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Timestamp:
May 19, 2016 2:50:55 PM (7 years ago)
Author:
vondreele
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  • Tutorials/StackingFaults-II/Stacking Faults II.htm

    r2274 r2281  
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    1044 <!--[if gte mso 10]>
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     221
    1067222</head>
    1068223
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    1070225
    1071226<div class=WordSection1>
    1072227
    1073 <h1><span style='mso-fareast-font-family:"Times New Roman"'>Stacking Fault
    1074 Simulations – II<o:p></o:p></span></h1>
    1075 
    1076 <p class=MsoNormal>In this exercise you will simulate some diffraction patterns
    1077 from kaolinite clays. Kaolinite, <span class=GramE>Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(</span>OH)<sub>4</sub>,
    1078 is a 1:1 layer silicate with a single unique sheet with AlO<sub>6</sub> <span
    1079 class=SpellE>octahedra</span> on one side and SiO<sub>4</sub> <span
    1080 class=SpellE>tetrahedra</span> on the other. The layers stack with an offset to
    1081 ideally form a triclinic C1 lattice (<span class=SpellE>Bish</span> &amp; Von
     228<h1>Stacking Fault Simulations – II</h1>
     229
     230<p class=MsoNormal>In this exercise and the next you will simulate some
     231diffraction patterns from kaolinite clays. Kaolinite, Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(OH)<sub>4</sub>,
     232is a 1:1 layer silicate with a single unique sheet with AlO<sub>6</sub>
     233octahedra on one side and SiO<sub>4</sub> tetrahedra on the other. The layers
     234stack with an offset to ideally form a triclinic C1 lattice (Bish &amp; Von
    1082235Dreele, 1989, Clay &amp; Clay Min. 37, 289-296) for a sample of the most
    1083 ordered form of kaolinite from Keokuk, Iowa. Kaolinites from other locations evidently
    1084 have stacking faults so that the peaks are displaced, have peculiar shapes and
    1085 are above a varying background. For the exercise we provide a laboratory
    1086 Bragg-Brentano pattern of Keokuk kaolinite and a less ordered one from
    1087 Washington County, Georgia (Clay Minerals Society Standard KGa-1b) collected
    1088 with <span class=SpellE>CuKa</span> radiation on a Bruker instrument and thus
    1089 in the Bruker RAW file format. The KGa-1b sample contains a small amount of <span
    1090 class=SpellE>anatase</span> (TiO<sub>2</sub>) and the Keokuk kaolinite has some
    1091 <span class=SpellE>dickite</span> (different ordered stacking of kaolinite
    1092 layers).</p>
     236ordered form of kaolinite from Keokuk, Iowa. Kaolinites from other locations
     237evidently have stacking faults so that the peaks are displaced, have peculiar
     238shapes and are above a varying background. For the exercise we provide a
     239laboratory Bragg-Brentano pattern of Keokuk kaolinite collected with CuKa
     240radiation on a Bruker instrument and thus in the Bruker RAW file format. The
     241Keokuk kaolinite has some dickite (different ordered stacking of kaolinite
     242layers). The next exercise Stacking Faults-III) covers a simple simulation of a
     243faulted kaolinite from Georgia.</p>
    1093244
    1094245<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
    1095246
    1096 <h2><span style='mso-fareast-font-family:"Times New Roman"'>Part 1. Creating
    1097 kaolinite layer<o:p></o:p></span></h2>
    1098 
    1099 <p class=MsoNormal>In this initial step we will load from a <span class=SpellE>cif</span>
    1100 file the structure of kaolinite, draw it to see the layer structure and then
    1101 transform it into forms suitable for stacking simulations. To begin do <b><span
     247<h2>Part 1. Creating kaolinite layer</h2>
     248
     249<p class=MsoNormal>In this initial step we will load from a cif file the
     250structure of kaolinite, draw it to see the layer structure and then transform
     251it into forms suitable for stacking simulations. To begin do <b><span
    1102252style='font-family:"Calibri",sans-serif'>Import/Phase/from CIF file</span></b>;
    1103 from the file dialog select <span class=SpellE><b><span style='font-family:
    1104 "Calibri",sans-serif'>kaolinite.cif</span></b></span>. After the “are you sure”
    1105 popup, there will be another warning you that 4 atom types (‘O-H’) were not
    1106 recognized chemical element symbols and they were substituted by <span
    1107 class=SpellE>Xe</span> to make them obvious in the atom list. Press <b><span
     253from the file dialog select <b><span style='font-family:"Calibri",sans-serif'>kaolinite.cif</span></b>.
