Changeset 2267


Ignore:
Timestamp:
May 13, 2016 3:51:35 PM (6 years ago)
Author:
vondreele
Message:
 
Location:
Tutorials/StackingFaults-II
Files:
38 deleted
9 edited

Legend:

Unmodified
Added
Removed
  • Tutorials/StackingFaults-II/Stacking Faults II.htm

    r2266 r2267  
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    80286pre
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    1070214</style>
    1071 <!--[if gte mso 10]>
    1072 <style>
    1073  /* Style Definitions */
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    1088 <![endif]--><!--[if gte mso 9]><xml>
    1089  <o:shapedefaults v:ext="edit" spidmax="1029"/>
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     215
    1097216</head>
    1098217
    1099 <body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
     218<body lang=EN-US link=blue vlink=purple>
    1100219
    1101220<div class=WordSection1>
    1102221
    1103 <h1><span style='mso-fareast-font-family:"Times New Roman"'>Stacking Fault
    1104 Simulations – II<o:p></o:p></span></h1>
     222<h1>Stacking Fault Simulations – II</h1>
    1105223
    1106224<p class=MsoNormal>In this exercise you will simulate some diffraction patterns
    1107 from kaolinite clays. Kaolinite, <span class=GramE>Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(</span>OH)<sub>4</sub>,
    1108 is a 1:1 layer silicate with a single unique sheet with AlO<sub>6</sub> <span
    1109 class=SpellE>octahedra</span> on one side and SiO<sub>4</sub> <span
    1110 class=SpellE>tetrahedra</span> on the other. The layers stack with an offset to
    1111 ideally form a triclinic C1 lattice (<span class=SpellE>Bish</span> &amp; Von
     225from kaolinite clays. Kaolinite, Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(OH)<sub>4</sub>,
     226is a 1:1 layer silicate with a single unique sheet with AlO<sub>6</sub>
     227octahedra on one side and SiO<sub>4</sub> tetrahedra on the other. The layers
     228stack with an offset to ideally form a triclinic C1 lattice (Bish &amp; Von
    1112229Dreele, 1989, Clay &amp; Clay Min. 37, 289-296) for a sample of the most
    1113230ordered form of kaolinite from Keokuk, Iowa. Kaolinites from other locations
     
    1116233laboratory Bragg-Brentano pattern of Keokuk kaolinite and a less ordered one
    1117234from Washington County, Georgia (Clay Minerals Society Standard KGa-1b)
    1118 collected with <span class=SpellE>CuKa</span> radiation on a Bruker instrument
    1119 and thus in the Bruker RAW file format. The KGa-1b sample contains a small
    1120 amount of <span class=SpellE>anatase</span> (TiO<sub>2</sub>) and the Keokuk
    1121 kaolinite has some <span class=SpellE>dickite</span> (different ordered
    1122 stacking of kaolinite layers).</p>
     235collected with CuKa radiation on a Bruker instrument and thus in the Bruker RAW
     236file format. The KGa-1b sample contains a small amount of anatase (TiO<sub>2</sub>)
     237and the Keokuk kaolinite has some dickite (different ordered stacking of
     238kaolinite layers).</p>
    1123239
    1124240<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
    1125241
    1126 <h2><span style='mso-fareast-font-family:"Times New Roman"'>Part 1. Creating
    1127 kaolinite layer<o:p></o:p></span></h2>
    1128 
    1129 <p class=MsoNormal>In this initial step we will load from a <span class=SpellE>cif</span>
    1130 file the structure of kaolinite, draw it to see the layer structure and then
    1131 transform it into forms suitable for stacking simulations. To begin do <b><span
     242<h2>Part 1. Creating kaolinite layer</h2>
     243
     244<p class=MsoNormal>In this initial step we will load from a cif file the
     245structure of kaolinite, draw it to see the layer structure and then transform
     246it into forms suitable for stacking simulations. To begin do <b><span
    1132247style='font-family:"Calibri",sans-serif'>Import/Phase/from CIF file</span></b>;
    1133 from the file dialog select <span class=SpellE><b><span style='font-family:
    1134 "Calibri",sans-serif'>kaolinite.cif</span></b></span>. After the “are you sure”
    1135 popup, there will be another warning you that 4 atom types (‘O-H’) were not
    1136 recognized chemical element symbols and they were substituted by <span
    1137 class=SpellE>Xe</span> to make them obvious in the atom list. Press <b><span
     248from the file dialog select <b><span style='font-family:"Calibri",sans-serif'>kaolinite.cif</span></b>.
     249After the “are you sure” popup, there will be another warning you that 4 atom
     250types (‘O-H’) were not recognized chemical element symbols and they were
     251substituted by Xe to make them obvious in the atom list. Press <b><span
    1138252style='font-family:"Calibri",sans-serif'>Ok</span></b>; you are offered a
    1139253chance to change the phase name, I used ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite</span></b>’.
