source: Tutorials/StackingFaults-I/Stacking Faults-I.htm @ 4633

Last change on this file since 4633 was 4457, checked in by toby, 18 months ago

add data link to tutorials

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402  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
403  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
404  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
405  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
406  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
407  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
408  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
409  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
410  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
411  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
412  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
413  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
414  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
415  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
416  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
417  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
418  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
419  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
420  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
421  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
422  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
423  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
424  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
425  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
426  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
427  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
428  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
429  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
430  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
431  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
432  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
433  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
434  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
435  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
436  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
437  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
438  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
439  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
440  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
441  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
442  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
443  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
444  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
445  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
446  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
447  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
448  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
449  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
450  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
451  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
452  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
453  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
454  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
455  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
456  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
457  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
458  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
459  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
460  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
461  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
462  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
463  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
464  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
465  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
466  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
467  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
468  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
469  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
470  <w:LsdException Locked="false" Priority="19" QFormat="true"
471   Name="Subtle Emphasis"/>
472  <w:LsdException Locked="false" Priority="21" QFormat="true"
473   Name="Intense Emphasis"/>
474  <w:LsdException Locked="false" Priority="31" QFormat="true"
475   Name="Subtle Reference"/>
476  <w:LsdException Locked="false" Priority="32" QFormat="true"
477   Name="Intense Reference"/>
478  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
479  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
480   UnhideWhenUsed="true" Name="Bibliography"/>
481  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
482   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
483  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
484  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
485  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
486  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
487  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
488  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
489  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
490  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
491  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
492  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
493  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
494  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
495  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
496  <w:LsdException Locked="false" Priority="46"
497   Name="Grid Table 1 Light Accent 1"/>
498  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
499  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
500  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
501  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
502  <w:LsdException Locked="false" Priority="51"
503   Name="Grid Table 6 Colorful Accent 1"/>
504  <w:LsdException Locked="false" Priority="52"
505   Name="Grid Table 7 Colorful Accent 1"/>
506  <w:LsdException Locked="false" Priority="46"
507   Name="Grid Table 1 Light Accent 2"/>
508  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
509  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
510  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
511  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
512  <w:LsdException Locked="false" Priority="51"
513   Name="Grid Table 6 Colorful Accent 2"/>
514  <w:LsdException Locked="false" Priority="52"
515   Name="Grid Table 7 Colorful Accent 2"/>
516  <w:LsdException Locked="false" Priority="46"
517   Name="Grid Table 1 Light Accent 3"/>
518  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
519  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
520  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
521  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
522  <w:LsdException Locked="false" Priority="51"
523   Name="Grid Table 6 Colorful Accent 3"/>
524  <w:LsdException Locked="false" Priority="52"
525   Name="Grid Table 7 Colorful Accent 3"/>
526  <w:LsdException Locked="false" Priority="46"
527   Name="Grid Table 1 Light Accent 4"/>
528  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
529  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
530  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
531  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
532  <w:LsdException Locked="false" Priority="51"
533   Name="Grid Table 6 Colorful Accent 4"/>
534  <w:LsdException Locked="false" Priority="52"
535   Name="Grid Table 7 Colorful Accent 4"/>
536  <w:LsdException Locked="false" Priority="46"
537   Name="Grid Table 1 Light Accent 5"/>
538  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
539  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
540  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
541  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
542  <w:LsdException Locked="false" Priority="51"
543   Name="Grid Table 6 Colorful Accent 5"/>
544  <w:LsdException Locked="false" Priority="52"
545   Name="Grid Table 7 Colorful Accent 5"/>
546  <w:LsdException Locked="false" Priority="46"
547   Name="Grid Table 1 Light Accent 6"/>
548  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
549  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
550  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
551  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
552  <w:LsdException Locked="false" Priority="51"
553   Name="Grid Table 6 Colorful Accent 6"/>
554  <w:LsdException Locked="false" Priority="52"
555   Name="Grid Table 7 Colorful Accent 6"/>
556  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