     254After the “are you sure” popup, there will be another warning you that 4 atom
     255types (‘O-H’) were not recognized chemical element symbols and they were
     256substituted by Xe to make them obvious in the atom list. Press <b><span
    1108257style='font-family:"Calibri",sans-serif'>Ok</span></b>; you are offered a
    1109258chance to change the phase name, I used ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite</span></b>’.
    1110 The General tab is displayed (notice the presence of <span class=SpellE>Xe</span>
    1111 in the element table).</p>
    1112 
    1113 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=930 height=500
    1114 id="_x0000_i1043" src="Stacking%20Faults%20II_files/image001.gif"></span></p>
    1115 
    1116 <p class=MsoNormal>To fix the <span class=SpellE>Xe</span> atoms (they should
    1117 be O), select <b><span style='font-family:"Calibri",sans-serif'>Atoms</span></b>
    1118 and then double click the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b>
    1119 column heading; a small popup will appear. Select <span class=SpellE><b><span
    1120 style='font-family:"Calibri",sans-serif'>Xe</span></b></span> &amp; press <b><span
    1121 style='font-family:"Calibri",sans-serif'>Ok</span></b>; the <span class=SpellE>Xe</span>
    1122 atoms at the bottom of the atom table will be highlighted. Next select <b><span
     259The General tab is displayed (notice the presence of Xe in the element table).</p>
     260
     261<p class=MsoNormal><img width=930 height=500
     262src="Stacking%20Faults%20II_files/image001.gif"></p>
     263
     264<p class=MsoNormal>To fix the Xe atoms (they should be O), select <b><span
     265style='font-family:"Calibri",sans-serif'>Atoms</span></b> and then double click
     266the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b> column
     267heading; a small popup will appear. Select <b><span style='font-family:"Calibri",sans-serif'>Xe</span></b>
     268&amp; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
     269the Xe atoms at the bottom of the atom table will be highlighted. Next select <b><span
    1123270style='font-family:"Calibri",sans-serif'>Edit/Modify atom parameters</span></b>
    1124271from the Phase Data menu; a new popup will appear. Select <b><span
    … …  
    1129276only.</p>
    1130277
    1131 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=479 height=358
    1132 id="_x0000_i1042" src="Stacking%20Faults%20II_files/image003.jpg"></span></p>
     278<p class=MsoNormal><img width=479 height=358
     279src="Stacking%20Faults%20II_files/image003.jpg"></p>
    1133280
    1134281<p class=MsoNormal>To better visualize the stacking layer, select the <b><span
    … …  
    1144291layering along the c-axis (blue line) will be evident.</p>
    1145292
    1146 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
    1147 id="_x0000_i1041" src="Stacking%20Faults%20II_files/image004.jpg"></span></p>
    1148 
    1149 <p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> <span
    1150 class=SpellE>tetrahedra</span> and AlO<sub>6</sub> <span class=SpellE>octahedra</span>.
