source: Tutorials/StackingFaults-I/Stacking Faults-I.htm @ 3553

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finish web tutorials for now

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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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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><B>A video version of this tutorial is available at
1134<A href="https://anl.box.com/v/StackingFaults-I" target="_blank">
1135https://anl.box.com/v/StackingFaults-I</A></B></P>
1136
1137<p class=MsoNormal>In this exercise you will use GSAS-II to simulate the
1138diffraction patterns from faulted diamond. Diamond most commonly has the
1139well-known cubic structure with the space group Fd3m and a=3.5668A. The C-atom
1140is at 1/8<span class=GramE>,1</span>/8,1/8 and can be viewed as a cubic
1141stacking of ruffled hexagonal nets along the cubic cell 111 diagonal. </p>
1142
1143<p class=MsoNormal><span style='mso-no-proof:yes'><img width=482 height=361
1144id="_x0000_i1052" src="Stacking%20Faults-I_files/image001.jpg"></span></p>
1145
1146<p class=MsoNormal>The structure of <span class=SpellE>londsdaleite</span> has
1147those layers stacked hexagonally and thus a faulted diamond structure may
1148occasionally have hexagonal stacked layers instead of all cubic ones. From
1149geometric considerations, these planar stacking faults must extend across the
1150entire crystal. If there are only a few such faults in a crystal then the
1151diffraction pattern will show two cubic diamond patterns in a twin law
1152relationship. Otherwise, if there are many such faults then the diffraction
1153pattern will show streaks. To simulate the streaks one must first develop a
1154model for the hexagonal net of C-atoms and then show how they stack in either
1155the cubic or hexagonal forms. GSAS-II uses a suite of subroutines from the <span
1156class=SpellE>DIFFaX</span> program (M.M.J. <span class=SpellE>Treacy</span>,
1157J.M. <span class=SpellE>Newsam</span> &amp; M.W. Deem, (1991), Proc. Roy. Soc. <span
1158class=SpellE>Lond</span>. 433A, 499-520) to calculate the diffraction pattern
1159via a general recursion algorithm and a randomized set of stacked layers. NB:
1160this calculation can be quite time consuming particularly if unreasonable
1161demands are made on it. </p>
1162
1163<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1164
1165<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 1.
1166Selected area diffraction for random faults in diamond<o:p></o:p></span></h2>
1167
1168<p class=MsoNormal>To begin we must have a phase to work with. In the main
1169GSAS-II data tree menu do <b><span style='font-family:"Calibri",sans-serif'>Data/Add
1170new phase</span></b>; a popup window will appear inviting you to name the
1171phase. I entered <b><span style='font-family:"Calibri",sans-serif'>‘random
1172faults</span></b>’. Then find this phase in the data tree under phases and
1173select it; the data window will display the default for the General tab.</p>
1174
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1199src="Stacking%20Faults-I_files/image002.gif" v:shapes="Picture_x0020_31"><![endif]></span></p>
1200
1201<p class=MsoNormal>Change the phase type to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
1202the window will be redrawn and a new tab (‘<b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>’)
1203will appear. Select it. Then save the project; I called it ‘<b><span
1204style='font-family:"Calibri",sans-serif'>diamond</span></b>’.</p>
1205
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1212
1213<p class=MsoNormal>First you need to describe the reference unit cell for the
1214stacking model. The cubic/hexagonal stacking in diamond is with layers
1215perpendicular to the 111 axis. This will become the new c-axis. The a- &amp;
1216b-axes are for the hexagonal net of C-atoms that are stacked in this structure.