557  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
558  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
559  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
560  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
561  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
562  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
563  <w:LsdException Locked="false" Priority="46"
564   Name="List Table 1 Light Accent 1"/>
565  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
566  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
567  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
568  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
569  <w:LsdException Locked="false" Priority="51"
570   Name="List Table 6 Colorful Accent 1"/>
571  <w:LsdException Locked="false" Priority="52"
572   Name="List Table 7 Colorful Accent 1"/>
573  <w:LsdException Locked="false" Priority="46"
574   Name="List Table 1 Light Accent 2"/>
575  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
576  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
577  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
578  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
579  <w:LsdException Locked="false" Priority="51"
580   Name="List Table 6 Colorful Accent 2"/>
581  <w:LsdException Locked="false" Priority="52"
582   Name="List Table 7 Colorful Accent 2"/>
583  <w:LsdException Locked="false" Priority="46"
584   Name="List Table 1 Light Accent 3"/>
585  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
586  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
587  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
588  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
589  <w:LsdException Locked="false" Priority="51"
590   Name="List Table 6 Colorful Accent 3"/>
591  <w:LsdException Locked="false" Priority="52"
592   Name="List Table 7 Colorful Accent 3"/>
593  <w:LsdException Locked="false" Priority="46"
594   Name="List Table 1 Light Accent 4"/>
595  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
596  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
597  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
598  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
599  <w:LsdException Locked="false" Priority="51"
600   Name="List Table 6 Colorful Accent 4"/>
601  <w:LsdException Locked="false" Priority="52"
602   Name="List Table 7 Colorful Accent 4"/>
603  <w:LsdException Locked="false" Priority="46"
604   Name="List Table 1 Light Accent 5"/>
605  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
606  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
607  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
608  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
609  <w:LsdException Locked="false" Priority="51"
610   Name="List Table 6 Colorful Accent 5"/>
611  <w:LsdException Locked="false" Priority="52"
612   Name="List Table 7 Colorful Accent 5"/>
613  <w:LsdException Locked="false" Priority="46"
614   Name="List Table 1 Light Accent 6"/>
615  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
616  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
617  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
618  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
619  <w:LsdException Locked="false" Priority="51"
620   Name="List Table 6 Colorful Accent 6"/>
621  <w:LsdException Locked="false" Priority="52"
622   Name="List Table 7 Colorful Accent 6"/>
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684h2
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732        mso-fareast-theme-font:minor-fareast;
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736        font-style:italic;}
737h5
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740        mso-style-qformat:yes;
741        mso-style-link:"Heading 5 Char";
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744        mso-margin-bottom-alt:auto;
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751        mso-fareast-theme-font:minor-fareast;
752        color:#4F4FFF;
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762        font-family:"Times New Roman",serif;
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768        mso-style-link:"Footer Char";
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1118<![endif]--><!--[if gte mso 9]><xml>
1119 <o:shapedefaults v:ext="edit" spidmax="1026"/>
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1125
1126<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1127
1128<div class=WordSection1>
1129
1130<h1><span style='mso-fareast-font-family:"Times New Roman"'>Stacking Fault
1131Simulations – I<o:p></o:p></span></h1>
1132
1133  <P><BL>
1134  <LI><B>A video version of this tutorial is available at
1135<A href="https://anl.box.com/v/StackingFaults-I" target="_blank">
1136https://anl.box.com/v/StackingFaults-I</A></B>
1137  <LI>No exercise files are needed for this tutorial</a>
1138</BL></P><P></P>
1139
1140<p class=MsoNormal>In this exercise you will use GSAS-II to simulate the
1141diffraction patterns from faulted diamond. Diamond most commonly has the
1142well-known cubic structure with the space group Fd3m and a=3.5668A. The C-atom
1143is at 1/8<span class=GramE>,1</span>/8,1/8 and can be viewed as a cubic
1144stacking of ruffled hexagonal nets along the cubic cell 111 diagonal. </p>
1145
1146<p class=MsoNormal><span style='mso-no-proof:yes'><img width=482 height=361
1147id="_x0000_i1052" src="Stacking%20Faults-I_files/image001.jpg"></span></p>
1148
1149<p class=MsoNormal>The structure of <span class=SpellE>londsdaleite</span> has
1150those layers stacked hexagonally and thus a faulted diamond structure may
1151occasionally have hexagonal stacked layers instead of all cubic ones. From
1152geometric considerations, these planar stacking faults must extend across the
1153entire crystal. If there are only a few such faults in a crystal then the
1154diffraction pattern will show two cubic diamond patterns in a twin law
1155relationship. Otherwise, if there are many such faults then the diffraction
1156pattern will show streaks. To simulate the streaks one must first develop a
1157model for the hexagonal net of C-atoms and then show how they stack in either
1158the cubic or hexagonal forms. GSAS-II uses a suite of subroutines from the <span
1159class=SpellE>DIFFaX</span> program (M.M.J. <span class=SpellE>Treacy</span>,
1160J.M. <span class=SpellE>Newsam</span> &amp; M.W. Deem, (1991), Proc. Roy. Soc. <span
1161class=SpellE>Lond</span>. 433A, 499-520) to calculate the diffraction pattern
1162via a general recursion algorithm and a randomized set of stacked layers. NB:
1163this calculation can be quite time consuming particularly if unreasonable
1164demands are made on it. </p>
1165
1166<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1167
1168<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 1.
1169Selected area diffraction for random faults in diamond<o:p></o:p></span></h2>
1170
1171<p class=MsoNormal>To begin we must have a phase to work with. In the main
1172GSAS-II data tree menu do <b><span style='font-family:"Calibri",sans-serif'>Data/Add
1173new phase</span></b>; a popup window will appear inviting you to name the
1174phase. I entered <b><span style='font-family:"Calibri",sans-serif'>‘random
1175faults</span></b>’. Then find this phase in the data tree under phases and
1176select it; the data window will display the default for the General tab.</p>
1177
1178<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
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1199 style='width:468pt;height:191.25pt;visibility:visible;mso-wrap-style:square'>
1200 <v:imagedata src="Stacking%20Faults-I_files/image001.png" o:title=""/>
1201</v:shape><![endif]--><![if !vml]><img width=624 height=255
1202src="Stacking%20Faults-I_files/image002.gif" v:shapes="Picture_x0020_31"><![endif]></span></p>
1203
1204<p class=MsoNormal>Change the phase type to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
1205the window will be redrawn and a new tab (‘<b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>’)
1206will appear. Select it. Then save the project; I called it ‘<b><span
1207style='font-family:"Calibri",sans-serif'>diamond</span></b>’.</p>
1208
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1213</v:shape><![endif]--><![if !vml]><img width=624 height=255
1214src="Stacking%20Faults-I_files/image004.gif" v:shapes="Picture_x0020_33"><![endif]></span></p>
1215
1216<p class=MsoNormal>First you need to describe the reference unit cell for the
1217stacking model. The cubic/hexagonal stacking in diamond is with layers
1218perpendicular to the 111 axis. This will become the new c-axis. The a- &amp;
1219b-axes are for the hexagonal net of C-atoms that are stacked in this structure.
