source: Tutorials/StackingFaults-II/Stacking Faults II.htm @ 2274

Last change on this file since 2274 was 2274, checked in by vondreele, 6 years ago

fix Stacking Faults II.htm

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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"/>
431  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
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"
582   Name="List Table 1 Light Accent 3"/>
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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1062 <o:shapedefaults v:ext="edit" spidmax="1026"/>
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1067</head>
1068
1069<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1070
1071<div class=WordSection1>
1072
1073<h1><span style='mso-fareast-font-family:"Times New Roman"'>Stacking Fault
1074Simulations – II<o:p></o:p></span></h1>
1075
1076<p class=MsoNormal>In this exercise you will simulate some diffraction patterns
1077from kaolinite clays. Kaolinite, <span class=GramE>Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(</span>OH)<sub>4</sub>,
1078is a 1:1 layer silicate with a single unique sheet with AlO<sub>6</sub> <span
1079class=SpellE>octahedra</span> on one side and SiO<sub>4</sub> <span
1080class=SpellE>tetrahedra</span> on the other. The layers stack with an offset to
1081ideally form a triclinic C1 lattice (<span class=SpellE>Bish</span> &amp; Von
1082Dreele, 1989, Clay &amp; Clay Min. 37, 289-296) for a sample of the most
1083ordered form of kaolinite from Keokuk, Iowa. Kaolinites from other locations evidently
1084have stacking faults so that the peaks are displaced, have peculiar shapes and
1085are above a varying background. For the exercise we provide a laboratory
1086Bragg-Brentano pattern of Keokuk kaolinite and a less ordered one from
1087Washington County, Georgia (Clay Minerals Society Standard KGa-1b) collected
1088with <span class=SpellE>CuKa</span> radiation on a Bruker instrument and thus
1089in the Bruker RAW file format. The KGa-1b sample contains a small amount of <span
1090class=SpellE>anatase</span> (TiO<sub>2</sub>) and the Keokuk kaolinite has some
1091<span class=SpellE>dickite</span> (different ordered stacking of kaolinite
1092layers).</p>
1093
1094<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1095
1096<h2><span style='mso-fareast-font-family:"Times New Roman"'>Part 1. Creating
1097kaolinite layer<o:p></o:p></span></h2>
1098
1099<p class=MsoNormal>In this initial step we will load from a <span class=SpellE>cif</span>
1100file the structure of kaolinite, draw it to see the layer structure and then
1101transform it into forms suitable for stacking simulations. To begin do <b><span
1102style='font-family:"Calibri",sans-serif'>Import/Phase/from CIF file</span></b>;
1103from the file dialog select <span class=SpellE><b><span style='font-family:
1104"Calibri",sans-serif'>kaolinite.cif</span></b></span>. After the “are you sure”
1105popup, there will be another warning you that 4 atom types (‘O-H’) were not
1106recognized chemical element symbols and they were substituted by <span
1107class=SpellE>Xe</span> to make them obvious in the atom list. Press <b><span
1108style='font-family:"Calibri",sans-serif'>Ok</span></b>; you are offered a
1109chance to change the phase name, I used ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite</span></b>’.