1217One can also anticipate that the resulting diffraction pattern will have
1218hexagonal <b><span style='font-family:"Calibri",sans-serif'>6/mmm</span></b>
1219symmetry so first select this from the pull down box near the top of the page;
1220the window will be redrawn.</p>
1221
1222<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1223 id="Picture_x0020_34" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:468pt;
1224 height:230.25pt;visibility:visible;mso-wrap-style:square'>
1225 <v:imagedata src="Stacking%20Faults-I_files/image005.png" o:title=""/>
1226</v:shape><![endif]--><![if !vml]><img width=624 height=307
1227src="Stacking%20Faults-I_files/image006.gif" v:shapes="Picture_x0020_34"><![endif]></span></p>
1228
1229<p class=MsoNormal><span class=GramE>The a</span> cell parameter for diamond
1230stacking can be assumed to be <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type
1231    m:val="lin"/><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:fPr><m:num><i
1234   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
1235      m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1236     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1237     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
1238     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
1239style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1240"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1241top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1242EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1243 type="#_x0000_t75" style='width:28.5pt;height:15.75pt'>
1244 <v:imagedata src="Stacking%20Faults-I_files/image007.png" o:title=""
1245  chromakey="white"/>
1246</v:shape><![endif]--><![if !vml]><img width=38 height=21
1247src="Stacking%20Faults-I_files/image008.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;=
1248<b><span style='font-family:"Calibri",sans-serif'>2.522</span></b> and the c
1249cell parameter is <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type m:val="lin"/><span
1250   style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
1251   mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
1252   normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
1253   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
1254      m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
1255     "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
1256     mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i
1257     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
1258style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
1259"Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
1260top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
1261EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
1262 type="#_x0000_t75" style='width:28.5pt;height:15.75pt'>
1263 <v:imagedata src="Stacking%20Faults-I_files/image009.png" o:title=""
1264  chromakey="white"/>
1265</v:shape><![endif]--><![if !vml]><img width=38 height=21
1266src="Stacking%20Faults-I_files/image010.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]>&nbsp;=
1267<b><span style='font-family:"Calibri",sans-serif'>2.059</span></b> since there
1268are 3 layers along the 111 diamond cell diagonal. Enter these in the
1269appropriate places; the cell volume will be revised.</p>
1270
1271<p class=MsoNormal>Now we have to describe the two hexagonal nets that will be
1272stacked for either cubic or hexagonal stacking. Select <b><span
1273style='font-family:"Calibri",sans-serif'>Add new layer?</span></b> <span
1274class=GramE>the</span> window will be redrawn.</p>
1275
1276<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1277 id="Picture_x0020_35" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:468pt;
1278 height:311.25pt;visibility:visible;mso-wrap-style:square'>
1279 <v:imagedata src="Stacking%20Faults-I_files/image011.png" o:title=""/>
1280</v:shape><![endif]--><![if !vml]><img width=624 height=415
1281src="Stacking%20Faults-I_files/image012.gif" v:shapes="Picture_x0020_35"><![endif]></span></p>
1282
1283<p class=MsoNormal>Name the layer (I chose ‘<b><span style='font-family:"Calibri",sans-serif'>layer
12841</span></b>’) and choose <b><span style='font-family:"Calibri",sans-serif'>‘-1</span></b>’
1285for the layer symmetry. The window will be redrawn after changing the name.
1286Next, select <b><span style='font-family:"Calibri",sans-serif'>Add atom?</span></b>
1287<span class=GramE>and</span> the window will be redrawn with one line in the
1288layer table.</p>
1289
1290<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1291 id="Picture_x0020_36" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:468pt;
1292 height:311.25pt;visibility:visible;mso-wrap-style:square'>
1293 <v:imagedata src="Stacking%20Faults-I_files/image013.png" o:title=""/>
1294</v:shape><![endif]--><![if !vml]><img width=624 height=415
1295src="Stacking%20Faults-I_files/image014.gif" v:shapes="Picture_x0020_36"><![endif]></span></p>
1296
1297<p class=MsoNormal>To make this a C-atom select the ‘<span class=SpellE><b><span
1298style='font-family:"Calibri",sans-serif'>Unk</span></b></span>’ under Type with
1299a double click; a Periodic table will popup. Select <b><span style='font-family:
1300"Calibri",sans-serif'>C</span></b>; the popup will disappear and the window
1301will be redrawn. The coordinates of this C-atom in the new stacking unit cell
1302is <b><span style='font-family:"Calibri",sans-serif'>-1/3,-1/6,-1/8</span></b>;
1303you may enter these as fractions. Select a table item to complete the entry;
1304the window should show the new position.</p>
1305
1306<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1307 id="Picture_x0020_38" o:spid="_x0000_i1046" type="#_x0000_t75" style='width:468pt;
1308 height:323.25pt;visibility:visible;mso-wrap-style:square'>
1309 <v:imagedata src="Stacking%20Faults-I_files/image015.png" o:title=""/>
1310</v:shape><![endif]--><![if !vml]><img width=624 height=431
1311src="Stacking%20Faults-I_files/image016.gif" v:shapes="Picture_x0020_38"><![endif]></span></p>
1312
1313<p class=MsoNormal>You can draw the layer to see what it looks like; select <b><span
1314style='font-family:"Calibri",sans-serif'>Draw layer?</span></b> <span
1315class=GramE>and</span> the drawing will appear. </p>
1316
1317<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1318 id="Picture_x0020_39" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:468pt;
1319 height:403.5pt;visibility:visible;mso-wrap-style:square'>
1320 <v:imagedata src="Stacking%20Faults-I_files/image017.png" o:title=""/>
1321</v:shape><![endif]--><![if !vml]><img width=624 height=538
1322src="Stacking%20Faults-I_files/image018.gif" v:shapes="Picture_x0020_39"><![endif]></span></p>
1323
1324<p class=MsoNormal>A unit cell box is drawn with a 5x5 suite of unit cells; the
1325ruffled hexagonal net perpendicular to the c-axis (blue line) is clear.</p>
1326
1327<p class=MsoNormal>Now we need a second layer (‘<b style='mso-bidi-font-weight:
1328normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1329minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>layer
13302</span></b>’); repeat the steps for making a layer using <b><span
1331style='font-family:"Calibri",sans-serif'>1/3<span class=GramE>,1</span>/6,-1/8</span></b>
1332for the C-atom position with <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>
1333for the layer symmetry. The window should look like this when done.</p>
1334
1335<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1336 id="Picture_x0020_40" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:468pt;
1337 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1338 <v:imagedata src="Stacking%20Faults-I_files/image019.png" o:title=""/>
1339</v:shape><![endif]--><![if !vml]><img width=624 height=485
1340src="Stacking%20Faults-I_files/image020.gif" v:shapes="Picture_x0020_40"><![endif]></span></p>
1341
1342<p class=MsoNormal>I’ve stretched it a bit to show the Layer-Layer transition probabilities.