    1151 Also notice that the next layer (represented by the 4 O atoms at the bottom of
    1152 the above drawing are offset giving a triclinic lattice.</p>
    1153 
    1154 <p class=MsoNormal>The stacking fault simulation calculation via <span
    1155 class=SpellE>DIFFaX</span> routines requires that the stacking layers be defined
    1156 in a coordinate system that has the stacking direction perpendicular to the
    1157 stacking plane defined as the c-axis. This requires transformation of the unit
    1158 cell and atom coordinates; a suitable tool exists in GSAS-II to do this. Select
    1159 the <b><span style='font-family:"Calibri",sans-serif'>General</span></b> tab and
    1160 do <b><span style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>;
    1161 a popup window will appear.</p>
    1162 
    1163 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=350 height=339
    1164 id="_x0000_i1040" src="Stacking%20Faults%20II_files/image005.gif"></span></p>
     293<p class=MsoNormal><img width=480 height=359
     294src="Stacking%20Faults%20II_files/image004.jpg"></p>
     295
     296<p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> tetrahedra
     297and AlO<sub>6</sub> octahedra. Also notice that the next layer (represented by
     298the 4 O atoms at the bottom of the above drawing are offset giving a triclinic
     299lattice.</p>
     300
     301<p class=MsoNormal>The stacking fault simulation calculation via DIFFaX
     302routines requires that the stacking layers be defined in a coordinate system
     303that has the stacking direction perpendicular to the stacking plane defined as
     304the c-axis. This requires transformation of the unit cell and atom coordinates;
     305a suitable tool exists in GSAS-II to do this. Select the <b><span
     306style='font-family:"Calibri",sans-serif'>General</span></b> tab and do <b><span
     307style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>; a popup
     308window will appear.</p>
     309
     310<p class=MsoNormal><img width=350 height=339
     311src="Stacking%20Faults%20II_files/image005.gif"></p>
    1165312
    1166313<p class=MsoNormal>Note that this allows one to transform the structure
    … …  
    1168315and then select those that are unique according to a selected space group. The
    1169316pulldown gives a selection of commonly used transformations; we want the last
    1170 one, <span class=SpellE><span class=GramE><b><span style='font-family:"Calibri",sans-serif'>abc</span></b></span></span><b><span
    1171 style='font-family:"Calibri",sans-serif'>*</span></b>, which satisfies the
    1172 stacking fault requirement. Select it; notice that the space group is changed
    1173 to P1. Leave this as the kaolinite layer has no symmetry; in other
    1174 circumstances the layer may have an inversion center in which case P-1 should
    1175 be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
     317one, <b><span style='font-family:"Calibri",sans-serif'>abc*</span></b>, which
     318satisfies the stacking fault requirement. Select it; notice that the space
     319group is changed to P1. Leave this as the kaolinite layer has no symmetry; in
     320other circumstances the layer may have an inversion center in which case P-1
     321should be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>,
    1176322the new lattice parameters will be shown.</p>
    1177323
    1178 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=350 height=339
    1179 id="_x0000_i1039" src="Stacking%20Faults%20II_files/image006.gif"></span></p>
    1180 
    1181 <p class=MsoNormal><span class=GramE>The a</span> &amp; b axes stay the same,
    1182 but c is now smaller (the interlayer distance in kaolinite) and <span
    1183 style='font-family:Symbol'>a</span> &amp; <span style='font-family:Symbol'>b</span>
    1184 = 90 (<span style='font-family:Symbol'>g</span> is unchanged). Press <b><span
    1185 style='font-family:"Calibri",sans-serif'>Ok</span></b>; a new phase (kaolinite <span
    1186 class=SpellE><span class=GramE>abc</span></span>*) will be made and its General
    1187 tab will be shown immediately. Select the <b><span style='font-family:"Calibri",sans-serif'>Draw
     324<p class=MsoNormal><img width=350 height=339
     325src="Stacking%20Faults%20II_files/image006.gif"></p>
     326
     327<p class=MsoNormal>The a &amp; b axes stay the same, but c is now smaller (the
     328interlayer distance in kaolinite) and <span style='font-family:Symbol'>a</span>
