source: Tutorials/StackingFaults-I/Stacking Faults-I.htm @ 3081

Last change on this file since 3081 was 3081, checked in by vondreele, 4 years ago

update to 2 layer

  • Property svn:mime-type set to text/html
File size: 94.1 KB
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400  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
401  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
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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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 class=MsoNormal>In this exercise you will use GSAS-II to simulate the
1134diffraction patterns from faulted diamond. Diamond most commonly has the
1135well-known cubic structure with the space group Fd3m and a=3.5668A. The C-atom
1136is at 1/8<span class=GramE>,1</span>/8,1/8 and can be viewed as a cubic
1137stacking of ruffled hexagonal nets along the cubic cell 111 diagonal. </p>
1138
1139<p class=MsoNormal><span style='mso-no-proof:yes'><img width=482 height=361
1140id="_x0000_i1052" src="Stacking%20Faults-I_files/image001.jpg"></span></p>
1141
1142<p class=MsoNormal>The structure of <span class=SpellE>londsdaleite</span> has
1143those layers stacked hexagonally and thus a faulted diamond structure may
1144occasionally have hexagonal stacked layers instead of all cubic ones. From
1145geometric considerations, these planar stacking faults must extend across the
1146entire crystal. If there are only a few such faults in a crystal then the
1147diffraction pattern will show two cubic diamond patterns in a twin law
1148relationship. Otherwise, if there are many such faults then the diffraction
1149pattern will show streaks. To simulate the streaks one must first develop a
1150model for the hexagonal net of C-atoms and then show how they stack in either
1151the cubic or hexagonal forms. GSAS-II uses a suite of subroutines from the <span
1152class=SpellE>DIFFaX</span> program (M.M.J. <span class=SpellE>Treacy</span>,
1153J.M. <span class=SpellE>Newsam</span> &amp; M.W. Deem, (1991), Proc. Roy. Soc. <span
1154class=SpellE>Lond</span>. 433A, 499-520) to calculate the diffraction pattern
1155via a general recursion algorithm and a randomized set of stacked layers. NB:
1156this calculation can be quite time consuming particularly if unreasonable
1157demands are made on it. </p>
1158
1159<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1160
1161<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 1.
1162Selected area diffraction for random faults in diamond<o:p></o:p></span></h2>
1163
1164<p class=MsoNormal>To begin we must have a phase to work with. In the main
1165GSAS-II data tree menu do <b><span style='font-family:"Calibri",sans-serif'>Data/Add
1166new phase</span></b>; a popup window will appear inviting you to name the
1167phase. I entered <b><span style='font-family:"Calibri",sans-serif'>‘random
1168faults</span></b>’. Then find this phase in the data tree under phases and
1169select it; the data window will display the default for the General tab.</p>
1170
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1196
1197<p class=MsoNormal>Change the phase type to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
1198the window will be redrawn and a new tab (‘<b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>’)
1199will appear. Select it. Then save the project; I called it ‘<b><span
1200style='font-family:"Calibri",sans-serif'>diamond</span></b>’.</p>
1201
1202<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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1208
1209<p class=MsoNormal>First you need to describe the reference unit cell for the
1210stacking model. The cubic/hexagonal stacking in diamond is with layers
1211perpendicular to the 111 axis. This will become the new c-axis. The a- &amp;
1212b-axes are for the hexagonal net of C-atoms that are stacked in this structure.
