source: Tutorials/StackingFaults-II/Stacking Faults II.htm @ 2390

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401  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
402  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
403  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
404  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
405  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
406  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
407  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
408  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
409  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
410  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
411  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
412  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
413  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
414  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
415  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
416  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
417  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
418  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
419  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
420  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
421  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
422  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
423  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
424  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
425  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
426  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
427  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
428  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
429  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
430  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
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432  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
433  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
434  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
435  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
436  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
437  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
438  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
439  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
440  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
441  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
442  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
443  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
444  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
445  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
446  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
447  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
448  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
449  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
450  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
451  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
452  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
453  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
454  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
455  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
456  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
457  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
458  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
459  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
460  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
461  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
462  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
463  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
464  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
465  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
466  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
467  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
468  <w:LsdException Locked="false" Priority="19" QFormat="true"
469   Name="Subtle Emphasis"/>
470  <w:LsdException Locked="false" Priority="21" QFormat="true"
471   Name="Intense Emphasis"/>
472  <w:LsdException Locked="false" Priority="31" QFormat="true"
473   Name="Subtle Reference"/>
474  <w:LsdException Locked="false" Priority="32" QFormat="true"
475   Name="Intense Reference"/>
476  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
477  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
478   UnhideWhenUsed="true" Name="Bibliography"/>
479  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
480   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
481  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
482  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
483  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
484  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
485  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
486  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
487  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
488  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
489  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
490  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
491  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
492  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
493  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
494  <w:LsdException Locked="false" Priority="46"
495   Name="Grid Table 1 Light Accent 1"/>
496  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
497  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
498  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
499  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
500  <w:LsdException Locked="false" Priority="51"
501   Name="Grid Table 6 Colorful Accent 1"/>
502  <w:LsdException Locked="false" Priority="52"
503   Name="Grid Table 7 Colorful Accent 1"/>
504  <w:LsdException Locked="false" Priority="46"
505   Name="Grid Table 1 Light Accent 2"/>
506  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
507  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
508  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
509  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
510  <w:LsdException Locked="false" Priority="51"
511   Name="Grid Table 6 Colorful Accent 2"/>
512  <w:LsdException Locked="false" Priority="52"
513   Name="Grid Table 7 Colorful Accent 2"/>
514  <w:LsdException Locked="false" Priority="46"
515   Name="Grid Table 1 Light Accent 3"/>
516  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
517  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
518  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
519  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
520  <w:LsdException Locked="false" Priority="51"
521   Name="Grid Table 6 Colorful Accent 3"/>
522  <w:LsdException Locked="false" Priority="52"
523   Name="Grid Table 7 Colorful Accent 3"/>
524  <w:LsdException Locked="false" Priority="46"
525   Name="Grid Table 1 Light Accent 4"/>
526  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
527  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
528  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
529  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
530  <w:LsdException Locked="false" Priority="51"