1220One can also anticipate that the resulting diffraction pattern will have
1221hexagonal <b><span style='font-family:"Calibri",sans-serif'>6/mmm</span></b>
1222symmetry so first select this from the pull down box near the top of the page;
1223the window will be redrawn.</p>
1224
1225<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1226 id="Picture_x0020_34" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:468pt;
1227 height:230.25pt;visibility:visible;mso-wrap-style:square'>
1228 <v:imagedata src="Stacking%20Faults-I_files/image005.png" o:title=""/>
1229</v:shape><![endif]--><![if !vml]><img width=624 height=307
1230src="Stacking%20Faults-I_files/image006.gif" v:shapes="Picture_x0020_34"><![endif]></span></p>
1231
1232<p class=MsoNormal><span class=GramE>The a</span> cell parameter for diamond
1233stacking can be assumed to be <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type
1234    m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1235   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1236   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
1237   style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:num><m:den><m:rad><m:radPr><m:degHide
1238      m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1239     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1240     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
1241     style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:e></m:rad></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
1242style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1243"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1244top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1245EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1246 type="#_x0000_t75" style='width:28.5pt;height:15.75pt'>
1247 <v:imagedata src="Stacking%20Faults-I_files/image007.png" o:title=""
1248  chromakey="white"/>
1249</v:shape><![endif]--><![if !vml]><img width=38 height=21
1250src="Stacking%20Faults-I_files/image008.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;=
1251<b><span style='font-family:"Calibri",sans-serif'>2.522</span></b> and the c
1252cell parameter is <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type m:val="lin"/><span
1253   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1254   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1255   normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
1256   normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:num><m:den><m:rad><m:radPr><m:degHide
1257      m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1258     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1259     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
1260     style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:e></m:rad></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
1261style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1262"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1263top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1264EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1265 type="#_x0000_t75" style='width:28.5pt;height:15.75pt'>
1266 <v:imagedata src="Stacking%20Faults-I_files/image009.png" o:title=""
1267  chromakey="white"/>
1268</v:shape><![endif]--><![if !vml]><img width=38 height=21
1269src="Stacking%20Faults-I_files/image010.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;=
1270<b><span style='font-family:"Calibri",sans-serif'>2.059</span></b> since there
1271are 3 layers along the 111 diamond cell diagonal. Enter these in the
1272appropriate places; the cell volume will be revised.</p>
1273
1274<p class=MsoNormal>Now we have to describe the two hexagonal nets that will be
1275stacked for either cubic or hexagonal stacking. Select <b><span
1276style='font-family:"Calibri",sans-serif'>Add new layer?</span></b> <span
1277class=GramE>the</span> window will be redrawn.</p>
1278
1279<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1280 id="Picture_x0020_35" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:468pt;
1281 height:311.25pt;visibility:visible;mso-wrap-style:square'>
1282 <v:imagedata src="Stacking%20Faults-I_files/image011.png" o:title=""/>
1283</v:shape><![endif]--><![if !vml]><img width=624 height=415
1284src="Stacking%20Faults-I_files/image012.gif" v:shapes="Picture_x0020_35"><![endif]></span></p>
1285
1286<p class=MsoNormal>Name the layer (I chose ‘<b><span style='font-family:"Calibri",sans-serif'>layer
12871</span></b>’) and choose <b><span style='font-family:"Calibri",sans-serif'>‘-1</span></b>’
1288for the layer symmetry. The window will be redrawn after changing the name.
1289Next, select <b><span style='font-family:"Calibri",sans-serif'>Add atom?</span></b>
1290<span class=GramE>and</span> the window will be redrawn with one line in the
1291layer table.</p>
1292
1293<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1294 id="Picture_x0020_36" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:468pt;
1295 height:311.25pt;visibility:visible;mso-wrap-style:square'>
1296 <v:imagedata src="Stacking%20Faults-I_files/image013.png" o:title=""/>
1297</v:shape><![endif]--><![if !vml]><img width=624 height=415
1298src="Stacking%20Faults-I_files/image014.gif" v:shapes="Picture_x0020_36"><![endif]></span></p>
1299
1300<p class=MsoNormal>To make this a C-atom select the ‘<span class=SpellE><b><span
1301style='font-family:"Calibri",sans-serif'>Unk</span></b></span>’ under Type with
1302a double click; a Periodic table will popup. Select <b><span style='font-family:
1303"Calibri",sans-serif'>C</span></b>; the popup will disappear and the window
1304will be redrawn. The coordinates of this C-atom in the new stacking unit cell
1305is <b><span style='font-family:"Calibri",sans-serif'>-1/3,-1/6,-1/8</span></b>;
1306you may enter these as fractions. Select a table item to complete the entry;
1307the window should show the new position.</p>
1308
1309<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1310 id="Picture_x0020_38" o:spid="_x0000_i1046" type="#_x0000_t75" style='width:468pt;
1311 height:323.25pt;visibility:visible;mso-wrap-style:square'>
1312 <v:imagedata src="Stacking%20Faults-I_files/image015.png" o:title=""/>
1313</v:shape><![endif]--><![if !vml]><img width=624 height=431
1314src="Stacking%20Faults-I_files/image016.gif" v:shapes="Picture_x0020_38"><![endif]></span></p>
1315
1316<p class=MsoNormal>You can draw the layer to see what it looks like; select <b><span
1317style='font-family:"Calibri",sans-serif'>Draw layer?</span></b> <span
1318class=GramE>and</span> the drawing will appear. </p>
1319
1320<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1321 id="Picture_x0020_39" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:468pt;
1322 height:403.5pt;visibility:visible;mso-wrap-style:square'>
1323 <v:imagedata src="Stacking%20Faults-I_files/image017.png" o:title=""/>
1324</v:shape><![endif]--><![if !vml]><img width=624 height=538
1325src="Stacking%20Faults-I_files/image018.gif" v:shapes="Picture_x0020_39"><![endif]></span></p>
1326
1327<p class=MsoNormal>A unit cell box is drawn with a 5x5 suite of unit cells; the
1328ruffled hexagonal net perpendicular to the c-axis (blue line) is clear.</p>
1329
1330<p class=MsoNormal>Now we need a second layer (‘<b style='mso-bidi-font-weight:
1331normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1332minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>layer
13332</span></b>’); repeat the steps for making a layer using <b><span
1334style='font-family:"Calibri",sans-serif'>1/3<span class=GramE>,1</span>/6,-1/8</span></b>
1335for the C-atom position with <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>
1336for the layer symmetry. The window should look like this when done.</p>
1337
1338<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1339 id="Picture_x0020_40" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:468pt;
1340 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1341 <v:imagedata src="Stacking%20Faults-I_files/image019.png" o:title=""/>
1342</v:shape><![endif]--><![if !vml]><img width=624 height=485
1343src="Stacking%20Faults-I_files/image020.gif" v:shapes="Picture_x0020_40"><![endif]></span></p>
1344
1345<p class=MsoNormal>I’ve stretched it a bit to show the Layer-Layer transition probabilities.
