sub>3</sub>
1587groups on the <span class=SpellE>Cp</span>* ring and one for each C-atom for
1588the NC<sub>5</sub>H<sub>5</sub> molecule. Press <b style='mso-bidi-font-weight:
1589normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1590minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; you will see the
1591H-atoms added in turn to the structure and they will be inserted immediately
1592after their respective C-atom. Their positions and thermal parameters are tied
1593to the C-atoms so that after refinement of the structure they can be shifted to
1594the <span class=SpellE>stereochemically</span> best positions. For the
1595refinement, double click the <b style='mso-bidi-font-weight:normal'><span
1596style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1597mso-hansi-theme-font:minor-latin'>Refine</span></b> column heading and select <b
1598style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1599mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>X</span></b>
1600and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1601mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>U</span></b>
1602from the popup; press <b style='mso-bidi-font-weight:normal'><span
1603style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1604mso-hansi-theme-font:minor-latin'>OK</span></b>. The Atom table will be redrawn
1605with XU in every entry under Refine. Now do <b style='mso-bidi-font-weight:
1606normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1607minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> (2-3
1608times until convergence<span class=GramE>)from</span> the main GSASII data tree
1609window; the <span class=SpellE>Rw</span> will drop to ~1.80%. If you look at
1610the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1611mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
1612tab the Twin element fractions are much clearer.</p>
1613
1614<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1615 id="Picture_x0020_59" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;
1616 height:342.75pt;visibility:visible;mso-wrap-style:square'>
1617 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image089.png"
1618  o:title=""/>
1619</v:shape><![endif]--><![if !vml]><img width=624 height=457
1620src="Merohedral%20twin%20refinement%20in%20GSAS_files/image090.gif" v:shapes="Picture_x0020_59"><![endif]></span><span
1621style='mso-spacerun:yes'> </span></p>
1622
1623<p class=MsoNormal>The identity Twin Law has virtually vanished along with the
16242-fold one leaving just the inverse and mirror Twin Laws.</p>
1625
1626<p class=MsoNormal>This means the structure is the inverse in space group P6<sub>5</sub>
1627but still Type 2 <span class=SpellE>merohedrally</span> twinned. </p>
1628
1629<p class=MsoNormal>To test this, we need to both change the space group and
1630invert the structure. First select the <b style='mso-bidi-font-weight:normal'><span
1631style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1632mso-hansi-theme-font:minor-latin'>General</span></b> tab and change the space
1633group to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1634mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P 65</span></b>;
1635you’ll see the Operators popup (press <b style='mso-bidi-font-weight:normal'><span
1636style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1637mso-hansi-theme-font:minor-latin'>Ok</span></b>) and the General tab will be
1638redrawn. Next select the <b style='mso-bidi-font-weight:normal'><span
1639style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1640mso-hansi-theme-font:minor-latin'>Atoms</span></b> tab; do <b style='mso-bidi-font-weight:
1641normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1642minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/Update H atoms</span></b>
1643to put them in their best positions.<span style='mso-spacerun:yes'> 
1644</span>Next select all the atoms by double clicking the empty box in upper left
1645corner of the table; all atoms will be highlighted &amp; plotted green. Do <b
1646style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1647mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
1648Atoms/On selected atoms…/Transform atoms</span></b>; a popup will appear.</p>
1649
1650<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1651 id="Picture_x0020_60" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:270pt;
1652 height:264pt;visibility:visible;mso-wrap-style:square'>
1653 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image091.png"
1654  o:title=""/>
1655</v:shape><![endif]--><![if !vml]><img width=360 height=352
1656src="Merohedral%20twin%20refinement%20in%20GSAS_files/image092.gif" v:shapes="Picture_x0020_60"><![endif]></span></p>
1657
1658<p class=MsoNormal>Check the <b style='mso-bidi-font-weight:normal'><span
1659style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1660mso-hansi-theme-font:minor-latin'>Choose inversion</span></b> box and
1661(important) set <b style='mso-bidi-font-weight:normal'><span style='font-family:
1662"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1663minor-latin'>Choose unit cell</span></b> to <b style='mso-bidi-font-weight:
1664normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1665minor-latin;mso-hansi-theme-font:minor-latin'>1 1 1</span></b>; this will put
1666the inverted structure back inside the unit cell. Press <b style='mso-bidi-font-weight:
1667normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1668minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; the table and plot
1669will both be redrawn. Now do <b style='mso-bidi-font-weight:normal'><span
1670style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1671mso-hansi-theme-font:minor-latin'>Calculate/Refine </span></b>2-3 times; the <span
1672class=SpellE>Rw</span> will drop back to where it was before and the <b
1673style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1674mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
1675tab will show new Twin fractions.</p>
1676
1677<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1678 id="Picture_x0020_61" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt;
1679 height:400.5pt;visibility:visible;mso-wrap-style:square'>
1680 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image093.png"
1681  o:title=""/>
1682</v:shape><![endif]--><![if !vml]><img width=624 height=534
1683src="Merohedral%20twin%20refinement%20in%20GSAS_files/image094.gif" v:shapes="Picture_x0020_61"><![endif]></span></p>
1684
1685<p class=MsoNormal>Now the identity Twin Law is ~2/3 and the 2-fold Twin Law is
1686the other ~1/3 while the other two are ~zero. You can delete them and repeat
1687the refinement; <span class=SpellE>Rw</span> ~1.7%. This completed the
1688merohedral twin exercises. You can save this project if desired.</p>
1689
1690<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1691
1692</span></div>
1693
1694</span></span></span></span></span></span></span></span></span></span>
1695</body>
1696
1697</html>
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