Changeset 3081
- Timestamp:
- Sep 18, 2017 2:52:30 PM (5 years ago)
- Location:
- Tutorials/StackingFaults-I
- Files:
-
- 49 added
- 13 edited
Legend:
- Unmodified
- Added
- Removed
-
Tutorials/StackingFaults-I/Stacking Faults-I.htm
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mso-ansi-font-size:10.0pt; 1086 mso-bidi-font-size:10.0pt; 1087 font-family:"Calibri",sans-serif; 1088 mso-ascii-font-family:Calibri; 1089 mso-hansi-font-family:Calibri; 1090 mso-bidi-font-family:Calibri;} 234 1091 @page WordSection1 235 1092 {size:8.5in 11.0in; 236 margin:1.0in 1.0in 1.0in 1.0in;} 1093 margin:1.0in 1.0in 1.0in 1.0in; 1094 mso-header-margin:.5in; 1095 mso-footer-margin:.5in; 1096 mso-paper-source:0;} 237 1097 div.WordSection1 238 1098 {page:WordSection1;} 239 1099 --> 240 1100 </style> 241 1101 <!--[if gte mso 10]> 1102 <style> 1103 /* Style Definitions */ 1104 table.MsoNormalTable 1105 {mso-style-name:"Table Normal"; 1106 mso-tstyle-rowband-size:0; 1107 mso-tstyle-colband-size:0; 1108 mso-style-noshow:yes; 1109 mso-style-priority:99; 1110 mso-style-parent:""; 1111 mso-padding-alt:0in 5.4pt 0in 5.4pt; 1112 mso-para-margin:0in; 1113 mso-para-margin-bottom:.0001pt; 1114 mso-pagination:widow-orphan; 1115 font-size:10.0pt; 1116 font-family:"Calibri",sans-serif;} 1117 </style> 1118 <![endif]--><!--[if gte mso 9]><xml> 1119 <o:shapedefaults v:ext="edit" spidmax="1026"/> 1120 </xml><![endif]--><!--[if gte mso 9]><xml> 1121 <o:shapelayout v:ext="edit"> 1122 <o:idmap v:ext="edit" data="1"/> 1123 </o:shapelayout></xml><![endif]--> 242 1124 </head> 243 1125 244 <body lang=EN-US link=blue vlink=purple >1126 <body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'> 245 1127 246 1128 <div class=WordSection1> 247 1129 248 <h1>Stacking Fault Simulations I</h1> 1130 <h1><span style='mso-fareast-font-family:"Times New Roman"'>Stacking Fault 1131 Simulations I<o:p></o:p></span></h1> 249 1132 250 1133 <p class=MsoNormal>In this exercise you will use GSAS-II to simulate the 251 1134 diffraction patterns from faulted diamond. Diamond most commonly has the 252 well-known cubic structure with the space group Fd3m and a=3.5668A. The C-atom is 253 at 1/8,1/8,1/8 and can be viewed as a cubic stacking of ruffled hexagonal nets 254 along the cubic cell 111 diagonal. </p> 255 256 <p class=MsoNormal><img width=482 height=361 257 src="Stacking%20Faults-I_files/image001.jpg"></p> 258 259 <p class=MsoNormal>The structure of londsdaleite has those layers stacked 260 hexagonally and thus a faulted diamond structure may occasionally have 261 hexagonal stacked layers instead of all cubic ones. From geometric 262 considerations, these planar stacking faults must extend across the entire 263 crystal. If there are only a few such faults in a crystal then the diffraction 264 pattern will show two cubic diamond patterns in a twin law relationship. 265 Otherwise, if there are many such faults then the diffraction pattern will show 266 streaks. To simulate the streaks one must first develop a model for the 267 hexagonal net of C-atoms and then show how they stack in either the cubic or 268 hexagonal forms. GSAS-II uses a suite of subroutines from the DIFFaX program 269 (M.M.J. Treacy, J.M. Newsam & M.W. Deem, (1991), Proc. Roy. Soc. Lond. 270 433A, 499-520) to calculate the diffraction pattern via a general recursion 271 algorithm and a randomized set of stacked layers. NB: this calculation can be 272 quite time consuming particularly if unreasonable demands are made on it. </p> 1135 well-known cubic structure with the space group Fd3m and a=3.5668A. The C-atom 1136 is at 1/8<span class=GramE>,1</span>/8,1/8 and can be viewed as a cubic 1137 stacking of ruffled hexagonal nets along the cubic cell 111 diagonal. </p> 1138 1139 <p class=MsoNormal><span style='mso-no-proof:yes'><img width=482 height=361 1140 id="_x0000_i1052" src="Stacking%20Faults-I_files/image001.jpg"></span></p> 1141 1142 <p class=MsoNormal>The structure of <span class=SpellE>londsdaleite</span> has 