    1140 The General tab is displayed (notice the presence of <span class=SpellE>Xe</span>
    1141 in the element table).</p>
    1142 
    1143 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
    1144  id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
    1145  path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
    1146  <v:stroke joinstyle="miter"/>
    1147  <v:formulas>
    1148   <v:f eqn="if lineDrawn pixelLineWidth 0"/>
    1149   <v:f eqn="sum @0 1 0"/>
    1150   <v:f eqn="sum 0 0 @1"/>
    1151   <v:f eqn="prod @2 1 2"/>
    1152   <v:f eqn="prod @3 21600 pixelWidth"/>
    1153   <v:f eqn="prod @3 21600 pixelHeight"/>
    1154   <v:f eqn="sum @0 0 1"/>
    1155   <v:f eqn="prod @6 1 2"/>
    1156   <v:f eqn="prod @7 21600 pixelWidth"/>
    1157   <v:f eqn="sum @8 21600 0"/>
    1158   <v:f eqn="prod @7 21600 pixelHeight"/>
    1159   <v:f eqn="sum @10 21600 0"/>
    1160  </v:formulas>
    1161  <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
    1162  <o:lock v:ext="edit" aspectratio="t"/>
    1163 </v:shapetype><v:shape id="Picture_x0020_8" o:spid="_x0000_i1043" type="#_x0000_t75"
    1164  style='width:697.5pt;height:375pt;visibility:visible;mso-wrap-style:square'>
    1165  <v:imagedata src="Stacking%20Faults%20II_files/image001.png" o:title=""/>
    1166 </v:shape><![endif]--><![if !vml]><img width=930 height=500
    1167 src="Stacking%20Faults%20II_files/image002.gif" v:shapes="Picture_x0020_8"><![endif]></span></p>
    1168 
    1169 <p class=MsoNormal>To fix the <span class=SpellE>Xe</span> atoms (they should be
    1170 O), select <b><span style='font-family:"Calibri",sans-serif'>Atoms</span></b>
    1171 and then double click the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
    1172 column heading; a small popup will appear. Select <span class=SpellE><b><span
    1173 style='font-family:"Calibri",sans-serif'>Xe</span></b></span> &amp; press <b><span
    1174 style='font-family:"Calibri",sans-serif'>Ok</span></b>; the <span class=SpellE>Xe</span>
    1175 atoms at the bottom of the atom table will be highlighted. Next select <b><span
     254The General tab is displayed (notice the presence of Xe in the element table).</p>
     255
     256<p class=MsoNormal><img width=930 height=500 id="Picture 8"
     257src="Stacking%20Faults%20II_files/image001.gif"></p>
     258
     259<p class=MsoNormal>To fix the Xe atoms (they should be O), select <b><span
     260style='font-family:"Calibri",sans-serif'>Atoms</span></b> and then double click
     261the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b> column
     262heading; a small popup will appear. Select <b><span style='font-family:"Calibri",sans-serif'>Xe</span></b>
     263&amp; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
     264the Xe atoms at the bottom of the atom table will be highlighted. Next select <b><span
    1176265style='font-family:"Calibri",sans-serif'>Edit/Modify atom parameters</span></b>
    1177266from the Phase Data menu; a new popup will appear.</p>
    1178267
    1179 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1180  id="Picture_x0020_9" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:171pt;
    1181  height:201pt;visibility:visible;mso-wrap-style:square'>
    1182  <v:imagedata src="Stacking%20Faults%20II_files/image003.png" o:title=""/>
    1183 </v:shape><![endif]--><![if !vml]><img width=228 height=268
    1184 src="Stacking%20Faults%20II_files/image004.gif" v:shapes="Picture_x0020_9"><![endif]></span></p>
     268<p class=MsoNormal><img width=228 height=268 id="Picture 9"
     269src="Stacking%20Faults%20II_files/image002.gif"></p>
    1185270
    1186271<p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
     
    1190275be drawn with Al, Si &amp; O atoms only.</p>
    1191276
    1192 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1193  id="Picture_x0020_10" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:359.25pt;
    1194  height:268.5pt;visibility:visible;mso-wrap-style:square'>
    1195  <v:imagedata src="Stacking%20Faults%20II_files/image005.jpg" o:title=""/>
    1196 </v:shape><![endif]--><![if !vml]><img width=479 height=358
    1197 src="Stacking%20Faults%20II_files/image006.jpg" v:shapes="Picture_x0020_10"><![endif]></span></p>
     277<p class=MsoNormal><img width=479 height=358 id="Picture 10"
     278src="Stacking%20Faults%20II_files/image003.jpg"></p>
    1198279
    1199280<p class=MsoNormal>To better visualize the stacking layer, select the <b><span
     
    1209290layering along the c-axis (blue line) will be evident.</p>
    1210291
    1211 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1212  id="Picture_x0020_11" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:5in;
    1213  height:269.25pt;visibility:visible;mso-wrap-style:square'>
    1214  <v:imagedata src="Stacking%20Faults%20II_files/image007.jpg" o:title=""/>
    1215 </v:shape><![endif]--><![if !vml]><img width=480 height=359
    1216 src="Stacking%20Faults%20II_files/image008.jpg" v:shapes="Picture_x0020_11"><![endif]></span></p>
    1217 
    1218 <p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> <span
    1219 class=SpellE>tetrahedra</span> and AlO<sub>6</sub> <span class=SpellE>octahedra</span>.
    1220 Also notice that the next layer (represented by the 4 O atoms at the bottom of
    1221 the above drawing are offset giving a triclinic lattice.</p>
    1222 
    1223 <p class=MsoNormal>The stacking fault simulation calculation via <span
    1224 class=SpellE>DIFFaX</span> routines requires that the stacking layers be
    1225 defined in a coordinate system that has the stacking direction perpendicular to
    1226 the stacking plane defined as the c-axis. This requires transformation of the
    1227 unit cell and atom coordinates; a suitable tool exists in GSAS-II to do this.
