Changeset 3059 for Tutorials


Ignore:
Timestamp:
Sep 9, 2017 8:20:15 AM (4 years ago)
Author:
vondreele
Message:

Update to 2 frame version

Location:
Tutorials/MerohedralTwins
Files:
47 added
12 deleted
19 edited

Legend:

Unmodified
Added
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  • Tutorials/MerohedralTwins/Merohedral twin refinement in GSAS.htm

    r2394 r3059  
    2424 <o:DocumentProperties>
    2525  <o:Author>Von Dreele</o:Author>
    26   <o:LastAuthor>Von Dreele</o:LastAuthor>
    27   <o:Revision>4</o:Revision>
    28   <o:TotalTime>3</o:TotalTime>
     26  <o:LastAuthor>vondreele</o:LastAuthor>
     27  <o:Revision>7</o:Revision>
     28  <o:TotalTime>1108</o:TotalTime>
    2929  <o:Created>2016-05-26T15:52:00Z</o:Created>
    30   <o:LastSaved>2016-07-28T19:27:00Z</o:LastSaved>
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    811813
    812814<p class=MsoNormal>In these exercises you will use GSAS-II to refine the
    813 structure of a few single crystal structures where there is merohedral twinning.
    814 There is a general discussion of twinning in International Tables for
    815 Crystallography (2006), Vol. C, Chapter 1.3, pp 10-14. Merohedral twinning
    816 occurs when the twin operation (2, m or <span style='position:relative;
    817 top:3pt'><span style='mso-no-proof:yes'><img width=9 height=19 id="_x0000_i1057"
    818 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image015.png"></span>)
    819 belongs to the point group of the vector lattice but not of the crystal
    820 structure. Of the 230 space groups only 159 of them may have merohedral
    821 twining. </p>
    822 
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     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:
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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"
     858 type="#_x0000_t75" style='position:absolute;margin-left:0;margin-top:0;
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    864878the Laue class of the crystal (only for space groups marked with * in above
    865879table) and multiple twin components may be found. For Type 1 the twin lattice
    866 exactly <span class=GramE>superimpose</span> so that if Friedel’s law is obeyed
    867 the twin components have the same value of |F|<sup>2</sup> (the twinning is
    868 undetectable!). However, in the presence of resonant scattering the |F|<sup>2</sup>
    869 components differ and if the twin components have unequal volumes then the
    870 Bragg intensities will differ from that obtained from the <span class=SpellE>untwinned</span>
    871 structure and then the twinning effects must be considered for
    872 refinement.&nbsp; Obviously all Type 1 crystals are <span class=SpellE>noncentrosymmetric</span>.
    873 For Type 2 the space group may be centrosymmetric from within a choice of just
    874 55 possible space groups. However, the diffraction pattern may display apparent
    875 higher symmetry especially if the twin components are all equally present in
    876 the crystal.&nbsp; Note that menu entries and user input are shown in bold face
    877 below as <b><span style='font-family:"Calibri",sans-serif'>Help/About GSAS-II</span></b>,
    878 which lists first the name of the menu (here <b><span style='font-family:"Calibri",sans-serif'>Help</span></b>)
     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>)
    879894and second the name of the entry in the menu (here <b><span style='font-family:
    880 "Calibri",sans-serif'>About GSAS-II</span></b>). If you have not done so
    881 already, start GSAS-II.</p>
     895"Calibri",sans-serif'>About GSAS-II</span></b>). If you have not done so already,
     896start GSAS-II.</p>
    882897
    883898<h2 style='margin-bottom:.25in'><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></h2>
     
    913928and you will see the General page for this phase</p>
    914929
    915 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=403 height=310
    916 id="_x0000_i1056"
    917 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image007.png"></span></p>
     930<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     931 id="Picture_x0020_1" o:spid="_x0000_i1052" type="#_x0000_t75" style='width:468pt;
     932 height:373.5pt;visibility:visible;mso-wrap-style:square'>
     933 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image005.png"
     934  o:title=""/>
     935</v:shape><![endif]--><![if !vml]><img width=624 height=498
     936src="Merohedral%20twin%20refinement%20in%20GSAS_files/image002.gif" v:shapes="Picture_x0020_1"><![endif]></span></p>
    918937
    919938<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
    920 Factor/from CIF file</span></b> (that is the format of a “<span class=SpellE>fcf</span>”
    921 file); a file selection dialog box will appear with the previously selected
    922 directory chosen. Select <b><span style='font-family:"Calibri",sans-serif'>1b.fcf</span></b>;
    923 a popup window will appear</p>
    924 
    925 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=447 height=249
    926 id="_x0000_i1055"
    927 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image008.png"></span></p>
    928 
    929 <p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
     939Factor/from CIF file</span></b> (that is the format of <span class=GramE>a</span>
     940“<span class=SpellE>fcf</span>” file); a file selection dialog box will appear
     941with the previously selected directory chosen. Select <b><span
     942style='font-family:"Calibri",sans-serif'>1b.fcf</span></b>; a popup window will
     943appear</p>
     944
     945<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     946 id="Picture_x0020_3" o:spid="_x0000_i1051" type="#_x0000_t75" style='width:274.5pt;
     947 height:208.5pt;visibility:visible;mso-wrap-style:square'>
     948 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image008.png"
     949  o:title=""/>
     950</v:shape><![endif]--><![if !vml]><img width=366 height=278
     951src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.gif" v:shapes="Picture_x0020_3"><![endif]></span></p>
     952
     953<p class=MsoNormal>Select <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Yes</span></b></span>;
    930954a new popup window allowing you to change the name</p>
    931955
    932 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=336 height=137
    933 id="_x0000_i1054"
    934 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image009.png"></span></p>
     956<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     957 id="Picture_x0020_4" o:spid="_x0000_i1050" type="#_x0000_t75" style='width:259.5pt;
     958 height:117pt;visibility:visible;mso-wrap-style:square'>
     959 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image021.png"
     960  o:title=""/>
     961</v:shape><![endif]--><![if !vml]><img width=346 height=156
     962src="Merohedral%20twin%20refinement%20in%20GSAS_files/image012.gif" v:shapes="Picture_x0020_4"><![endif]></span></p>
    935963
    936964<p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
    937965after a pause and some activity a popup window will appear</p>
    938966
    939 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=320 height=310
    940 id="_x0000_i1053"
    941 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.png"></span></p>
     967<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     968 id="Picture_x0020_5" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:233.25pt;
     969 height:228.75pt;visibility:visible;mso-wrap-style:square'>
     970 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image023.png"
     971  o:title=""/>
     972</v:shape><![endif]--><![if !vml]><img width=311 height=305
     973src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.gif" v:shapes="Picture_x0020_5"><![endif]></span></p>
    942974
    943975<p class=MsoNormal>This makes the connection between the data set and the
     