1143 those layers stacked hexagonally and thus a faulted diamond structure may 1144 occasionally have hexagonal stacked layers instead of all cubic ones. From 1145 geometric considerations, these planar stacking faults must extend across the 1146 entire crystal. If there are only a few such faults in a crystal then the 1147 diffraction pattern will show two cubic diamond patterns in a twin law 1148 relationship. Otherwise, if there are many such faults then the diffraction 1149 pattern will show streaks. To simulate the streaks one must first develop a 1150 model for the hexagonal net of C-atoms and then show how they stack in either 1151 the cubic or hexagonal forms. GSAS-II uses a suite of subroutines from the <span 1152 class=SpellE>DIFFaX</span> program (M.M.J. <span class=SpellE>Treacy</span>, 1153 J.M. <span class=SpellE>Newsam</span> & M.W. Deem, (1991), Proc. Roy. Soc. <span 1154 class=SpellE>Lond</span>. 433A, 499-520) to calculate the diffraction pattern 1155 via a general recursion algorithm and a randomized set of stacked layers. NB: 1156 this calculation can be quite time consuming particularly if unreasonable 1157 demands are made on it. </p> 273 1158 274 1159 <p class=MsoNormal>If you have not done so already, start GSAS-II.</p> 275 1160 276 <h2>Simulation 1. Selected area diffraction for random faults in diamond</h2> 1161 <h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 1. 1162 Selected area diffraction for random faults in diamond<o:p></o:p></span></h2> 277 1163 278 1164 <p class=MsoNormal>To begin we must have a phase to work with. In the main … … 283 1169 select it; the data window will display the default for the General tab.</p> 284 1170 285 <p class=MsoNormal><img width=620 height=334 286 src="Stacking%20Faults-I_files/image002.gif"></p> 1171 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype 1172 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" 1173 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> 1174 <v:stroke joinstyle="miter"/> 1175 <v:formulas> 1176 <v:f eqn="if lineDrawn pixelLineWidth 0"/> 1177 <v:f eqn="sum @0 1 0"/> 1178 <v:f eqn="sum 0 0 @1"/> 1179 <v:f eqn="prod @2 1 2"/> 1180 <v:f eqn="prod @3 21600 pixelWidth"/> 1181 <v:f eqn="prod @3 21600 pixelHeight"/> 1182 <v:f eqn="sum @0 0 1"/> 1183 <v:f eqn="prod @6 1 2"/> 1184 <v:f eqn="prod @7 21600 pixelWidth"/> 1185 <v:f eqn="sum @8 21600 0"/> 1186 <v:f eqn="prod @7 21600 pixelHeight"/> 1187 <v:f eqn="sum @10 21600 0"/> 1188 </v:formulas> 1189 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> 1190 <o:lock v:ext="edit" aspectratio="t"/> 1191 </v:shapetype><v:shape id="Picture_x0020_31" o:spid="_x0000_i1051" type="#_x0000_t75" 1192 style='width:468pt;height:191.25pt;visibility:visible;mso-wrap-style:square'> 1193 <v:imagedata src="Stacking%20Faults-I_files/image001.png" o:title=""/> 1194 </v:shape><![endif]--><![if !vml]><img width=624 height=255 1195 src="Stacking%20Faults-I_files/image002.gif" v:shapes="Picture_x0020_31"><![endif]></span></p> 287 1196 288 1197 <p class=MsoNormal>Change the phase type to <b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>; … … 291 1200 style='font-family:"Calibri",sans-serif'>diamond</span></b>.</p> 292 1201 293 <p class=MsoNormal><img width=624 height=370 294 src="Stacking%20Faults-I_files/image003.gif"></p> 1202 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1203 id="Picture_x0020_33" o:spid="_x0000_i1050" type="#_x0000_t75" style='width:468pt; 1204 height:191.25pt;visibility:visible;mso-wrap-style:square'> 1205 <v:imagedata src="Stacking%20Faults-I_files/image003.png" o:title=""/> 1206 </v:shape><![endif]--><![if !vml]><img width=624 height=255 1207 src="Stacking%20Faults-I_files/image004.gif" v:shapes="Picture_x0020_33"><![endif]></span></p> 295 1208 296 1209 <p class=MsoNormal>First you need to describe the reference unit cell for the … … 300 1213 One can also anticipate that the resulting diffraction pattern will have 301 1214 hexagonal <b><span style='font-family:"Calibri",sans-serif'>6/mmm</span></b> 302 symmetry so first select this from the pull down box nea tthe top of the page;1215 symmetry so first select this from the pull down box near the top of the page; 303 1216 the window will be redrawn.