    1228 Select the <b><span style='font-family:"Calibri",sans-serif'>General</span></b>
    1229 tab and do <b><span style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>;
    1230 a popup window will appear.</p>
    1231 
    1232 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1233  id="Picture_x0020_12" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:262.5pt;
    1234  height:254.25pt;visibility:visible;mso-wrap-style:square'>
    1235  <v:imagedata src="Stacking%20Faults%20II_files/image009.png" o:title=""/>
    1236 </v:shape><![endif]--><![if !vml]><img width=350 height=339
    1237 src="Stacking%20Faults%20II_files/image010.gif" v:shapes="Picture_x0020_12"><![endif]></span></p>
     292<p class=MsoNormal><img width=480 height=359 id="Picture 11"
     293src="Stacking%20Faults%20II_files/image004.jpg"></p>
     294
     295<p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> tetrahedra
     296and AlO<sub>6</sub> octahedra. Also notice that the next layer (represented by
     297the 4 O atoms at the bottom of the above drawing are offset giving a triclinic
     298lattice.</p>
     299
     300<p class=MsoNormal>The stacking fault simulation calculation via DIFFaX
     301routines requires that the stacking layers be defined in a coordinate system
     302that has the stacking direction perpendicular to the stacking plane defined as
     303the c-axis. This requires transformation of the unit cell and atom coordinates;
     304a suitable tool exists in GSAS-II to do this. Select the <b><span
     305style='font-family:"Calibri",sans-serif'>General</span></b> tab and do <b><span
     306style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>; a popup
     307window will appear.</p>
     308
     309<p class=MsoNormal><img width=350 height=339 id="Picture 12"
     310src="Stacking%20Faults%20II_files/image005.gif"></p>
    1238311
    1239312<p class=MsoNormal>Note that this allows one to transform the structure
     
    1241314and then select those that are unique according to a selected space group. The
    1242315pulldown gives a selection of commonly used transformations; we want the last
    1243 one, <span class=SpellE><span class=GramE><b><span style='font-family:"Calibri",sans-serif'>abc</span></b></span></span><b><span
    1244 style='font-family:"Calibri",sans-serif'>*</span></b>, which satisfies the
    1245 stacking fault requirement. Select it; notice that the space group is changed
    1246 to P1. Leave this as the kaolinite layer has no symmetry; in other
    1247 circumstances the layer may have an inversion center in which P-1 should be
    1248 used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
     316one, <b><span style='font-family:"Calibri",sans-serif'>abc*</span></b>, which
     317satisfies the stacking fault requirement. Select it; notice that the space
     318group is changed to P1. Leave this as the kaolinite layer has no symmetry; in
     319other circumstances the layer may have an inversion center in which P-1 should
     320be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
    1249321the new lattice parameters will be shown.</p>
    1250322
    1251 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1252  id="Picture_x0020_13" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:262.5pt;
    1253  height:254.25pt;visibility:visible;mso-wrap-style:square'>
    1254  <v:imagedata src="Stacking%20Faults%20II_files/image011.png" o:title=""/>
    1255 </v:shape><![endif]--><![if !vml]><img width=350 height=339
    1256 src="Stacking%20Faults%20II_files/image012.gif" v:shapes="Picture_x0020_13"><![endif]></span></p>
    1257 
    1258 <p class=MsoNormal><span class=GramE>The a</span> &amp; b axes stay the same,
    1259 but c is now smaller (the interlayer distance in kaolinite) and <span
    1260 style='font-family:Symbol'>a</span> &amp; <span style='font-family:Symbol'>b</span>
    1261 = 90 (<span style='font-family:Symbol'>g</span> is unchanged). Press <b><span
    1262 style='font-family:"Calibri",sans-serif'>Ok</span></b>; a new phase (kaolinite <span
    1263 class=SpellE><span class=GramE>abc</span></span>*) will be made and its General
    1264 tab will be shown immediately. Select the <b><span style='font-family:"Calibri",sans-serif'>Draw
     323<p class=MsoNormal><img width=350 height=339 id="Picture 13"
     324src="Stacking%20Faults%20II_files/image006.gif"></p>
     325
     326<p class=MsoNormal>The a &amp; b axes stay the same, but c is now smaller (the
     327interlayer distance in kaolinite) and <span style='font-family:Symbol'>a</span>
     328&amp; <span style='font-family:Symbol'>b</span> = 90 (<span style='font-family:
     329Symbol'>g</span> is unchanged). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
     330a new phase (kaolinite abc*) will be made and its General tab will be shown
     331immediately. Select the <b><span style='font-family:"Calibri",sans-serif'>Draw
    1265332Atoms</span></b> tab to see the resulting structure.</p>
    1266333
    1267 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1268  id="Picture_x0020_14" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:353.25pt;
    1269  height:264pt;visibility:visible;mso-wrap-style:square'>
    1270  <v:imagedata src="Stacking%20Faults%20II_files/image013.jpg" o:title=""/>
    1271 </v:shape><![endif]--><![if !vml]><img width=471 height=352
    1272 src="Stacking%20Faults%20II_files/image014.jpg" v:shapes="Picture_x0020_14"><![endif]></span></p>
     334<p class=MsoNormal><img width=471 height=352 id="Picture 14"
     335src="Stacking%20Faults%20II_files/image007.jpg"></p>
    1273336
    1274337<p class=MsoNormal>To see what this layer looks like with more of it drawn, you
    1275338can add more unit cells to the drawing; select all the atoms by double clicking
    1276 the upper left empty box of the Draw atoms table. Do <b style='mso-bidi-font-weight:
    1277 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1278 minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add atoms</span></b> and <b
    1279 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1280 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>increment</span></b>
    1281 the 1<sup>st</sup> <b style='mso-bidi-font-weight:normal'><span
    1282 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1283 mso-hansi-theme-font:minor-latin'>Choose unit cel</span></b>l and press <b
    1284 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1285 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>;
    1286 this will add one unit cell along x. Now select all the atoms again, do <b
    1287 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1288 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add
    1289 atoms</span></b> and now <b style='mso-bidi-font-weight:normal'><span
    1290 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1291 mso-hansi-theme-font:minor-latin'>decrement</span></b> the 1<sup>st</sup> <b
    1292 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1293 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Choose unit
    1294 cell</span></b>. Press <b style='mso-bidi-font-weight:normal'><span