     329&amp; <span style='font-family:Symbol'>b</span> = 90 (<span style='font-family:
     330Symbol'>g</span> is unchanged). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
     331a new phase (kaolinite abc*) will be made and its General tab will be shown
     332immediately. Select the <b><span style='font-family:"Calibri",sans-serif'>Draw
    1188333Atoms</span></b> tab to see the resulting structure.</p>
    1189334
    1190 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=471 height=352
    1191 id="_x0000_i1038" src="Stacking%20Faults%20II_files/image007.jpg"></span></p>
     335<p class=MsoNormal><img width=471 height=352
     336src="Stacking%20Faults%20II_files/image007.jpg"></p>
    1192337
    1193338<p class=MsoNormal>To see what this layer looks like with more of it drawn, you
    … …  
    1209354style='font-family:"Calibri",sans-serif'>Style</span></b> column heading and
    1210355select <b><span style='font-family:"Calibri",sans-serif'>Balls and sticks</span></b>;
    1211 the drawing should look like (after some zooming/shifting/rotation).<o:p></o:p></p>
    1212 
    1213 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=477 height=357 id="_x0000_i1037"
    1214 src="Stacking%20Faults%20II_files/image009.jpg"></span></p>
    1215 
    1216 <p class=MsoNormal>This structure is now suitable for use in <span
    1217 class=SpellE>DIFFaX</span> calculations; the cell has a c-axis that is
    1218 perpendicular to the ab plane with a length that is the stacking repeat
    1219 distance. This is a good place to save your project (I called it ‘<b><span
    1220 style='font-family:"Calibri",sans-serif'>kaolinite’</span></b>).</p>
    1221 
    1222 <h2><span style='mso-fareast-font-family:"Times New Roman"'>Part 2. Set up
    1223 simulation of ideal kaolinite stacking<o:p></o:p></span></h2>
     356the drawing should look like (after some zooming/shifting/rotation).</p>
     357
     358<p class=MsoNormal><img width=477 height=357
     359src="Stacking%20Faults%20II_files/image009.jpg"></p>
     360
     361<p class=MsoNormal>This structure is now suitable for use in DIFFaX
     362calculations; the cell has a c-axis that is perpendicular to the ab plane with
     363a length that is the stacking repeat distance. This is a good place to save
     364your project (I called it ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite’</span></b>).</p>
     365
     366<h2>Part 2. Set up simulation of ideal kaolinite stacking</h2>
    1224367
    1225368<p class=MsoNormal>In this part of the tutorial we’ll create a stacking model
    1226 for Keokuk kaolinite and use <span class=SpellE>DIFFaX</span> to simulate the
    1227 powder pattern and compare it to some real data. To begin we need a new phase
    1228 that we can declare as “faulted’. In the main GSAS-II data tree menu do <b><span
    1229 style='font-family:"Calibri",sans-serif'>Data/Add new phase</span></b>; I named
    1230 it ‘<b><span style='font-family:"Calibri",sans-serif'>Keokuk</span></b>’. The
    1231 General tab for it will immediately appear.</p>
    1232 
    1233 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=930 height=500
    1234 id="_x0000_i1036" src="Stacking%20Faults%20II_files/image010.gif"></span></p>
     369for Keokuk kaolinite and use DIFFaX to simulate the powder pattern and compare
     370it to some real data. To begin we need a new phase that we can declare as
     371“faulted’. In the main GSAS-II data tree menu do <b><span style='font-family:
     372"Calibri",sans-serif'>Data/Add new phase</span></b>; I named it ‘<b><span
     373style='font-family:"Calibri",sans-serif'>Keokuk</span></b>’. The General tab
     374for it will immediately appear.</p>
     375
     376<p class=MsoNormal><img width=930 height=500
     377src="Stacking%20Faults%20II_files/image010.gif"></p>
    1235378
    1236379<p class=MsoNormal>Change the <b><span style='font-family:"Calibri",sans-serif'>Phase
    … …  
    1239382will appear. Select it.</p>
    1240383
    1241 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=817 height=484
    1242 id="_x0000_i1035" src="Stacking%20Faults%20II_files/image011.gif"></span></p>
     384<p class=MsoNormal><img width=817 height=484
     385src="Stacking%20Faults%20II_files/image011.gif"></p>
    1243386
    1244387<p class=MsoNormal>We can anticipate (given that kaolinite space group is C1)
    1245388that the <b><span style='font-family:"Calibri",sans-serif'>Diffraction Laue
    1246389symmetry</span></b> is <b><span style='font-family:"Calibri",sans-serif'>-1</span></b>.