1346Change <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dz</span></b></span>
1347for each entry to <b><span style='font-family:"Calibri",sans-serif'>1.0</span></b>
1348to properly space out the stacked layers. If you select the first box in the
1349plot column for layer 1 you will see the two layers stacked but in a way
1350reminiscent of how carbon sheets stack in graphite. </p>
1351
1352<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1353 id="Picture_x0020_41" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:468pt;
1354 height:406.5pt;visibility:visible;mso-wrap-style:square'>
1355 <v:imagedata src="Stacking%20Faults-I_files/image021.png" o:title=""/>
1356</v:shape><![endif]--><![if !vml]><img width=624 height=542
1357src="Stacking%20Faults-I_files/image022.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
1358
1359<p class=MsoNormal>Clearly not diamond stacking. The table defines how the next
1360layer is displaced relative to the reference layer. You can shift this layer by
1361using the <b><span style='font-family:"Calibri",sans-serif'>X<span class=GramE>,Y,Z</span></span></b>
1362&amp; <b><span style='font-family:"Calibri",sans-serif'>shift-X,Y,Z</span></b>
1363keys; the plot will be redrawn and the table entry updated each time you shift the
1364layer. When you get to the right offset for diamond additional bonds will
1365appear connecting the layers together. The correct shift is <span class=SpellE><b><span
1366style='font-family:"Calibri",sans-serif'>Dx</span></b></span><b><span
1367style='font-family:"Calibri",sans-serif'>=2/3</span></b>, <span class=SpellE><b><span
1368style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span
1369style='font-family:"Calibri",sans-serif'>=1/3</span></b> and <span
1370class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dz</span></b></span><b><span
1371style='font-family:"Calibri",sans-serif'>=1.0</span></b> for the layer 1 to
1372layer 1 transition and for layer 2 to layer 2 the shifts are <span
1373class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dx</span></b></span><b><span
1374style='font-family:"Calibri",sans-serif'>=-2/3</span></b>, <span class=SpellE><b><span
1375style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span
1376style='font-family:"Calibri",sans-serif'>=-1/3</span></b> and <span
1377class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dz</span></b></span><b><span
1378style='font-family:"Calibri",sans-serif'>=1.0</span></b>. For the remaining
1379layer 1-layer 2 and <i>vice versa</i> transitions <span class=SpellE><b><span
1380style='font-family:"Calibri",sans-serif'>Dx</span></b></span><b><span
1381style='font-family:"Calibri",sans-serif'>=<span class=SpellE>Dy</span>=0</span></b>.
1382Layer 1 to layer 1 stacking looks like.</p>
1383
1384<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1385 id="Picture_x0020_42" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:468pt;
1386 height:404.25pt;visibility:visible;mso-wrap-style:square'>
1387 <v:imagedata src="Stacking%20Faults-I_files/image023.png" o:title=""/>
1388</v:shape><![endif]--><![if !vml]><img width=624 height=539
1389src="Stacking%20Faults-I_files/image024.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
1390
1391<p class=MsoNormal>You can explore the result of various stacking sequences in
1392the next block of commands; enter <b><span style='font-family:"Calibri",sans-serif'>1
13931 1 1 2 2 2</span></b> into the box (remember to include spaces in between each number) and press <b><span style='font-family:"Calibri",sans-serif'>Enter</span></b>.