531   Name="Grid Table 6 Colorful Accent 4"/>
532  <w:LsdException Locked="false" Priority="52"
533   Name="Grid Table 7 Colorful Accent 4"/>
534  <w:LsdException Locked="false" Priority="46"
535   Name="Grid Table 1 Light Accent 5"/>
536  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
537  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
538  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
539  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
540  <w:LsdException Locked="false" Priority="51"
541   Name="Grid Table 6 Colorful Accent 5"/>
542  <w:LsdException Locked="false" Priority="52"
543   Name="Grid Table 7 Colorful Accent 5"/>
544  <w:LsdException Locked="false" Priority="46"
545   Name="Grid Table 1 Light Accent 6"/>
546  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
547  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
548  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
549  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
550  <w:LsdException Locked="false" Priority="51"
551   Name="Grid Table 6 Colorful Accent 6"/>
552  <w:LsdException Locked="false" Priority="52"
553   Name="Grid Table 7 Colorful Accent 6"/>
554  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
555  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
556  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
557  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
558  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
559  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
560  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
561  <w:LsdException Locked="false" Priority="46"
562   Name="List Table 1 Light Accent 1"/>
563  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
564  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
565  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
566  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
567  <w:LsdException Locked="false" Priority="51"
568   Name="List Table 6 Colorful Accent 1"/>
569  <w:LsdException Locked="false" Priority="52"
570   Name="List Table 7 Colorful Accent 1"/>
571  <w:LsdException Locked="false" Priority="46"
572   Name="List Table 1 Light Accent 2"/>
573  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
574  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
575  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
576  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
577  <w:LsdException Locked="false" Priority="51"
578   Name="List Table 6 Colorful Accent 2"/>
579  <w:LsdException Locked="false" Priority="52"
580   Name="List Table 7 Colorful Accent 2"/>
581  <w:LsdException Locked="false" Priority="46"
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583  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
584  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
585  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
586  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
587  <w:LsdException Locked="false" Priority="51"
588   Name="List Table 6 Colorful Accent 3"/>
589  <w:LsdException Locked="false" Priority="52"
590   Name="List Table 7 Colorful Accent 3"/>
591  <w:LsdException Locked="false" Priority="46"
592   Name="List Table 1 Light Accent 4"/>
593  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
594  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
595  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
596  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
597  <w:LsdException Locked="false" Priority="51"
598   Name="List Table 6 Colorful Accent 4"/>
599  <w:LsdException Locked="false" Priority="52"
600   Name="List Table 7 Colorful Accent 4"/>
601  <w:LsdException Locked="false" Priority="46"
602   Name="List Table 1 Light Accent 5"/>
603  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
604  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
605  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
606  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
607  <w:LsdException Locked="false" Priority="51"
608   Name="List Table 6 Colorful Accent 5"/>
609  <w:LsdException Locked="false" Priority="52"
610   Name="List Table 7 Colorful Accent 5"/>
611  <w:LsdException Locked="false" Priority="46"
612   Name="List Table 1 Light Accent 6"/>
613  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
614  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
615  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
616  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
617  <w:LsdException Locked="false" Priority="51"
618   Name="List Table 6 Colorful Accent 6"/>
619  <w:LsdException Locked="false" Priority="52"
620   Name="List Table 7 Colorful Accent 6"/>
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1073 <o:shapedefaults v:ext="edit" spidmax="1026"/>
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1079
1080<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1081
1082<div class=WordSection1>
1083
1084<h1><span style='mso-fareast-font-family:"Times New Roman"'>Stacking Fault
1085Simulations – II<o:p></o:p></span></h1>
1086
1087<p class=MsoNormal>In this exercise and the next you will simulate some
1088diffraction patterns from kaolinite clays. Kaolinite, Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(OH)<sub>4</sub>,
1089is a 1:<span class=GramE>1 layer</span> silicate with a single unique sheet
1090with AlO<sub>6</sub> <span class=SpellE>octahedra</span> on one side and SiO<sub>4</sub>
1091<span class=SpellE>tetrahedra</span> on the other. The layers stack with an
1092offset to ideally form a triclinic C1 lattice (<span class=SpellE>Bish</span>
1093&amp; Von Dreele, 1989, Clay &amp; Clay Min. 37, 289-296) for a sample of the
1094most ordered form of kaolinite from Keokuk, Iowa. Kaolinites from other
1095locations evidently have stacking faults so that the peaks are displaced, have
1096peculiar shapes and are above a varying background. For the exercise we provide
1097a laboratory Bragg-Brentano pattern of Keokuk kaolinite collected with <span
1098class=SpellE>CuKa</span> radiation on a Bruker instrument and thus in the
1099Bruker RAW file format. The Keokuk kaolinite has some <span class=SpellE>dickite</span>
1100(different ordered stacking of kaolinite layers). The next exercise Stacking
1101Faults-III) covers a simple simulation of a faulted kaolinite from Georgia.</p>
1102
1103<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1104
1105<h2><span style='mso-fareast-font-family:"Times New Roman"'>Part 1. Creating
1106kaolinite layer<o:p></o:p></span></h2>
1107
1108<p class=MsoNormal>In this initial step we will load from a <span class=SpellE>cif</span>
1109file the structure of kaolinite, draw it to see the layer structure and then
1110transform it into forms suitable for stacking simulations. To begin do <b><span
1111style='font-family:"Calibri",sans-serif'>Import/Phase/from CIF file</span></b>;
1112from the file dialog select <span class=SpellE><b style='mso-bidi-font-weight:
1113normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1114minor-latin;mso-hansi-theme-font:minor-latin'>StackingFaults</span></b></span><b
1115style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1116mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-II/data/</span></b><span
1117class=SpellE><b><span style='font-family:"Calibri",sans-serif'>kaolinite.cif</span></b></span>.