1110The General tab is displayed (notice the presence of <span class=SpellE>Xe</span>
1111in the element table).</p>
1112
1113<p class=MsoNormal><span style='mso-no-proof:yes'><img width=930 height=500
1114id="_x0000_i1043" src="Stacking%20Faults%20II_files/image001.gif"></span></p>
1115
1116<p class=MsoNormal>To fix the <span class=SpellE>Xe</span> atoms (they should
1117be O), select <b><span style='font-family:"Calibri",sans-serif'>Atoms</span></b>
1118and then double click the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
1119column heading; a small popup will appear. Select <span class=SpellE><b><span
1120style='font-family:"Calibri",sans-serif'>Xe</span></b></span> &amp; press <b><span
1121style='font-family:"Calibri",sans-serif'>Ok</span></b>; the <span class=SpellE>Xe</span>
1122atoms at the bottom of the atom table will be highlighted. Next select <b><span
1123style='font-family:"Calibri",sans-serif'>Edit/Modify atom parameters</span></b>
1124from the Phase Data menu; a new popup will appear. Select <b><span
1125style='font-family:"Calibri",sans-serif'>Type</span></b> &amp; press <b><span
1126style='font-family:"Calibri",sans-serif'>Ok</span></b>; a periodic table of the
1127element will appear. Select <b><span style='font-family:"Calibri",sans-serif'>O</span></b>
1128from the O-atom pulldown; the structure will be drawn with Al, Si &amp; O atoms
1129only.</p>
1130
1131<p class=MsoNormal><span style='mso-no-proof:yes'><img width=479 height=358
1132id="_x0000_i1042" src="Stacking%20Faults%20II_files/image003.jpg"></span></p>
1133
1134<p class=MsoNormal>To better visualize the stacking layer, select the <b><span
1135style='font-family:"Calibri",sans-serif'>Draw Atoms</span></b> tab and then
1136double click the empty upper left corner box of the table. All atoms will turn
1137green. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit/Fill unit
1138cell</span></b>; the structure will be redrawn with all atoms that belong in
1139the unit cell. Finally, double click on the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
1140column heading, select <b><span style='font-family:"Calibri",sans-serif'>Al</span></b>
1141&amp; <b><span style='font-family:"Calibri",sans-serif'>Si</span></b> (they
1142will turn green) and then do <b><span style='font-family:"Calibri",sans-serif'>Edit/Fill
1143CN sphere</span></b>. After a bit of rotating the structure around, the
1144layering along the c-axis (blue line) will be evident.</p>
1145
1146<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
1147id="_x0000_i1041" src="Stacking%20Faults%20II_files/image004.jpg"></span></p>
1148
1149<p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> <span
1150class=SpellE>tetrahedra</span> and AlO<sub>6</sub> <span class=SpellE>octahedra</span>.
1151Also notice that the next layer (represented by the 4 O atoms at the bottom of
1152the above drawing are offset giving a triclinic lattice.</p>
1153
1154<p class=MsoNormal>The stacking fault simulation calculation via <span
1155class=SpellE>DIFFaX</span> routines requires that the stacking layers be defined
1156in a coordinate system that has the stacking direction perpendicular to the
1157stacking plane defined as the c-axis. This requires transformation of the unit
1158cell and atom coordinates; a suitable tool exists in GSAS-II to do this. Select
1159the <b><span style='font-family:"Calibri",sans-serif'>General</span></b> tab and
1160do <b><span style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>;
1161a popup window will appear.</p>
1162
1163<p class=MsoNormal><span style='mso-no-proof:yes'><img width=350 height=339
1164id="_x0000_i1040" src="Stacking%20Faults%20II_files/image005.gif"></span></p>
1165
1166<p class=MsoNormal>Note that this allows one to transform the structure
1167according to a matrix and then shift the resultant positions along some vector
1168and then select those that are unique according to a selected space group. The
1169pulldown gives a selection of commonly used transformations; we want the last
1170one, <span class=SpellE><span class=GramE><b><span style='font-family:"Calibri",sans-serif'>abc</span></b></span></span><b><span
1171style='font-family:"Calibri",sans-serif'>*</span></b>, which satisfies the
1172stacking fault requirement. Select it; notice that the space group is changed
1173to P1. Leave this as the kaolinite layer has no symmetry; in other
1174circumstances the layer may have an inversion center in which case P-1 should
1175be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
1176the new lattice parameters will be shown.</p>
1177
1178<p class=MsoNormal><span style='mso-no-proof:yes'><img width=350 height=339
1179id="_x0000_i1039" src="Stacking%20Faults%20II_files/image006.gif"></span></p>
1180
1181<p class=MsoNormal><span class=GramE>The a</span> &amp; b axes stay the same,
1182but c is now smaller (the interlayer distance in kaolinite) and <span
1183style='font-family:Symbol'>a</span> &amp; <span style='font-family:Symbol'>b</span>
1184= 90 (<span style='font-family:Symbol'>g</span> is unchanged). Press <b><span
1185style='font-family:"Calibri",sans-serif'>Ok</span></b>; a new phase (kaolinite <span
1186class=SpellE><span class=GramE>abc</span></span>*) will be made and its General
1187tab will be shown immediately. Select the <b><span style='font-family:"Calibri",sans-serif'>Draw
1188Atoms</span></b> tab to see the resulting structure.</p>
1189
1190<p class=MsoNormal><span style='mso-no-proof:yes'><img width=471 height=352
1191id="_x0000_i1038" src="Stacking%20Faults%20II_files/image007.jpg"></span></p>
1192
1193<p class=MsoNormal>To see what this layer looks like with more of it drawn, you
1194can add more unit cells to the drawing; select all the atoms by double clicking
1195the upper left empty box of the Draw atoms table. Do <b><span style='font-family:
1196"Calibri",sans-serif'>Edit/Add atoms</span></b> and <b><span style='font-family:
1197"Calibri",sans-serif'>increment</span></b> the 1<sup>st</sup> <b><span
1198style='font-family:"Calibri",sans-serif'>Choose unit cel</span></b>l and press <b><span
1199style='font-family:"Calibri",sans-serif'>Ok</span></b>; this will add one unit
1200cell along x. Now select all the atoms again, do <b><span style='font-family:
1201"Calibri",sans-serif'>Edit/Add atoms</span></b> and now <b><span
1202style='font-family:"Calibri",sans-serif'>decrement</span></b> the 1<sup>st</sup>
1203<b><span style='font-family:"Calibri",sans-serif'>Choose unit cell</span></b>.