</p> 304 1217 305 <p class=MsoNormal><img width=624 height=464 306 src="Stacking%20Faults-I_files/image004.gif"></p> 307 308 <p class=MsoNormal>The a cell parameter for diamond stacking can be assumed to 309 be a<span style='position:relative;top:3pt'><img width=27 height=21 310 src="Stacking%20Faults-I_files/image005.gif"> = <b><span style='font-family: 311 "Calibri",sans-serif'>2.522</span></b> and the c cell parameter is a<span 312 style='position:relative;top:3pt'><img width=27 height=21 313 src="Stacking%20Faults-I_files/image006.gif"> = <b><span style='font-family: 314 "Calibri",sans-serif'>2.059</span></b> since there are 3 layers along the 111 315 diamond cell diagonal. Enter these in the appropriate places; the cell volume 316 will be revised.</p> 1218 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1219 id="Picture_x0020_34" o:spid="_x0000_i1049" type="#_x0000_t75" style='width:468pt; 1220 height:230.25pt;visibility:visible;mso-wrap-style:square'> 1221 <v:imagedata src="Stacking%20Faults-I_files/image005.png" o:title=""/> 1222 </v:shape><![endif]--><![if !vml]><img width=624 height=307 1223 src="Stacking%20Faults-I_files/image006.gif" v:shapes="Picture_x0020_34"><![endif]></span></p> 1224 1225 <p class=MsoNormal><span class=GramE>The a</span> cell parameter for diamond 1226 stacking can be assumed to be <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type 1227 m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family: 1228 "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic; 1229 mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i 1230 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:num><m:den><m:rad><m:radPr><m:degHide 1231 m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family: 1232 "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic; 1233 mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i 1234 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:e></m:rad></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span 1235 style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: 1236 "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; 1237 top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: 1238 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1239 type="#_x0000_t75" style='width:28.5pt;height:15.75pt'> 1240 <v:imagedata src="Stacking%20Faults-I_files/image007.png" o:title="" 1241 chromakey="white"/> 1242 </v:shape><![endif]--><![if !vml]><img width=38 height=21 1243 src="Stacking%20Faults-I_files/image008.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]> = 1244 <b><span style='font-family:"Calibri",sans-serif'>2.522</span></b> and the c 1245 cell parameter is <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type m:val="lin"/><span 1246 style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; 1247 mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: 1248 normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style: 1249 normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:num><m:den><m:rad><m:radPr><m:degHide 1250 m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family: 1251 "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic; 1252 mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i 1253 style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>3</m:r></span></i></m:e></m:rad></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span 1254 style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: 1255 "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; 1256 top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: 1257 EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" 1258 type="#_x0000_t75" style='width:28.5pt;height:15.75pt'> 1259 <v:imagedata src="Stacking%20Faults-I_files/image009.png" o:title="" 1260 chromakey="white"/> 1261 </v:shape><![endif]--><![if !vml]><img width=38 height=21 1262 src="Stacking%20Faults-I_files/image010.gif" v:shapes="_x0000_i1025"><![endif]></span><![endif]> = 1263 <b><span style='font-family:"Calibri",sans-serif'>2.059</span></b> since there 1264 are 3 layers along the 111 diamond cell diagonal. Enter these in the 1265 appropriate places; the cell volume will be revised.