1213One can also anticipate that the resulting diffraction pattern will have
1214hexagonal <b><span style='font-family:"Calibri",sans-serif'>6/mmm</span></b>
1215symmetry so first select this from the pull down box near the top of the page;
1216the window will be redrawn.</p>
1217
1218<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1219 id="Picture_x0020_34" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:468pt;
1220 height:230.25pt;visibility:visible;mso-wrap-style:square'>
1221 <v:imagedata src="Stacking%20Faults-I_files/image005.png" o:title=""/>
1222</v:shape><![endif]--><![if !vml]><img width=624 height=307
1223src="Stacking%20Faults-I_files/image006.gif" v:shapes="Picture_x0020_34"><![endif]></span></p>
1224
1225<p class=MsoNormal><span class=GramE>The a</span> cell parameter for diamond
1226stacking can be assumed to be <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type
1227    m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1228   "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1229   mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
1230   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
1231      m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1232     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1233     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
1234     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
1235style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1236"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1237top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1238EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1239 type="#_x0000_t75" style='width:28.5pt;height:15.75pt'>
1240 <v:imagedata src="Stacking%20Faults-I_files/image007.png" o:title=""
1241  chromakey="white"/>
1242</v:shape><![endif]--><![if !vml]><img width=38 height=21
1243src="Stacking%20Faults-I_files/image008.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;=
1244<b><span style='font-family:"Calibri",sans-serif'>2.522</span></b> and the c
1245cell parameter is <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type m:val="lin"/><span
1246   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1247   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1248   normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
1249   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
1250      m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1251     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1252     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
1253     style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:e></m:rad></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
1254style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1255"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1256top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1257EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1258 type="#_x0000_t75" style='width:28.5pt;height:15.75pt'>
1259 <v:imagedata src="Stacking%20Faults-I_files/image009.png" o:title=""
1260  chromakey="white"/>
1261</v:shape><![endif]--><![if !vml]><img width=38 height=21
1262src="Stacking%20Faults-I_files/image010.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;=
1263<b><span style='font-family:"Calibri",sans-serif'>2.059</span></b> since there
1264are 3 layers along the 111 diamond cell diagonal. Enter these in the
1265appropriate places; the cell volume will be revised.</p>
1266
1267<p class=MsoNormal>Now we have to describe the two hexagonal nets that will be
1268stacked for either cubic or hexagonal stacking. Select <b><span
1269style='font-family:"Calibri",sans-serif'>Add new layer?</span></b> <span
1270class=GramE>the</span> window will be redrawn.</p>
1271
1272<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1273 id="Picture_x0020_35" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:468pt;
1274 height:311.25pt;visibility:visible;mso-wrap-style:square'>
1275 <v:imagedata src="Stacking%20Faults-I_files/image011.png" o:title=""/>
1276</v:shape><![endif]--><![if !vml]><img width=624 height=415
1277src="Stacking%20Faults-I_files/image012.gif" v:shapes="Picture_x0020_35"><![endif]></span></p>
1278
1279<p class=MsoNormal>Name the layer (I chose ‘<b><span style='font-family:"Calibri",sans-serif'>layer
12801</span></b>’) and choose <b><span style='font-family:"Calibri",sans-serif'>‘-1</span></b>’
1281for the layer symmetry. The window will be redrawn after changing the name.
1282Next, select <b><span style='font-family:"Calibri",sans-serif'>Add atom?</span></b>
1283<span class=GramE>and</span> the window will be redrawn with one line in the
1284layer table.</p>
1285
1286<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1287 id="Picture_x0020_36" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:468pt;
1288 height:311.25pt;visibility:visible;mso-wrap-style:square'>
1289 <v:imagedata src="Stacking%20Faults-I_files/image013.png" o:title=""/>
1290</v:shape><![endif]--><![if !vml]><img width=624 height=415
1291src="Stacking%20Faults-I_files/image014.gif" v:shapes="Picture_x0020_36"><![endif]></span></p>
1292
1293<p class=MsoNormal>To make this a C-atom select the ‘<span class=SpellE><b><span
1294style='font-family:"Calibri",sans-serif'>Unk</span></b></span>’ under Type with
1295a double click; a Periodic table will popup. Select <b><span style='font-family:
1296"Calibri",sans-serif'>C</span></b>; the popup will disappear and the window
1297will be redrawn. The coordinates of this C-atom in the new stacking unit cell
1298is <b><span style='font-family:"Calibri",sans-serif'>-1/3,-1/6,-1/8</span></b>;
1299you may enter these as fractions. Select a table item to complete the entry;
1300the window should show the new position.</p>
1301
1302<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1303 id="Picture_x0020_38" o:spid="_x0000_i1046" type="#_x0000_t75" style='width:468pt;
1304 height:323.25pt;visibility:visible;mso-wrap-style:square'>
1305 <v:imagedata src="Stacking%20Faults-I_files/image015.png" o:title=""/>
1306</v:shape><![endif]--><![if !vml]><img width=624 height=431
1307src="Stacking%20Faults-I_files/image016.gif" v:shapes="Picture_x0020_38"><![endif]></span></p>
1308
1309<p class=MsoNormal>You can draw the layer to see what it looks like; select <b><span
1310style='font-family:"Calibri",sans-serif'>Draw layer?</span></b> <span
1311class=GramE>and</span> the drawing will appear. </p>
1312
1313<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1314 id="Picture_x0020_39" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:468pt;
1315 height:403.5pt;visibility:visible;mso-wrap-style:square'>
1316 <v:imagedata src="Stacking%20Faults-I_files/image017.png" o:title=""/>
1317</v:shape><![endif]--><![if !vml]><img width=624 height=538
1318src="Stacking%20Faults-I_files/image018.gif" v:shapes="Picture_x0020_39"><![endif]></span></p>
1319
1320<p class=MsoNormal>A unit cell box is drawn with a 5x5 suite of unit cells; the
1321ruffled hexagonal net perpendicular to the c-axis (blue line) is clear.</p>
1322
1323<p class=MsoNormal>Now we need a second layer (‘<b style='mso-bidi-font-weight:
1324normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1325minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>layer
13262</span></b>’); repeat the steps for making a layer using <b><span
1327style='font-family:"Calibri",sans-serif'>1/3<span class=GramE>,1</span>/6,-1/8</span></b>
1328for the C-atom position with <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>
1329for the layer symmetry. The window should look like this when done.</p>
1330
1331<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1332 id="Picture_x0020_40" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:468pt;
1333 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1334 <v:imagedata src="Stacking%20Faults-I_files/image019.png" o:title=""/>
1335</v:shape><![endif]--><![if !vml]><img width=624 height=485
1336src="Stacking%20Faults-I_files/image020.gif" v:shapes="Picture_x0020_40"><![endif]></span></p>
1337
1338<p class=MsoNormal>I’ve stretched it a bit to show the Layer-Layer transition probabilities.