1204Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; the
1205drawing will now be 3 unit cells wide along x. Repeat this once more <b><span
1206style='font-family:"Calibri",sans-serif'>decrementing</span></b> the 2<sup>nd</sup>
1207<b><span style='font-family:"Calibri",sans-serif'>Choose unit cell</span></b>
1208to give a 3x2 unit cell block of atoms. Double click the <b><span
1209style='font-family:"Calibri",sans-serif'>Style</span></b> column heading and
1210select <b><span style='font-family:"Calibri",sans-serif'>Balls and sticks</span></b>;
1211the drawing should look like (after some zooming/shifting/rotation).<o:p></o:p></p>
1212
1213<p class=MsoNormal><span style='mso-no-proof:yes'><img width=477 height=357 id="_x0000_i1037"
1214src="Stacking%20Faults%20II_files/image009.jpg"></span></p>
1215
1216<p class=MsoNormal>This structure is now suitable for use in <span
1217class=SpellE>DIFFaX</span> calculations; the cell has a c-axis that is
1218perpendicular to the ab plane with a length that is the stacking repeat
1219distance. This is a good place to save your project (I called it ‘<b><span
1220style='font-family:"Calibri",sans-serif'>kaolinite’</span></b>).</p>
1221
1222<h2><span style='mso-fareast-font-family:"Times New Roman"'>Part 2. Set up
1223simulation of ideal kaolinite stacking<o:p></o:p></span></h2>
1224
1225<p class=MsoNormal>In this part of the tutorial we’ll create a stacking model
1226for Keokuk kaolinite and use <span class=SpellE>DIFFaX</span> to simulate the
1227powder pattern and compare it to some real data. To begin we need a new phase
1228that we can declare as “faulted’. In the main GSAS-II data tree menu do <b><span
1229style='font-family:"Calibri",sans-serif'>Data/Add new phase</span></b>; I named
1230it ‘<b><span style='font-family:"Calibri",sans-serif'>Keokuk</span></b>’. The
1231General tab for it will immediately appear.</p>
1232
1233<p class=MsoNormal><span style='mso-no-proof:yes'><img width=930 height=500
1234id="_x0000_i1036" src="Stacking%20Faults%20II_files/image010.gif"></span></p>
1235
1236<p class=MsoNormal>Change the <b><span style='font-family:"Calibri",sans-serif'>Phase
1237type</span></b> to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
1238the General tab will be redrawn and a new tab <b><span style='font-family:"Calibri",sans-serif'>‘Layers</span></b>’
1239will appear. Select it.</p>
1240
1241<p class=MsoNormal><span style='mso-no-proof:yes'><img width=817 height=484
1242id="_x0000_i1035" src="Stacking%20Faults%20II_files/image011.gif"></span></p>
1243
1244<p class=MsoNormal>We can anticipate (given that kaolinite space group is C1)
1245that the <b><span style='font-family:"Calibri",sans-serif'>Diffraction Laue
1246symmetry</span></b> is <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>.