    959991GSAS-II data tree.</p>
    960992
    961 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
    962 id="_x0000_i1052"
    963 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
     993<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     994 id="Picture_x0020_6" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:468pt;
     995 height:209.25pt;visibility:visible;mso-wrap-style:square'>
     996 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"
     997  o:title=""/>
     998</v:shape><![endif]--><![if !vml]><img width=624 height=279
     999src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.gif" v:shapes="Picture_x0020_6"><![endif]></span></p>
    9641000
    9651001<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
     
    9671003"Calibri",sans-serif'>2.0</span></b>. Next, select the <b><span
    9681004style='font-family:"Calibri",sans-serif'>Phases/C8 H25 Al0.84 Ga1.16</span></b>
    969 <span class=GramE>entry</span> in the GSAS-II data tree and choose the <b><span
    970 style='font-family:"Calibri",sans-serif'>Data</span></b> tab</p>
    971 
    972 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
    973 id="_x0000_i1051"
    974 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image011.png"></span></p>
     1005entry in the GSAS-II data tree and choose the <b><span style='font-family:"Calibri",sans-serif'>Data</span></b>
     1006tab</p>
     1007
     1008<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1009 id="Picture_x0020_23" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:468pt;
     1010 height:261.75pt;visibility:visible;mso-wrap-style:square'>
     1011 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image028.png"
     1012  o:title=""/>
     1013</v:shape><![endif]--><![if !vml]><img width=624 height=349
     1014src="Merohedral%20twin%20refinement%20in%20GSAS_files/image018.gif" v:shapes="Picture_x0020_23"><![endif]></span></p>
    9751015
    9761016<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
     
    9861026let’s test this; select the <b><span style='font-family:"Calibri",sans-serif'>Flack
    9871027parameter</span></b> for refinement and do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>
    988 from the main GSAS-II data tree menu. The structure will quickly refine to give
    989 <span class=SpellE>R<sub>w</sub></span>=2.087% which is a considerable
    990 improvement on Scale factor alone. The Flack parameter is now 0.452, meaning
    991 that both hands somehow exist in the structure. This can happen if the crystal
    992 is <span class=SpellE>merohedrally</span> inversion twinned.</p>
     1028from the main GSAS-II data tree menu. You’ll be asked to save the project; pick
     1029a directory &amp; a name – I chose <b style='mso-bidi-font-weight:normal'><span
     1030style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1031mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>1b</span></b>.
     1032The structure will quickly refine to give <span class=SpellE>R<sub>w</sub></span>=2.155%
     1033which is a considerable improvement on Scale factor alone. The Flack parameter
     1034is now 0.433, meaning that both hands somehow exist in the structure. This can
     1035happen if the crystal is <span class=SpellE>merohedrally</span> inversion twinned.</p>
    9931036
    9941037<p class=MsoNormal>To introduce this twin, press the <b><span style='font-family:
    9951038"Calibri",sans-serif'>Add Twin Law</span></b> box; the window will be redrawn.</p>
    9961039
    997 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
    998 id="_x0000_i1050"
    999 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image013.png"></span></p>
    1000 
    1001 <p class=MsoNormal>Notice that two Twin Law matrices have been generated; one
    1002 is the identity for the reference structure and the other by default is the
     1040<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1041 id="_x0000_i1046" type="#_x0000_t75" style='width:468pt;height:334.5pt;
     1042 visibility:visible;mso-wrap-style:square'>
     1043 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image030.png"
     1044  o:title=""/>
     1045</v:shape><![endif]--><![if !vml]><img width=624 height=446
     1046src="Merohedral%20twin%20refinement%20in%20GSAS_files/image019.gif" v:shapes="_x0000_i1046"><![endif]></span></p>
     1047
     1048<p class=MsoNormal>Notice that two Twin Law matrices have been generated; one is
     1049the identity for the reference structure and the other by default is the
    10031050merohedral inverse. If some other twin law is desired, then the matrix elements
    10041051need to be changed. Moreover, the Flack parameter has vanished as it is no
     
    10071054fraction</span></b> and rerun the refinement. The Data window now has.</p>
    10081055
    1009 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=449 height=500
    1010 id="_x0000_i1049"
    1011 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.png"></span></p>
     1056<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1057 id="Picture_x0020_42" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:468pt;
     1058 height:337.5pt;visibility:visible;mso-wrap-style:square'>
     1059 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image032.png"
     1060  o:title=""/>
     1061</v:shape><![endif]--><![if !vml]><img width=624 height=450
     1062src="Merohedral%20twin%20refinement%20in%20GSAS_files/image062.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
    10121063
    10131064<p class=MsoNormal>The refinement quickly converged to where it was before but
     