1118After the “are you sure” popup, there will be another warning you that 4 atom
1119types (‘O-H’) were not recognized chemical element symbols and they were
1120substituted by <span class=SpellE>Xe</span> to make them obvious in the atom
1121list. Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1122you are offered a chance to change the phase name, I used ‘<b><span
1123style='font-family:"Calibri",sans-serif'>kaolinite</span></b>’. The General tab
1124is displayed (notice the presence of <span class=SpellE>Xe</span> in the
1125element table).</p>
1126
1127<p class=MsoNormal><span style='mso-no-proof:yes'><img width=930 height=500
1128id="_x0000_i1043" src="Stacking%20Faults%20II_files/image001.gif"></span></p>
1129
1130<p class=MsoNormal>To fix the <span class=SpellE>Xe</span> atoms (they should
1131be O), select <b><span style='font-family:"Calibri",sans-serif'>Atoms</span></b>
1132and then double click the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
1133column heading; a small popup will appear. Select <span class=SpellE><b><span
1134style='font-family:"Calibri",sans-serif'>Xe</span></b></span> &amp; press <b><span
1135style='font-family:"Calibri",sans-serif'>Ok</span></b>; the <span class=SpellE>Xe</span>
1136atoms at the bottom of the atom table will be highlighted. Next select <b><span
1137style='font-family:"Calibri",sans-serif'>Edit/Modify atom parameters</span></b>
1138from the Phase Data menu; a new popup will appear. Select <b><span
1139style='font-family:"Calibri",sans-serif'>Type</span></b> &amp; press <b><span
1140style='font-family:"Calibri",sans-serif'>Ok</span></b>; a periodic table of the
1141element will appear. Select <b><span style='font-family:"Calibri",sans-serif'>O</span></b>
1142from the O-atom pulldown; the structure will be drawn with Al, Si &amp; O atoms
1143only.</p>
1144
1145<p class=MsoNormal><span style='mso-no-proof:yes'><img width=479 height=358
1146id="_x0000_i1042" src="Stacking%20Faults%20II_files/image003.jpg"></span></p>
1147
1148<p class=MsoNormal>To better visualize the stacking layer, select the <b><span
1149style='font-family:"Calibri",sans-serif'>Draw Atoms</span></b> tab and then
1150double click the empty upper left corner box of the table. All atoms will turn
1151green. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit/Fill unit
1152cell</span></b>; the structure will be redrawn with all atoms that belong in
1153the unit cell. Finally, double click on the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
1154column heading, select <b><span style='font-family:"Calibri",sans-serif'>Al</span></b>
1155&amp; <b><span style='font-family:"Calibri",sans-serif'>Si</span></b> (they
1156will turn green) and then do <b><span style='font-family:"Calibri",sans-serif'>Edit/Fill
1157CN sphere</span></b>. After a bit of rotating the structure around, the
1158layering along the c-axis (blue line) will be evident.</p>
1159
1160<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
1161id="_x0000_i1041" src="Stacking%20Faults%20II_files/image004.jpg"></span></p>
1162
1163<p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> <span
1164class=SpellE>tetrahedra</span> and AlO<sub>6</sub> <span class=SpellE>octahedra</span>.