1343Change <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dz</span></b></span>
1344for each entry to <b><span style='font-family:"Calibri",sans-serif'>1.0</span></b>
1345to properly space out the stacked layers. If you select the first box in the
1346plot column for layer 1 you will see the two layers stacked but in a way
1347reminiscent of how carbon sheets stack in graphite. </p>
1348
1349<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1350 id="Picture_x0020_41" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:468pt;
1351 height:406.5pt;visibility:visible;mso-wrap-style:square'>
1352 <v:imagedata src="Stacking%20Faults-I_files/image021.png" o:title=""/>
1353</v:shape><![endif]--><![if !vml]><img width=624 height=542
1354src="Stacking%20Faults-I_files/image022.gif" v:shapes="Picture_x0020_41"><![endif]></span></p>
1355
1356<p class=MsoNormal>Clearly not diamond stacking. The table defines how the next
1357layer is displaced relative to the reference layer. You can shift this layer by
1358using the <b><span style='font-family:"Calibri",sans-serif'>X<span class=GramE>,Y,Z</span></span></b>
1359&amp; <b><span style='font-family:"Calibri",sans-serif'>shift-X,Y,Z</span></b>
1360keys; the plot will be redrawn and the table entry updated each time you shift the
1361layer. When you get to the right offset for diamond additional bonds will
1362appear connecting the layers together. The correct shift is <span class=SpellE><b><span
1363style='font-family:"Calibri",sans-serif'>Dx</span></b></span><b><span
1364style='font-family:"Calibri",sans-serif'>=2/3</span></b>, <span class=SpellE><b><span
1365style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span
1366style='font-family:"Calibri",sans-serif'>=1/3</span></b> and <span
1367class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dz</span></b></span><b><span
1368style='font-family:"Calibri",sans-serif'>=1.0</span></b> for the layer 1 to
1369layer 1 transition and for layer 2 to layer 2 the shifts are <span
1370class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dx</span></b></span><b><span
1371style='font-family:"Calibri",sans-serif'>=-2/3</span></b>, <span class=SpellE><b><span
1372style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span
1373style='font-family:"Calibri",sans-serif'>=-1/3</span></b> and <span
1374class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dz</span></b></span><b><span
1375style='font-family:"Calibri",sans-serif'>=1.0</span></b>. For the remaining
1376layer 1-layer 2 and <i>vice versa</i> transitions <span class=SpellE><b><span
1377style='font-family:"Calibri",sans-serif'>Dx</span></b></span><b><span
1378style='font-family:"Calibri",sans-serif'>=<span class=SpellE>Dy</span>=0</span></b>.
1379Layer 1 to layer 1 stacking looks like.</p>
1380
1381<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1382 id="Picture_x0020_42" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:468pt;
1383 height:404.25pt;visibility:visible;mso-wrap-style:square'>
1384 <v:imagedata src="Stacking%20Faults-I_files/image023.png" o:title=""/>
1385</v:shape><![endif]--><![if !vml]><img width=624 height=539
1386src="Stacking%20Faults-I_files/image024.gif" v:shapes="Picture_x0020_42"><![endif]></span></p>
1387
1388<p class=MsoNormal>You can explore the result of various stacking sequences in
1389the next block of commands; enter <b><span style='font-family:"Calibri",sans-serif'>1
13901 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>.