1394A plot showing the result of a single twin fault will be shown.</p>
1395
1396<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1397 id="Picture_x0020_43" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:468pt;
1398 height:404.25pt;visibility:visible;mso-wrap-style:square'>
1399 <v:imagedata src="Stacking%20Faults-I_files/image025.png" o:title=""/>
1400</v:shape><![endif]--><![if !vml]><img width=624 height=539
1401src="Stacking%20Faults-I_files/image026.gif" v:shapes="Picture_x0020_43"><![endif]></span></p>
1402
1403<p class=MsoNormal>If you enter 1 2 1 2 1 2 1 2 then the structure of <span
1404class=SpellE>londsdaleite</span> will be shown; 1 1 1 1 1 1 or 2 2 2 2 2 2
1405gives the diamond structure. </p>
1406
1407<p class=MsoNormal>Finally we must select transition probabilities; they should
1408sum to 1.0 for each block. Use <b><span style='font-family:"Calibri",sans-serif'>0.7</span></b>
1409for layer 1 to layer 1 and layer 2 to layer 2; the cross terms are then <b><span
1410style='font-family:"Calibri",sans-serif'>0.3</span></b> to give</p>
1411
1412<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1413 id="Picture_x0020_44" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:468pt;
1414 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1415 <v:imagedata src="Stacking%20Faults-I_files/image027.png" o:title=""/>
1416</v:shape><![endif]--><![if !vml]><img width=624 height=485
1417src="Stacking%20Faults-I_files/image028.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
1418
1419<p class=MsoNormal>We are now ready to do a single crystal simulation; select <b><span
1420style='font-family:"Calibri",sans-serif'>Operations/Simulate pattern</span></b>
1421from the Phase data window menu. A small popup will appear</p>
1422
1423<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1424 id="Picture_x0020_45" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:209.25pt;
1425 height:102.75pt;visibility:visible;mso-wrap-style:square'>
1426 <v:imagedata src="Stacking%20Faults-I_files/image029.png" o:title=""/>
1427</v:shape><![endif]--><![if !vml]><img width=279 height=137
1428src="Stacking%20Faults-I_files/image030.gif" v:shapes="Picture_x0020_45"><![endif]></span></p>
1429
1430<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>selected
1431area</span></b> for the calculation type; the popup will be redrawn with new
1432options.</p>
1433
1434<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1435 id="Picture_x0020_46" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:181.5pt;
1436 height:102.75pt;visibility:visible;mso-wrap-style:square'>
1437 <v:imagedata src="Stacking%20Faults-I_files/image031.png" o:title=""/>
1438</v:shape><![endif]--><![if !vml]><img width=242 height=137
1439src="Stacking%20Faults-I_files/image032.gif" v:shapes="Picture_x0020_46"><![endif]></span></p>
1440
1441<p class=MsoNormal>To make it interesting select <b><span style='font-family:
1442"Calibri",sans-serif'>Max. <span class=GramE>l</span> index</span></b> of <b><span
1443style='font-family:"Calibri",sans-serif'>6</span></b> and press <b><span
1444style='font-family:"Calibri",sans-serif'>Ok</span></b>. Very quickly a new
1445popup will appear letting you know the simulation is finished; press <b><span
1446style='font-family:"Calibri",sans-serif'>Ok</span></b>. The data window will be
1447redrawn</p>
1448
1449<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1450 id="Picture_x0020_47" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:468pt;
1451 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1452 <v:imagedata src="Stacking%20Faults-I_files/image033.png" o:title=""/>
1453</v:shape><![endif]--><![if !vml]><img width=624 height=485
1454src="Stacking%20Faults-I_files/image034.gif" v:shapes="Picture_x0020_47"><![endif]></span></p>
1455
1456<p class=MsoNormal>At the top is a new item <b><span style='font-family:"Calibri",sans-serif'>Plot
1457selected area diffraction?</span></b> Select it and a new plot will appear. The
1458intensity scale is adjusted by pressing <b><span style='font-family:"Calibri",sans-serif'>D</span></b>
1459(or <b><span style='font-family:"Calibri",sans-serif'>U</span></b>); I got</p>
1460
1461<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1462 id="Picture_x0020_48" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt;
1463 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1464 <v:imagedata src="Stacking%20Faults-I_files/image035.png" o:title=""/>
1465</v:shape><![endif]--><![if !vml]><img width=624 height=535
1466src="Stacking%20Faults-I_files/image036.gif" v:shapes="Picture_x0020_48"><![endif]></span></p>
1467
1468<p class=MsoNormal>The streaking intermixed with sharp spots is clearly obvious
1469in this plot. Save this project; you’ll need it for the next simulation.</p>
1470
1471<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 2.
1472Laboratory powder diffraction simulation for random faults in diamond<o:p></o:p></span></h2>
1473
1474<p class=MsoNormal>The setup for a powder pattern simulation is the same as
1475above for selected are diffraction with one crucial difference. We need a dummy
1476powder pattern to define the simulation limits. Using the same project as
1477above, do <b><span style='font-family:"Calibri",sans-serif'>Import/Powder
1478data/Simulate a data set</span></b> from the main GSAS-II data tree window. A
1479popup will appear requesting the selection of an instrument parameter file;
1480here we will use one of the built in defaults. Press <b><span style='font-family:
1481"Calibri",sans-serif'>Cancel</span></b> and a new popup will appear offering
1482some choices.</p>
1483
1484<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1485 id="Picture_x0020_49" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:241.5pt;
1486 height:201.75pt;visibility:visible;mso-wrap-style:square'>
1487 <v:imagedata src="Stacking%20Faults-I_files/image037.png" o:title=""/>
1488</v:shape><![endif]--><![if !vml]><img width=322 height=269
1489src="Stacking%20Faults-I_files/image038.gif" v:shapes="Picture_x0020_49"><![endif]></span></p>
1490
1491<p class=MsoNormal>Use the first one for <span class=SpellE><b><span
1492style='font-family:"Calibri",sans-serif'>CuKa</span></b></span><b><span
1493style='font-family:"Calibri",sans-serif'> lab data</span></b>; a new popup will
1494appear</p>
1495
1496<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1497 id="Picture_x0020_50" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:238.5pt;
1498 height:257.25pt;visibility:visible;mso-wrap-style:square'>
1499 <v:imagedata src="Stacking%20Faults-I_files/image039.png" o:title=""/>
1500</v:shape><![endif]--><![if !vml]><img width=318 height=343
1501src="Stacking%20Faults-I_files/image040.gif" v:shapes="Picture_x0020_50"><![endif]></span></p>
1502
1503<p class=MsoNormal>Change the end angle to <b><span style='font-family:"Calibri",sans-serif'>150</span></b>
1504and the step size to <b><span style='font-family:"Calibri",sans-serif'>0.02</span></b>;
1505press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and
1506choose <b><span style='font-family:"Calibri",sans-serif'>random faults </span></b>(your
1507phase name). Notice the small data window lets you know that you can clear the
1508observed intensities in the simulation by doing an <b><span style='font-family:
1509"Calibri",sans-serif'>Edit range</span></b> (no need to change anything). The
1510tree will have a new item <b><span style='font-family:"Calibri",sans-serif'>PWDR
1511CW x-ray simulation</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Background</span></b>
1512&amp; enter <b><span style='font-family:"Calibri",sans-serif'>50</span></b> for
1513the 1<sup>st</sup> coefficient. Next select <b><span style='font-family:"Calibri",sans-serif'>Sample
1514parameters</span></b> and enter <b><span style='font-family:"Calibri",sans-serif'>1000</span></b>
1515for the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale
1516factor</span></b> and change the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
1517type</span></b> to <b><span
1518style='font-family:"Calibri",sans-serif'>Bragg-Brentano</span></b> (if
1519not already set to that).