1247We can enter by hand the lattice parameters from the kaolinite <span
1248class=SpellE><span class=GramE>abc</span></span>* phase but an easier method is
1249available. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Copy
1250phase cell</span></b>; a file selection dialog will appear for your current
1251directory and the file <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b></span>
1252should be there. Select it; a small popup will appear listing the available
1253phases. Choose ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite <span
1254class=SpellE><span class=GramE>abc</span></span>*</span></b>’ and press <b><span
1255style='font-family:"Calibri",sans-serif'>Ok</span></b>; the Layers window will
1256be redrawn with the new lattice parameters.</p>
1257
1258<p class=MsoNormal><span style='mso-no-proof:yes'><img width=829 height=484
1259id="_x0000_i1034" src="Stacking%20Faults%20II_files/image012.gif"></span></p>
1260
1261<p class=MsoNormal>Next, you need to define the layer. As it would be very
1262tedious to enter 24 atoms by hand, the alternative is to get them from the previously
1263created kaolinite <span class=SpellE><span class=GramE>abc</span></span>*
1264phase. Select the <b><span style='font-family:"Calibri",sans-serif'>Import new
1265layer</span></b> box; the file dialog with <span class=SpellE><b><span
1266style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b></span> will
1267appear. Select the file and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>;
1268again a small popup with two phases listed will appear. Again select <b><span
1269style='font-family:"Calibri",sans-serif'>kaolinite <span class=SpellE><span
1270class=GramE>abc</span></span>*</span></b> and press <b><span style='font-family:
1271"Calibri",sans-serif'>Ok</span></b>; the Layers page will be redrawn with a
1272layer (named kaolinite) will be filled out.</p>
1273
1274<p class=MsoNormal><span style='mso-no-proof:yes'><img width=829 height=500
1275id="_x0000_i1033" src="Stacking%20Faults%20II_files/image013.gif"></span></p>
1276
1277<p class=MsoNormal>If you move down to the bottom of the page (if there isn’t a
1278scroll bar, just grab an edge of the window &amp; shift it slightly) to find
1279the one line <b><span style='font-family:"Calibri",sans-serif'>Layer-Layer
1280Transition probabilities</span></b>. Change <span class=SpellE><b><span
1281style='font-family:"Calibri",sans-serif'>Dz</span></b></span><b><span
1282style='font-family:"Calibri",sans-serif'>=1.0</span></b> and press the plot
1283box; the drawing will show a layer of kaolinite stacked directly above another
1284one.</p>
1285
1286<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
1287id="_x0000_i1032" src="Stacking%20Faults%20II_files/image014.jpg"></span></p>
1288
1289<p class=MsoNormal>Compare that to the stacking in kaolinite.</p>
1290
1291<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
1292id="_x0000_i1031" src="Stacking%20Faults%20II_files/image015.jpg"></span></p>
1293
1294<p class=MsoNormal>Notice the effect of the offset. The 1<sup>st</sup> row of
1295SiO<sub>4</sub> <span class=SpellE>tetrahedra</span> are positioned directly
1296above the AlO<sub>6</sub> <span class=SpellE>octahedra</span> in the real
1297structure but not in the vertically stacked structure. We can use a bit of
1298simple geometry to work out what the offset is but first let us see what
1299happens in the simulation and how it compares to real data.</p>
1300
1301<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 3. Import
1302Keokuk kaolinite data and do 1<sup>st</sup> simulation<o:p></o:p></span></h2>
1303
1304<p class=MsoNormal>First we need to import the Keokuk kaolinite powder data; do
1305<b><span style='font-family:"Calibri",sans-serif'>Import/Powder Data/from
1306Bruker RAW file</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Keokuk
1307<span class=SpellE>kaolinite.RAW</span></span></b> from the file dialog box;
1308press <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Yes</span></b></span>
1309in the next popup. A new file dialog appears requesting an instrument parameter
1310file; we will use an internal default instead. Press <b><span style='font-family:
1311"Calibri",sans-serif'>Cancel</span></b> and select <b><span style='font-family:
1312"Calibri",sans-serif'>Defaults for <span class=SpellE>CuKa</span> lab data</span></b>
1313from the next popup. This process will repeat since the RAW file contains two
1314scans. In the next popup, select only <b><span style='font-family:"Calibri",sans-serif'>kaolinite
1315<span class=SpellE><span class=GramE>abc</span></span>*</span></b>. There will
1316be two PWDR scans in the GSAS-II data tree; one covers 2<span style='font-family:
1317Symbol'>Q</span>= 10-90<span style='font-family:"Calibri",sans-serif'>°</span>
1318and the other covers 2<span style='font-family:Symbol'>Q</span>=80-150°. Only
1319the lower part of the first one is going to be used in our simulation work as
1320the calculations become very time consuming for complex structures and high
1321angle data. Select <b><span style='font-family:"Calibri",sans-serif'>PWDR