1391A plot showing the result of a single twin fault will be shown.</p>
1392
1393<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1394 id="Picture_x0020_43" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:468pt;
1395 height:404.25pt;visibility:visible;mso-wrap-style:square'>
1396 <v:imagedata src="Stacking%20Faults-I_files/image025.png" o:title=""/>
1397</v:shape><![endif]--><![if !vml]><img width=624 height=539
1398src="Stacking%20Faults-I_files/image026.gif" v:shapes="Picture_x0020_43"><![endif]></span></p>
1399
1400<p class=MsoNormal>If you enter 1 2 1 2 1 2 1 2 then the structure of <span
1401class=SpellE>londsdaleite</span> will be shown; 1 1 1 1 1 1 or 2 2 2 2 2 2
1402gives the diamond structure. </p>
1403
1404<p class=MsoNormal>Finally we must select transition probabilities; they should
1405sum to 1.0 for each block. Use <b><span style='font-family:"Calibri",sans-serif'>0.7</span></b>
1406for layer 1 to layer 1 and layer 2 to layer 2; the cross terms are then <b><span
1407style='font-family:"Calibri",sans-serif'>0.3</span></b> to give</p>
1408
1409<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1410 id="Picture_x0020_44" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:468pt;
1411 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1412 <v:imagedata src="Stacking%20Faults-I_files/image027.png" o:title=""/>
1413</v:shape><![endif]--><![if !vml]><img width=624 height=485
1414src="Stacking%20Faults-I_files/image028.gif" v:shapes="Picture_x0020_44"><![endif]></span></p>
1415
1416<p class=MsoNormal>We are now ready to do a single crystal simulation; select <b><span
1417style='font-family:"Calibri",sans-serif'>Operations/Simulate pattern</span></b>
1418from the Phase data window menu. A small popup will appear</p>
1419
1420<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1421 id="Picture_x0020_45" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:209.25pt;
1422 height:102.75pt;visibility:visible;mso-wrap-style:square'>
1423 <v:imagedata src="Stacking%20Faults-I_files/image029.png" o:title=""/>
1424</v:shape><![endif]--><![if !vml]><img width=279 height=137
1425src="Stacking%20Faults-I_files/image030.gif" v:shapes="Picture_x0020_45"><![endif]></span></p>
1426
1427<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>selected
1428area</span></b> for the calculation type; the popup will be redrawn with new
1429options.</p>
1430
1431<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1432 id="Picture_x0020_46" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:181.5pt;
1433 height:102.75pt;visibility:visible;mso-wrap-style:square'>
1434 <v:imagedata src="Stacking%20Faults-I_files/image031.png" o:title=""/>
1435</v:shape><![endif]--><![if !vml]><img width=242 height=137
1436src="Stacking%20Faults-I_files/image032.gif" v:shapes="Picture_x0020_46"><![endif]></span></p>
1437
1438<p class=MsoNormal>To make it interesting select <b><span style='font-family:
1439"Calibri",sans-serif'>Max. <span class=GramE>l</span> index</span></b> of <b><span
1440style='font-family:"Calibri",sans-serif'>6</span></b> and press <b><span
1441style='font-family:"Calibri",sans-serif'>Ok</span></b>. Very quickly a new
1442popup will appear letting you know the simulation is finished; press <b><span
1443style='font-family:"Calibri",sans-serif'>Ok</span></b>. The data window will be
1444redrawn</p>
1445
1446<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1447 id="Picture_x0020_47" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:468pt;
1448 height:363.75pt;visibility:visible;mso-wrap-style:square'>
1449 <v:imagedata src="Stacking%20Faults-I_files/image033.png" o:title=""/>
1450</v:shape><![endif]--><![if !vml]><img width=624 height=485
1451src="Stacking%20Faults-I_files/image034.gif" v:shapes="Picture_x0020_47"><![endif]></span></p>
1452
1453<p class=MsoNormal>At the top is a new item <b><span style='font-family:"Calibri",sans-serif'>Plot
1454selected area diffraction?</span></b> Select it and a new plot will appear. The
1455intensity scale is adjusted by pressing <b><span style='font-family:"Calibri",sans-serif'>D</span></b>
1456(or <b><span style='font-family:"Calibri",sans-serif'>U</span></b>); I got</p>
1457
1458<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1459 id="Picture_x0020_48" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt;
1460 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1461 <v:imagedata src="Stacking%20Faults-I_files/image035.png" o:title=""/>
1462</v:shape><![endif]--><![if !vml]><img width=624 height=535
1463src="Stacking%20Faults-I_files/image036.gif" v:shapes="Picture_x0020_48"><![endif]></span></p>
1464
1465<p class=MsoNormal>The streaking intermixed with sharp spots is clearly obvious
1466in this plot. Save this project; you’ll need it for the next simulation.</p>
1467
1468<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 2.