</p> 317 1266 318 1267 <p class=MsoNormal>Now we have to describe the two hexagonal nets that will be 319 1268 stacked for either cubic or hexagonal stacking. Select <b><span 320 style='font-family:"Calibri",sans-serif'>Add new layer?</span></b> the window 321 will be redrawn.</p> 322 323 <p class=MsoNormal><img width=624 height=479 324 src="Stacking%20Faults-I_files/image007.gif"></p> 1269 style='font-family:"Calibri",sans-serif'>Add new layer?</span></b> <span 1270 class=GramE>the</span> window will be redrawn.</p> 1271 1272 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1273 id="Picture_x0020_35" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:468pt; 1274 height:311.25pt;visibility:visible;mso-wrap-style:square'> 1275 <v:imagedata src="Stacking%20Faults-I_files/image011.png" o:title=""/> 1276 </v:shape><![endif]--><![if !vml]><img width=624 height=415 1277 src="Stacking%20Faults-I_files/image012.gif" v:shapes="Picture_x0020_35"><![endif]></span></p> 325 1278 326 1279 <p class=MsoNormal>Name the layer (I chose <b><span style='font-family:"Calibri",sans-serif'>layer … … 328 1281 for the layer symmetry. The window will be redrawn after changing the name. 329 1282 Next, select <b><span style='font-family:"Calibri",sans-serif'>Add atom?</span></b> 330 and the window will be redrawn with one line in the layer table.</p> 331 332 <p class=MsoNormal><img width=624 height=479 333 src="Stacking%20Faults-I_files/image008.gif"></p> 334 335 <p class=MsoNormal>To make this a C-atom select the <b><span style='font-family: 336 "Calibri",sans-serif'>Unk</span></b> under Type with a double click; a 337 Periodic table will popup. Select <b><span style='font-family:"Calibri",sans-serif'>C</span></b>; 338 the popup will disappear and the window will be redrawn. The coordinates of 339 this C-atom in the new stacking unit cell is <b><span style='font-family:"Calibri",sans-serif'>-1/3,-1/6,-1/8</span></b>; 1283 <span class=GramE>and</span> the window will be redrawn with one line in the 1284 layer table.</p> 1285 1286 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1287 id="Picture_x0020_36" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:468pt; 1288 height:311.25pt;visibility:visible;mso-wrap-style:square'> 1289 <v:imagedata src="Stacking%20Faults-I_files/image013.png" o:title=""/> 1290 </v:shape><![endif]--><![if !vml]><img width=624 height=415 1291 src="Stacking%20Faults-I_files/image014.gif" v:shapes="Picture_x0020_36"><![endif]></span></p> 1292 1293 <p class=MsoNormal>To make this a C-atom select the <span class=SpellE><b><span 1294 style='font-family:"Calibri",sans-serif'>Unk</span></b></span> under Type with 1295 a double click; a Periodic table will popup. Select <b><span style='font-family: 1296 "Calibri",sans-serif'>C</span></b>; the popup will disappear and the window 1297 will be redrawn. The coordinates of this C-atom in the new stacking unit cell 1298 is <b><span style='font-family:"Calibri",sans-serif'>-1/3,-1/6,-1/8</span></b>; 340 1299 you may enter these as fractions. Select a table item to complete the entry; 341 1300 the window should show the new position.