    1295 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1296 mso-hansi-theme-font:minor-latin'>Ok</span></b>; the drawing will now be 3 unit
    1297 cells wide along x. Repeat this once more <b style='mso-bidi-font-weight:normal'><span
    1298 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1299 mso-hansi-theme-font:minor-latin'>decrementing</span></b> the 2<sup>nd</sup> <b
    1300 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1301 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Choose unit
    1302 cell</span></b> to give a 3x2 unit cell block of atoms. Double click the <b
    1303 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1304 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Style</span></b>
    1305 column heading and select <b style='mso-bidi-font-weight:normal'><span
    1306 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1307 mso-hansi-theme-font:minor-latin'>Balls and sticks</span></b>; the drawing
    1308 should look like (after some zooming/shifting/rotation).</p>
    1309 
    1310 <p class=MsoNormal><!--[if gte vml 1]><v:line id="Straight_x0020_Connector_x0020_16"
    1311  o:spid="_x0000_s1028" style='position:absolute;z-index:251659264;visibility:visible;
    1312  mso-wrap-style:square;mso-width-percent:0;mso-height-percent:0;
    1313  mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
    1314  mso-wrap-distance-bottom:0;mso-position-horizontal:absolute;
    1315  mso-position-horizontal-relative:text;mso-position-vertical:absolute;
    1316  mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0;
    1317  mso-width-relative:page;mso-height-relative:page' from="9.75pt,78.7pt" to="275.25pt,227.95pt"
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    1347 " strokecolor="#ed7d31 [3205]" strokeweight="1.5pt">
    1348  <v:stroke dashstyle="longDash" joinstyle="miter"/>
    1349  <o:lock v:ext="edit" shapetype="f"/>
    1350 </v:line><![endif]--><![if !vml]><span style='mso-ignore:vglayout;position:
    1351 absolute;z-index:251659264;margin-left:12px;margin-top:103px;width:356px;
    1352 height:202px'><img width=356 height=202
    1353 src="Stacking%20Faults%20II_files/image015.gif" v:shapes="Straight_x0020_Connector_x0020_16"></span><![endif]><span
    1354 style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15"
    1355  o:spid="_x0000_i1036" type="#_x0000_t75" style='width:357.75pt;height:267.75pt;
    1356  visibility:visible;mso-wrap-style:square'>
    1357  <v:imagedata src="Stacking%20Faults%20II_files/image016.jpg" o:title=""/>
    1358 </v:shape><![endif]--><![if !vml]><img width=477 height=357
    1359 src="Stacking%20Faults%20II_files/image017.jpg" v:shapes="Picture_x0020_15"><![endif]></span></p>
     339the upper left empty box of the Draw atoms table. Do <b><span style='font-family:
     340"Calibri",sans-serif'>Edit/Add atoms</span></b> and <b><span style='font-family:
     341"Calibri",sans-serif'>increment</span></b> the 1<sup>st</sup> <b><span
     342style='font-family:"Calibri",sans-serif'>Choose unit cel</span></b>l and press <b><span
     343style='font-family:"Calibri",sans-serif'>Ok</span></b>; this will add one unit
     344cell along x. Now select all the atoms again, do <b><span style='font-family:
     345"Calibri",sans-serif'>Edit/Add atoms</span></b> and now <b><span
     346style='font-family:"Calibri",sans-serif'>decrement</span></b> the 1<sup>st</sup>
     347<b><span style='font-family:"Calibri",sans-serif'>Choose unit cell</span></b>.
     348Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; the
     349drawing will now be 3 unit cells wide along x. Repeat this once more <b><span
     350style='font-family:"Calibri",sans-serif'>decrementing</span></b> the 2<sup>nd</sup>
     351<b><span style='font-family:"Calibri",sans-serif'>Choose unit cell</span></b>
     352to give a 3x2 unit cell block of atoms. Double click the <b><span
     353style='font-family:"Calibri",sans-serif'>Style</span></b> column heading and
     354select <b><span style='font-family:"Calibri",sans-serif'>Balls and sticks</span></b>;
     355the drawing should look like (after some zooming/shifting/rotation).</p>
     356
     357<p class=MsoNormal><span style='position:absolute;z-index:251659264;margin-left:
     35812px;margin-top:104px;width:356px;height:201px'><img width=356 height=201
     359src="Stacking%20Faults%20II_files/image008.gif"></span><img width=477
     360height=357 id="Picture 15" src="Stacking%20Faults%20II_files/image009.jpg"></p>
    1360361
    1361362<p class=MsoNormal>I’ll say more about that diagonal line later. This structure
    1362 is now suitable for use in <span class=SpellE>DIFFaX</span> calculations; the
    1363 cell has a c-axis that is perpendicular to the ab plane with a length that is
    1364 the stacking repeat distance. This is a good place to save your project (I
    1365 called it ‘<b style='mso-bidi-font-weight:normal'><span style='font-family:
    1366 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    1367 minor-latin'>kaolinite’</span></b>).</p>
     363is now suitable for use in DIFFaX calculations; the cell has a c-axis that is
     364perpendicular to the ab plane with a length that is the stacking repeat
     365distance. This is a good place to save your project (I called it ‘<b><span
     366style='font-family:"Calibri",sans-serif'>kaolinite’</span></b>).</p>
    1368367
    1369368<h2>Part 2. Set up simulation of ideal kaolinite stacking</h2>
    1370369
    1371370<p class=MsoNormal>In this part of the tutorial we’ll create a stacking model
    1372 for Keokuk kaolinite and use <span class=SpellE>DIFFaX</span> to simulate the
    1373 powder pattern and compare it to some real data. To begin we need a new phase
    1374 that we can declare as “faulted’. In the main GSAS-II data tree menu do <b
    1375 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1376 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Add new
    1377 phase</span></b>; I named it ‘<b style='mso-bidi-font-weight:normal'><span
    1378 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1379 mso-hansi-theme-font:minor-latin'>Keokuk</span></b>’. The General tab for it
    1380 will immediately appear.</p>
    1381 
    1382 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1383  id="Picture_x0020_17" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:697.5pt;
    1384  height:375pt;visibility:visible;mso-wrap-style:square'>
    1385  <v:imagedata src="Stacking%20Faults%20II_files/image018.png" o:title=""/>
    1386 </v:shape><![endif]--><![if !vml]><img width=930 height=500
    1387 src="Stacking%20Faults%20II_files/image019.gif" v:shapes="Picture_x0020_17"><![endif]></span></p>
    1388 
    1389 <p class=MsoNormal>Change the <b style='mso-bidi-font-weight:normal'><span
    1390 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1391 mso-hansi-theme-font:minor-latin'>Phase type</span></b> to ‘<b
    1392 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1393 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>faulted</span></b>’;
    1394 the General tab will be redrawn and a new tab <b style='mso-bidi-font-weight:
    1395 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1396 minor-latin;mso-hansi-theme-font:minor-latin'>‘Layers</span></b>’ will appear.