1469Laboratory powder diffraction simulation for random faults in diamond<o:p></o:p></span></h2>
1470
1471<p class=MsoNormal>The setup for a powder pattern simulation is the same as
1472above for selected are diffraction with one crucial difference. We need a dummy
1473powder pattern to define the simulation limits. Using the same project as
1474above, do <b><span style='font-family:"Calibri",sans-serif'>Import/Powder
1475data/Simulate a data set</span></b> from the main GSAS-II data tree window. A
1476popup will appear requesting the selection of an instrument parameter file;
1477here we will use one of the built in defaults. Press <b><span style='font-family:
1478"Calibri",sans-serif'>Cancel</span></b> and a new popup will appear offering
1479some choices.</p>
1480
1481<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1482 id="Picture_x0020_49" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:241.5pt;
1483 height:201.75pt;visibility:visible;mso-wrap-style:square'>
1484 <v:imagedata src="Stacking%20Faults-I_files/image037.png" o:title=""/>
1485</v:shape><![endif]--><![if !vml]><img width=322 height=269
1486src="Stacking%20Faults-I_files/image038.gif" v:shapes="Picture_x0020_49"><![endif]></span></p>
1487
1488<p class=MsoNormal>Use the first one for <span class=SpellE><b><span
1489style='font-family:"Calibri",sans-serif'>CuKa</span></b></span><b><span
1490style='font-family:"Calibri",sans-serif'> lab data</span></b>; a new popup will
1491appear</p>
1492
1493<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1494 id="Picture_x0020_50" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:238.5pt;
1495 height:257.25pt;visibility:visible;mso-wrap-style:square'>
1496 <v:imagedata src="Stacking%20Faults-I_files/image039.png" o:title=""/>
1497</v:shape><![endif]--><![if !vml]><img width=318 height=343
1498src="Stacking%20Faults-I_files/image040.gif" v:shapes="Picture_x0020_50"><![endif]></span></p>
1499
1500<p class=MsoNormal>Change the end angle to <b><span style='font-family:"Calibri",sans-serif'>150</span></b>
1501and the step size to <b><span style='font-family:"Calibri",sans-serif'>0.02</span></b>;
1502press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and
1503choose <b><span style='font-family:"Calibri",sans-serif'>random faults </span></b>(your
1504phase name). Notice the small data window lets you know that you can clear the
1505observed intensities in the simulation by doing an <b><span style='font-family:
1506"Calibri",sans-serif'>Edit range</span></b> (no need to change anything). The
1507tree will have a new item <b><span style='font-family:"Calibri",sans-serif'>PWDR
1508CW x-ray simulation</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Background</span></b>
1509&amp; enter <b><span style='font-family:"Calibri",sans-serif'>50</span></b> for
1510the 1<sup>st</sup> coefficient. Next select <b><span style='font-family:"Calibri",sans-serif'>Sample
1511parameters</span></b> and enter <b><span style='font-family:"Calibri",sans-serif'>1000</span></b>
1512for the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale
1513factor</span></b> and change the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
1514type</span></b> to <b><span
1515style='font-family:"Calibri",sans-serif'>Bragg-Brentano</span></b> (if
1516not already set to that).
1517Finally, find your phase (<b><span style='font-family:"Calibri",sans-serif'>random
1518faults</span></b>) and select it and then the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
1519tab. It should be unchanged from when the selected area simulation was
1520finished.</p>
1521
1522<p class=MsoNormal>To do the simulation do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
1523pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1524from the popup. The calculated pattern will by default be broadened using U, V,
1525&amp; W from the Instrument parameters for the chosen powder pattern. Other
1526choices use a mean Gaussian broadening (faster) or no broadening (even faster).
1527The only choice for the pattern is given in the next popup; press <b><span
1528style='font-family:"Calibri",sans-serif'>Ok</span></b> and the simulation will
1529proceed. After a few seconds a small popup will appear letting you know it is
1530done; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and
1531the powder pattern will be displayed with the result. On the plot press the ‘<b><span
1532style='font-family:"Calibri",sans-serif'>+</span></b>’ key to suppress the ‘+’
1533marks. The plot should look like: </p>
1534
1535<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1536 id="Picture_x0020_51" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt;
1537 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1538 <v:imagedata src="Stacking%20Faults-I_files/image041.png" o:title=""/>
1539</v:shape><![endif]--><![if !vml]><img width=624 height=535
1540src="Stacking%20Faults-I_files/image042.gif" v:shapes="Picture_x0020_51"><![endif]></span></p>
1541(I’ve expanded the scale to show the
1542interesting stuff around each peak.)
1543<p></p>
1544<p class=MsoNormal>The blue line is a simulated observed pattern with imposed
1545Poisson noise, the red line is the calculated background and the green curve is
1546the smooth calculated pattern. A difference curve is also shown. You can play
1547with changing the transition probabilities and/or the layer offsets to see what
1548effect these have on the pattern; changing these will change the calculated
1549pattern unless you reset the dummy profile as noted above.</p>
1550
1551<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 3.