1165Also notice that the next layer (represented by the 4 O atoms at the bottom of
1166the above drawing are offset giving a triclinic lattice.</p>
1167
1168<p class=MsoNormal>The stacking fault simulation calculation via <span
1169class=SpellE>DIFFaX</span> routines requires that the stacking layers be
1170defined in a coordinate system that has the stacking direction perpendicular to
1171the stacking plane defined as the c-axis. This requires transformation of the
1172unit cell and atom coordinates; a suitable tool exists in GSAS-II to do this.
1173Select the <b><span style='font-family:"Calibri",sans-serif'>General</span></b>
1174tab and do <b><span style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>;
1175a popup window will appear.</p>
1176
1177<p class=MsoNormal><span style='mso-no-proof:yes'><img width=350 height=339
1178id="_x0000_i1040" src="Stacking%20Faults%20II_files/image005.gif"></span></p>
1179
1180<p class=MsoNormal>Note that this allows one to transform the structure
1181according to a matrix and then shift the resultant positions along some vector
1182and then select those that are unique according to a selected space group. The
1183pulldown gives a selection of commonly used transformations; we want the last
1184one, <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>abc</span></b></span><b><span
1185style='font-family:"Calibri",sans-serif'>*</span></b>, which satisfies the
1186stacking fault requirement. Select it; notice that the space group is changed
1187to P1. Leave this as the kaolinite layer has no symmetry; in other
1188circumstances the layer may have an inversion center in which case P-1 should
1189be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
1190the new lattice parameters will be shown.</p>
1191
1192<p class=MsoNormal><span style='mso-no-proof:yes'><img width=350 height=339
1193id="_x0000_i1039" src="Stacking%20Faults%20II_files/image006.gif"></span></p>
1194
1195<p class=MsoNormal>The a &amp; b axes stay the same, but c is now smaller (the
1196interlayer distance in kaolinite) and <span style='font-family:Symbol'>a</span>
1197&amp; <span style='font-family:Symbol'>b</span> = 90 (<span style='font-family:
1198Symbol'>g</span> is unchanged). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1199a new phase (kaolinite <span class=SpellE>abc</span>*) will be made and its
1200General tab will be shown immediately. Select the <b><span style='font-family:
1201"Calibri",sans-serif'>Draw Atoms</span></b> tab to see the resulting structure.</p>
1202
1203<p class=MsoNormal><span style='mso-no-proof:yes'><img width=471 height=352
1204id="_x0000_i1038" src="Stacking%20Faults%20II_files/image007.jpg"></span></p>
1205
1206<p class=MsoNormal>To see what this layer looks like with more of it drawn, you
1207can add more unit cells to the drawing; select all the atoms by double clicking
1208the upper left empty box of the Draw atoms table. Do <b><span style='font-family:
1209"Calibri",sans-serif'>Edit/Add atoms</span></b> and <b><span style='font-family:
1210"Calibri",sans-serif'>increment</span></b> the 1<sup>st</sup> <b><span
1211style='font-family:"Calibri",sans-serif'>Choose unit cel</span></b>l and press <b><span
1212style='font-family:"Calibri",sans-serif'>Ok</span></b>; this will add <span
1213class=GramE>one unit</span> cell along x. Now select all the atoms again, do <b><span
1214style='font-family:"Calibri",sans-serif'>Edit/Add atoms</span></b> and now <b><span
1215style='font-family:"Calibri",sans-serif'>decrement</span></b> the 1<sup>st</sup>
1216<b><span style='font-family:"Calibri",sans-serif'>Choose unit cell</span></b>.