    1397 Select it.</p>
    1398 
    1399 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1400  id="Picture_x0020_18" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:612.75pt;
    1401  height:363pt;visibility:visible;mso-wrap-style:square'>
    1402  <v:imagedata src="Stacking%20Faults%20II_files/image020.png" o:title=""/>
    1403 </v:shape><![endif]--><![if !vml]><img width=817 height=484
    1404 src="Stacking%20Faults%20II_files/image021.gif" v:shapes="Picture_x0020_18"><![endif]></span></p>
     371for Keokuk kaolinite and use DIFFaX to simulate the powder pattern and compare
     372it to some real data. To begin we need a new phase that we can declare as
     373“faulted’. In the main GSAS-II data tree menu do <b><span style='font-family:
     374"Calibri",sans-serif'>Data/Add new phase</span></b>; I named it ‘<b><span
     375style='font-family:"Calibri",sans-serif'>Keokuk</span></b>’. The General tab
     376for it will immediately appear.</p>
     377
     378<p class=MsoNormal><img width=930 height=500 id="Picture 17"
     379src="Stacking%20Faults%20II_files/image010.gif"></p>
     380
     381<p class=MsoNormal>Change the <b><span style='font-family:"Calibri",sans-serif'>Phase
     382type</span></b> to ‘<b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>’;
     383the General tab will be redrawn and a new tab <b><span style='font-family:"Calibri",sans-serif'>‘Layers</span></b>’
     384will appear. Select it.</p>
     385
     386<p class=MsoNormal><img width=817 height=484 id="Picture 18"
     387src="Stacking%20Faults%20II_files/image011.gif"></p>
    1405388
    1406389<p class=MsoNormal>We can anticipate (given that kaolinite space group is C1)
    1407 that the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1408 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Diffraction
    1409 Laue symmetry</span></b> is <b style='mso-bidi-font-weight:normal'><span
    1410 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1411 mso-hansi-theme-font:minor-latin'>-1</span></b>. We can enter by hand the
    1412 lattice parameters from the kaolinite <span class=SpellE><span class=GramE>abc</span></span>*
    1413 phase but an easier method is available. Do <b style='mso-bidi-font-weight:
    1414 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1415 minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Copy phase cell</span></b>;
    1416 a file selection dialog will appear for your current directory and the file <span
    1417 class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
    1418 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    1419 minor-latin'>kaolinite.gpx</span></b></span> should be there. Select it; a
    1420 small popup will appear listing the available phases. Choose ‘<b
    1421 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1422 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>kaolinite <span
    1423 class=SpellE><span class=GramE>abc</span></span>*</span></b>’ and press <b
    1424 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1425 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>;
     390that the <b><span style='font-family:"Calibri",sans-serif'>Diffraction Laue
     391symmetry</span></b> is <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>.
     392We can enter by hand the lattice parameters from the kaolinite abc* phase but
     393an easier method is available. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Copy
     394phase cell</span></b>; a file selection dialog will appear for your current
     395directory and the file <b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b>
     396should be there. Select it; a small popup will appear listing the available
     397phases. Choose ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite
     398abc*</span></b>’ and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
    1426399the Layers window will be redrawn with the new lattice parameters.</p>
    1427400
    1428 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1429  id="Picture_x0020_19" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:621.75pt;
    1430  height:363pt;visibility:visible;mso-wrap-style:square'>
    1431  <v:imagedata src="Stacking%20Faults%20II_files/image022.png" o:title=""/>
    1432 </v:shape><![endif]--><![if !vml]><img width=829 height=484
    1433 src="Stacking%20Faults%20II_files/image023.gif" v:shapes="Picture_x0020_19"><![endif]></span></p>
    1434 
    1435 <p class=MsoNormal>Next, you need to define the layer. As it would be very tedious
    1436 to enter 24 atoms by hand, the alternative is to get them from the previously
    1437 created kaolinite <span class=SpellE><span class=GramE>abc</span></span>*
    1438 phase. Select the <b style='mso-bidi-font-weight:normal'><span
    1439 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1440 mso-hansi-theme-font:minor-latin'>Import new layer</span></b> box; the file
    1441 dialog with <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
    1442 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1443 mso-hansi-theme-font:minor-latin'>kaolinite.gpx</span></b></span> will appear.
    1444 Select the file and press <b style='mso-bidi-font-weight:normal'><span
    1445 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1446 mso-hansi-theme-font:minor-latin'>Open</span></b>; again a small popup with two
    1447 phases listed will appear. Again select <b style='mso-bidi-font-weight:normal'><span
    1448 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1449 mso-hansi-theme-font:minor-latin'>kaolinite <span class=SpellE><span
    1450 class=GramE>abc</span></span>*</span></b> and press <b style='mso-bidi-font-weight:
    1451 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1452 minor-latin;mso-hansi-theme-font:minor-latin'>Ok</span></b>; the Layers page
    1453 will be redrawn with a layer (named kaolinite) will be filled out.</p>
    1454 
    1455 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1456  id="Picture_x0020_20" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:621.75pt;
    1457  height:375pt;visibility:visible;mso-wrap-style:square'>
    1458  <v:imagedata src="Stacking%20Faults%20II_files/image024.png" o:title=""/>
    1459 </v:shape><![endif]--><![if !vml]><img width=829 height=500
    1460 src="Stacking%20Faults%20II_files/image025.gif" v:shapes="Picture_x0020_20"><![endif]></span></p>
     401<p class=MsoNormal><img width=829 height=484 id="Picture 19"
     402src="Stacking%20Faults%20II_files/image012.gif"></p>
     403
     404<p class=MsoNormal>Next, you need to define the layer. As it would be very
     405tedious to enter 24 atoms by hand, the alternative is to get them from the
     406previously created kaolinite abc* phase. Select the <b><span style='font-family:
     407"Calibri",sans-serif'>Import new layer</span></b> box; the file dialog with <b><span
     408style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b> will appear.