1339Change <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dz</span></b></span>
1340for each entry to <b><span style='font-family:"Calibri",sans-serif'>1.0</span></b>
1341to properly space out the stacked layers. If you select the first box in the
1342plot column for layer 1 you will see the two layers stacked but in a way
1343reminiscent of how carbon sheets stack in graphite. </p>
1344
1345<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1346 id="Picture_x0020_41" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:468pt;
1347 height:406.5pt;visibility:visible;mso-wrap-style:square'>
1348 <v:imagedata src="Stacking%20Faults-I_files/image021.png" o:title=""/>
1349</v:shape><![endif]--><![if !vml]><img width=624 height=542
1350src="Stacking%20Faults-I_files/image022.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
1351
1352<p class=MsoNormal>Clearly not diamond stacking. The table defines how the next
1353layer is displaced relative to the reference layer. You can shift this layer by
1354using the <b><span style='font-family:"Calibri",sans-serif'>X<span class=GramE>,Y,Z</span></span></b>
1355&amp; <b><span style='font-family:"Calibri",sans-serif'>shift-X,Y,Z</span></b>
1356keys; the plot will be redrawn and the table entry updated each time you shift the
1357layer. When you get to the right offset for diamond additional bonds will
1358appear connecting the layers together. The correct shift is <span class=SpellE><b><span
1359style='font-family:"Calibri",sans-serif'>Dx</span></b></span><b><span
1360style='font-family:"Calibri",sans-serif'>=2/3</span></b>, <span class=SpellE><b><span
1361style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span
1362style='font-family:"Calibri",sans-serif'>=1/3</span></b> and <span
1363class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dz</span></b></span><b><span
1364style='font-family:"Calibri",sans-serif'>=1.0</span></b> for the layer 1 to
1365layer 1 transition and for layer 2 to layer 2 the shifts are <span
1366class=SpellE><b><span style='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 remaining
1372layer 1-layer 2 and <i>vice versa</i> transitions <span class=SpellE><b><span
1373style='font-family:"Calibri",sans-serif'>Dx</span></b></span><b><span
1374style='font-family:"Calibri",sans-serif'>=<span class=SpellE>Dy</span>=0</span></b>.
1375Layer 1 to layer 1 stacking looks like.</p>
1376
1377<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1378 id="Picture_x0020_42" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:468pt;
1379 height:404.25pt;visibility:visible;mso-wrap-style:square'>
1380 <v:imagedata src="Stacking%20Faults-I_files/image023.png" o:title=""/>
1381</v:shape><![endif]--><![if !vml]><img width=624 height=539
1382src="Stacking%20Faults-I_files/image024.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
1383
1384<p class=MsoNormal>You can explore the result of various stacking sequences in
1385the next block of commands; enter <b><span style='font-family:"Calibri",sans-serif'>1
13861 1 1 2 2 2</span></b> into the box and press <b><span style='font-family:"Calibri",sans-serif'>Enter</span></b>.
