source: Tutorials/StackingFaults-II/Stacking Faults II.htm @ 2812

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401  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
402  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
403  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
404  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
405  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
406  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
407  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
408  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
409  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
410  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
411  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
412  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
413  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
414  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
415  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
416  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
417  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
418  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
419  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
420  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
421  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
422  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
423  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
424  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
425  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
426  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
427  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
428  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
429  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
430  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
431  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
432  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
433  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
434  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
435  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
436  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
437  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
438  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
439  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
440  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
441  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
442  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
443  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
444  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
445  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
446  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
447  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
448  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
449  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
450  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
451  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
452  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
453  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
454  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
455  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
456  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
457  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
458  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
459  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
460  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
461  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
462  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
463  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
464  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
465  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
466  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
467  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
468  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
469  <w:LsdException Locked="false" Priority="19" QFormat="true"
470   Name="Subtle Emphasis"/>
471  <w:LsdException Locked="false" Priority="21" QFormat="true"
472   Name="Intense Emphasis"/>
473  <w:LsdException Locked="false" Priority="31" QFormat="true"
474   Name="Subtle Reference"/>
475  <w:LsdException Locked="false" Priority="32" QFormat="true"
476   Name="Intense Reference"/>
477  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
478  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
479   UnhideWhenUsed="true" Name="Bibliography"/>
480  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
481   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
482  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
483  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
484  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
485  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
486  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
487  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
488  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
489  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
490  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
491  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
492  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
493  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
494  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
495  <w:LsdException Locked="false" Priority="46"
496   Name="Grid Table 1 Light Accent 1"/>
497  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
498  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
499  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
500  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
501  <w:LsdException Locked="false" Priority="51"
502   Name="Grid Table 6 Colorful Accent 1"/>
503  <w:LsdException Locked="false" Priority="52"
504   Name="Grid Table 7 Colorful Accent 1"/>
505  <w:LsdException Locked="false" Priority="46"
506   Name="Grid Table 1 Light Accent 2"/>
507  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
508  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
509  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
510  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
511  <w:LsdException Locked="false" Priority="51"
512   Name="Grid Table 6 Colorful Accent 2"/>
513  <w:LsdException Locked="false" Priority="52"
514   Name="Grid Table 7 Colorful Accent 2"/>
515  <w:LsdException Locked="false" Priority="46"
516   Name="Grid Table 1 Light Accent 3"/>
517  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
518  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
519  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
520  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
521  <w:LsdException Locked="false" Priority="51"
522   Name="Grid Table 6 Colorful Accent 3"/>
523  <w:LsdException Locked="false" Priority="52"
524   Name="Grid Table 7 Colorful Accent 3"/>
525  <w:LsdException Locked="false" Priority="46"
526   Name="Grid Table 1 Light Accent 4"/>
527  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
528  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
529  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
530  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