1217Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; the
1218drawing will now be 3 unit cells wide along x. Repeat this once more <b><span
1219style='font-family:"Calibri",sans-serif'>decrementing</span></b> the 2<sup>nd</sup>
1220<b><span style='font-family:"Calibri",sans-serif'>Choose unit cell</span></b>
1221to give a 3x2 unit cell block of atoms. Double click the <b><span
1222style='font-family:"Calibri",sans-serif'>Style</span></b> column heading and
1223select <b><span style='font-family:"Calibri",sans-serif'>Balls and sticks</span></b>;
1224the drawing should look like (after some zooming/shifting/rotation).</p>
1225
1226<p class=MsoNormal><span style='mso-no-proof:yes'><img width=477 height=357
1227id="_x0000_i1037" src="Stacking%20Faults%20II_files/image009.jpg"></span></p>
1228
1229<p class=MsoNormal>This structure is now suitable for use in <span
1230class=SpellE>DIFFaX</span> calculations; the cell has a c-axis that is
1231perpendicular to the ab plane with a length that is the stacking repeat
1232distance. This is a good place to save your project (I called it ‘<b><span
1233style='font-family:"Calibri",sans-serif'>kaolinite’</span></b>).</p>
1234
1235<h2><span style='mso-fareast-font-family:"Times New Roman"'>Part 2. Set up
1236simulation of ideal kaolinite stacking<o:p></o:p></span></h2>
1237
1238<p class=MsoNormal>In this part of the tutorial we’ll create a stacking model
1239for Keokuk kaolinite and use <span class=SpellE>DIFFaX</span> to simulate the
1240powder pattern and compare it to some real data. To begin we need a new phase
1241that we can declare as “faulted’. In the main GSAS-II data tree menu do <b><span
1242style='font-family:"Calibri",sans-serif'>Data/Add new phase</span></b>; I named
1243it ‘<b><span style='font-family:"Calibri",sans-serif'>Keokuk</span></b>’. The
1244General tab for it will immediately appear.</p>
1245
1246<p class=MsoNormal><span style='mso-no-proof:yes'><img width=930 height=500
1247id="_x0000_i1036" src="Stacking%20Faults%20II_files/image010.gif"></span></p>
1248
1249<p class=MsoNormal>Change the <b><span style='font-family:"Calibri",sans-serif'>Phase
1250type</span></b> to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
1251the General tab will be redrawn and a new tab <b><span style='font-family:"Calibri",sans-serif'>‘Layers</span></b>’
1252will appear. Select it.</p>
1253
1254<p class=MsoNormal><span style='mso-no-proof:yes'><img width=817 height=484
1255id="_x0000_i1035" src="Stacking%20Faults%20II_files/image011.gif"></span></p>
1256
1257<p class=MsoNormal>We can anticipate (given that kaolinite space group is C1)
1258that the <b><span style='font-family:"Calibri",sans-serif'>Diffraction Laue
1259symmetry</span></b> is <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>.
1260We can enter by hand the lattice parameters from the kaolinite <span
1261class=SpellE>abc</span>* phase but an easier method is available. Do <b><span
1262style='font-family:"Calibri",sans-serif'>Operations/Copy phase cell</span></b>;
1263a file selection dialog will appear for your current directory and the file <span
1264class=SpellE><b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b></span>
1265should be there. Select it; a small popup will appear listing the available
1266phases. Choose ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite <span
1267class=SpellE>abc</span>*</span></b>’ and press <b><span style='font-family:
1268"Calibri",sans-serif'>Ok</span></b>; the Layers window will be redrawn with the
1269new lattice parameters.</p>
1270
1271<p class=MsoNormal><span style='mso-no-proof:yes'><img width=829 height=484
1272id="_x0000_i1034" src="Stacking%20Faults%20II_files/image012.gif"></span></p>
1273
1274<p class=MsoNormal>Next, you need to define the layer. As it would be very tedious
1275to enter 24 atoms by hand, the alternative is to get them from the previously
1276created kaolinite <span class=SpellE>abc</span>* phase. Select the <b><span
1277style='font-family:"Calibri",sans-serif'>Import new layer</span></b> box; the
1278file dialog with <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b></span>
1279will appear. Select the file and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>;
1280again a small popup with two phases listed will appear. Again select <b><span