1520Finally, find your phase (<b><span style='font-family:"Calibri",sans-serif'>random
1521faults</span></b>) and select it and then the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
1522tab. It should be unchanged from when the selected area simulation was
1523finished.</p>
1524
1525<p class=MsoNormal>To do the simulation do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
1526pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1527from the popup. The calculated pattern will by default be broadened using U, V,
1528&amp; W from the Instrument parameters for the chosen powder pattern. Other
1529choices use a mean Gaussian broadening (faster) or no broadening (even faster).
1530The only choice for the pattern is given in the next popup; press <b><span
1531style='font-family:"Calibri",sans-serif'>Ok</span></b> and the simulation will
1532proceed. After a few seconds a small popup will appear letting you know it is
1533done; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and
1534the powder pattern will be displayed with the result. On the plot press the ‘<b><span
1535style='font-family:"Calibri",sans-serif'>+</span></b>’ key to suppress the ‘+’
1536marks. The plot should look like: </p>
1537
1538<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1539 id="Picture_x0020_51" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt;
1540 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1541 <v:imagedata src="Stacking%20Faults-I_files/image041.png" o:title=""/>
1542</v:shape><![endif]--><![if !vml]><img width=624 height=535
1543src="Stacking%20Faults-I_files/image042.gif" v:shapes="Picture_x0020_51"><![endif]></span></p>
1544(I’ve expanded the scale to show the
1545interesting stuff around each peak.)
1546<p></p>
1547<p class=MsoNormal>The blue line is a simulated observed pattern with imposed
1548Poisson noise, the red line is the calculated background and the green curve is
1549the smooth calculated pattern. A difference curve is also shown. You can play
1550with changing the transition probabilities and/or the layer offsets to see what
1551effect these have on the pattern; changing these will change the calculated
1552pattern unless you reset the dummy profile as noted above.</p>
1553
1554<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 3.
1555Sequential parameter change<o:p></o:p></span></h2>
1556
1557<p class=MsoNormal>A perhaps useful means of exploring the effects of changing
1558stacking parameters is doing a sequence of simulations varying one parameter
1559over a range. To try this out do <b><span style='font-family:"Calibri",sans-serif'>Operations/Sequence
1560simulations</span></b> from the Layers menu; a popup will appear</p>
1561
1562<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1563 id="Picture_x0020_52" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:209.25pt;
1564 height:2in;visibility:visible;mso-wrap-style:square'>
1565 <v:imagedata src="Stacking%20Faults-I_files/image043.png" o:title=""/>
1566</v:shape><![endif]--><![if !vml]><img width=279 height=192
1567src="Stacking%20Faults-I_files/image044.gif" v:shapes="Picture_x0020_52"><![endif]></span></p>
1568
1569<p class=MsoNormal>Here you select the parameter, range and number of steps
1570(both ends will be used). From the <b><span style='font-family:"Calibri",sans-serif'>Select
1571parameter</span></b> pulldown choose <b><span style='font-family:"Calibri",sans-serif'>TransP<span
1572class=GramE>;0</span>;0</span></b>; this is the layer 1 to layer 1 transition
1573probability. Then change the no. steps to <b><span style='font-family:"Calibri",sans-serif'>10</span></b>
1574(11 will be calculated). We have the same choices for instrument broadening as
1575above; use the default. Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1576the next popup allows selection of a powder pattern (e.g. for comparison and
1577the range for the calculation). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1578for this one; the sequential simulation will proceed. The console displays
1579progress and the transition matrix for each step. A popup will appear when the
1580sequence is finished after several seconds. Notice that the matrix is not
1581symmetric (see console) so that layer1 to layer 1 probability is not the same
1582as layer 2 to layer 2 at each step in the simulation. We can force this by
1583selecting <b><span style='font-family:"Calibri",sans-serif'>Symmetric
1584probabilities?</span></b> <span class=GramE>on</span> the Layers tab. Do this
1585and repeat the sequential simulation as above. Now the matrices are symmetric
1586as one could expect. When the simulation is finished, select the <b><span
1587style='font-family:"Calibri",sans-serif'>Plot sequential result?</span></b> <span
1588class=GramE>box</span>; a new plot will appear.</p>
1589
1590<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1591 id="Picture_x0020_61" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
1592 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1593 <v:imagedata src="Stacking%20Faults-I_files/image046.png" o:title=""/>
1594</v:shape><![endif]--><![if !vml]><img width=624 height=535
1595src="Stacking%20Faults-I_files/image048.gif" v:shapes="Picture_x0020_61"><![endif]></span></p>
1596
1597<p class=MsoNormal>This is a multiline plot; you can shift the lines with the <b><span
1598style='font-family:"Calibri",sans-serif'>U<span class=GramE>,D,L,R</span></span></b>
1599keys (<b><span style='font-family:"Calibri",sans-serif'>O</span></b> resets
1600offsets to zero). I’ve done this for the next plot.</p>
1601
1602<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1603 id="Picture_x0020_62" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;
1604 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1605 <v:imagedata src="Stacking%20Faults-I_files/image083.png" o:title=""/>
1606</v:shape><![endif]--><![if !vml]><img width=624 height=535
1607src="Stacking%20Faults-I_files/image084.gif" v:shapes="Picture_x0020_62"><![endif]></span></p>
1608
1609<p class=MsoNormal>The first blue line is for pure hexagonal <span
1610class=SpellE>londsdaleite</span> stacking and the last magenta line is for pure
1611cubic diamond stacking. You can see how some lines quickly vanish with the
1612introduction of stacking faults while other persist across the entire sequence.