531  <w:LsdException Locked="false" Priority="51"
532   Name="Grid Table 6 Colorful Accent 4"/>
533  <w:LsdException Locked="false" Priority="52"
534   Name="Grid Table 7 Colorful Accent 4"/>
535  <w:LsdException Locked="false" Priority="46"
536   Name="Grid Table 1 Light Accent 5"/>
537  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
538  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
539  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
540  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
541  <w:LsdException Locked="false" Priority="51"
542   Name="Grid Table 6 Colorful Accent 5"/>
543  <w:LsdException Locked="false" Priority="52"
544   Name="Grid Table 7 Colorful Accent 5"/>
545  <w:LsdException Locked="false" Priority="46"
546   Name="Grid Table 1 Light Accent 6"/>
547  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
548  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
549  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
550  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
551  <w:LsdException Locked="false" Priority="51"
552   Name="Grid Table 6 Colorful Accent 6"/>
553  <w:LsdException Locked="false" Priority="52"
554   Name="Grid Table 7 Colorful Accent 6"/>
555  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
556  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
557  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
558  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
559  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
560  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
561  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
562  <w:LsdException Locked="false" Priority="46"
563   Name="List Table 1 Light Accent 1"/>
564  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
565  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
566  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
567  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
568  <w:LsdException Locked="false" Priority="51"
569   Name="List Table 6 Colorful Accent 1"/>
570  <w:LsdException Locked="false" Priority="52"
571   Name="List Table 7 Colorful Accent 1"/>
572  <w:LsdException Locked="false" Priority="46"
573   Name="List Table 1 Light Accent 2"/>
574  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
575  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
576  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
577  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
578  <w:LsdException Locked="false" Priority="51"
579   Name="List Table 6 Colorful Accent 2"/>
580  <w:LsdException Locked="false" Priority="52"
581   Name="List Table 7 Colorful Accent 2"/>
582  <w:LsdException Locked="false" Priority="46"
583   Name="List Table 1 Light Accent 3"/>
584  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
585  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
586  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
587  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
588  <w:LsdException Locked="false" Priority="51"
589   Name="List Table 6 Colorful Accent 3"/>
590  <w:LsdException Locked="false" Priority="52"
591   Name="List Table 7 Colorful Accent 3"/>
592  <w:LsdException Locked="false" Priority="46"
593   Name="List Table 1 Light Accent 4"/>
594  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
595  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
596  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
597  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
598  <w:LsdException Locked="false" Priority="51"
599   Name="List Table 6 Colorful Accent 4"/>
600  <w:LsdException Locked="false" Priority="52"
601   Name="List Table 7 Colorful Accent 4"/>
602  <w:LsdException Locked="false" Priority="46"
603   Name="List Table 1 Light Accent 5"/>
604  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
605  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
606  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
607  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
608  <w:LsdException Locked="false" Priority="51"
609   Name="List Table 6 Colorful Accent 5"/>
610  <w:LsdException Locked="false" Priority="52"
611   Name="List Table 7 Colorful Accent 5"/>
612  <w:LsdException Locked="false" Priority="46"
613   Name="List Table 1 Light Accent 6"/>
614  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
615  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
616  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
617  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
618  <w:LsdException Locked="false" Priority="51"
619   Name="List Table 6 Colorful Accent 6"/>
620  <w:LsdException Locked="false" Priority="52"
621   Name="List Table 7 Colorful Accent 6"/>
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1089<![endif]--><!--[if gte mso 9]><xml>
1090 <o:shapedefaults v:ext="edit" spidmax="1026"/>
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1098
1099<div class=WordSection1>
1100
1101<h1><span style='mso-fareast-font-family:"Times New Roman"'>Stacking Fault
1102Simulations – II<o:p></o:p></span></h1>
1103
1104<p class=MsoNormal>In this exercise and the next you will simulate some
1105diffraction patterns from kaolinite clays. Kaolinite, <span class=GramE>Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(</span>OH)<sub>4</sub>,
1106is a 1:1 layer silicate with a single unique sheet with AlO<sub>6</sub> <span
1107class=SpellE>octahedra</span> on one side and SiO<sub>4</sub> <span
1108class=SpellE>tetrahedra</span> on the other. The layers stack with an offset to
1109ideally form a triclinic C1 lattice (<span class=SpellE>Bish</span> &amp; Von <span
1110class=SpellE>Dreele</span>, 1989, Clay &amp; Clay Min. 37, 289-296) for a
1111sample of the most ordered form of kaolinite from Keokuk, Iowa. Kaolinites from
1112other locations evidently have stacking faults so that the peaks are displaced,
1113have peculiar shapes and are above a varying background. For the exercise we
1114provide a laboratory Bragg-Brentano pattern of Keokuk kaolinite collected with <span
1115class=SpellE>CuKa</span> radiation on a Bruker instrument and thus in the
1116Bruker RAW file format. The Keokuk kaolinite has some <span class=SpellE>dickite</span>
1117(different ordered stacking of kaolinite layers). The next exercise Stacking
1118Faults-III) covers a simple simulation of a faulted kaolinite from Georgia.</p>
1119
1120<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1121
1122<h2><span style='mso-fareast-font-family:"Times New Roman"'>Part 1. Creating
1123kaolinite layer<o:p></o:p></span></h2>
1124
1125<p class=MsoNormal>In this initial step we will load from a <span class=SpellE>cif</span>
1126file the structure of kaolinite, draw it to see the layer structure and then
1127transform it into forms suitable for stacking simulations. To begin do <b><span
1128style='font-family:"Calibri",sans-serif'>Import/Phase/from CIF file</span></b>;
1129from the file dialog select <span class=SpellE><b style='mso-bidi-font-weight:
1130normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1131minor-latin;mso-hansi-theme-font:minor-latin'>StackingFaults</span></b></span><b
1132style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1133mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-II/data/</span></b><span
1134class=SpellE><b><span style='font-family:"Calibri",sans-serif'>kaolinite.cif</span></b></span>.