1281style='font-family:"Calibri",sans-serif'>kaolinite <span class=SpellE>abc</span>*</span></b>
1282and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; the
1283Layers page will be redrawn with a layer (named kaolinite) will be filled out.</p>
1284
1285<p class=MsoNormal><span style='mso-no-proof:yes'><img width=829 height=500
1286id="_x0000_i1033" src="Stacking%20Faults%20II_files/image013.gif"></span></p>
1287
1288<p class=MsoNormal>If you move down to the bottom of the page (if there isn’t a
1289scroll bar, just grab an edge of the window &amp; shift it slightly) to find
1290the <span class=GramE>one line</span> <b><span style='font-family:"Calibri",sans-serif'>Layer-Layer
1291Transition probabilities</span></b>. Change <span class=SpellE><b><span
1292style='font-family:"Calibri",sans-serif'>Dz</span></b></span><b><span
1293style='font-family:"Calibri",sans-serif'>=1.0</span></b> and press the plot
1294box; the drawing will show a layer of kaolinite stacked directly above another
1295one.</p>
1296
1297<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
1298id="_x0000_i1032" src="Stacking%20Faults%20II_files/image014.jpg"></span></p>
1299
1300<p class=MsoNormal>Compare that to the stacking in kaolinite.</p>
1301
1302<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
1303id="_x0000_i1031" src="Stacking%20Faults%20II_files/image015.jpg"></span></p>
1304
1305<p class=MsoNormal>Notice the effect of the offset. The 1<sup>st</sup> row of
1306SiO<sub>4</sub> <span class=SpellE>tetrahedra</span> are positioned directly
1307above the AlO<sub>6</sub> <span class=SpellE>octahedra</span> in the real
1308structure but not in the vertically stacked structure. We can use a bit of
1309simple geometry to work out what the offset is but first let us see what
1310happens in the simulation and how it compares to real data.</p>
1311
1312<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 3. Import
1313Keokuk kaolinite data and do 1<sup>st</sup> simulation<o:p></o:p></span></h2>
1314
1315<p class=MsoNormal>First we need to import the Keokuk kaolinite powder data; do
1316<b><span style='font-family:"Calibri",sans-serif'>Import/Powder Data/from
1317Bruker RAW file</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Keokuk
1318<span class=SpellE>kaolinite.RAW</span></span></b> from the file dialog box;
1319press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b> in the
1320next popup. A new file dialog appears requesting an instrument parameter file;
1321we will use an internal default instead. Press <b><span style='font-family:
1322"Calibri",sans-serif'>Cancel</span></b> and select <b><span style='font-family:
1323"Calibri",sans-serif'>Defaults for <span class=SpellE>CuKa</span> lab data</span></b>
1324from the next popup. This process will repeat since the RAW file contains two
1325scans. In the next popup, select only <b><span style='font-family:"Calibri",sans-serif'>kaolinite
1326<span class=SpellE>abc</span>*</span></b>. There will be two PWDR scans in the
1327GSAS-II data tree; one covers 2<span style='font-family:Symbol'>Q</span>= 10-90<span
1328style='font-family:"Calibri",sans-serif'>°</span> and the other covers 2<span
1329style='font-family:Symbol'>Q</span>=80-150°. Only the lower part of the first
1330one is going to be used in our simulation work as the calculations become very
1331time consuming for complex structures and high angle data. Select <b><span
1332style='font-family:"Calibri",sans-serif'>PWDR Keokuk <span class=SpellE>kaolinite.RAW</span>
1333Scan 1</span></b> from the GSAS-II data tree make sure it expands; its plot
1334will also show.</p>
1335
1336<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1337id="_x0000_i1030" src="Stacking%20Faults%20II_files/image016.gif"></span></p>
1338
1339<p class=MsoNormal>Go to <b><span style='font-family:"Calibri",sans-serif'>Limits</span></b>
1340and set <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Tmax</span></b></span>
1341to <b><span style='font-family:"Calibri",sans-serif'>52.0</span></b>; that puts
1342the upper limit in a relatively clear part of the pattern. Then go to
1343Background and set the 1<sup>st</sup> coefficient to 20 (approximately the
1344background at 2Q=18). Next go to <b><span style='font-family:"Calibri",sans-serif'>Sample