</p> 342 1301 343 <p class=MsoNormal><img width=624 height=479 344 src="Stacking%20Faults-I_files/image009.gif"></p> 1302 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1303 id="Picture_x0020_38" o:spid="_x0000_i1046" type="#_x0000_t75" style='width:468pt; 1304 height:323.25pt;visibility:visible;mso-wrap-style:square'> 1305 <v:imagedata src="Stacking%20Faults-I_files/image015.png" o:title=""/> 1306 </v:shape><![endif]--><![if !vml]><img width=624 height=431 1307 src="Stacking%20Faults-I_files/image016.gif" v:shapes="Picture_x0020_38"><![endif]></span></p> 345 1308 346 1309 <p class=MsoNormal>You can draw the layer to see what it looks like; select <b><span 347 style='font-family:"Calibri",sans-serif'>Draw layer?</span></b> and the drawing 348 will appear. </p> 349 350 <p class=MsoNormal><img width=486 height=363 351 src="Stacking%20Faults-I_files/image010.jpg"></p> 1310 style='font-family:"Calibri",sans-serif'>Draw layer?</span></b> <span 1311 class=GramE>and</span> the drawing will appear. </p> 1312 1313 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1314 id="Picture_x0020_39" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:468pt; 1315 height:403.5pt;visibility:visible;mso-wrap-style:square'> 1316 <v:imagedata src="Stacking%20Faults-I_files/image017.png" o:title=""/> 1317 </v:shape><![endif]--><![if !vml]><img width=624 height=538 1318 src="Stacking%20Faults-I_files/image018.gif" v:shapes="Picture_x0020_39"><![endif]></span></p> 352 1319 353 1320 <p class=MsoNormal>A unit cell box is drawn with a 5x5 suite of unit cells; the 354 1321 ruffled hexagonal net perpendicular to the c-axis (blue line) is clear.</p> 355 1322 356 <p class=MsoNormal>Now we need a second layer; repeat the steps for making a 357 layer using <b><span style='font-family:"Calibri",sans-serif'>1/3,1/6,-1/8</span></b> 1323 <p class=MsoNormal>Now we need a second layer (<b style='mso-bidi-font-weight: 1324 normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: 1325 minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>layer 1326 2</span></b>); repeat the steps for making a layer using <b><span 1327 style='font-family:"Calibri",sans-serif'>1/3<span class=GramE>,1</span>/6,-1/8</span></b> 358 1328 for the C-atom position with <b><span style='font-family:"Calibri",sans-serif'>-1</span></b> 359 1329 for the layer symmetry. The window should look like this when done.</p> 360 1330 361 <p class=MsoNormal><img width=624 height=624 362 src="Stacking%20Faults-I_files/image011.gif"></p> 363 364 <p class=MsoNormal>Ive stretched it a bit to show the Layer-Layer transition 365 probabilities. Change <b><span style='font-family:"Calibri",sans-serif'>Dz</span></b> 1331 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1332 id="Picture_x0020_40" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:468pt; 1333 height:363.75pt;visibility:visible;mso-wrap-style:square'> 1334 <v:imagedata src="Stacking%20Faults-I_files/image019.png" o:title=""/> 1335 </v:shape><![endif]--><![if !vml]><img width=624 height=485 1336 src="Stacking%20Faults-I_files/image020.gif" v:shapes="Picture_x0020_40"><![endif]></span></p> 1337 1338 <p class=MsoNormal>Ive stretched it a bit to show the Layer-Layer transition probabilities. 1339 Change <span class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dz</span></b></span> 366 1340 for each entry to <b><span style='font-family:"Calibri",sans-serif'>1.0</span></b> 367 1341 to properly space out the stacked layers. If you select the first box in the … … 369 1343 reminiscent of how carbon sheets stack in graphite. </p> 370 1344 371 <p class=MsoNormal><img width=479 height=358 372 src="Stacking%20Faults-I_files/image012.jpg"></p> 1345 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1346 id="Picture_x0020_41" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:468pt; 1347 height:406.5pt;visibility:visible;mso-wrap-style:square'> 1348 <v:imagedata src="Stacking%20Faults-I_files/image021.png" o:title=""/> 1349 </v:shape><![endif]--><![if !vml]><img width=624 height=542 1350 src="Stacking%20Faults-I_files/image022.gif" v:shapes="Picture_x0020_41"><![endif]></span></p> 373 1351 374 1352 <p class=MsoNormal>Clearly not diamond stacking. The table defines how the next 375 1353 layer is displaced relative to the reference layer. You can shift this layer