1135After the “are you sure” popup, there will be another warning you that 4 atom
1136types (‘O-H’) were not recognized chemical element symbols and they were
1137substituted by <span class=SpellE>Xe</span> to make them obvious in the atom
1138list. Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1139you are offered a chance to change the phase name, I used ‘<b><span
1140style='font-family:"Calibri",sans-serif'>kaolinite</span></b>’. The General tab
1141is displayed (notice the presence of <span class=SpellE>Xe</span> in the
1142element table).</p>
1143
1144<p class=MsoNormal><span style='mso-no-proof:yes'><img width=930 height=500
1145id="_x0000_i1043" src="Stacking%20Faults%20II_files/image001.gif"></span></p>
1146
1147<p class=MsoNormal>To fix the <span class=SpellE>Xe</span> atoms (they should
1148be O), select <b><span style='font-family:"Calibri",sans-serif'>Atoms</span></b>
1149and then double click the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
1150column heading; a small popup will appear. Select <span class=SpellE><b><span
1151style='font-family:"Calibri",sans-serif'>Xe</span></b></span> &amp; press <b><span
1152style='font-family:"Calibri",sans-serif'>Ok</span></b>; the <span class=SpellE>Xe</span>
1153atoms at the bottom of the atom table will be highlighted. Next select <b><span
1154style='font-family:"Calibri",sans-serif'>Edit/On selected atoms…/Modify parameters</span></b>
1155from the Phase Data menu; a new popup will appear. Select <b><span
1156style='font-family:"Calibri",sans-serif'>Type</span></b> &amp; press <b><span
1157style='font-family:"Calibri",sans-serif'>Ok</span></b>; a periodic table of the
1158element will appear. Select <b><span style='font-family:"Calibri",sans-serif'>O</span></b>
1159from the O-atom pulldown; the structure will be drawn with Al, Si &amp; O atoms
1160only.</p>
1161
1162<p class=MsoNormal><span style='mso-no-proof:yes'><img width=479 height=358
1163id="_x0000_i1042" src="Stacking%20Faults%20II_files/image003.jpg"></span></p>
1164
1165<p class=MsoNormal>To better visualize the stacking layer, select the <b><span
1166style='font-family:"Calibri",sans-serif'>Draw Atoms</span></b> tab and then
1167double click the empty upper left corner box of the table. All atoms will turn
1168green. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit Figure/Fill
1169unit cell</span></b>; the structure will be redrawn with all atoms that belong
1170in the unit cell. Finally, double click on the <b><span style='font-family:
1171"Calibri",sans-serif'>Type</span></b> column heading, select <b><span
1172style='font-family:"Calibri",sans-serif'>Al</span></b> &amp; <b><span
1173style='font-family:"Calibri",sans-serif'>Si</span></b> (they will turn green)
1174and then do <b><span style='font-family:"Calibri",sans-serif'>Edit Figure/Fill
1175CN sphere</span></b>. After a bit of rotating the structure around, the
1176layering along the c-axis (blue line) will be evident.</p>
1177
1178<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
1179id="_x0000_i1041" src="Stacking%20Faults%20II_files/image004.jpg"></span></p>
1180
1181<p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> <span
1182class=SpellE>tetrahedra</span> and AlO<sub>6</sub> <span class=SpellE>octahedra</span>.