     409Select the file and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>;
     410again a small popup with two phases listed will appear. Again select <b><span
     411style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b> and press <b><span
     412style='font-family:"Calibri",sans-serif'>Ok</span></b>; the Layers page will be
     413redrawn with a layer (named kaolinite) will be filled out.</p>
     414
     415<p class=MsoNormal><img width=829 height=500 id="Picture 20"
     416src="Stacking%20Faults%20II_files/image013.gif"></p>
    1461417
    1462418<p class=MsoNormal>If you move down to the bottom of the page (if there isn’t a
    1463419scroll bar, just grab an edge of the window &amp; shift it slightly) to find
    1464 the one line <b style='mso-bidi-font-weight:normal'><span style='font-family:
    1465 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    1466 minor-latin'>Layer-Layer Transition probabilities</span></b>. Change <span
    1467 class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
    1468 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    1469 minor-latin'>Dz</span></b></span><b style='mso-bidi-font-weight:normal'><span
    1470 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1471 mso-hansi-theme-font:minor-latin'>=1.0</span></b> and press the plot box; the
    1472 drawing will show a layer of kaolinite stacked directly above another one.</p>
    1473 
    1474 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1475  id="Picture_x0020_24" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:5in;
    1476  height:269.25pt;visibility:visible;mso-wrap-style:square'>
    1477  <v:imagedata src="Stacking%20Faults%20II_files/image026.jpg" o:title=""/>
    1478 </v:shape><![endif]--><![if !vml]><img width=480 height=359
    1479 src="Stacking%20Faults%20II_files/image027.jpg" v:shapes="Picture_x0020_24"><![endif]></span></p>
     420the one line <b><span style='font-family:"Calibri",sans-serif'>Layer-Layer
     421Transition probabilities</span></b>. Change <b><span style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b>
     422and press the plot box; the drawing will show a layer of kaolinite stacked
     423directly above another one.</p>
     424
     425<p class=MsoNormal><img width=480 height=359 id="Picture 24"
     426src="Stacking%20Faults%20II_files/image014.jpg"></p>
    1480427
    1481428<p class=MsoNormal>Compare that to the stacking in kaolinite.</p>
    1482429
    1483 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1484  id="Picture_x0020_26" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:5in;
    1485  height:269.25pt;visibility:visible;mso-wrap-style:square'>
    1486  <v:imagedata src="Stacking%20Faults%20II_files/image028.jpg" o:title=""/>
    1487 </v:shape><![endif]--><![if !vml]><img width=480 height=359
    1488 src="Stacking%20Faults%20II_files/image029.jpg" v:shapes="Picture_x0020_26"><![endif]></span></p>
     430<p class=MsoNormal><img width=480 height=359 id="Picture 26"
     431src="Stacking%20Faults%20II_files/image015.jpg"></p>
    1489432
    1490433<p class=MsoNormal>Notice the effect of the offset. The 1<sup>st</sup> row of
    1491 SiO<sub>4</sub> <span class=SpellE>tetrahedra</span> are positioned directly
    1492 above the AlO<sub>6</sub> <span class=SpellE>octahedra</span> in the real
    1493 structure but not in the vertically stacked structure. We can use a bit of
    1494 simple geometry to work out what the offset is but first let us see what
    1495 happens in the simulation and how it compares to real data.</p>
     434SiO<sub>4</sub> tetrahedra are positioned directly above the AlO<sub>6</sub>
     435octahedra in the real structure but not in the vertically stacked structure. We
     436can use a bit of simple geometry to work out what the offset is but first let
     437us see what happens in the simulation and how it compares to real data.</p>
    1496438
    1497439<h2>Step 3. Import Keokuk kaolinite data and do 1<sup>st</sup> simulation</h2>
    1498440
    1499441<p class=MsoNormal>First we need to import the Keokuk kaolinite powder data; do
    1500 <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1501 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Import/Powder
    1502 Data/from Bruker RAW file</span></b>. Select <b style='mso-bidi-font-weight:
    1503 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1504 minor-latin;mso-hansi-theme-font:minor-latin'>Keokuk <span class=SpellE>kaolinite.RAW</span></span></b>
    1505 from the file dialog box; press <span class=GramE><b style='mso-bidi-font-weight:
    1506 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1507 minor-latin;mso-hansi-theme-font:minor-latin'>Yes</span></b></span> in the next
    1508 popup. A new file dialog appears requesting an instrument parameter file; we
    1509 will use an internal default instead. Press <b style='mso-bidi-font-weight:
    1510 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1511 minor-latin;mso-hansi-theme-font:minor-latin'>Cancel</span></b> and select <b
    1512 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1513 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Defaults for
    1514 <span class=SpellE>CuKa</span> lab data</span></b> from the next popup. This process
    1515 will repeat since the RAW file contains two scans. In the next popup, select
    1516 only <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1517 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>kaolinite <span
    1518 class=SpellE><span class=GramE>abc</span></span>*</span></b>. There will be two
    1519 PWDR scans in the GSAS-II data tree; one covers 2<span style='font-family:Symbol'>Q</span>=
    1520 10-90<span style='font-family:"Calibri",sans-serif'>°</span> and the other
    1521 covers 2<span style='font-family:Symbol'>Q</span>=80-150°. Only the lower part
    1522 of the first one is going to be used in our simulation work as the calculations
    1523 become very time consuming for complex structures and high angle data. Select <b
    1524 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1525 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR Keokuk <span
    1526 class=SpellE>kaolinite.RAW</span> Scan 1</span></b> from the GSAS-II data tree
    1527 make sure it expands; its plot will also show.</p>
    1528 
    1529 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1530  id="Picture_x0020_27" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:525pt;
    1531  height:450pt;visibility:visible;mso-wrap-style:square'>
    1532  <v:imagedata src="Stacking%20Faults%20II_files/image030.png" o:title=""/>
    1533 </v:shape><![endif]--><![if !vml]><img width=700 height=600
    1534 src="Stacking%20Faults%20II_files/image031.gif" v:shapes="Picture_x0020_27"><![endif]></span></p>
    1535 
    1536 <p class=MsoNormal>Go to <b style='mso-bidi-font-weight:normal'><span
    1537 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1538 mso-hansi-theme-font:minor-latin'>Limits</span></b> and set <span class=SpellE><b
    1539 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1540 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Tmax</span></b></span>
    1541 to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1542 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>52.0</span></b>;
    1543 that puts the upper limit in a relatively clear part of the pattern. Then go to
    1544 Background and set the 1<sup>st</sup> coefficient to 20 (approximately the