1387A plot showing the result of a single twin fault will be shown.</p>
1388
1389<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1390 id="Picture_x0020_43" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:468pt;
1391 height:404.25pt;visibility:visible;mso-wrap-style:square'>
1392 <v:imagedata src="Stacking%20Faults-I_files/image025.png" o:title=""/>
1393</v:shape><![endif]--><![if !vml]><img width=624 height=539
1394src="Stacking%20Faults-I_files/image026.gif" v:shapes="Picture_x0020_43"><![endif]></span></p>
1395
1396<p class=MsoNormal>If you enter 1 2 1 2 1 2 1 2 then the structure of <span
1397class=SpellE>londsdaleite</span> will be shown; 1 1 1 1 1 1 or 2 2 2 2 2 2
1398gives the diamond structure. </p>
1399
1400<p class=MsoNormal>Finally we must select transition probabilities; they should
1401sum to 1.0 for each block. Use <b><span style='font-family:"Calibri",sans-serif'>0.7</span></b>
1402for layer 1 to layer 1 and layer 2 to layer 2; the cross terms are then <b><span
1403style='font-family:"Calibri",sans-serif'>0.3</span></b> to give</p>
1404
1405<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1406 id="Picture_x0020_44" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:468pt;
1407 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1408 <v:imagedata src="Stacking%20Faults-I_files/image027.png" o:title=""/>
1409</v:shape><![endif]--><![if !vml]><img width=624 height=485
1410src="Stacking%20Faults-I_files/image028.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
1411
1412<p class=MsoNormal>We are now ready to do a single crystal simulation; select <b><span
1413style='font-family:"Calibri",sans-serif'>Operations/Simulate pattern</span></b>
1414from the Phase data window menu. A small popup will appear</p>
1415
1416<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1417 id="Picture_x0020_45" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:209.25pt;
1418 height:102.75pt;visibility:visible;mso-wrap-style:square'>
1419 <v:imagedata src="Stacking%20Faults-I_files/image029.png" o:title=""/>
1420</v:shape><![endif]--><![if !vml]><img width=279 height=137
1421src="Stacking%20Faults-I_files/image030.gif" v:shapes="Picture_x0020_45"><![endif]></span></p>
1422
1423<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>selected
1424area</span></b> for the calculation type; the popup will be redrawn with new
1425options.</p>
1426
1427<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1428 id="Picture_x0020_46" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:181.5pt;
1429 height:102.75pt;visibility:visible;mso-wrap-style:square'>
1430 <v:imagedata src="Stacking%20Faults-I_files/image031.png" o:title=""/>
1431</v:shape><![endif]--><![if !vml]><img width=242 height=137
1432src="Stacking%20Faults-I_files/image032.gif" v:shapes="Picture_x0020_46"><![endif]></span></p>
1433
1434<p class=MsoNormal>To make it interesting select <b><span style='font-family:
1435"Calibri",sans-serif'>Max. <span class=GramE>l</span> index</span></b> of <b><span
1436style='font-family:"Calibri",sans-serif'>6</span></b> and press <b><span
1437style='font-family:"Calibri",sans-serif'>Ok</span></b>. Very quickly a new
1438popup will appear letting you know the simulation is finished; press <b><span
1439style='font-family:"Calibri",sans-serif'>Ok</span></b>. The data window will be
1440redrawn</p>
1441
1442<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1443 id="Picture_x0020_47" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:468pt;
1444 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1445 <v:imagedata src="Stacking%20Faults-I_files/image033.png" o:title=""/>
1446</v:shape><![endif]--><![if !vml]><img width=624 height=485
1447src="Stacking%20Faults-I_files/image034.gif" v:shapes="Picture_x0020_47"><![endif]></span></p>
1448
1449<p class=MsoNormal>At the top is a new item <b><span style='font-family:"Calibri",sans-serif'>Plot
1450selected area diffraction?</span></b> Select it and a new plot will appear. The
1451intensity scale is adjusted by pressing <b><span style='font-family:"Calibri",sans-serif'>D</span></b>
1452(or <b><span style='font-family:"Calibri",sans-serif'>U</span></b>); I got</p>
1453
1454<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1455 id="Picture_x0020_48" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt;
1456 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1457 <v:imagedata src="Stacking%20Faults-I_files/image035.png" o:title=""/>
1458</v:shape><![endif]--><![if !vml]><img width=624 height=535
1459src="Stacking%20Faults-I_files/image036.gif" v:shapes="Picture_x0020_48"><![endif]></span></p>
1460
1461<p class=MsoNormal>The streaking intermixed with sharp spots is clearly obvious
1462in this plot. Save this project; you’ll need it for the next simulation.</p>
1463
1464<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 2.