1552Sequential parameter change<o:p></o:p></span></h2>
1553
1554<p class=MsoNormal>A perhaps useful means of exploring the effects of changing
1555stacking parameters is doing a sequence of simulations varying one parameter
1556over a range. To try this out do <b><span style='font-family:"Calibri",sans-serif'>Operations/Sequence
1557simulations</span></b> from the Layers menu; a popup will appear</p>
1558
1559<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1560 id="Picture_x0020_52" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:209.25pt;
1561 height:2in;visibility:visible;mso-wrap-style:square'>
1562 <v:imagedata src="Stacking%20Faults-I_files/image043.png" o:title=""/>
1563</v:shape><![endif]--><![if !vml]><img width=279 height=192
1564src="Stacking%20Faults-I_files/image044.gif" v:shapes="Picture_x0020_52"><![endif]></span></p>
1565
1566<p class=MsoNormal>Here you select the parameter, range and number of steps
1567(both ends will be used). From the <b><span style='font-family:"Calibri",sans-serif'>Select
1568parameter</span></b> pulldown choose <b><span style='font-family:"Calibri",sans-serif'>TransP<span
1569class=GramE>;0</span>;0</span></b>; this is the layer 1 to layer 1 transition
1570probability. Then change the no. steps to <b><span style='font-family:"Calibri",sans-serif'>10</span></b>
1571(11 will be calculated). We have the same choices for instrument broadening as
1572above; use the default. Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1573the next popup allows selection of a powder pattern (e.g. for comparison and
1574the range for the calculation). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1575for this one; the sequential simulation will proceed. The console displays
1576progress and the transition matrix for each step. A popup will appear when the
1577sequence is finished after several seconds. Notice that the matrix is not
1578symmetric (see console) so that layer1 to layer 1 probability is not the same
1579as layer 2 to layer 2 at each step in the simulation. We can force this by
1580selecting <b><span style='font-family:"Calibri",sans-serif'>Symmetric
1581probabilities?</span></b> <span class=GramE>on</span> the Layers tab. Do this
1582and repeat the sequential simulation as above. Now the matrices are symmetric
1583as one could expect. When the simulation is finished, select the <b><span
1584style='font-family:"Calibri",sans-serif'>Plot sequential result?</span></b> <span
1585class=GramE>box</span>; a new plot will appear.</p>
1586
1587<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1588 id="Picture_x0020_61" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
1589 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1590 <v:imagedata src="Stacking%20Faults-I_files/image046.png" o:title=""/>
1591</v:shape><![endif]--><![if !vml]><img width=624 height=535
1592src="Stacking%20Faults-I_files/image048.gif" v:shapes="Picture_x0020_61"><![endif]></span></p>
1593
1594<p class=MsoNormal>This is a multiline plot; you can shift the lines with the <b><span
1595style='font-family:"Calibri",sans-serif'>U<span class=GramE>,D,L,R</span></span></b>
1596keys (<b><span style='font-family:"Calibri",sans-serif'>O</span></b> resets
1597offsets to zero). I’ve done this for the next plot.</p>
1598
1599<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1600 id="Picture_x0020_62" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;
1601 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1602 <v:imagedata src="Stacking%20Faults-I_files/image083.png" o:title=""/>
1603</v:shape><![endif]--><![if !vml]><img width=624 height=535
1604src="Stacking%20Faults-I_files/image084.gif" v:shapes="Picture_x0020_62"><![endif]></span></p>
1605
1606<p class=MsoNormal>The first blue line is for pure hexagonal <span
1607class=SpellE>londsdaleite</span> stacking and the last magenta line is for pure
1608cubic diamond stacking. You can see how some lines quickly vanish with the
1609introduction of stacking faults while other persist across the entire sequence.
1610This is a good place to save your project file; the sequential result will be
1611included.</p>
1612
1613<h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 4.
1614Modelling clustering in diamond<o:p></o:p></span></h2>
1615
1616<p class=MsoNormal>In this simulation we will explore the possibility that the
1617stacking history affects the probability of a fault. In the case of diamond, a
1618fault to form <span class=SpellE>londsdaleite</span> could be followed by
1619similar layers until a lower probability fault converts the structure back to
1620diamond. The crystal then has blocks of diamond structure interleaved with
1621blocks of <span class=SpellE>londsdaleite</span>. This is best done in a new
1622phase so we don’t mess up the above simulations, but most of the data in the
1623current phase is useful for the cluster model. The easiest way is to import the
1624new phase from the current project. <b><span style='font-family:"Calibri",sans-serif'>Do
1625Import/Phase/from GSAS-II <span class=SpellE>gpx</span> file</span></b> from
1626the main GSAS-II data tree <span class=GramE>menu.</span> A file selection
1627dialog box will appear; select the current project file (<span class=SpellE><b><span
1628style='font-family:"Calibri",sans-serif'>diamond.gpx</span></b></span>) and
1629press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>. A
1630small popup will appear confirming your choice; press <span class=GramE><b><span
1631style='font-family:"Calibri",sans-serif'>Yes</span></b></span>. The next popup
1632offers the change to name the phase, I chose <b><span style='font-family:"Calibri",sans-serif'>clustered</span></b>
1633for the name. Next select the PWDR data set to be linked to this phase. The
1634General tab for the new phase will appear.</p>
1635
1636<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1637 id="Picture_x0020_55" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:468pt;
1638 height:173.25pt;visibility:visible;mso-wrap-style:square'>
1639 <v:imagedata src="Stacking%20Faults-I_files/image073.png" o:title=""/>