    10551106you want.</p>
    10561107
    1057 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=410 height=262
    1058 id="_x0000_i1048"
    1059 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image012.png"></span></p>
    1060 
    1061 <p class=MsoNormal>Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>;
     1108<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1109 id="Picture_x0020_43" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:314.25pt;
     1110 height:159pt;visibility:visible;mso-wrap-style:square'>
     1111 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image034.png"
     1112  o:title=""/>
     1113</v:shape><![endif]--><![if !vml]><img width=419 height=212
     1114src="Merohedral%20twin%20refinement%20in%20GSAS_files/image063.gif" v:shapes="Picture_x0020_43"><![endif]></span></p>
     1115
     1116<p class=MsoNormal>Press <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Yes</span></b></span>;
    10621117a Read Warning will appear.</p>
    10631118
    10641119<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1065  id="Picture_x0020_39" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:371.25pt;
    1066  height:176.25pt;visibility:visible;mso-wrap-style:square'>
    1067  <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image001.png"
    1068   o:title=""/>
    1069 </v:shape><![endif]--><![if !vml]><img width=495 height=235
    1070 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image002.gif" v:shapes="Picture_x0020_39"><![endif]></span></p>
     1120 id="Picture_x0020_44" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:378.75pt;
     1121 height:177pt;visibility:visible;mso-wrap-style:square'>
     1122 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image036.png"
     1123  o:title=""/>
     1124</v:shape><![endif]--><![if !vml]><img width=505 height=236
     1125src="Merohedral%20twin%20refinement%20in%20GSAS_files/image064.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
    10711126
    10721127<p class=MsoNormal>There are two significant warnings concerning <span
     
    10851140the General tab for this phase is shown. </p>
    10861141
    1087 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=336
    1088 id="_x0000_i1046"
    1089 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image027.png"></span></p>
     1142<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1143 id="Picture_x0020_45" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:468pt;
     1144 height:206.25pt;visibility:visible;mso-wrap-style:square'>
     1145 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image038.png"
     1146  o:title=""/>
     1147</v:shape><![endif]--><![if !vml]><img width=624 height=275
     1148src="Merohedral%20twin%20refinement%20in%20GSAS_files/image065.gif" v:shapes="Picture_x0020_45"><![endif]></span></p>
    10901149
    10911150<p class=MsoNormal>Change the Space group to <b><span style='font-family:"Calibri",sans-serif'>P
     
    10941153Atoms</span></b>.</p>
    10951154
    1096 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=478 height=358
    1097 id="_x0000_i1045"
    1098 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image028.jpg"></span></p>
     1155<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1156 id="Picture_x0020_47" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:468pt;
     1157 height:405pt;visibility:visible;mso-wrap-style:square'>
     1158 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image040.png"
     1159  o:title=""/>
     1160</v:shape><![endif]--><![if !vml]><img width=624 height=540
     1161src="Merohedral%20twin%20refinement%20in%20GSAS_files/image066.gif" v:shapes="Picture_x0020_47"><![endif]></span></p>
    10991162
    11001163<p class=MsoNormal>&nbsp;</p>
     
    11081171from the file dialog box; a popup will appear showing a few lines.</p>
    11091172
    1110 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=366 height=262
    1111 id="_x0000_i1044"
    1112 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image022.png"></span></p>
     1173<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1174 id="Picture_x0020_48" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:274.5pt;
     1175 height:186pt;visibility:visible;mso-wrap-style:square'>
     1176 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image042.png"
     1177  o:title=""/>
     1178</v:shape><![endif]--><![if !vml]><img width=366 height=248
     1179src="Merohedral%20twin%20refinement%20in%20GSAS_files/image067.gif" v:shapes="Picture_x0020_48"><![endif]></span></p>
    11131180
    11141181<p class=MsoNormal>This is the right file; a <span class=SpellE>Shelx</span>
    1115 HKLF 4 file consists of records with just <span class=SpellE><span class=GramE>h,k</span>,l</span>,
    1116 F<sup>2</sup> and <span style='font-family:Symbol'>s</span>(F<sup>2</sup>).
    1117 Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b> and <b><span
    1118 style='font-family:"Calibri",sans-serif'>OK</span></b> on the next one (we’ll
    1119 keep the name as it is). Choose the phase with the long name on the next popup
    1120 and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>; a 2D
    1121 display of the hk0 zone is plotted.</p>
    1122 
    1123 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=535
    1124 id="_x0000_i1043"
    1125 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image029.png"></span></p>
    1126 
    1127 <p class=MsoNormal>The size of the green circles <span class=GramE>are</span>
    1128 proportional to <span class=SpellE>Fo</span> (after a structure factor
     1182HKLF 4 file consists of records with just <span class=SpellE>h<span
     1183class=GramE>,k,l</span></span>, F<sup>2</sup> and <span style='font-family:
     1184Symbol'>s</span>(F<sup>2</sup>). Press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
     1185and <b><span style='font-family:"Calibri",sans-serif'>OK</span></b> on the next
     1186one (we’ll keep the name as it is). Choose the phase with the long name on the
     1187next popup and press <b><span style='font-family:"Calibri",sans-serif'>OK</span></b>;
     1188select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
     1189"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
     1190minor-latin;mso-bidi-theme-font:minor-latin'>Structure factors</span></b> tab, a
     11912D display of the hk0 zone is plotted.</p>
     1192
     1193<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1194 id="Picture_x0020_49" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:468pt;
     1195 height:401.25pt;visibility:visible;mso-wrap-style:square'>
     1196 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image044.png"
     1197  o:title=""/>
     1198</v:shape><![endif]--><![if !vml]><img width=624 height=535
     1199src="Merohedral%20twin%20refinement%20in%20GSAS_files/image068.gif" v:shapes="Picture_x0020_49"><![endif]></span></p>
     1200
     1201<p class=MsoNormal>The size of the green circles are proportional to <span
     1202class=SpellE><span class=GramE>Fo</span></span> (after a structure factor
    11291203calculation blue rings will appear for Fc).</p>
    11301204
     