by 376 using the <b><span style='font-family:"Calibri",sans-serif'>X ,Y,Z</span></b>1354 using the <b><span style='font-family:"Calibri",sans-serif'>X<span class=GramE>,Y,Z</span></span></b> 377 1355 & <b><span style='font-family:"Calibri",sans-serif'>shift-X,Y,Z</span></b> 378 keys; the plot will be redrawn and the table entry updated each time you shift 379 the layer. When you get to the right offset for diamond additional bonds will 380 appear connecting the layers together. The correct shift is <b><span 381 style='font-family:"Calibri",sans-serif'>Dx=2/3</span></b>, <b><span 382 style='font-family:"Calibri",sans-serif'>Dy=1/3</span></b> and <b><span 383 style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b> for the layer 1 to 384 layer 1 transition and for layer 2 to layer 2 the shifts are <b><span 385 style='font-family:"Calibri",sans-serif'>Dx=-2/3</span></b>, <b><span 386 style='font-family:"Calibri",sans-serif'>Dy=-1/3</span></b> and <b><span 387 style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b>. For the remaining 388 layer 1-layer 2 and <i>vice versa</i> transitions <b><span style='font-family: 389 "Calibri",sans-serif'>Dx=Dy=0</span></b>. Layer 1 to layer 1 stacking looks 390 like.</p> 391 392 <p class=MsoNormal><img width=477 height=357 393 src="Stacking%20Faults-I_files/image013.jpg"></p> 1356 keys; the plot will be redrawn and the table entry updated each time you shift the 1357 layer. When you get to the right offset for diamond additional bonds will 1358 appear connecting the layers together. The correct shift is <span class=SpellE><b><span 1359 style='font-family:"Calibri",sans-serif'>Dx</span></b></span><b><span 1360 style='font-family:"Calibri",sans-serif'>=2/3</span></b>, <span class=SpellE><b><span 1361 style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span 1362 style='font-family:"Calibri",sans-serif'>=1/3</span></b> and <span 1363 class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dz</span></b></span><b><span 1364 style='font-family:"Calibri",sans-serif'>=1.0</span></b> for the layer 1 to 1365 layer 1 transition and for layer 2 to layer 2 the shifts are <span 1366 class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dx</span></b></span><b><span 1367 style='font-family:"Calibri",sans-serif'>=-2/3</span></b>, <span class=SpellE><b><span 1368 style='font-family:"Calibri",sans-serif'>Dy</span></b></span><b><span 1369 style='font-family:"Calibri",sans-serif'>=-1/3</span></b> and <span 1370 class=SpellE><b><span style='font-family:"Calibri",sans-serif'>Dz</span></b></span><b><span 1371 style='font-family:"Calibri",sans-serif'>=1.0</span></b>. For the remaining 1372 layer 1-layer 2 and <i>vice versa</i> transitions <span class=SpellE><b><span 1373 style='font-family:"Calibri",sans-serif'>Dx</span></b></span><b><span 1374 style='font-family:"Calibri",sans-serif'>=<span class=SpellE>Dy</span>=0</span></b>. 1375 Layer 1 to layer 1 stacking looks like.</p> 1376 1377 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1378 id="Picture_x0020_42" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:468pt; 1379 height:404.25pt;visibility:visible;mso-wrap-style:square'> 1380 <v:imagedata src="Stacking%20Faults-I_files/image023.png" o:title=""/> 1381 </v:shape><![endif]--><![if !vml]><img width=624 height=539 1382 src="Stacking%20Faults-I_files/image024.gif" v:shapes="Picture_x0020_42"><![endif]></span></p> 394 1383 395 1384 <p class=MsoNormal>You can explore the result of various stacking sequences in 396 1385 the next block of commands; enter <b><span style='font-family:"Calibri",sans-serif'>1 397 1 1 1 2 2 2 2</span></b> into the box and press <b><span style='font-family: 398 "Calibri",sans-serif'>Enter</span></b>. A plot showing the result of a single 399 twin fault will be shown.