1183Also notice that the next layer (represented by the 4 O atoms at the bottom of
1184the above drawing are offset giving a triclinic lattice.</p>
1185
1186<p class=MsoNormal>The stacking fault simulation calculation via <span
1187class=SpellE>DIFFaX</span> routines requires that the stacking layers be
1188defined in a coordinate system that has the stacking direction perpendicular to
1189the stacking plane defined as the c-axis. This requires transformation of the
1190unit cell and atom coordinates; a suitable tool exists in GSAS-II to do this. Select
1191the <b><span style='font-family:"Calibri",sans-serif'>General</span></b> tab
1192and do <b><span style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>;
1193a popup window will appear.</p>
1194
1195<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
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1197 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1198 <v:stroke joinstyle="miter"/>
1199 <v:formulas>
1200  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
1201  <v:f eqn="sum @0 1 0"/>
1202  <v:f eqn="sum 0 0 @1"/>
1203  <v:f eqn="prod @2 1 2"/>
1204  <v:f eqn="prod @3 21600 pixelWidth"/>
1205  <v:f eqn="prod @3 21600 pixelHeight"/>
1206  <v:f eqn="sum @0 0 1"/>
1207  <v:f eqn="prod @6 1 2"/>
1208  <v:f eqn="prod @7 21600 pixelWidth"/>
1209  <v:f eqn="sum @8 21600 0"/>
1210  <v:f eqn="prod @7 21600 pixelHeight"/>
1211  <v:f eqn="sum @10 21600 0"/>
1212 </v:formulas>
1213 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1214 <o:lock v:ext="edit" aspectratio="t"/>
1215</v:shapetype><v:shape id="Picture_x0020_20" o:spid="_x0000_i1040" type="#_x0000_t75"
1216 style='width:262.5pt;height:301.5pt;visibility:visible;mso-wrap-style:square'>
1217 <v:imagedata src="Stacking%20Faults%20II_files/image001.png" o:title=""/>
1218</v:shape><![endif]--><![if !vml]><img width=350 height=402
1219src="Stacking%20Faults%20II_files/image002.gif" v:shapes="Picture_x0020_20"><![endif]></span></p>
1220
1221<p class=MsoNormal>Note that this allows one to transform the structure
1222according to a matrix and then shift the resultant positions along some vector
1223and then select those that are unique according to a selected space group. The
1224pulldown gives a selection of commonly used transformations; we want the last
1225one, <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>abc</span></b></span><b><span
1226style='font-family:"Calibri",sans-serif'>*</span></b>, which satisfies the
1227stacking fault requirement. Select it; notice that the space group is changed
1228to P1. Leave this as the kaolinite layer has no symmetry; in other
1229circumstances the layer may have an inversion center in which case P-1 should
1230be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
1231the new lattice parameters will be shown.</p>
1232
1233<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1234 id="Picture_x0020_21" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:262.5pt;
1235 height:301.5pt;visibility:visible;mso-wrap-style:square'>
1236 <v:imagedata src="Stacking%20Faults%20II_files/image003.png" o:title=""/>
1237</v:shape><![endif]--><![if !vml]><img width=350 height=402
1238src="Stacking%20Faults%20II_files/image004.gif" v:shapes="Picture_x0020_21"><![endif]></span></p>
1239
1240<p class=MsoNormal><span class=GramE>The a</span> &amp; b axes stay the same,
1241but c is now smaller (the interlayer distance in kaolinite) and <span
1242style='font-family:Symbol'>a</span> &amp; <span style='font-family:Symbol'>b</span>
1243= 90 (<span style='font-family:Symbol'>g</span> is unchanged). Press <b><span
1244style='font-family:"Calibri",sans-serif'>Ok</span></b>; a new phase (kaolinite <span
1245class=SpellE>abc</span>*) will be made and its General tab will be shown
1246immediately. Select the <b><span style='font-family:"Calibri",sans-serif'>Draw