1613This is a good place to save your project file; the sequential result will be
1614included.</p>
1615
1616<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 4.
1617Modelling clustering in diamond<o:p></o:p></span></h2>
1618
1619<p class=MsoNormal>In this simulation we will explore the possibility that the
1620stacking history affects the probability of a fault. In the case of diamond, a
1621fault to form <span class=SpellE>londsdaleite</span> could be followed by
1622similar layers until a lower probability fault converts the structure back to
1623diamond. The crystal then has blocks of diamond structure interleaved with
1624blocks of <span class=SpellE>londsdaleite</span>. This is best done in a new
1625phase so we don’t mess up the above simulations, but most of the data in the
1626current phase is useful for the cluster model. The easiest way is to import the
1627new phase from the current project. <b><span style='font-family:"Calibri",sans-serif'>Do
1628Import/Phase/from GSAS-II <span class=SpellE>gpx</span> file</span></b> from
1629the main GSAS-II data tree <span class=GramE>menu.</span> A file selection
1630dialog box will appear; select the current project file (<span class=SpellE><b><span
1631style='font-family:"Calibri",sans-serif'>diamond.gpx</span></b></span>) and
1632press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>. A
1633small popup will appear confirming your choice; press <span class=GramE><b><span
1634style='font-family:"Calibri",sans-serif'>Yes</span></b></span>. The next popup
1635offers the change to name the phase, I chose <b><span style='font-family:"Calibri",sans-serif'>clustered</span></b>
1636for the name. Next select the PWDR data set to be linked to this phase. The
1637General tab for the new phase will appear.</p>
1638
1639<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1640 id="Picture_x0020_55" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:468pt;
1641 height:173.25pt;visibility:visible;mso-wrap-style:square'>
1642 <v:imagedata src="Stacking%20Faults-I_files/image073.png" o:title=""/>
1643</v:shape><![endif]--><![if !vml]><img width=624 height=231
1644src="Stacking%20Faults-I_files/image085.gif" v:shapes="Picture_x0020_55"><![endif]></span></p>
1645
1646<p class=MsoNormal>Notice that the Phase type is faulted and that Layers is one
1647of the tabs; select it.</p>
1648
1649<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1650 id="Picture_x0020_56" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:468pt;
1651 height:276pt;visibility:visible;mso-wrap-style:square'>
1652 <v:imagedata src="Stacking%20Faults-I_files/image075.png" o:title=""/>
1653</v:shape><![endif]--><![if !vml]><img width=624 height=368
1654src="Stacking%20Faults-I_files/image086.gif" v:shapes="Picture_x0020_56"><![endif]></span></p>
1655
1656<p class=MsoNormal>This is all the same information as for the random faults
1657phase. To simulate clustering we need two new layers which are the same as
1658these two listed here. Do <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Add</span></b></span><b><span
1659style='font-family:"Calibri",sans-serif'> new layer?</span></b> <span
1660class=GramE>twice</span> so two new layers appear. Name them <b><span
1661style='font-family:"Calibri",sans-serif'>layer 3</span></b> and <b><span
1662style='font-family:"Calibri",sans-serif'>layer 4</span></b>. Make layer 3 <span
1663class=GramE><b><span style='font-family:"Calibri",sans-serif'>Same</span></b></span><b><span
1664style='font-family:"Calibri",sans-serif'> as layer</span></b> 1 (select from
1665the pull down) and layer 4 <b><span style='font-family:"Calibri",sans-serif'>Same
1666as layer 2</span></b>. Each time the window is redrawn so that the transition
1667probability tables reflect these changes. You should also change the <b><span
1668style='font-family:"Calibri",sans-serif'>Diffraction Laue symmetry</span></b>
1669to <b><span style='font-family:"Calibri",sans-serif'>-3m</span></b>. When you
1670are done the upper part of the Layers window should look like.</p>
1671
1672<p class=MsoNormal>&nbsp;</p>
1673
1674<p class=MsoNormal>&nbsp;</p>
1675
1676<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1677 id="Picture_x0020_57" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;
1678 height:276pt;visibility:visible;mso-wrap-style:square'>
1679 <v:imagedata src="Stacking%20Faults-I_files/image077.png" o:title=""/>
1680</v:shape><![endif]--><![if !vml]><img width=624 height=368
1681src="Stacking%20Faults-I_files/image087.gif" v:shapes="Picture_x0020_57"><![endif]></span></p>
1682
1683<p class=MsoNormal>&nbsp;</p>
1684
1685<p class=MsoNormal>The transition vectors for the cluster model are similar to
1686the random faults model, i.e. layer 1-1 and layer 3-1 transitions are <b><span
1687style='font-family:"Calibri",sans-serif'>2/3,1/3,1</span></b> for <span
1688class=SpellE>Dx</span>, <span class=SpellE>Dy</span> &amp; <span class=SpellE>Dz</span>,
1689layer, and layer 2-4 and 4-4 transitions are <b><span style='font-family:"Calibri",sans-serif'>-2/3,-1/3,1</span></b>
1690for <span class=SpellE>Dx</span>, <span class=SpellE>Dy</span> &amp; Dz. All
1691the rest are <b><span style='font-family:"Calibri",sans-serif'>0<span
1692class=GramE>,0,1</span></span></b> for <span class=SpellE>Dx</span>,,<span
1693class=SpellE>Dy</span> &amp; Dz. The probabilities can best be seen from the
1694following array</p>
1695
1696<p class=MsoNormal>&nbsp;</p>
1697
1698<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
1699 style='border-collapse:collapse;mso-yfti-tbllook:1184;mso-padding-alt:0in 0in 0in 0in'>
1700 <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;height:21.45pt'>
1701  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1702  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1703  <p class=MsoNormal>Layer</p>
1704  </td>
1705  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1706  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1707  <p class=MsoNormal>1</p>
1708  </td>
1709  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1710  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1711  <p class=MsoNormal>2</p>
1712  </td>
1713  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1714  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1715  <p class=MsoNormal>3</p>
1716  </td>
1717  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1718  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1719  <p class=MsoNormal>4</p>
1720  </td>
1721 </tr>
1722 <tr style='mso-yfti-irow:1;height:21.45pt'>
1723  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1724  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1725  <p class=MsoNormal>1</p>
1726  </td>
1727  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1728  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1729  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1730  <p class=MsoNormal>CS</p>
1731  </td>
1732  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1733  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1734  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1735  <p class=MsoNormal>CF</p>