    1247 We can enter by hand the lattice parameters from the kaolinite <span
    1248 class=SpellE><span class=GramE>abc</span></span>* phase but an easier method is
    1249 available. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Copy
     390We can enter by hand the lattice parameters from the kaolinite abc* phase but
     391an easier method is available. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Copy
    1250392phase cell</span></b>; a file selection dialog will appear for your current
    1251 directory and the file <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b></span>
     393directory and the file <b><span style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b>
    1252394should be there. Select it; a small popup will appear listing the available
    1253 phases. Choose ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite <span
    1254 class=SpellE><span class=GramE>abc</span></span>*</span></b>’ and press <b><span
    1255 style='font-family:"Calibri",sans-serif'>Ok</span></b>; the Layers window will
    1256 be redrawn with the new lattice parameters.</p>
    1257 
    1258 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=829 height=484
    1259 id="_x0000_i1034" src="Stacking%20Faults%20II_files/image012.gif"></span></p>
     395phases. Choose ‘<b><span style='font-family:"Calibri",sans-serif'>kaolinite
     396abc*</span></b>’ and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;
     397the Layers window will be redrawn with the new lattice parameters.</p>
     398
     399<p class=MsoNormal><img width=829 height=484
     400src="Stacking%20Faults%20II_files/image012.gif"></p>
    1260401
    1261402<p class=MsoNormal>Next, you need to define the layer. As it would be very
    1262 tedious to enter 24 atoms by hand, the alternative is to get them from the previously
    1263 created kaolinite <span class=SpellE><span class=GramE>abc</span></span>*
    1264 phase. Select the <b><span style='font-family:"Calibri",sans-serif'>Import new
    1265 layer</span></b> box; the file dialog with <span class=SpellE><b><span
    1266 style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b></span> will
    1267 appear. Select the file and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>;
     403tedious to enter 24 atoms by hand, the alternative is to get them from the
     404previously created kaolinite abc* phase. Select the <b><span style='font-family:
     405"Calibri",sans-serif'>Import new layer</span></b> box; the file dialog with <b><span
     406style='font-family:"Calibri",sans-serif'>kaolinite.gpx</span></b> will appear.
     407Select the file and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>;
    1268408again a small popup with two phases listed will appear. Again select <b><span
    1269 style='font-family:"Calibri",sans-serif'>kaolinite <span class=SpellE><span
    1270 class=GramE>abc</span></span>*</span></b> and press <b><span style='font-family:
    1271 "Calibri",sans-serif'>Ok</span></b>; the Layers page will be redrawn with a
    1272 layer (named kaolinite) will be filled out.</p>
    1273 
    1274 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=829 height=500
    1275 id="_x0000_i1033" src="Stacking%20Faults%20II_files/image013.gif"></span></p>
     409style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b> and press <b><span
     410style='font-family:"Calibri",sans-serif'>Ok</span></b>; the Layers page will be
     411redrawn with a layer (named kaolinite) will be filled out.</p>
     412
     413<p class=MsoNormal><img width=829 height=500
     414src="Stacking%20Faults%20II_files/image013.gif"></p>
    1276415
    1277416<p class=MsoNormal>If you move down to the bottom of the page (if there isn’t a
    1278417scroll bar, just grab an edge of the window &amp; shift it slightly) to find
    1279418the one line <b><span style='font-family:"Calibri",sans-serif'>Layer-Layer
    1280 Transition probabilities</span></b>. Change <span class=SpellE><b><span
    1281 style='font-family:"Calibri",sans-serif'>Dz</span></b></span><b><span