    11451219GSAS-II data tree.</p>
    11461220
    1147 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
    1148 id="_x0000_i1042"
    1149 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
     1221<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1222 id="Picture_x0020_50" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:468pt;
     1223 height:215.25pt;visibility:visible;mso-wrap-style:square'>
     1224 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image046.png"
     1225  o:title=""/>
     1226</v:shape><![endif]--><![if !vml]><img width=624 height=287
     1227src="Merohedral%20twin%20refinement%20in%20GSAS_files/image069.gif" v:shapes="Picture_x0020_50"><![endif]></span></p>
    11501228
    11511229<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
     
    11581236
    11591237<p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=444
    1160 id="_x0000_i1041"
     1238id="_x0000_i1037"
    11611239src="Merohedral%20twin%20refinement%20in%20GSAS_files/image030.png"></span></p>
    11621240
     
    11641242factor</span></b> is selected for refinement by default. If you refine it, you
    11651243will get an <span class=SpellE>R<sub>w</sub></span>~ 25% which is terrible. If
    1166 you try refining atom positions &amp; thermal parameters you could possibly <span
    1167 class=GramE>lower</span> it to ~15% (still terrible) and the resulting
    1168 structure would not be very satisfactory. However, we have suspected from the
    1169 equivalence of <span style='position:relative;top:3pt'><span style='mso-no-proof:
    1170 yes'><img width=9 height=19 id="_x0000_i1040"
    1171 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image031.png"></span>&nbsp;and
    1172 <span style='position:relative;top:3pt'><span style='mso-no-proof:yes'><img
    1173 width=9 height=19 id="_x0000_i1039"
    1174 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m1
     1244you try refining atom positions &amp; thermal parameters you could possibly
     1245lower it to ~15% (still terrible) and the resulting structure would not be very
     1246satisfactory. However, we have suspected from the equivalence of <span
     1247style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
     1248    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     1249   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1250   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
     1251   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
     1252style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1253"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1254top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1255EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1256 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
     1257 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
     1258  o:title="" chromakey="white"/>
     1259</v:shape><![endif]--><![if !vml]><img width=9 height=21
     1260src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;and
     1261<span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
     1262    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     1263   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1264   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
     1265   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
     1266style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1267"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1268top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1269EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1270 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
     1271 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
     1272  o:title="" chromakey="white"/>
     1273</v:shape><![endif]--><![if !vml]><img width=9 height=21
     1274src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>m1
    11751275Laue data symmetries that there is twinning so don’t bother trying to make it
    11761276better by refining the structure. To determine the possible twin law we refer
    11771277to Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
    1178 that indeed Laue <span style='position:relative;top:3pt'><span
    1179 style='mso-no-proof:yes'><img width=9 height=19 id="_x0000_i1038"
    1180 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>m1
     1278that indeed Laue <span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
     1279    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     1280   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1281   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
     1282   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
     1283style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1284"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1285top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1286EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1287 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
     1288 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
     1289  o:title="" chromakey="white"/>
     1290</v:shape><![endif]--><![if !vml]><img width=9 height=21
     1291src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>m1
    11811292as P3<sub>2</sub>21 can be simulated by twinned Laue <span style='position:
    1182 relative;top:3pt'><span style='mso-no-proof:yes'><img width=9 height=19
    1183 id="_x0000_i1037"
    1184 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image026.png"></span>&nbsp;crystals
     1293relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:bar><m:barPr><m:pos
     1294    m:val="top"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
     1295   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     1296   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:barPr><m:e><i
     1297   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
     1298style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
     1299"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
     1300top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
     1301EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
     1302 type="#_x0000_t75" style='width:6.75pt;height:15.75pt'>
     1303 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image048.png"
     1304  o:title="" chromakey="white"/>
     1305</v:shape><![endif]--><![if !vml]><img width=9 height=21
     1306src="Merohedral%20twin%20refinement%20in%20GSAS_files/image070.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;crystals
    11851307in P3<sub>2</sub>; the possible operator is shown in Table 1.3.4.1 (reproduced
    1186 above) as either a mirror or a 2-fold. The detailed symbolism in the table (‘m.<span
    1187 class=GramE>., ..</span>2/.2.’) indicates (perhaps obscurely) the operator
    1188 specifics. See P3m1 and P3<sub>2</sub>21 space groups in International Tables
    1189 for Crystallography, Vol A for the operations m as <span style='position:relative;
    1190 top:3pt'><span style='mso-no-proof:yes'>-y-xz</span>&nbsp;or 2 as <span
    1191 style='position:relative;top:3pt'><span style='mso-no-proof:yes'>yx-z</span>;
    1192 we will use the 2-fold since the m inverts the structure which we are not
    1193 sensitive to in this experiment.</p>
     1308above) as either a mirror or a 2-fold. The detailed symbolism in the table
     1309(‘m.., ..2/.2.’) indicates (perhaps obscurely) the operator specifics. See P3m1
     1310and P3<sub>2</sub>21 space groups in International Tables for Crystallography,
     1311Vol A for the operations m as <span style='position:relative;top:3pt'><span
     1312style='mso-no-proof:yes'>-y-xz</span>&nbsp;or 2 as <span style='position:relative;
     1313top:3pt'><span style='mso-no-proof:yes'>yx-z</span>; we will use the 2-fold
     1314since the m inverts the structure which we are not sensitive to in this
     1315experiment.</p>
    11941316
    11951317<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Add
     