1247Atoms</span></b> tab to see the resulting structure.</p>
1248
1249<p class=MsoNormal><span style='mso-no-proof:yes'><img width=471 height=352
1250id="_x0000_i1038" src="Stacking%20Faults%20II_files/image007.jpg"></span></p>
1251
1252<p class=MsoNormal>To see what this layer looks like with more of it drawn, you
1253can add more unit cells to the drawing; select all the atoms by double clicking
1254the upper left empty box of the Draw atoms table. Do <b><span style='font-family:
1255"Calibri",sans-serif'>Edit Figure/Add atoms</span></b> and <b><span
1256style='font-family:"Calibri",sans-serif'>increment</span></b> the 1<sup>st</sup>
1257<b><span style='font-family:"Calibri",sans-serif'>Choose unit cel</span></b>l
1258and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; this
1259will add one unit cell along x. Now select all the atoms again, do <b><span
1260style='font-family:"Calibri",sans-serif'>Edit Figure/Add atoms</span></b> and
1261now <b><span style='font-family:"Calibri",sans-serif'>decrement</span></b> the
12621<sup>st</sup> <b><span style='font-family:"Calibri",sans-serif'>Choose unit
1263cell</span></b>. Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1264the drawing will now be 3 unit cells wide along x. Repeat this once more <b><span
1265style='font-family:"Calibri",sans-serif'>decrementing</span></b> the 2<sup>nd</sup>
1266<b><span style='font-family:"Calibri",sans-serif'>Choose unit cell</span></b>
1267to give a 3x2 unit cell block of atoms. Double click the <b><span
1268style='font-family:"Calibri",sans-serif'>Style</span></b> column heading and
1269select <b><span style='font-family:"Calibri",sans-serif'>Balls and sticks</span></b>;
1270the drawing should look like (after some zooming/shifting/rotation).</p>
1271
1272<p class=MsoNormal><span style='mso-no-proof:yes'><img width=477 height=357
1273id="_x0000_i1037" src="Stacking%20Faults%20II_files/image009.jpg"></span></p>
1274
1275<p class=MsoNormal>This structure is now suitable for use in <span
1276class=SpellE>DIFFaX</span> calculations; the cell has a c-axis that is
1277perpendicular to the ab plane with a length that is the stacking repeat
1278distance. This is a good place to save your project (I called it ‘<b><span
1279style='font-family:"Calibri",sans-serif'>kaolinite’</span></b>).</p>
1280
1281<h2><span style='mso-fareast-font-family:"Times New Roman"'>Part 2. Set up
1282simulation of ideal kaolinite stacking<o:p></o:p></span></h2>
1283
1284<p class=MsoNormal>In this part of the tutorial we’ll create a stacking model
1285for Keokuk kaolinite and use <span class=SpellE>DIFFaX</span> to simulate the powder
1286pattern and compare it to some real data. To begin we need a new phase that we
1287can declare as “faulted’. In the main GSAS-II data tree menu do <b><span
1288style='font-family:"Calibri",sans-serif'>Data/Add new phase</span></b>; I named
1289it ‘<b><span style='font-family:"Calibri",sans-serif'>Keokuk</span></b>’. The
1290General tab for it will immediately appear.</p>
1291
1292<p class=MsoNormal><span style='mso-no-proof:yes'><img width=930 height=500
1293id="_x0000_i1036" src="Stacking%20Faults%20II_files/image010.gif"></span></p>
1294
1295<p class=MsoNormal>Change the <b><span style='font-family:"Calibri",sans-serif'>Phase
1296type</span></b> to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
1297the General tab will be redrawn and a new tab <b><span style='font-family:"Calibri",sans-serif'>‘Layers</span></b>’
1298will appear. Select it.</p>
1299
1300<p class=MsoNormal><span style='mso-no-proof:yes'><img width=817 height=484
1301id="_x0000_i1035" src="Stacking%20Faults%20II_files/image011.gif"></span></p>
1302
1303<p class=MsoNormal>We can anticipate (given that kaolinite space group is C1)
1304that the <b><span style='font-family:"Calibri",sans-serif'>Diffraction Laue
1305symmetry</span></b> is <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>.