    1282 style='font-family:"Calibri",sans-serif'>=1.0</span></b> and press the plot
    1283 box; the drawing will show a layer of kaolinite stacked directly above another
    1284 one.</p>
    1285 
    1286 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
    1287 id="_x0000_i1032" src="Stacking%20Faults%20II_files/image014.jpg"></span></p>
     419Transition probabilities</span></b>. Change <b><span style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b>
     420and press the plot box; the drawing will show a layer of kaolinite stacked
     421directly above another one.</p>
     422
     423<p class=MsoNormal><img width=480 height=359
     424src="Stacking%20Faults%20II_files/image014.jpg"></p>
    1288425
    1289426<p class=MsoNormal>Compare that to the stacking in kaolinite.</p>
    1290427
    1291 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=359
    1292 id="_x0000_i1031" src="Stacking%20Faults%20II_files/image015.jpg"></span></p>
     428<p class=MsoNormal><img width=480 height=359
     429src="Stacking%20Faults%20II_files/image015.jpg"></p>
    1293430
    1294431<p class=MsoNormal>Notice the effect of the offset. The 1<sup>st</sup> row of
    1295 SiO<sub>4</sub> <span class=SpellE>tetrahedra</span> are positioned directly
    1296 above the AlO<sub>6</sub> <span class=SpellE>octahedra</span> in the real
    1297 structure but not in the vertically stacked structure. We can use a bit of
    1298 simple geometry to work out what the offset is but first let us see what
    1299 happens in the simulation and how it compares to real data.</p>
    1300 
    1301 <h2><span style='mso-fareast-font-family:"Times New Roman"'>Step 3. Import
    1302 Keokuk kaolinite data and do 1<sup>st</sup> simulation<o:p></o:p></span></h2>
     432SiO<sub>4</sub> tetrahedra are positioned directly above the AlO<sub>6</sub>
     433octahedra in the real structure but not in the vertically stacked structure. We
     434can use a bit of simple geometry to work out what the offset is but first let
     435us see what happens in the simulation and how it compares to real data.</p>
     436
     437<h2>Step 3. Import Keokuk kaolinite data and do 1<sup>st</sup> simulation</h2>
    1303438
    1304439<p class=MsoNormal>First we need to import the Keokuk kaolinite powder data; do
    1305440<b><span style='font-family:"Calibri",sans-serif'>Import/Powder Data/from
    1306441Bruker RAW file</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Keokuk
    1307 <span class=SpellE>kaolinite.RAW</span></span></b> from the file dialog box;
    1308 press <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Yes</span></b></span>
    1309 in the next popup. A new file dialog appears requesting an instrument parameter
    1310 file; we will use an internal default instead. Press <b><span style='font-family:
    1311 "Calibri",sans-serif'>Cancel</span></b> and select <b><span style='font-family:
    1312 "Calibri",sans-serif'>Defaults for <span class=SpellE>CuKa</span> lab data</span></b>
    1313 from the next popup. This process will repeat since the RAW file contains two
    1314 scans. In the next popup, select only <b><span style='font-family:"Calibri",sans-serif'>kaolinite
    1315 <span class=SpellE><span class=GramE>abc</span></span>*</span></b>. There will
     442kaolinite.RAW</span></b> from the file dialog box; press <b><span
     443style='font-family:"Calibri",sans-serif'>Yes</span></b> in the next popup. A
     444new file dialog appears requesting an instrument parameter file; we will use an
     445internal default instead. Press <b><span style='font-family:"Calibri",sans-serif'>Cancel</span></b>
     446and select <b><span style='font-family:"Calibri",sans-serif'>Defaults for CuKa
     447lab data</span></b> from the next popup. This process will repeat since the RAW
     448file contains two scans. In the next popup, select only <b><span
     449style='font-family:"Calibri",sans-serif'>kaolinite abc*</span></b>. There will
    1316450be two PWDR scans in the GSAS-II data tree; one covers 2<span style='font-family:
    1317451Symbol'>Q</span>= 10-90<span style='font-family:"Calibri",sans-serif'>°</span>
    1318452and the other covers 2<span style='font-family:Symbol'>Q</span>=80-150°. Only
    1319 the lower part of the first one is going to be used in our simulation work as
    1320 the calculations become very time consuming for complex structures and high
    1321 angle data. Select <b><span style='font-family:"Calibri",sans-serif'>PWDR
    1322 Keokuk <span class=SpellE>kaolinite.RAW</span> Scan 1</span></b> from the
    1323 GSAS-II data tree make sure it expands; its plot will also show.</p>
    1324 
    1325 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
    1326 id="_x0000_i1030" src="Stacking%20Faults%20II_files/image016.gif"></span></p>
     453the lower part of the first one is going to be used in our simulation work as the
     454calculations become very time consuming for complex structures and high angle
     455data. Select <b><span style='font-family:"Calibri",sans-serif'>PWDR Keokuk
     456kaolinite.RAW Scan 1</span></b> from the GSAS-II data tree make sure it
     457expands; its plot will also show.</p>
     458
     459<p class=MsoNormal><img width=700 height=600
     460src="Stacking%20Faults%20II_files/image016.gif"></p>
    1327461
    1328462<p class=MsoNormal>Go to <b><span style='font-family:"Calibri",sans-serif'>Limits</span></b>
    1329 and set <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Tmax</span></b></span>
    1330 to <b><span style='font-family:"Calibri",sans-serif'>52.0</span></b>; that puts
    1331 the upper limit in a relatively clear part of the pattern. Then go to
    1332 Background and set the 1<sup>st</sup> coefficient to 20 (approximately the
    1333 background at 2Q=18). Next go to <b><span style='font-family:"Calibri",sans-serif'>Sample
    1334 parameters</span></b> and set the <b><span style='font-family:"Calibri",sans-serif'>Histogram
    1335 scale</span></b> to something reasonable (I chose <b><span style='font-family:
    1336 "Calibri",sans-serif'>20.0</span></b>) and make sure the <b><span
    1337 style='font-family:"Calibri",sans-serif'>Diffractometer type is Bragg-Brentano</span></b>.</p>
     463and set <b><span style='font-family:"Calibri",sans-serif'>Tmax</span></b> to <b><span
     464style='font-family:"Calibri",sans-serif'>52.0</span></b>; that puts the upper limit
     465in a relatively clear part of the pattern. Then go to Background and set the 1<sup>st</sup>
     466coefficient to 20 (approximately the background at 2Q=18). Next go to <b><span
     467style='font-family:"Calibri",sans-serif'>Sample parameters</span></b> and set
     468the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale</span></b>
     469to something reasonable (I chose <b><span style='font-family:"Calibri",sans-serif'>20.0</span></b>)
     470and make sure the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer
     471type is Bragg-Brentano</span></b>.</p>
    1338472
    1339473<p class=MsoNormal>Now we are ready for our 1<sup>st</sup> kaolinite
    … …  
    1347481and the new plot will be displayed (I’ve zoomed in a bit).</p>
    1348482
    1349 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
    1350 id="_x0000_i1029" src="Stacking%20Faults%20II_files/image017.gif"></span>.</p>
     483<p class=MsoNormal><img width=700 height=600
     484src="Stacking%20Faults%20II_files/image017.gif">.</p>
    1351485
    1352486<p class=MsoNormal>As you can see the simulation (green curve) does not fit the
    1353487data (blue crosses) at all mostly due to the incorrect layer offset although
    1354488the 1<sup>st</sup> peak seems to be positioned correctly. To work out the
    1355 offset consider the drawing of kaolinite.<o:p></o:p></p>
    1356 
    1357 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=480 height=338 id="_x0000_i1028"
    1358 src="Stacking%20Faults%20II_files/image002.gif"></span></p>
    1359 
    1360 <p class=MsoNormal>The offset <span class=SpellE>Dx</span> is given by the blue
    1361 arrow in the above drawing of kaolinite and is in fractional coordinates.