    11991321box. It should look like.</p>
    12001322
    1201 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=507 height=500
    1202 id="_x0000_i1036"
    1203 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image034.png"></span></p>
     1323<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1324 id="Picture_x0020_51" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt;
     1325 height:352.5pt;visibility:visible;mso-wrap-style:square'>
     1326 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image050.png"
     1327  o:title=""/>
     1328</v:shape><![endif]--><![if !vml]><img width=624 height=470
     1329src="Merohedral%20twin%20refinement%20in%20GSAS_files/image071.gif" v:shapes="Picture_x0020_51"><![endif]></span></p>
    12041330
    12051331<p class=MsoNormal>Now do <b><span style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b>;
    1206 there will be an immediate improvement in the fit to <span class=SpellE>Rw</span>=5.05%
    1207 and the twin fractions will be ~50/50. Clearly this crystal is Type 2 <span
    1208 class=SpellE>merohedrally</span> twinned; we cannot determine if there is any
    1209 Type 1 twinning because we lack sufficient resonant scattering to see it. This
    1210 ends the second example; you can save the project file.</p>
     1332you’ll have to save the project. Pick a directory &amp; file name - I used <b
     1333style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     1334mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
     1335minor-latin'>2b</span></b>. <span class=GramE>there</span> will be an immediate
     1336improvement in the fit to <span class=SpellE>Rw</span>=5.05% and the twin
     1337fractions will be ~50/50. Clearly this crystal is Type 2 <span class=SpellE>merohedrally</span>
     1338twinned; we cannot determine if there is any Type 1 twinning because we lack
     1339sufficient resonant scattering to see it. This ends the second example; you can
     1340save the project file.</p>
    12111341
    12121342<h2><span style='mso-fareast-font-family:"Times New Roman"'>Example 3. A Type 1
    1213 &amp; 2 merohedral twin – <span class=SpellE>Cp</span>*Cs(NC<sub>5</sub>H<sub>5</sub>)<o:p></o:p></span></h2>
     1343&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>
    12141344
    12151345<p class=MsoNormal>This <span class=SpellE>ecample</span> is very similar to
     
    12371367you want.</p>
    12381368
    1239 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=366 height=262
    1240 id="_x0000_i1035"
    1241 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image035.png"></span></p>
     1369<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1370 id="Picture_x0020_52" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:274.5pt;
     1371 height:174.75pt;visibility:visible;mso-wrap-style:square'>
     1372 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image072.png"
     1373  o:title=""/>
     1374</v:shape><![endif]--><![if !vml]><img width=366 height=233
     1375src="Merohedral%20twin%20refinement%20in%20GSAS_files/image073.gif" v:shapes="Picture_x0020_52"><![endif]></span></p>
    12421376
    12431377<p class=MsoNormal>It is; press the <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b>
     
    1248138261</span></b>; the General tab will be redrawn after showing you the operators.</p>
    12491383
    1250 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=624 height=467
    1251 id="_x0000_i1034"
    1252 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image036.png"></span></p>
     1384<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1385 id="Picture_x0020_53" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:468pt;
     1386 height:234.75pt;visibility:visible;mso-wrap-style:square'>
     1387 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image074.png"
     1388  o:title=""/>
     1389</v:shape><![endif]--><![if !vml]><img width=624 height=313
     1390src="Merohedral%20twin%20refinement%20in%20GSAS_files/image075.gif" v:shapes="Picture_x0020_53"><![endif]></span></p>
    12531391
    12541392<p class=MsoNormal>Next do <b><span style='font-family:"Calibri",sans-serif'>Import/Structure
     
    12651403class=SpellE>Shelx</span>.</p>
    12661404
    1267 <p class=MsoNormal>You now have loaded all that is needed for the third
    1268 example. The structure had previously been solved and refined with <span
    1269 class=SpellE>Shelx</span> so you need not trouble about those steps. You can
    1270 try to solve the structure in GSAS-II via charge flipping but this is not part
    1271 of this exercise (it isn’t easy because of the twinning; charge flipping will
    1272 readily give the Cs position &amp; most of the rest. It can be completed via
    1273 difference Fourier techniques); we will only explore the twin analysis features
    1274 of GSAS-II.</p>
     1405<p class=MsoNormal>You now have loaded all that is needed for the third example.
     1406The structure had previously been solved and refined with <span class=SpellE>Shelx</span>
     1407so you need not trouble about those steps. You can try to solve the structure
     1408in GSAS-II via charge flipping but this is not part of this exercise (it isn’t
     1409easy because of the twinning; charge flipping will readily give the Cs position
     1410&amp; most of the rest. It can be completed via difference Fourier techniques);
     1411we will only explore the twin analysis features of GSAS-II.</p>
    12751412
    12761413<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 2. Refinement
     