1465Laboratory powder diffraction simulation for random faults in diamond<o:p></o:p></span></h2>
1466
1467<p class=MsoNormal>The setup for a powder pattern simulation is the same as
1468above for selected are diffraction with one crucial difference. We need a dummy
1469powder pattern to define the simulation limits. Using the same project as
1470above, do <b><span style='font-family:"Calibri",sans-serif'>Import/Powder
1471data/Simulate a data set</span></b> from the main GSAS-II data tree window. A
1472popup will appear requesting the selection of an instrument parameter file;
1473here we will use one of the built in defaults. Press <b><span style='font-family:
1474"Calibri",sans-serif'>Cancel</span></b> and a new popup will appear offering
1475some choices.</p>
1476
1477<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1478 id="Picture_x0020_49" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:241.5pt;
1479 height:201.75pt;visibility:visible;mso-wrap-style:square'>
1480 <v:imagedata src="Stacking%20Faults-I_files/image037.png" o:title=""/>
1481</v:shape><![endif]--><![if !vml]><img width=322 height=269
1482src="Stacking%20Faults-I_files/image038.gif" v:shapes="Picture_x0020_49"><![endif]></span></p>
1483
1484<p class=MsoNormal>Use the first one for <span class=SpellE><b><span
1485style='font-family:"Calibri",sans-serif'>CuKa</span></b></span><b><span
1486style='font-family:"Calibri",sans-serif'> lab data</span></b>; a new popup will
1487appear</p>
1488
1489<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1490 id="Picture_x0020_50" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:238.5pt;
1491 height:257.25pt;visibility:visible;mso-wrap-style:square'>
1492 <v:imagedata src="Stacking%20Faults-I_files/image039.png" o:title=""/>
1493</v:shape><![endif]--><![if !vml]><img width=318 height=343
1494src="Stacking%20Faults-I_files/image040.gif" v:shapes="Picture_x0020_50"><![endif]></span></p>
1495
1496<p class=MsoNormal>Change the end angle to <b><span style='font-family:"Calibri",sans-serif'>150</span></b>
1497and the step size to <b><span style='font-family:"Calibri",sans-serif'>0.02</span></b>;
1498press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and
1499choose <b><span style='font-family:"Calibri",sans-serif'>random faults </span></b>(your
1500phase name). Notice the small data window lets you know that you can clear the
1501observed intensities in the simulation by doing an <b><span style='font-family:
1502"Calibri",sans-serif'>Edit range</span></b> (no need to change anything). The
1503tree will have a new item <b><span style='font-family:"Calibri",sans-serif'>PWDR
1504CW x-ray simulation</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Background</span></b>
1505&amp; enter <b><span style='font-family:"Calibri",sans-serif'>50</span></b> for
1506the 1<sup>st</sup> coefficient. Next select <b><span style='font-family:"Calibri",sans-serif'>Sample
1507parameters</span></b> and enter <b><span style='font-family:"Calibri",sans-serif'>1000</span></b>
1508for the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale
1509factor</span></b> and change the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
1510type</span></b> to <b><span style='font-family:"Calibri",sans-serif'>Bragg-Brentano</span></b>.
1511Finally, find your phase (<b><span style='font-family:"Calibri",sans-serif'>random
1512faults</span></b>) and select it and then the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
1513tab. It should be unchanged from when the selected area simulation was
1514finished.</p>
1515
1516<p class=MsoNormal>To do the simulation do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
1517pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1518from the popup. The calculated pattern will by default be broadened using U, V,
1519&amp; W from the Instrument parameters for the chosen powder pattern. Other
1520choices use a mean Gaussian broadening (faster) or no broadening (even faster).
1521The only choice for the pattern is given in the next popup; press <b><span
1522style='font-family:"Calibri",sans-serif'>Ok</span></b> and the simulation will
1523proceed. After a few seconds a small popup will appear letting you know it is
1524done; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and
1525the powder pattern will be displayed with the result. On the plot press the ‘<b><span
1526style='font-family:"Calibri",sans-serif'>+</span></b>’ key to suppress the ‘+’
1527marks. The plot should look like: I’ve expanded the scale to show the
1528interesting stuff around each peak.</p>
1529
1530<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1531 id="Picture_x0020_51" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt;
1532 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1533 <v:imagedata src="Stacking%20Faults-I_files/image041.png" o:title=""/>
1534</v:shape><![endif]--><![if !vml]><img width=624 height=535
1535src="Stacking%20Faults-I_files/image042.gif" v:shapes="Picture_x0020_51"><![endif]></span></p>
1536
1537<p class=MsoNormal>The blue line is a simulated observed pattern with imposed
1538Poisson noise, the red line is the calculated background and the green curve is
1539the smooth calculated pattern. A difference curve is also shown. You can play
1540with changing the transition probabilities and/or the layer offsets to see what
1541effect these have on the pattern; changing these will change the calculated
1542pattern unless you reset the dummy profile as noted above.</p>
1543
1544<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 3.