1345parameters</span></b> and set the <b><span style='font-family:"Calibri",sans-serif'>Histogram
1346scale</span></b> to something reasonable (I chose <b><span style='font-family:
1347"Calibri",sans-serif'>20.0</span></b>) and make sure the <b><span
1348style='font-family:"Calibri",sans-serif'>Diffractometer type is Bragg-Brentano</span></b>.</p>
1349
1350<p class=MsoNormal>Now we are ready for our 1<sup>st</sup> kaolinite
1351simulation. Go to <b><span style='font-family:"Calibri",sans-serif'>Phases/Keokuk</span></b>
1352and select the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
1353tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
1354pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1355in the popup. Select the <b><span style='font-family:"Calibri",sans-serif'>Scan
13561</span></b> pattern and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1357the simulation will finish quickly (press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>)
1358and the new plot will be displayed (I’ve zoomed in a bit).</p>
1359
1360<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1361id="_x0000_i1029" src="Stacking%20Faults%20II_files/image017.gif"></span>.</p>
1362
1363<p class=MsoNormal>As you can see the simulation (green curve) does not fit the
1364data (blue crosses) at all mostly due to the incorrect layer offset although
1365the 1<sup>st</sup> peak seems to be positioned correctly. To work out the
1366offset consider the drawing of kaolinite.</p>
1367
1368<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=338
1369id="_x0000_i1028" src="Stacking%20Faults%20II_files/image002.gif"></span></p>
1370
1371<p class=MsoNormal>The offset <span class=SpellE>Dx</span> is given by the blue
1372arrow in the above drawing of kaolinite and is in fractional coordinates.
1373Geometry gives<o:p></o:p></p>
1374
1375<p class=MsoNormal><span style='position:relative;top:3pt'><span
1376style='mso-no-proof:yes'><img width=106 height=26 id="_x0000_i1027"
1377src="Stacking%20Faults%20II_files/image021.gif"></span>&nbsp;Or in this case <b><span
1378style='font-family:"Calibri",sans-serif'>-0.368</span></b>. Set <span
1379class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dx</span></b></span>
1380to this value &amp; repeat simulation.</p>
1381
1382<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1383id="_x0000_i1026" src="Stacking%20Faults%20II_files/image022.gif"></span></p>
1384
1385<p class=MsoNormal>There is some improvement but some parts are not very well
1386represented. Recall from the triclinic kaolinite lattice parameters that <span
1387style='font-family:Symbol'>a</span> was 91.7°; that will produce a small offset
1388in Dy. Using the same kind of geometry math gives <span class=SpellE><b><span
1389style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span
1390style='font-family:"Calibri",sans-serif'>=-0.0246</span></b>. Enter this value
1391&amp; repeat the simulation again. This gives a much better fit to the observed
1392pattern, but the simulated peaks are too sharp; this can be fixed by changing
1393the <span class=GramE>U,V</span>,W Instrument parameters. I’d just set <b><span
1394style='font-family:"Calibri",sans-serif'>W=40</span></b> and the <b><span
1395style='font-family:"Calibri",sans-serif'>Histogram scale</span></b> (in <b><span
1396style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>) to <b><span
1397style='font-family:"Calibri",sans-serif'>40</span></b> and try again.</p>
1398
1399<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1400id="_x0000_i1025" src="Stacking%20Faults%20II_files/image023.gif"></span></p>
1401
1402<p class=MsoNormal>That is a pretty good fit for a stacking simulation. By
1403further hand tweaking of the parameters one can further improve the simulation
1404but based on what we see here we do have the right description of stacking in
1405Keokuk kaolinite. Doing sequence simulations varying each parameter over a
1406small range can be used to help with optimization, but in this case it would be
1407far easier to do a Rietveld refinement for this well ordered kaolinite. Save
1408your project as you will need it for the next exercise (Stacking Faults-III).<o:p></o:p></p>
1409
1410</span></div>
1411
1412</body>
1413
1414</html>
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