    12781415
    12791416<p class=MsoNormal>Before beginning the refinement, it usually the practice to
    1280 eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub> &lt;
    1281 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
     1417eliminate the poorly measured reflections where F<sup>2</sup><sub>obs</sub>
     1418&lt; 2<span style='font-family:Symbol'>s</span>(F<sup>2</sup>). Select the <b><span
    12821419style='font-family:"Calibri",sans-serif'>Controls</span></b> entry from the
    12831420GSAS-II data tree.</p>
    12841421
    1285 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=522 height=301
    1286 id="_x0000_i1033"
    1287 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.png"></span></p>
     1422<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1423 id="Picture_x0020_54" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt;
     1424 height:205.5pt;visibility:visible;mso-wrap-style:square'>
     1425 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image076.png"
     1426  o:title=""/>
     1427</v:shape><![endif]--><![if !vml]><img width=624 height=274
     1428src="Merohedral%20twin%20refinement%20in%20GSAS_files/image077.gif" v:shapes="Picture_x0020_54"><![endif]></span></p>
    12881429
    12891430<p class=MsoNormal>Change <b><span style='font-family:"Calibri",sans-serif'>Min
     
    12951436tab.</p>
    12961437
    1297 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
    1298 id="_x0000_i1032"
    1299 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image037.png"></span></p>
     1438<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1439 id="Picture_x0020_55" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:468pt;
     1440 height:303.75pt;visibility:visible;mso-wrap-style:square'>
     1441 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image078.png"
     1442  o:title=""/>
     1443</v:shape><![endif]--><![if !vml]><img width=624 height=405
     1444src="Merohedral%20twin%20refinement%20in%20GSAS_files/image079.gif" v:shapes="Picture_x0020_55"><![endif]></span></p>
    13001445
    13011446<p class=MsoNormal>Notice that the <b><span style='font-family:"Calibri",sans-serif'>Scale
     
    13031448will get an <span class=SpellE>R<sub>w</sub></span>~ 17% which is terrible. It
    13041449doesn’t change much if you add the Flack parameter (~0.36). If you try refining
    1305 atom positions &amp; thermal parameters you could possibly <span class=GramE>lower</span>
    1306 it but the resulting structure would not be very satisfactory. However, we have
    1307 suspected from the equivalence of 6/m and 6/mmm Laue data symmetries that there
    1308 is twinning so don’t bother trying to make it better by refining the structure.
    1309 To determine the possible twin <span class=GramE>laws</span> we again refer to
    1310 Table 1.3.4.2 of the International Tables for Crystallography Vol C. and see
    1311 that indeed Laue 6/mmm as P6<sub>1</sub>22 can be simulated by twinned Laue 6/m
    1312 crystals in P6<sub>1</sub>; the possible operator is shown in Table 1.3.4.1
    1313 (reproduced above) as either a mirror or a 2-fold. The detailed symbolism in the
    1314 table (‘m.., ..2/.2.’) indicates (perhaps obscurely) the operator specifics;
    1315 they are m as <span style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:acc><m:accPr><m:chr
     1450atom positions &amp; thermal parameters you could possibly lower it but the
     1451resulting structure would not be very satisfactory. However, we have suspected
     1452from the equivalence of 6/m and 6/mmm Laue data symmetries that there is
     1453twinning so don’t bother trying to make it better by refining the structure. To
     1454determine the possible twin laws we again refer to Table 1.3.4.2 of the
     1455International Tables for Crystallography Vol C. and see that indeed Laue 6/mmm
     1456as P6<sub>1</sub>22 can be simulated by twinned Laue 6/m crystals in P6<sub>1</sub>;
     1457the possible operator is shown in Table 1.3.4.1 (reproduced above) as either a
     1458mirror or a 2-fold. The detailed symbolism in the table (‘m.., ..2/.2.’)
     1459indicates (perhaps obscurely) the operator specifics; they are m as <span
     1460style='position:relative;top:3pt'><!--[if gte msEquation 12]><m:oMath><m:acc><m:accPr><m:chr
    13161461    m:val="&#773;"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
    13171462   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
     
    13281473EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    13291474 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
    1330  <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image004.png"
     1475 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image052.png"
    13311476  o:title="" chromakey="white"/>
    13321477</v:shape><![endif]--><![if !vml]><img width=26 height=19
    1333 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image005.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;or
     1478src="Merohedral%20twin%20refinement%20in%20GSAS_files/image080.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;or
    133414792 as <!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:normal'><span
    13351480 style='font-family:"Cambria Math",serif'><span style='position:relative;
     
    13441489EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    13451490 type="#_x0000_t75" style='width:19.5pt;height:14.25pt'>
    1346  <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image006.png"
     1491 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image054.png"
    13471492  o:title="" chromakey="white"/>
    13481493</v:shape><![endif]--><![if !vml]><img width=26 height=19
    1349 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image008.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
     1494src="Merohedral%20twin%20refinement%20in%20GSAS_files/image081.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    13501495style='font-family:"Cambria Math",serif'>; we will use the 2-fold, m and
    13511496inversion operators to fully test for presence of the 4 possible twin laws.
     
    13561501redrawn. When done you should see.<o:p></o:p></span></p>
    13571502
    1358 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=434 height=444
    1359 id="_x0000_i1031"
    1360 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image038.png"></span>&nbsp;</p>
     1503<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1504 id="Picture_x0020_56" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
     1505 height:405.75pt;visibility:visible;mso-wrap-style:square'>
     1506 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image082.png"
     1507  o:title=""/>
     1508</v:shape><![endif]--><![if !vml]><img width=624 height=541
     1509src="Merohedral%20twin%20refinement%20in%20GSAS_files/image083.gif" v:shapes="Picture_x0020_56"><![endif]></span>&nbsp;</p>
    13611510
    13621511<p class=MsoNormal>For the third and fourth matrix enter <b><span
     