1640</v:shape><![endif]--><![if !vml]><img width=624 height=231
1641src="Stacking%20Faults-I_files/image085.gif" v:shapes="Picture_x0020_55"><![endif]></span></p>
1642
1643<p class=MsoNormal>Notice that the Phase type is faulted and that Layers is one
1644of the tabs; select it.</p>
1645
1646<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1647 id="Picture_x0020_56" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:468pt;
1648 height:276pt;visibility:visible;mso-wrap-style:square'>
1649 <v:imagedata src="Stacking%20Faults-I_files/image075.png" o:title=""/>
1650</v:shape><![endif]--><![if !vml]><img width=624 height=368
1651src="Stacking%20Faults-I_files/image086.gif" v:shapes="Picture_x0020_56"><![endif]></span></p>
1652
1653<p class=MsoNormal>This is all the same information as for the random faults
1654phase. To simulate clustering we need two new layers which are the same as
1655these two listed here. Do <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Add</span></b></span><b><span
1656style='font-family:"Calibri",sans-serif'> new layer?</span></b> <span
1657class=GramE>twice</span> so two new layers appear. Name them <b><span
1658style='font-family:"Calibri",sans-serif'>layer 3</span></b> and <b><span
1659style='font-family:"Calibri",sans-serif'>layer 4</span></b>. Make layer 3 <span
1660class=GramE><b><span style='font-family:"Calibri",sans-serif'>Same</span></b></span><b><span
1661style='font-family:"Calibri",sans-serif'> as layer</span></b> 1 (select from
1662the pull down) and layer 4 <b><span style='font-family:"Calibri",sans-serif'>Same
1663as layer 2</span></b>. Each time the window is redrawn so that the transition
1664probability tables reflect these changes. You should also change the <b><span
1665style='font-family:"Calibri",sans-serif'>Diffraction Laue symmetry</span></b>
1666to <b><span style='font-family:"Calibri",sans-serif'>-3m</span></b>. When you
1667are done the upper part of the Layers window should look like.</p>
1668
1669<p class=MsoNormal>&nbsp;</p>
1670
1671<p class=MsoNormal>&nbsp;</p>
1672
1673<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1674 id="Picture_x0020_57" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;
1675 height:276pt;visibility:visible;mso-wrap-style:square'>
1676 <v:imagedata src="Stacking%20Faults-I_files/image077.png" o:title=""/>
1677</v:shape><![endif]--><![if !vml]><img width=624 height=368
1678src="Stacking%20Faults-I_files/image087.gif" v:shapes="Picture_x0020_57"><![endif]></span></p>
1679
1680<p class=MsoNormal>&nbsp;</p>
1681
1682<p class=MsoNormal>The transition vectors for the cluster model are similar to
1683the random faults model, i.e. layer 1-1 and layer 3-1 transitions are <b><span
1684style='font-family:"Calibri",sans-serif'>2/3,1/3,1</span></b> for <span
1685class=SpellE>Dx</span>, <span class=SpellE>Dy</span> &amp; <span class=SpellE>Dz</span>,
1686layer, and layer 2-4 and 4-4 transitions are <b><span style='font-family:"Calibri",sans-serif'>-2/3,-1/3,1</span></b>
1687for <span class=SpellE>Dx</span>, <span class=SpellE>Dy</span> &amp; Dz. All
1688the rest are <b><span style='font-family:"Calibri",sans-serif'>0<span
1689class=GramE>,0,1</span></span></b> for <span class=SpellE>Dx</span>,,<span
1690class=SpellE>Dy</span> &amp; Dz. The probabilities can best be seen from the
1691following array</p>
1692
1693<p class=MsoNormal>&nbsp;</p>
1694
1695<table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0
1696 style='border-collapse:collapse;mso-yfti-tbllook:1184;mso-padding-alt:0in 0in 0in 0in'>
1697 <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;height:21.45pt'>
1698  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1699  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1700  <p class=MsoNormal>Layer</p>
1701  </td>
1702  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1703  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1704  <p class=MsoNormal>1</p>
1705  </td>
1706  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1707  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1708  <p class=MsoNormal>2</p>
1709  </td>
1710  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1711  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1712  <p class=MsoNormal>3</p>
1713  </td>
1714  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1715  border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1716  <p class=MsoNormal>4</p>
1717  </td>
1718 </tr>
1719 <tr style='mso-yfti-irow:1;height:21.45pt'>
1720  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1721  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1722  <p class=MsoNormal>1</p>
1723  </td>
1724  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1725  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1726  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1727  <p class=MsoNormal>CS</p>
1728  </td>
1729  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1730  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1731  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1732  <p class=MsoNormal>CF</p>
1733  </td>
1734  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1735  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1736  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1737  <p class=MsoNormal>x</p>
1738  </td>
1739  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1740  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1741  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1742  <p class=MsoNormal>x</p>
1743  </td>
1744 </tr>
1745 <tr style='mso-yfti-irow:2;height:21.45pt'>
1746  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1747  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1748  <p class=MsoNormal>2</p>
1749  </td>
1750  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1751  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1752  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1753  <p class=MsoNormal>x</p>
1754  </td>