    1545 background at 2Q=18). Next go to <b style='mso-bidi-font-weight:normal'><span
    1546 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1547 mso-hansi-theme-font:minor-latin'>Sample parameters</span></b> and set the <b
    1548 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1549 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Histogram
    1550 scale</span></b> to something reasonable (I chose <b style='mso-bidi-font-weight:
    1551 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1552 minor-latin;mso-hansi-theme-font:minor-latin'>20.0</span></b>) and make sure
    1553 the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1554 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Diffractometer
     442<b><span style='font-family:"Calibri",sans-serif'>Import/Powder Data/from
     443Bruker RAW file</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Keokuk
     444kaolinite.RAW</span></b> from the file dialog box; press <b><span
     445style='font-family:"Calibri",sans-serif'>Yes</span></b> in the next popup. A
     446new file dialog appears requesting an instrument parameter file; we will use an
     447internal default instead. Press <b><span style='font-family:"Calibri",sans-serif'>Cancel</span></b>
     448and select <b><span style='font-family:"Calibri",sans-serif'>Defaults for CuKa
     449lab data</span></b> from the next popup. This process will repeat since the RAW
     450file contains two scans. In the next popup, select only <b><span
     451style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b>. There will
     452be two PWDR scans in the GSAS-II data tree; one covers 2<span style='font-family:
     453Symbol'>Q</span>= 10-90<span style='font-family:"Calibri",sans-serif'>°</span>
     454and the other covers 2<span style='font-family:Symbol'>Q</span>=80-150°. Only
     455the lower part of the first one is going to be used in our simulation work as
     456the calculations become very time consuming for complex structures and high
     457angle data. Select <b><span style='font-family:"Calibri",sans-serif'>PWDR
     458Keokuk kaolinite.RAW Scan 1</span></b> from the GSAS-II data tree make sure it
     459expands; its plot will also show.</p>
     460
     461<p class=MsoNormal><img width=700 height=600 id="Picture 27"
     462src="Stacking%20Faults%20II_files/image016.gif"></p>
     463
     464<p class=MsoNormal>Go to <b><span style='font-family:"Calibri",sans-serif'>Limits</span></b>
     465and set <b><span style='font-family:"Calibri",sans-serif'>Tmax</span></b> to <b><span
     466style='font-family:"Calibri",sans-serif'>52.0</span></b>; that puts the upper
     467limit in a relatively clear part of the pattern. Then go to Background and set
     468the 1<sup>st</sup> coefficient to 20 (approximately the background at 2Q=18).
     469Next go to <b><span style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>
     470and set the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale</span></b>
     471to something reasonable (I chose <b><span style='font-family:"Calibri",sans-serif'>20.0</span></b>)
     472and make sure the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
    1555473type is Bragg-Brentano</span></b>.</p>
    1556474
    1557475<p class=MsoNormal>Now we are ready for our 1<sup>st</sup> kaolinite
    1558 simulation. Go to <b style='mso-bidi-font-weight:normal'><span
    1559 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1560 mso-hansi-theme-font:minor-latin'>Phases/Keokuk</span></b> and select the <b
    1561 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1562 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Layers</span></b>
    1563 tab. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1564 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Simulate
    1565 pattern</span></b> and press <b style='mso-bidi-font-weight:normal'><span
    1566 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1567 mso-hansi-theme-font:minor-latin'>Ok</span></b> in the popup. Select the <b
    1568 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1569 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Scan 1</span></b>
    1570 pattern and press <b style='mso-bidi-font-weight:normal'><span
    1571 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1572 mso-hansi-theme-font:minor-latin'>Ok</span></b>; the simulation will finish
    1573 quickly (press <b style='mso-bidi-font-weight:normal'><span style='font-family:
    1574 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    1575 minor-latin'>Ok</span></b>) and the new plot will be displayed (I’ve zoomed in
    1576 a bit).</p>
    1577 
    1578 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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    1583 src="Stacking%20Faults%20II_files/image033.gif" v:shapes="Picture_x0020_29"><![endif]></span>.</p>
     476simulation. Go to <b><span style='font-family:"Calibri",sans-serif'>Phases/Keokuk</span></b>
     477and select the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>
     478tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate
     479pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>
     480in the popup. Select the <b><span style='font-family:"Calibri",sans-serif'>Scan
     4811</span></b> pattern and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
     482the simulation will finish quickly (press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>)
     483and the new plot will be displayed (I’ve zoomed in a bit).</p>
     484
     485<p class=MsoNormal><img width=700 height=600 id="Picture 29"
     486src="Stacking%20Faults%20II_files/image017.gif">.</p>
    1584487
    1585488<p class=MsoNormal>As you can see the simulation (green curve) does not fit the
     
    1588491offset consider the drawing of kaolinite.</p>
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    1674 ochdx9kBAAD4AwAADgAAAAAAAAAAAAAAAAAuAgAAZHJzL2Uyb0RvYy54bWxQSwECLQAUAAYACAAA
    1675 ACEANv84Z+AAAAALAQAADwAAAAAAAAAAAAAAAAAzBAAAZHJzL2Rvd25yZXYueG1sUEsFBgAAAAAE
    1676 AAQA8wAAAEAFAAAAAA==
    1677 " strokecolor="#ed7d31 [3205]" strokeweight="1.5pt">
    1678  <v:stroke joinstyle="miter"/>
    1679  <o:lock v:ext="edit" shapetype="f"/>
    1680 </v:line><![endif]--><![if !vml]><span style='mso-ignore:vglayout;position:
     493<p class=MsoNormal><span style='position:absolute;z-index:251661312;margin-left:
     494104px;margin-top:123px;width:46px;height:22px'><img width=46 height=22
     495src="Stacking%20Faults%20II_files/image018.gif"></span><span style='position:
    1681496absolute;z-index:251660288;margin-left:153px;margin-top:135px;width:3px;
    1682497height:199px'><img width=3 height=199
    1683 src="Stacking%20Faults%20II_files/image035.gif" v:shapes="Straight_x0020_Connector_x0020_31"></span><![endif]><span
    1684 style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_30"
    1685  o:spid="_x0000_i1027" type="#_x0000_t75" style='width:360.75pt;height:270pt;
    1686  visibility:visible;mso-wrap-style:square'>
    1687  <v:imagedata src="Stacking%20Faults%20II_files/image036.jpg" o:title=""/>
    1688 </v:shape><![endif]--><![if !vml]><img width=481 height=360
    1689 src="Stacking%20Faults%20II_files/image037.jpg" v:shapes="Picture_x0020_30"><![endif]></span></p>
    1690 
    1691 <p class=MsoNormal>The offset <span class=SpellE>Dx</span> is given by the blue
    1692 arrow in the above drawing of kaolinite and is in fractional coordinates.