</p> 400 401 <p class=MsoNormal><img width=483 height=361 402 src="Stacking%20Faults-I_files/image014.jpg"></p> 403 404 <p class=MsoNormal>If you enter 1 2 1 2 1 2 1 2 then the structure of londsdaleite 405 will be shown; 1 1 1 1 1 1 or 2 2 2 2 2 2 gives the diamond structure. </p> 1386 1 1 1 2 2 2</span></b> into the box and press <b><span style='font-family:"Calibri",sans-serif'>Enter</span></b>. 1387 A plot showing the result of a single twin fault will be shown.</p> 1388 1389 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1390 id="Picture_x0020_43" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:468pt; 1391 height:404.25pt;visibility:visible;mso-wrap-style:square'> 1392 <v:imagedata src="Stacking%20Faults-I_files/image025.png" o:title=""/> 1393 </v:shape><![endif]--><![if !vml]><img width=624 height=539 1394 src="Stacking%20Faults-I_files/image026.gif" v:shapes="Picture_x0020_43"><![endif]></span></p> 1395 1396 <p class=MsoNormal>If you enter 1 2 1 2 1 2 1 2 then the structure of <span 1397 class=SpellE>londsdaleite</span> will be shown; 1 1 1 1 1 1 or 2 2 2 2 2 2 1398 gives the diamond structure. </p> 406 1399 407 1400 <p class=MsoNormal>Finally we must select transition probabilities; they should … … 410 1403 style='font-family:"Calibri",sans-serif'>0.3</span></b> to give</p> 411 1404 412 <p class=MsoNormal><img width=624 height=448 413 src="Stacking%20Faults-I_files/image015.gif"></p> 1405 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1406 id="Picture_x0020_44" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:468pt; 1407 height:363.75pt;visibility:visible;mso-wrap-style:square'> 1408 <v:imagedata src="Stacking%20Faults-I_files/image027.png" o:title=""/> 1409 </v:shape><![endif]--><![if !vml]><img width=624 height=485 1410 src="Stacking%20Faults-I_files/image028.gif" v:shapes="Picture_x0020_44"><![endif]></span></p> 414 1411 415 1412 <p class=MsoNormal>We are now ready to do a single crystal simulation; select <b><span … … 417 1414 from the Phase data window menu. A small popup will appear</p> 418 1415 419 <p class=MsoNormal><img width=279 height=136 420 src="Stacking%20Faults-I_files/image016.gif"></p> 1416 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1417 id="Picture_x0020_45" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:209.25pt; 1418 height:102.75pt;visibility:visible;mso-wrap-style:square'> 1419 <v:imagedata src="Stacking%20Faults-I_files/image029.png" o:title=""/> 1420 </v:shape><![endif]--><![if !vml]><img width=279 height=137 1421 src="Stacking%20Faults-I_files/image030.gif" v:shapes="Picture_x0020_45"><![endif]></span></p> 421 1422 422 1423 <p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>selected … … 424 1425 options.</p> 425 1426 426 <p class=MsoNormal><img width=242 height=136 427 src="Stacking%20Faults-I_files/image017.gif"></p> 1427 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1428 id="Picture_x0020_46" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:181.5pt; 1429 height:102.75pt;visibility:visible;mso-wrap-style:square'> 1430 <v:imagedata src="Stacking%20Faults-I_files/image031.png" o:title=""/> 1431 </v:shape><![endif]--><![if !vml]><img width=242 height=137 1432 src="Stacking%20Faults-I_files/image032.gif" v:shapes="Picture_x0020_46"><![endif]></span></p> 428 1433 429 1434 <p class=MsoNormal>To make it interesting select <b><span style='font-family: 430 "Calibri",sans-serif'>Max. l index</span></b> of <b><span style='font-family: 431 "Calibri",sans-serif'>6</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>. 432 Very quickly a new popup will appear letting you know the simulation is 433 finished; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>. 