1322Keokuk <span class=SpellE>kaolinite.RAW</span> Scan 1</span></b> from the
1323GSAS-II data tree make sure it expands; its plot will also show.</p>
1324
1325<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1326id="_x0000_i1030" src="Stacking%20Faults%20II_files/image016.gif"></span></p>
1327
1328<p class=MsoNormal>Go to <b><span style='font-family:"Calibri",sans-serif'>Limits</span></b>
1329and set <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Tmax</span></b></span>
1330to <b><span style='font-family:"Calibri",sans-serif'>52.0</span></b>; that puts
1331the upper limit in a relatively clear part of the pattern. Then go to
1332Background and set the 1<sup>st</sup> coefficient to 20 (approximately the
1333background at 2Q=18). Next go to <b><span style='font-family:"Calibri",sans-serif'>Sample
1334parameters</span></b> and set the <b><span style='font-family:"Calibri",sans-serif'>Histogram
1335scale</span></b> to something reasonable (I chose <b><span style='font-family:
1336"Calibri",sans-serif'>20.0</span></b>) and make sure the <b><span
1337style='font-family:"Calibri",sans-serif'>Diffractometer type is Bragg-Brentano</span></b>.</p>
1338
1339<p class=MsoNormal>Now we are ready for our 1<sup>st</sup> kaolinite
1340simulation. Go to <b><span style='font-family:"Calibri",sans-serif'>Phases/Keokuk</span></b>
1341and select the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
1342tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
1343pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1344in the popup. Select the <b><span style='font-family:"Calibri",sans-serif'>Scan
13451</span></b> pattern and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1346the simulation will finish quickly (press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>)
1347and the new plot will be displayed (I’ve zoomed in a bit).</p>
1348
1349<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1350id="_x0000_i1029" src="Stacking%20Faults%20II_files/image017.gif"></span>.</p>
1351
1352<p class=MsoNormal>As you can see the simulation (green curve) does not fit the
1353data (blue crosses) at all mostly due to the incorrect layer offset although
1354the 1<sup>st</sup> peak seems to be positioned correctly. To work out the
1355offset consider the drawing of kaolinite.<o:p></o:p></p>
1356
1357<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=338 id="_x0000_i1028"
1358src="Stacking%20Faults%20II_files/image002.gif"></span></p>
1359
1360<p class=MsoNormal>The offset <span class=SpellE>Dx</span> is given by the blue
1361arrow in the above drawing of kaolinite and is in fractional coordinates.
1362Geometry gives<o:p></o:p></p>
1363
1364<p class=MsoNormal><span style='position:relative;top:3pt'><span
1365style='mso-no-proof:yes'><img width=106 height=26 id="_x0000_i1027"
1366src="Stacking%20Faults%20II_files/image021.gif"></span>&nbsp;Or in this case <b><span
1367style='font-family:"Calibri",sans-serif'>-0.368</span></b>. Set <span
1368class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dx</span></b></span>
1369to this value &amp; repeat simulation.</p>
1370
1371<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1372id="_x0000_i1026" src="Stacking%20Faults%20II_files/image022.gif"></span></p>
1373
1374<p class=MsoNormal>There is some improvement but some parts are not very well
1375represented. Recall from the triclinic kaolinite lattice parameters that <span
1376style='font-family:Symbol'>a</span> was 91.7°; that will produce a small offset
1377in Dy. Using the same kind of geometry math gives <span class=SpellE><b><span
1378style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span
1379style='font-family:"Calibri",sans-serif'>=-0.0246</span></b>. Enter this value
1380&amp; repeat the simulation again. This gives a much better fit to the observed
1381pattern, but the simulated peaks are too sharp; this can be fixed by changing
1382the U<span class=GramE>,V,W</span> Instrument parameters. I’d just set <b><span
1383style='font-family:"Calibri",sans-serif'>W=40</span></b> and the <b><span
1384style='font-family:"Calibri",sans-serif'>Histogram scale</span></b> (in <b><span
1385style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>) to <b><span
1386style='font-family:"Calibri",sans-serif'>40</span></b> and try again.</p>
1387
1388<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1389id="_x0000_i1025" src="Stacking%20Faults%20II_files/image023.gif"></span></p>
1390
1391<p class=MsoNormal>That is a pretty good fit for a stacking simulation. By
1392further hand tweaking of the parameters one can further improve the simulation
1393but based on what we see here we do have the right description of stacking in
1394Keokuk kaolinite. Doing sequence simulations varying each parameter over a
1395small range can be used to help with optimization, but in this case it would be
1396far easier to do a Rietveld refinement for this well ordered kaolinite. Save
1397your project as you will need it for the next part of the exercise.<o:p></o:p></p>
1398
1399</span></div>
1400
1401</span></span></span>
1402</body>
1403
1404</html>
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