    13671516style='font-family:"Calibri",sans-serif'>Refine</span></b> button and do <b><span
    13681517style='font-family:"Calibri",sans-serif'>Calculate/Refine</span></b> from the
    1369 main menu. The <span class=SpellE>Rw</span> will immediately drop to ~2.26%
    1370 (RF~2.05%). The four twin element fractions will show various values.</p>
    1371 
    1372 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1373  id="Picture_x0020_40" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:336.75pt;
    1374  height:375pt;visibility:visible;mso-wrap-style:square'>
    1375  <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image007.png"
    1376   o:title=""/>
    1377 </v:shape><![endif]--><![if !vml]><img width=449 height=500
    1378 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image010.gif" v:shapes="Picture_x0020_40"><![endif]></span></p>
    1379 
    1380 <p class=MsoNormal>The negative one for the 3<sup>rd</sup> twin fraction is
    1381 nonphysical and the 1<sup>st</sup> twin fraction is small. It is likely that
    1382 the true space group is P6<sub>5</sub> and Type 2 <span class=SpellE>merohedrally</span>
     1518main menu; again you’ll have to save the project file – I called it 3a. The <span
     1519class=SpellE>Rw</span> will immediately drop to ~2.26% (RF~2.05%). The four
     1520twin element fractions will show various values</p>
     1521
     1522<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1523 id="Picture_x0020_57" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;
     1524 height:405.75pt;visibility:visible;mso-wrap-style:square'>
     1525 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image084.png"
     1526  o:title=""/>
     1527</v:shape><![endif]--><![if !vml]><img width=624 height=541
     1528src="Merohedral%20twin%20refinement%20in%20GSAS_files/image085.gif" v:shapes="Picture_x0020_57"><![endif]></span></p>
     1529
     1530<p class=MsoNormal>The negative one for the 3<sup>rd</sup> twin fraction is nonphysical
     1531and the 1<sup>st</sup> twin fraction is small. It is likely that the true space
     1532group is P6<sub>5</sub> and Type 2 <span class=SpellE>merohedrally</span>
    13831533twinned (twin fractions 2 &amp; 4). We can improve it by refining the atom
    13841534positions and thermal parameters, but first we need to replace the hydrogen
     
    13941544  o:title=""/>
    13951545</v:shape><![endif]--><![if !vml]><img width=700 height=300
    1396 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image012.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
     1546src="Merohedral%20twin%20refinement%20in%20GSAS_files/image086.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
    13971547
    13981548<p class=MsoNormal>If you scroll down the page, you’ll see H-atoms with default
     
    14071557The H-atoms will be highlighted (and plotted in green). Do <b style='mso-bidi-font-weight:
    14081558normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1409 minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Delete atom</span></b> from
    1410 the menu; the H-atoms will be deleted and the structure will be redrawn. Next
    1411 double <span class=GramE>click</span> the <b style='mso-bidi-font-weight:normal'><span
     1559minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/On selected atoms
     1560/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
    14121563style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    14131564mso-hansi-theme-font:minor-latin'>Type</span></b> column heading and select <b
     
    14161567all the C-atoms will be selected (and shown in green on the plot). Do <b
    14171568style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1418 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Insert
    1419 H atoms</span></b>; a Distance Angle Controls will appear. Occasionally these
    1420 values may need to be changed but not this time; press <b style='mso-bidi-font-weight:
    1421 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1422 minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>. The next popup is
    1423 for the H atoms add controls.</p>
    1424 
    1425 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1426  id="Picture_x0020_42" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:300pt;
    1427  height:363.75pt;visibility:visible;mso-wrap-style:square'>
    1428  <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image011.png"
    1429   o:title=""/>
    1430 </v:shape><![endif]--><![if !vml]><img width=400 height=485
    1431 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image014.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
     1569mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/On
     1570selected atoms
     1571/<span class=SpellE>Calc</span> H atoms</span></b>; a Distance
     1572Angle Controls will appear. Occasionally these values may need to be changed
     1573but not this time; press <b style='mso-bidi-font-weight:normal'><span
     1574style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1575mso-hansi-theme-font:minor-latin'>Ok</span></b>. The next popup is for the H
     1576atoms add controls.</p>
     1577
     1578<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1579 id="Picture_x0020_58" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:300pt;
     1580 height:187.5pt;visibility:visible;mso-wrap-style:square'>
     1581 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image087.png"
     1582  o:title=""/>
     1583</v:shape><![endif]--><![if !vml]><img width=400 height=250
     1584src="Merohedral%20twin%20refinement%20in%20GSAS_files/image088.gif" v:shapes="Picture_x0020_58"><![endif]></span></p>
    14321585
    14331586<p class=MsoNormal>It specifies the expected geometry around each C-atom for
     
    14401593after their respective C-atom. Their positions and thermal parameters are tied
    14411594to the C-atoms so that after refinement of the structure they can be shifted to
    1442 the <span class=SpellE>stereochemically</span> best positions. For the refinement,
    1443 double click the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    1444 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    1445 minor-latin'>Refine</span></b> column heading and select <b style='mso-bidi-font-weight:
    1446 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1447 minor-latin;mso-hansi-theme-font:minor-latin'>X</span></b> and <b
     1595the <span class=SpellE>stereochemically</span> best positions. For the
     1596refinement, double click the <b style='mso-bidi-font-weight:normal'><span
     1597style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
     1598mso-hansi-theme-font:minor-latin'>Refine</span></b> column heading and select <b
    14481599style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     1600mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>X</span></b>
     1601and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    14491602mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>U</span></b>
    14501603from the popup; press <b style='mso-bidi-font-weight:normal'><span
     