1736  </td>
1737  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1738  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1739  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1740  <p class=MsoNormal>x</p>
1741  </td>
1742  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1743  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1744  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1745  <p class=MsoNormal>x</p>
1746  </td>
1747 </tr>
1748 <tr style='mso-yfti-irow:2;height:21.45pt'>
1749  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1750  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1751  <p class=MsoNormal>2</p>
1752  </td>
1753  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1754  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1755  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1756  <p class=MsoNormal>x</p>
1757  </td>
1758  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1759  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1760  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1761  <p class=MsoNormal>x</p>
1762  </td>
1763  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1764  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1765  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1766  <p class=MsoNormal>HS</p>
1767  </td>
1768  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1769  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1770  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1771  <p class=MsoNormal>HF</p>
1772  </td>
1773 </tr>
1774 <tr style='mso-yfti-irow:3;height:21.45pt'>
1775  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1776  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1777  <p class=MsoNormal>3</p>
1778  </td>
1779  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1780  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1781  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1782  <p class=MsoNormal>HF</p>
1783  </td>
1784  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1785  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1786  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1787  <p class=MsoNormal>HS</p>
1788  </td>
1789  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1790  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1791  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1792  <p class=MsoNormal>x</p>
1793  </td>
1794  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1795  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1796  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1797  <p class=MsoNormal>x</p>
1798  </td>
1799 </tr>
1800 <tr style='mso-yfti-irow:4;mso-yfti-lastrow:yes;height:21.45pt'>
1801  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1802  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1803  <p class=MsoNormal>4</p>
1804  </td>
1805  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1806  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1807  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1808  <p class=MsoNormal>x</p>
1809  </td>
1810  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1811  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1812  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1813  <p class=MsoNormal>x</p>
1814  </td>
1815  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1816  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1817  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1818  <p class=MsoNormal>CF</p>
1819  </td>
1820  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1821  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1822  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1823  <p class=MsoNormal>CS</p>
1824  </td>
1825 </tr>
1826</table>
1827
1828<p class=MsoNormal>Where CS – cubic stacking, CF – cubic fault, HS – hexagonal
1829stacking, HF – hexagonal fault and x – not allowed. A suitable model might be
1830CS = <b><span style='font-family:"Calibri",sans-serif'>0.9</span></b>, CF = <b><span
1831style='font-family:"Calibri",sans-serif'>0.1</span></b>, HS = <b><span
1832style='font-family:"Calibri",sans-serif'>0.8</span></b> and HF = <b><span
1833style='font-family:"Calibri",sans-serif'>0.2</span></b>. This will give more and
1834thicker cubic blocks than hexagonal ones. Set these values and the Transition
1835tables should look like</p>
1836
1837<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1838 id="Picture_x0020_59" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:468pt;
1839 height:457.5pt;visibility:visible;mso-wrap-style:square'>
1840 <v:imagedata src="Stacking%20Faults-I_files/image079.png" o:title=""/>
1841</v:shape><![endif]--><![if !vml]><img width=624 height=610
1842src="Stacking%20Faults-I_files/image088.gif" v:shapes="Picture_x0020_59"><![endif]></span></p>
1843
1844<p class=MsoNormal>Before doing the simulation we need to clear away the old
1845one; select the <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b>
1846entry from the GSAS-II data tree and then select <b><span style='font-family:
1847"Calibri",sans-serif'>Edit range</span></b> from the data window. Don’t change
1848anything, just press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1849this will clear the previous simulation. Then return to the random
1850faults phase
1851Layers tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
1852pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1853twice. The simulation will require some seconds to finish; the powder profile
1854will look like</p>
1855
1856<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1857 id="Picture_x0020_60" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt;
1858 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1859 <v:imagedata src="Stacking%20Faults-I_files/image081.png" o:title=""/>
1860</v:shape><![endif]--><![if !vml]><img width=624 height=535
1861src="Stacking%20Faults-I_files/image089.gif" v:shapes="Picture_x0020_60"><![endif]></span></p>
1862
1863<p class=MsoNormal>Again, I have used ‘<b><span style='font-family:"Calibri",sans-serif'>+</span></b>’
1864and zoomed in to show the interesting part of the pattern. </p>
1865
1866<p class=MsoNormal>As additional work you can do sequential simulations to
1867explore the effect of changing probabilities. Try varying <b><span
1868style='font-family:"Calibri",sans-serif'>TransP;0;0</span></b>, i.e. layer 1 –
1869layer 1 (CS) transition probability and <b><span style='font-family:"Calibri",sans-serif'>TransP;2;1</span></b>,
1870i.e. layer 3 – layer – 2 (HS) transition probability. Be sure the <b><span
1871style='font-family:"Calibri",sans-serif'>Symmetric probabilities</span></b> box
1872is checked otherwise you’ll get nonsense. This ends this stacking fault
1873tutorial; the next one involves using kaolinite layers to simulate diffraction
1874patterns from kaolinite clays.<o:p></o:p></p>
1875
1876</div>
1877
1878</span></span>
1879</body>
1880
1881</html>
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