1306We can enter by hand the lattice parameters from the kaolinite <span
1307class=SpellE>abc</span>* phase but an easier method is available. Do <b><span
1308style='font-family:"Calibri",sans-serif'>Operations/Copy phase cell</span></b>;
1309a file selection dialog will appear for your current directory and the file <span
1310class=SpellE><b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b></span>
1311should be there. Select it; a small popup will appear listing the available
1312phases. Choose ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite <span
1313class=SpellE>abc</span>*</span></b>’ and press <b><span style='font-family:
1314"Calibri",sans-serif'>Ok</span></b>; the Layers window will be redrawn with the
1315new lattice parameters.</p>
1316
1317<p class=MsoNormal><span style='mso-no-proof:yes'><img width=829 height=484
1318id="_x0000_i1034" src="Stacking%20Faults%20II_files/image012.gif"></span></p>
1319
1320<p class=MsoNormal>Next, you need to define the layer. As it would be very
1321tedious to enter 24 atoms by hand, the alternative is to get them from the
1322previously created kaolinite <span class=SpellE>abc</span>* phase. Select the <b><span
1323style='font-family:"Calibri",sans-serif'>Import new layer</span></b> box; the
1324file dialog with <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b></span>
1325will appear. Select the file and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>;
1326again a small popup with two phases listed will appear. Again select <b><span
1327style='font-family:"Calibri",sans-serif'>kaolinite <span class=SpellE>abc</span>*</span></b>
1328and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; the
1329Layers page will be redrawn with a layer (named kaolinite) will be filled out.</p>
1330
1331<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1332 id="Picture_x0020_22" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt;
1333 height:282.75pt;visibility:visible;mso-wrap-style:square'>
1334 <v:imagedata src="Stacking%20Faults%20II_files/image005.png" o:title=""/>
1335</v:shape><![endif]--><![if !vml]><img width=624 height=377
1336src="Stacking%20Faults%20II_files/image006.gif" v:shapes="Picture_x0020_22"><![endif]></span></p>
1337
1338<p class=MsoNormal>If you move down to the bottom of the page to find the one
1339line <b><span style='font-family:"Calibri",sans-serif'>Layer-Layer Transition
1340probabilities</span></b>. Change <span class=SpellE><b><span style='font-family:
1341"Calibri",sans-serif'>Dz</span></b></span><b><span style='font-family:"Calibri",sans-serif'>=1.0</span></b>
1342and press the plot box; the drawing will show a layer of kaolinite stacked
1343directly above another one.</p>
1344
1345<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
1346id="_x0000_i1032" src="Stacking%20Faults%20II_files/image014.jpg"></span></p>
1347
1348<p class=MsoNormal>Compare that to the stacking in kaolinite.</p>
1349
1350<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
1351id="_x0000_i1031" src="Stacking%20Faults%20II_files/image015.jpg"></span></p>
1352
1353<p class=MsoNormal>Notice the effect of the offset. The 1<sup>st</sup> row of
1354SiO<sub>4</sub> <span class=SpellE>tetrahedra</span> are positioned directly
1355above the AlO<sub>6</sub> <span class=SpellE>octahedra</span> in the real
1356structure but not in the vertically stacked structure. We can use a bit of
1357simple geometry to work out what the offset is but first let us see what
1358happens in the simulation and how it compares to real data.</p>
1359
1360<h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 3. Import
1361Keokuk kaolinite data and do 1<sup>st</sup> simulation<o:p></o:p></span></h2>
1362
1363<p class=MsoNormal>First we need to import the Keokuk kaolinite powder data; do
1364<b><span style='font-family:"Calibri",sans-serif'>Import/Powder Data/from
1365Bruker RAW file</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Keokuk
1366<span class=SpellE>kaolinite.RAW</span></span></b> from the file dialog box;
1367press <b><span style='font-family:"Calibri",sans-serif'>Yes</span></b> in the
1368next popup. A new file dialog appears requesting an instrument parameter file;
1369we will use an internal default instead. Press <b><span style='font-family:
1370"Calibri",sans-serif'>Cancel</span></b> and select <b><span style='font-family:
1371"Calibri",sans-serif'>Defaults for <span class=SpellE>CuKa</span> lab data</span></b>
1372from the next popup. This process will repeat since the RAW file contains two
1373scans. In the next popup, select only <b><span style='font-family:"Calibri",sans-serif'>kaolinite
1374<span class=SpellE>abc</span>*</span></b>. There will be two PWDR scans in the
1375GSAS-II data tree; one covers 2<span style='font-family:Symbol'>Q</span>= 10-90<span
1376style='font-family:"Calibri",sans-serif'>°</span> and the other covers 2<span
1377style='font-family:Symbol'>Q</span>=80-150°. Only the lower part of the first
1378one is going to be used in our simulation work as the calculations become very
1379time consuming for complex structures and high angle data. Select <b><span
1380style='font-family:"Calibri",sans-serif'>PWDR Keokuk <span class=SpellE>kaolinite.RAW</span>
1381Scan 1</span></b> from the GSAS-II data tree make sure it expands; its plot
1382will also show.</p>
1383
1384<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1385id="_x0000_i1030" src="Stacking%20Faults%20II_files/image016.gif"></span></p>
1386
1387<p class=MsoNormal>Go to <b><span style='font-family:"Calibri",sans-serif'>Limits</span></b>
1388and set <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Tmax</span></b></span>
1389to <b><span style='font-family:"Calibri",sans-serif'>52.0</span></b>; that puts
1390the upper limit in a relatively clear part of the pattern. Then go to
1391Background and set the 1<sup>st</sup> coefficient to 20 (approximately the
1392background at 2<span style='font-family:Symbol;mso-ascii-font-family:"Times New Roman";
1393mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-font-family:
1394Symbol'><span style='mso-char-type:symbol;mso-symbol-font-family:Symbol'>Q</span></span>=18).