    1362 Geometry gives<o:p></o:p></p>
    1363 
    1364 <p class=MsoNormal><span style='position:relative;top:3pt'><span
    1365 style='mso-no-proof:yes'><img width=106 height=26 id="_x0000_i1027"
    1366 src="Stacking%20Faults%20II_files/image021.gif"></span>&nbsp;Or in this case <b><span
    1367 style='font-family:"Calibri",sans-serif'>-0.368</span></b>. Set <span
    1368 class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dx</span></b></span>
    1369 to this value &amp; repeat simulation.</p>
    1370 
    1371 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
    1372 id="_x0000_i1026" src="Stacking%20Faults%20II_files/image022.gif"></span></p>
     489offset consider the drawing of kaolinite.</p>
     490
     491<p class=MsoNormal><img width=480 height=338
     492src="Stacking%20Faults%20II_files/image002.gif"></p>
     493
     494<p class=MsoNormal>The offset Dx is given by the blue arrow in the above
     495drawing of kaolinite and is in fractional coordinates. Geometry gives</p>
     496
     497<p class=MsoNormal><span style='position:relative;top:3pt'><img width=106
     498height=26 src="Stacking%20Faults%20II_files/image021.gif">&nbsp;Or in this case
     499<b><span style='font-family:"Calibri",sans-serif'>-0.368</span></b>. Set <b><span
     500style='font-family:"Calibri",sans-serif'>Dx</span></b> to this value &amp;
     501repeat simulation.</p>
     502
     503<p class=MsoNormal><img width=700 height=600
     504src="Stacking%20Faults%20II_files/image022.gif"></p>
    1373505
    1374506<p class=MsoNormal>There is some improvement but some parts are not very well
    1375507represented. Recall from the triclinic kaolinite lattice parameters that <span
    1376508style='font-family:Symbol'>a</span> was 91.7°; that will produce a small offset
    1377 in Dy. Using the same kind of geometry math gives <span class=SpellE><b><span
    1378 style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span
    1379 style='font-family:"Calibri",sans-serif'>=-0.0246</span></b>. Enter this value
    1380 &amp; repeat the simulation again. This gives a much better fit to the observed
    1381 pattern, but the simulated peaks are too sharp; this can be fixed by changing
    1382 the U<span class=GramE>,V,W</span> Instrument parameters. I’d just set <b><span
    1383 style='font-family:"Calibri",sans-serif'>W=40</span></b> and the <b><span
    1384 style='font-family:"Calibri",sans-serif'>Histogram scale</span></b> (in <b><span
    1385 style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>) to <b><span
    1386 style='font-family:"Calibri",sans-serif'>40</span></b> and try again.</p>
    1387 
    1388 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=700 height=600
    1389 id="_x0000_i1025" src="Stacking%20Faults%20II_files/image023.gif"></span></p>
     509in Dy. Using the same kind of geometry math gives <b><span style='font-family:
     510"Calibri",sans-serif'>Dy=-0.0246</span></b>. Enter this value &amp; repeat the
     511simulation again. This gives a much better fit to the observed pattern, but the
     512simulated peaks are too sharp; this can be fixed by changing the U,V,W
     513Instrument parameters. I’d just set <b><span style='font-family:"Calibri",sans-serif'>W=40</span></b>
     514and the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale</span></b>
     515(in <b><span style='font-family:"Calibri",sans-serif'>Sample parameters</span></b>)
     516to <b><span style='font-family:"Calibri",sans-serif'>40</span></b> and try
     517again.</p>
     518
     519<p class=MsoNormal><img width=700 height=600
     520src="Stacking%20Faults%20II_files/image023.gif"></p>
    1390521
    1391522<p class=MsoNormal>That is a pretty good fit for a stacking simulation. By
    … …  
    1395526small range can be used to help with optimization, but in this case it would be
    1396527far easier to do a Rietveld refinement for this well ordered kaolinite. Save
    1397 your project as you will need it for the next part of the exercise.<o:p></o:p></p>
     528your project as you will need it for the next exercise (Stacking Faults-III).</p>
    1398529
    1399530</span></div>
    1400531
    1401 </span></span></span>
    1402532</body>
    1403533
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