1545Sequential parameter change<o:p></o:p></span></h2>
1546
1547<p class=MsoNormal>A perhaps useful means of exploring the effects of changing
1548stacking parameters is doing a sequence of simulations varying one parameter
1549over a range. To try this out do <b><span style='font-family:"Calibri",sans-serif'>Operations/Sequence
1550simulations</span></b> from the Layers menu; a popup will appear</p>
1551
1552<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1553 id="Picture_x0020_52" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:209.25pt;
1554 height:2in;visibility:visible;mso-wrap-style:square'>
1555 <v:imagedata src="Stacking%20Faults-I_files/image043.png" o:title=""/>
1556</v:shape><![endif]--><![if !vml]><img width=279 height=192
1557src="Stacking%20Faults-I_files/image044.gif" v:shapes="Picture_x0020_52"><![endif]></span></p>
1558
1559<p class=MsoNormal>Here you select the parameter, range and number of steps
1560(both ends will be used). From the <b><span style='font-family:"Calibri",sans-serif'>Select
1561parameter</span></b> pulldown choose <b><span style='font-family:"Calibri",sans-serif'>TransP<span
1562class=GramE>;0</span>;0</span></b>; this is the layer 1 to layer 1 transition
1563probability. Then change the no. steps to <b><span style='font-family:"Calibri",sans-serif'>10</span></b>
1564(11 will be calculated). We have the same choices for instrument broadening as
1565above; use the default. Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1566the next popup allows selection of a powder pattern (e.g. for comparison and
1567the range for the calculation). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1568for this one; the sequential simulation will proceed. The console displays
1569progress and the transition matrix for each step. A popup will appear when the
1570sequence is finished after several seconds. Notice that the matrix is not
1571symmetric (see console) so that layer1 to layer 1 probability is not the same
1572as layer 2 to layer 2 at each step in the simulation. We can force this by
1573selecting <b><span style='font-family:"Calibri",sans-serif'>Symmetric
1574probabilities?</span></b> <span class=GramE>on</span> the Layers page. Do this
1575and repeat the sequential simulation as above. Now the matrices are symmetric
1576as one could expect. When the simulation is finished, select the <b><span
1577style='font-family:"Calibri",sans-serif'>Plot sequential result?</span></b> <span
1578class=GramE>box</span>; a new plot will appear.</p>
1579
1580<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1581 id="Picture_x0020_61" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
1582 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1583 <v:imagedata src="Stacking%20Faults-I_files/image046.png" o:title=""/>
1584</v:shape><![endif]--><![if !vml]><img width=624 height=535
1585src="Stacking%20Faults-I_files/image048.gif" v:shapes="Picture_x0020_61"><![endif]></span></p>
1586
1587<p class=MsoNormal>This is a multiline plot; you can shift the lines with the <b><span
1588style='font-family:"Calibri",sans-serif'>U<span class=GramE>,D,L,R</span></span></b>
1589keys (<b><span style='font-family:"Calibri",sans-serif'>O</span></b> resets
1590offsets to zero). I’ve done this for the next plot.</p>
1591
1592<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1593 id="Picture_x0020_62" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;
1594 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1595 <v:imagedata src="Stacking%20Faults-I_files/image083.png" o:title=""/>
1596</v:shape><![endif]--><![if !vml]><img width=624 height=535
1597src="Stacking%20Faults-I_files/image084.gif" v:shapes="Picture_x0020_62"><![endif]></span></p>
1598
1599<p class=MsoNormal>The first blue line is for pure hexagonal <span
1600class=SpellE>londsdaleite</span> stacking and the last magenta line is for pure
1601cubic diamond stacking. You can see how some lines quickly vanish with the
1602introduction of stacking faults while other persist across the entire sequence.
1603This is a good place to save your project file; the sequential result will be
1604included.</p>
1605
1606<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 4.