1395Next go to <b><span style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>
1396and set the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale</span></b>
1397to something reasonable (I chose <b><span style='font-family:"Calibri",sans-serif'>20.0</span></b>)
1398and make sure the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
1399type is Bragg-Brentano</span></b>.</p>
1400
1401<p class=MsoNormal>Now we are ready for our 1<sup>st</sup> kaolinite
1402simulation. Go to <b><span style='font-family:"Calibri",sans-serif'>Phases/Keokuk</span></b>
1403and select the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
1404tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
1405pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
1406in the popup. Select the <b><span style='font-family:"Calibri",sans-serif'>Scan
14071</span></b> pattern and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
1408the simulation will finish quickly (press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>)
1409and the new plot will be displayed (I’ve zoomed in a bit).</p>
1410
1411<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1412id="_x0000_i1029" src="Stacking%20Faults%20II_files/image017.gif"></span>.</p>
1413
1414<p class=MsoNormal>As you can see the simulation (green curve) does not fit the
1415data (blue crosses) at all mostly due to the incorrect layer offset although
1416the 1<sup>st</sup> peak seems to be positioned correctly. To work out the
1417offset consider the drawing of kaolinite.</p>
1418
1419<p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=338
1420id="_x0000_i1028" src="Stacking%20Faults%20II_files/image002.gif"></span></p>
1421
1422<p class=MsoNormal>The offset <span class=SpellE>Dx</span> is given by the blue
1423arrow in the above drawing of kaolinite and is in fractional coordinates.
1424Geometry gives<o:p></o:p></p>
1425
1426<p class=MsoNormal><span style='position:relative;top:3pt'><span
1427style='mso-no-proof:yes'><img width=106 height=26 id="_x0000_i1027"
1428src="Stacking%20Faults%20II_files/image021.gif"></span>&nbsp;Or in this case <b><span
1429style='font-family:"Calibri",sans-serif'>-0.368</span></b>. Set <span
1430class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dx</span></b></span>
1431to this value &amp; repeat simulation.</p>
1432
1433<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1434id="_x0000_i1026" src="Stacking%20Faults%20II_files/image022.gif"></span></p>
1435
1436<p class=MsoNormal>There is some improvement but some parts are not very well
1437represented. Recall from the triclinic kaolinite lattice parameters that <span
1438style='font-family:Symbol'>a</span> was 91.7°; that will produce a small offset
1439in Dy. Using the same kind of geometry math gives <span class=SpellE><b><span
1440style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span
1441style='font-family:"Calibri",sans-serif'>=-0.0246</span></b>. Enter this value
1442&amp; repeat the simulation again. This gives a much better fit to the observed
1443pattern, but the simulated peaks are too sharp; this can be fixed by changing
1444the U<span class=GramE>,V,W</span> Instrument parameters. I’d just set <b><span
1445style='font-family:"Calibri",sans-serif'>W=40</span></b> and the <b><span
1446style='font-family:"Calibri",sans-serif'>Histogram scale</span></b> (in <b><span
1447style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>) to <b><span
1448style='font-family:"Calibri",sans-serif'>40</span></b> and try again.</p>
1449
1450<p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
1451id="_x0000_i1025" src="Stacking%20Faults%20II_files/image023.gif"></span></p>
1452
1453<p class=MsoNormal>That is a pretty good fit for a stacking simulation. By
1454further hand tweaking of the parameters one can further improve the simulation
1455but based on what we see here we do have the right description of stacking in
1456Keokuk kaolinite. Doing sequence simulations varying each parameter over a
1457small range can be used to help with optimization, but in this case it would be
1458far easier to do a Rietveld refinement for this well ordered kaolinite. Save
1459your project as you will need it for the next exercise (Stacking Faults-III).<o:p></o:p></p>
1460
1461</span></div>
1462
1463</body>
1464
1465</html>
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