1755  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1756  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1757  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1758  <p class=MsoNormal>x</p>
1759  </td>
1760  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1761  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1762  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1763  <p class=MsoNormal>HS</p>
1764  </td>
1765  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1766  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1767  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1768  <p class=MsoNormal>HF</p>
1769  </td>
1770 </tr>
1771 <tr style='mso-yfti-irow:3;height:21.45pt'>
1772  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1773  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1774  <p class=MsoNormal>3</p>
1775  </td>
1776  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1777  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1778  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1779  <p class=MsoNormal>HF</p>
1780  </td>
1781  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1782  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1783  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1784  <p class=MsoNormal>HS</p>
1785  </td>
1786  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1787  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1788  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1789  <p class=MsoNormal>x</p>
1790  </td>
1791  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1792  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1793  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1794  <p class=MsoNormal>x</p>
1795  </td>
1796 </tr>
1797 <tr style='mso-yfti-irow:4;mso-yfti-lastrow:yes;height:21.45pt'>
1798  <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt;
1799  border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1800  <p class=MsoNormal>4</p>
1801  </td>
1802  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1803  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1804  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1805  <p class=MsoNormal>x</p>
1806  </td>
1807  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1808  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1809  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1810  <p class=MsoNormal>x</p>
1811  </td>
1812  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1813  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1814  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1815  <p class=MsoNormal>CF</p>
1816  </td>
1817  <td width=72 valign=top style='width:54.05pt;border-top:none;border-left:
1818  none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;
1819  padding:0in 5.4pt 0in 5.4pt;height:21.45pt'>
1820  <p class=MsoNormal>CS</p>
1821  </td>
1822 </tr>
1823</table>
1824
1825<p class=MsoNormal>Where CS – cubic stacking, CF – cubic fault, HS – hexagonal
1826stacking, HF – hexagonal fault and x – not allowed. A suitable model might be
1827CS = <b><span style='font-family:"Calibri",sans-serif'>0.9</span></b>, CF = <b><span
1828style='font-family:"Calibri",sans-serif'>0.1</span></b>, HS = <b><span
1829style='font-family:"Calibri",sans-serif'>0.8</span></b> and HF = <b><span
1830style='font-family:"Calibri",sans-serif'>0.2</span></b>. This will give more and
1831thicker cubic blocks than hexagonal ones. Set these values and the Transition
1832tables should look like</p>
1833
1834<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1835 id="Picture_x0020_59" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:468pt;
1836 height:457.5pt;visibility:visible;mso-wrap-style:square'>
1837 <v:imagedata src="Stacking%20Faults-I_files/image079.png" o:title=""/>
1838</v:shape><![endif]--><![if !vml]><img width=624 height=610
1839src="Stacking%20Faults-I_files/image088.gif" v:shapes="Picture_x0020_59"><![endif]></span></p>
1840
1841<p class=MsoNormal>Before doing the simulation we need to clear away the old
1842one; select the <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b>
1843entry from the GSAS-II data tree and then select <b><span style='font-family:
1844"Calibri",sans-serif'>Edit range</span></b> from the data window. Don’t change
1845anything, just press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1846this will clear the previous simulation. Then return to the random
1847faults phase
1848Layers tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
1849pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1850twice. The simulation will require some seconds to finish; the powder profile
1851will look like</p>
1852
1853<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1854 id="Picture_x0020_60" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt;
1855 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1856 <v:imagedata src="Stacking%20Faults-I_files/image081.png" o:title=""/>
1857</v:shape><![endif]--><![if !vml]><img width=624 height=535
1858src="Stacking%20Faults-I_files/image089.gif" v:shapes="Picture_x0020_60"><![endif]></span></p>
1859
1860<p class=MsoNormal>Again, I have used ‘<b><span style='font-family:"Calibri",sans-serif'>+</span></b>’
1861and zoomed in to show the interesting part of the pattern. </p>
1862
1863<p class=MsoNormal>As additional work you can do sequential simulations to
1864explore the effect of changing probabilities. Try varying <b><span
1865style='font-family:"Calibri",sans-serif'>TransP;0;0</span></b>, i.e. layer 1 –
1866layer 1 (CS) transition probability and <b><span style='font-family:"Calibri",sans-serif'>TransP;2;1</span></b>,
1867i.e. layer 3 – layer – 2 (HS) transition probability. Be sure the <b><span
1868style='font-family:"Calibri",sans-serif'>Symmetric probabilities</span></b> box
1869is checked otherwise you’ll get nonsense. This ends this stacking fault
1870tutorial; the next one involves using kaolinite layers to simulate diffraction
1871patterns from kaolinite clays.<o:p></o:p></p>
1872
1873</div>
1874
1875</span></span>
1876</body>
1877
1878</html>
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