1607Modelling clustering in diamond<o:p></o:p></span></h2>
1608
1609<p class=MsoNormal>In this simulation we will explore the possibility that the
1610stacking history affects the probability of a fault. In the case of diamond, a
1611fault to form <span class=SpellE>londsdaleite</span> could be followed by
1612similar layers until a lower probability fault converts the structure back to
1613diamond. The crystal then has blocks of diamond structure interleaved with
1614blocks of <span class=SpellE>londsdaleite</span>. This is best done in a new
1615phase so we don’t mess up the above simulations, but most of the data in the
1616current phase is useful for the cluster model. The easiest way is to import the
1617new phase from the current project. <b><span style='font-family:"Calibri",sans-serif'>Do
1618Import/Phase/from GSAS-II <span class=SpellE>gpx</span> file</span></b> from
1619the main GSAS-II data tree <span class=GramE>menu.</span> A file selection
1620dialog box will appear; select the current project file (<span class=SpellE><b><span
1621style='font-family:"Calibri",sans-serif'>diamond.gpx</span></b></span>) and
1622press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>. A
1623small popup will appear confirming your choice; press <span class=GramE><b><span
1624style='font-family:"Calibri",sans-serif'>Yes</span></b></span>. The next popup
1625offers the change to name the phase, I chose <b><span style='font-family:"Calibri",sans-serif'>clustered</span></b>
1626for the name. Next select the PWDR data set to be linked to this phase. The
1627General tab for the new phase will appear.</p>
1628
1629<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1630 id="Picture_x0020_55" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:468pt;
1631 height:173.25pt;visibility:visible;mso-wrap-style:square'>
1632 <v:imagedata src="Stacking%20Faults-I_files/image073.png" o:title=""/>
1633</v:shape><![endif]--><![if !vml]><img width=624 height=231
1634src="Stacking%20Faults-I_files/image085.gif" v:shapes="Picture_x0020_55"><![endif]></span></p>
1635
1636<p class=MsoNormal>Notice that the Phase type is faulted and that Layers is one
1637of the tabs; select it.</p>
1638
1639<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1640 id="Picture_x0020_56" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:468pt;
1641 height:276pt;visibility:visible;mso-wrap-style:square'>
1642 <v:imagedata src="Stacking%20Faults-I_files/image075.png" o:title=""/>
1643</v:shape><![endif]--><![if !vml]><img width=624 height=368
1644src="Stacking%20Faults-I_files/image086.gif" v:shapes="Picture_x0020_56"><![endif]></span></p>
1645
1646<p class=MsoNormal>This is all the same information as for the random faults
1647phase. To simulate clustering we need two new layers which are the same as
1648these two listed here. Do <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Add</span></b></span><b><span
1649style='font-family:"Calibri",sans-serif'> new layer?</span></b> <span
1650class=GramE>twice</span> so two new layers appear. Name them <b><span
1651style='font-family:"Calibri",sans-serif'>layer 3</span></b> and <b><span
1652style='font-family:"Calibri",sans-serif'>layer 4</span></b>. Make layer 3 <span
1653class=GramE><b><span style='font-family:"Calibri",sans-serif'>Same</span></b></span><b><span
1654style='font-family:"Calibri",sans-serif'> as layer</span></b> 1 (select from
1655the pull down) and layer 4 <b><span style='font-family:"Calibri",sans-serif'>Same
1656as layer 2</span></b>. Each time the window is redrawn so that the transition
1657probability tables reflect these changes. You should also change the <b><span
1658style='font-family:"Calibri",sans-serif'>Diffraction Laue symmetry</span></b>
1659to <b><span style='font-family:"Calibri",sans-serif'>-3m</span></b>. When you
1660are done the upper part of the Layers window should look like.</p>
1661
1662<p class=MsoNormal>&nbsp;</p>
1663
1664<p class=MsoNormal>&nbsp;</p>
1665
1666<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1667 id="Picture_x0020_57" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;
1668 height:276pt;visibility:visible;mso-wrap-style:square'>
1669 <v:imagedata src="Stacking%20Faults-I_files/image077.png" o:title=""/>
1670</v:shape><![endif]--><![if !vml]><img width=624 height=368
1671src="Stacking%20Faults-I_files/image087.gif" v:shapes="Picture_x0020_57"><![endif]></span></p>
1672
1673<p class=MsoNormal>&nbsp;</p>
1674
1675<p class=MsoNormal>The transition vectors for the cluster model are similar to
1676the random faults model, i.e. layer 1-1 and layer 3-1 transitions are <b><span
1677style='font-family:"Calibri",sans-serif'>2/3,1/3,1</span></b> for <span
1678class=SpellE>Dx</span>, <span class=SpellE>Dy</span> &amp; <span class=SpellE>Dz</span>,
1679layer, and layer 2-4 and 4-4 transitions are <b><span style='font-family:"Calibri",sans-serif'>-2/3,-1/3,1</span></b>
1680for <span class=SpellE>Dx</span>, <span class=SpellE>Dy</span> &amp; Dz. All
1681the rest are <b><span style='font-family:"Calibri",sans-serif'>0<span
1682class=GramE>,0,1</span></span></b> for <span class=SpellE>Dx</span>,,<span
1683class=SpellE>Dy</span> &amp; Dz. The probabilities can best be seen from the
1684following array</p>
1685
1686<p class=MsoNormal>&nbsp;</p>
1687
1688<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
1689 style='border-collapse:collapse;mso-yfti-tbllook:1184;mso-padding-alt:0in 0in 0in 0in'>
1690 <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;height:21.45pt'>
1691  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1692  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1693  <p class=MsoNormal>Layer</p>
1694  </td>
1695  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1696  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1697  <p class=MsoNormal>1</p>
1698  </td>
1699  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1700  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1701  <p class=MsoNormal>2</p>
1702  </td>
1703  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1704  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1705  <p class=MsoNormal>3</p>
1706  </td>
1707  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1708  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1709  <p class=MsoNormal>4</p>
1710  </td>
1711 </tr>