    1693 Geometry gives</p>
    1694 
    1695 <p class=MsoNormal><!--[if gte msEquation 12]><m:oMath><i style='mso-bidi-font-style:
    1696  normal'><span style='font-family:"Cambria Math",serif'><m:r>Dx</m:r><m:r>= </m:r></span></i><m:f><m:fPr><m:type
    1697     m:val="skw"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family:
    1698    "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic;
    1699    mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
    1700    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>c</m:r></span></i><m:func><m:funcPr><span
    1701      style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    1702      mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    1703      normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span
    1704      style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty
    1705         m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style:
    1706      normal'><span style='font-family:"Cambria Math",serif'><m:r>&#946;</m:r></span></i></m:e></m:func></m:num><m:den><i
    1707    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
    1708 style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family:
    1709 "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative;
    1710 top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language:
    1711 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025"
    1712  type="#_x0000_t75" style='width:79.5pt;height:19.5pt'>
    1713  <v:imagedata src="Stacking%20Faults%20II_files/image038.png" o:title=""
    1714   chromakey="white"/>
    1715 </v:shape><![endif]--><![if !vml]><img width=106 height=26
    1716 src="Stacking%20Faults%20II_files/image039.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    1717 style='mso-spacerun:yes'> </span>Or in this case <b style='mso-bidi-font-weight:
    1718 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
    1719 minor-latin;mso-hansi-theme-font:minor-latin'>-0.368</span></b>. Set <span
    1720 class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
    1721 "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
    1722 minor-latin'>Dx</span></b></span> to this value &amp; repeat simulation.</p>
    1723 
    1724 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1725  id="Picture_x0020_33" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:525pt;
    1726  height:450pt;visibility:visible;mso-wrap-style:square'>
    1727  <v:imagedata src="Stacking%20Faults%20II_files/image040.png" o:title=""/>
    1728 </v:shape><![endif]--><![if !vml]><img width=700 height=600
    1729 src="Stacking%20Faults%20II_files/image041.gif" v:shapes="Picture_x0020_33"><![endif]></span></p>
     498src="Stacking%20Faults%20II_files/image019.gif"></span><img width=481
     499height=360 id="Picture 30" src="Stacking%20Faults%20II_files/image020.jpg"></p>
     500
     501<p class=MsoNormal>The offset Dx is given by the blue arrow in the above
     502drawing of kaolinite and is in fractional coordinates. Geometry gives</p>
     503
     504<p class=MsoNormal><span
     505style='font-size:12.0pt;font-family:"Times New Roman",serif;position:relative;
     506top:3.0pt'><img width=106 height=26
     507src="Stacking%20Faults%20II_files/image021.gif"></span> Or in this case <b><span
     508style='font-family:"Calibri",sans-serif'>-0.368</span></b>. Set <b><span
     509style='font-family:"Calibri",sans-serif'>Dx</span></b> to this value &amp;
     510repeat simulation.</p>
     511
     512<p class=MsoNormal><img width=700 height=600 id="Picture 33"
     513src="Stacking%20Faults%20II_files/image022.gif"></p>
    1730514
    1731515<p class=MsoNormal>There is some improvement but some parts are not very well
    1732516represented. Recall from the triclinic kaolinite lattice parameters that <span
    1733517style='font-family:Symbol'>a</span> was 91.7°; that will produce a small offset
    1734 in Dy. Using the same kind of geometry math gives <span class=SpellE><b
    1735 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1736 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dy</span></b></span><b
    1737 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1738 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>=-0.0246</span></b>.
    1739 Enter this value &amp; repeat the simulation again. This gives a much better
    1740 fit to the observed pattern, but the simulated peaks are too sharp; this can be
    1741 fixed by changing the U<span class=GramE>,V,W</span> Instrument parameters. I’d
    1742 just set <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1743 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>W=40</span></b>
    1744 and the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1745 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Histogram
    1746 scale</span></b> (in <b style='mso-bidi-font-weight:normal'><span
    1747 style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
    1748 mso-hansi-theme-font:minor-latin'>Sample parameters</span></b>) to <b
    1749 style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
    1750 mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>40</span></b>
    1751 and try again.</p>
    1752 
    1753 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
    1754  id="Picture_x0020_34" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:525pt;
    1755  height:450pt;visibility:visible;mso-wrap-style:square'>
    1756  <v:imagedata src="Stacking%20Faults%20II_files/image042.png" o:title=""/>
    1757 </v:shape><![endif]--><![if !vml]><img width=700 height=600
    1758 src="Stacking%20Faults%20II_files/image043.gif" v:shapes="Picture_x0020_34"><![endif]></span></p>
     518in Dy. Using the same kind of geometry math gives <b><span style='font-family:
     519"Calibri",sans-serif'>Dy=-0.0246</span></b>. Enter this value &amp; repeat the
     520simulation again. This gives a much better fit to the observed pattern, but the
     521simulated peaks are too sharp; this can be fixed by changing the U,V,W
     522Instrument parameters. I’d just set <b><span style='font-family:"Calibri",sans-serif'>W=40</span></b>
     523and the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale</span></b>
     524(in <b><span style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>)
     525to <b><span style='font-family:"Calibri",sans-serif'>40</span></b> and try
     526again.</p>
     527
     528<p class=MsoNormal><img width=700 height=600 id="Picture 34"
     529src="Stacking%20Faults%20II_files/image023.gif"></p>
    1759530
    1760531<p class=MsoNormal>That is a pretty good fit for a stacking simulation. By
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