    14531606with XU in every entry under Refine. Now do <b style='mso-bidi-font-weight:
    14541607normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1455 minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from
    1456 the main GSASII data tree window; the <span class=SpellE>Rw</span> will drop to
    1457 ~1.92%. If you look at the <b style='mso-bidi-font-weight:normal'><span
    1458 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1459 mso-hansi-theme-font:minor-latin'>Data</span></b> tab the Twin element
    1460 fractions are much clearer.</p>
    1461 
    1462 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1463  id="Picture_x0020_43" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:336.75pt;
    1464  height:375pt;visibility:visible;mso-wrap-style:square'>
    1465  <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image013.png"
    1466   o:title=""/>
    1467 </v:shape><![endif]--><![if !vml]><img width=449 height=500
    1468 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image016.gif" v:shapes="Picture_x0020_43"><![endif]></span><span
     1608minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> (2-3
     1609times until convergence<span class=GramE>)from</span> the main GSASII data tree
     1610window; the <span class=SpellE>Rw</span> will drop to ~1.80%. If you look at
     1611the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     1612mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b>
     1613tab the Twin element fractions are much clearer.</p>
     1614
     1615<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1616 id="Picture_x0020_59" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;
     1617 height:342.75pt;visibility:visible;mso-wrap-style:square'>
     1618 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image089.png"
     1619  o:title=""/>
     1620</v:shape><![endif]--><![if !vml]><img width=624 height=457
     1621src="Merohedral%20twin%20refinement%20in%20GSAS_files/image090.gif" v:shapes="Picture_x0020_59"><![endif]></span><span
    14691622style='mso-spacerun:yes'> </span></p>
    14701623
     
    14831636you’ll see the Operators popup (press <b style='mso-bidi-font-weight:normal'><span
    14841637style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1485 mso-hansi-theme-font:minor-latin'>Ok</span></b>) and the General tab will be redrawn.
    1486 Next select the <b style='mso-bidi-font-weight:normal'><span style='font-family:
    1487 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    1488 minor-latin'>Atoms</span></b> tab; do <b style='mso-bidi-font-weight:normal'><span
     1638mso-hansi-theme-font:minor-latin'>Ok</span></b>) and the General tab will be
     1639redrawn. Next select the <b style='mso-bidi-font-weight:normal'><span
    14891640style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1490 mso-hansi-theme-font:minor-latin'>Edit/Update H atoms</span></b> to put them in
    1491 their best positions.<span style='mso-spacerun:yes'>  </span>Next select all
    1492 the atoms by double clicking the empty box in upper left corner of the table;
    1493 all atoms will be highlighted &amp; plotted green. Do <b style='mso-bidi-font-weight:
     1641mso-hansi-theme-font:minor-latin'>Atoms</span></b> tab; do <b style='mso-bidi-font-weight:
    14941642normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1495 minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Transform atoms</span></b>;
    1496 a popup will appear.</p>
    1497 
    1498 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1499  id="Picture_x0020_44" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:270pt;
    1500  height:263.25pt;visibility:visible;mso-wrap-style:square'>
    1501  <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image015.png"
    1502   o:title=""/>
    1503 </v:shape><![endif]--><![if !vml]><img width=360 height=351
    1504 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image018.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
     1643minor-latin;mso-hansi-theme-font:minor-latin'>Edit Atoms/Update H atoms</span></b>
     1644to put them in their best positions.<span style='mso-spacerun:yes'> 
     1645</span>Next select all the atoms by double clicking the empty box in upper left
     1646corner of the table; all atoms will be highlighted &amp; plotted green. Do <b
     1647style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     1648mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
     1649Atoms/On selected atoms
     1650/Transform atoms</span></b>; a popup will appear.</p>
     1651
     1652<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
     1653 id="Picture_x0020_60" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:270pt;
     1654 height:264pt;visibility:visible;mso-wrap-style:square'>
     1655 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image091.png"
     1656  o:title=""/>
     1657</v:shape><![endif]--><![if !vml]><img width=360 height=352
     1658src="Merohedral%20twin%20refinement%20in%20GSAS_files/image092.gif" v:shapes="Picture_x0020_60"><![endif]></span></p>
    15051659
    15061660<p class=MsoNormal>Check the <b style='mso-bidi-font-weight:normal'><span
     
    15171671will both be redrawn. Now do <b style='mso-bidi-font-weight:normal'><span
    15181672style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1519 mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b>; the <span
     1673mso-hansi-theme-font:minor-latin'>Calculate/Refine </span></b>2-3 times; the <span
    15201674class=SpellE>Rw</span> will drop back to where it was before and the <b
    15211675style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
     
    15241678
    15251679<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1526  id="Picture_x0020_46" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:336.75pt;
    1527  height:375pt;visibility:visible;mso-wrap-style:square'>
    1528  <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image017.png"
    1529   o:title=""/>
    1530 </v:shape><![endif]--><![if !vml]><img width=449 height=500
    1531 src="Merohedral%20twin%20refinement%20in%20GSAS_files/image019.gif" v:shapes="Picture_x0020_46"><![endif]></span></p>
     1680 id="Picture_x0020_61" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt;
     1681 height:400.5pt;visibility:visible;mso-wrap-style:square'>
     1682 <v:imagedata src="Merohedral%20twin%20refinement%20in%20GSAS_files/image093.png"
     1683  o:title=""/>
     1684</v:shape><![endif]--><![if !vml]><img width=624 height=534
     1685src="Merohedral%20twin%20refinement%20in%20GSAS_files/image094.gif" v:shapes="Picture_x0020_61"><![endif]></span></p>
    15321686
    15331687<p class=MsoNormal>Now the identity Twin Law is ~2/3 and the 2-fold Twin Law is
  • Tutorials/MerohedralTwins/Merohedral twin refinement in GSAS_files/filelist.xml

    r2394 r3059  
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