1712 <tr style='mso-yfti-irow:1;height:21.45pt'>
1713  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1714  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1715  <p class=MsoNormal>1</p>
1716  </td>
1717  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1718  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1719  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1720  <p class=MsoNormal>CS</p>
1721  </td>
1722  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1723  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1724  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1725  <p class=MsoNormal>CF</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>x</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>x</p>
1736  </td>
1737 </tr>
1738 <tr style='mso-yfti-irow:2;height:21.45pt'>
1739  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1740  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1741  <p class=MsoNormal>2</p>
1742  </td>
1743  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1744  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1745  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1746  <p class=MsoNormal>x</p>
1747  </td>
1748  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1749  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1750  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1751  <p class=MsoNormal>x</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>HS</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>HF</p>
1762  </td>
1763 </tr>
1764 <tr style='mso-yfti-irow:3;height:21.45pt'>
1765  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1766  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1767  <p class=MsoNormal>3</p>
1768  </td>
1769  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1770  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1771  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1772  <p class=MsoNormal>HF</p>
1773  </td>
1774  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1775  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1776  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1777  <p class=MsoNormal>HS</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>x</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>x</p>
1788  </td>
1789 </tr>
1790 <tr style='mso-yfti-irow:4;mso-yfti-lastrow:yes;height:21.45pt'>
1791  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1792  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1793  <p class=MsoNormal>4</p>
1794  </td>
1795  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1796  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1797  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1798  <p class=MsoNormal>x</p>
1799  </td>
1800  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1801  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1802  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1803  <p class=MsoNormal>x</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>CF</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>CS</p>
1814  </td>
1815 </tr>
1816</table>
1817
1818<p class=MsoNormal>Where CS – cubic stacking, CF – cubic fault, HS – hexagonal
1819stacking, HF – hexagonal fault and x – not allowed. A suitable model might be
1820CS = <b><span style='font-family:"Calibri",sans-serif'>0.9</span></b>, CF = <b><span
1821style='font-family:"Calibri",sans-serif'>0.1</span></b>, HS = <b><span
1822style='font-family:"Calibri",sans-serif'>0.8</span></b> and HF = <b><span
1823style='font-family:"Calibri",sans-serif'>0.2</span></b>. This will give more and
1824thicker cubic blocks than hexagonal ones. Set these values and the Transition
1825tables should look like</p>
1826
1827<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1828 id="Picture_x0020_59" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:468pt;
1829 height:457.5pt;visibility:visible;mso-wrap-style:square'>
1830 <v:imagedata src="Stacking%20Faults-I_files/image079.png" o:title=""/>
1831</v:shape><![endif]--><![if !vml]><img width=624 height=610
1832src="Stacking%20Faults-I_files/image088.gif" v:shapes="Picture_x0020_59"><![endif]></span></p>
1833
1834<p class=MsoNormal>Before doing the simulation we need to clear away the old
1835one; select the <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b>
1836entry from the GSAS-II data tree and then select <b><span style='font-family:
1837"Calibri",sans-serif'>Edit range</span></b> from the data window. Don’t change
1838anything, just press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1839this will clear the previous simulation. Then return to the clustered phase
1840Layers tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
1841pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1842twice. The simulation will require some seconds to finish; the powder profile
1843will look like</p>
1844
1845<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1846 id="Picture_x0020_60" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt;
1847 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1848 <v:imagedata src="Stacking%20Faults-I_files/image081.png" o:title=""/>
1849</v:shape><![endif]--><![if !vml]><img width=624 height=535
1850src="Stacking%20Faults-I_files/image089.gif" v:shapes="Picture_x0020_60"><![endif]></span></p>
1851
1852<p class=MsoNormal>Again, I have used ‘<b><span style='font-family:"Calibri",sans-serif'>+</span></b>’
1853and zoomed in to show the interesting part of the pattern. </p>
1854
1855<p class=MsoNormal>As additional work you can do sequential simulations to
1856explore the effect of changing probabilities. Try varying <b><span
1857style='font-family:"Calibri",sans-serif'>TransP;0;0</span></b>, i.e. layer 1 –
1858layer 1 (CS) transition probability and <b><span style='font-family:"Calibri",sans-serif'>TransP;2;1</span></b>,
1859i.e. layer 3 – layer – 2 (HS) transition probability. Be sure the <b><span
1860style='font-family:"Calibri",sans-serif'>Symmetric probabilities</span></b> box
1861is checked otherwise you’ll get nonsense. This ends this stacking fault
1862tutorial; the next one involves using kaolinite layers to simulate diffraction
1863patterns from kaolinite clays.<o:p></o:p></p>
1864
1865</div>
1866
1867</span></span>
1868</body>
1869
1870</html>
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