434 The data window will be redrawn</p> 435 436 <p class=MsoNormal><img width=624 height=474 437 src="Stacking%20Faults-I_files/image018.gif"></p> 1435 "Calibri",sans-serif'>Max. <span class=GramE>l</span> index</span></b> of <b><span 1436 style='font-family:"Calibri",sans-serif'>6</span></b> and press <b><span 1437 style='font-family:"Calibri",sans-serif'>Ok</span></b>. Very quickly a new 1438 popup will appear letting you know the simulation is finished; press <b><span 1439 style='font-family:"Calibri",sans-serif'>Ok</span></b>. The data window will be 1440 redrawn</p> 1441 1442 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1443 id="Picture_x0020_47" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:468pt; 1444 height:363.75pt;visibility:visible;mso-wrap-style:square'> 1445 <v:imagedata src="Stacking%20Faults-I_files/image033.png" o:title=""/> 1446 </v:shape><![endif]--><![if !vml]><img width=624 height=485 1447 src="Stacking%20Faults-I_files/image034.gif" v:shapes="Picture_x0020_47"><![endif]></span></p> 438 1448 439 1449 <p class=MsoNormal>At the top is a new item <b><span style='font-family:"Calibri",sans-serif'>Plot … … 442 1452 (or <b><span style='font-family:"Calibri",sans-serif'>U</span></b>); I got</p> 443 1453 444 <p class=MsoNormal><img width=484 height=455 445 src="Stacking%20Faults-I_files/image019.gif"></p> 1454 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1455 id="Picture_x0020_48" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt; 1456 height:401.25pt;visibility:visible;mso-wrap-style:square'> 1457 <v:imagedata src="Stacking%20Faults-I_files/image035.png" o:title=""/> 1458 </v:shape><![endif]--><![if !vml]><img width=624 height=535 1459 src="Stacking%20Faults-I_files/image036.gif" v:shapes="Picture_x0020_48"><![endif]></span></p> 446 1460 447 1461 <p class=MsoNormal>The streaking intermixed with sharp spots is clearly obvious 448 1462 in this plot. Save this project; youll need it for the next simulation.</p> 449 1463 450 <h2> Simulation 2. Laboratory powder diffraction simulation for random faults in451 diamond</h2>1464 <h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 2. 1465 Laboratory powder diffraction simulation for random faults in diamond<o:p></o:p></span></h2> 452 1466 453 1467 <p class=MsoNormal>The setup for a powder pattern simulation is the same as … … 461 1475 some choices.</p> 462 1476 463 <p class=MsoNormal><img width=322 height=268 464 src="Stacking%20Faults-I_files/image020.gif"></p> 465 466 <p class=MsoNormal>Use the first one for <b><span style='font-family:"Calibri",sans-serif'>CuKa 467 lab data</span></b>; a new popup will appear</p> 468 469 <p class=MsoNormal><img width=318 height=342 470 src="Stacking%20Faults-I_files/image021.gif"></p> 1477 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1478 id="Picture_x0020_49" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:241.5pt; 1479 height:201.75pt;visibility:visible;mso-wrap-style:square'> 1480 <v:imagedata src="Stacking%20Faults-I_files/image037.png" o:title=""/> 1481 </v:shape><![endif]--><![if !vml]><img width=322 height=269 1482 src="Stacking%20Faults-I_files/image038.gif" v:shapes="Picture_x0020_49"><![endif]></span></p> 1483 1484 <p class=MsoNormal>Use the first one for <span class=SpellE><b><span 1485 style='font-family:"Calibri",sans-serif'>CuKa</span></b></span><b><span 1486 style='font-family:"Calibri",sans-serif'> lab data</span></b>; a new popup will 1487 appear</p> 1488 1489 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1490 id="Picture_x0020_50" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:238.5pt; 1491 height:257.25pt;visibility:visible;mso-wrap-style:square'> 1492 <v:imagedata src="Stacking%20Faults-I_files/image039.png" o:title=""/> 1493 </v:shape><![endif]--><![if !vml]><img width=318 height=343 1494 src="Stacking%20Faults-I_files/image040.gif" v:shapes="Picture_x0020_50"><![endif]></span></p> 471 1495 472 1496 <p class=MsoNormal>Change the end angle to <b><span style='font-family:"Calibri",sans-serif'>150</span></b> … … 504 1528 interesting stuff around each peak.</p> 505 1529 506 <p class=MsoNormal><img width=624 height=587 507 src="Stacking%20Faults-I_files/image022.gif"></p> 1530 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1531 id="Picture_x0020_51" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt; 1532 height:401.25pt;visibility:visible;mso-wrap-style:square'> 1533 <v:imagedata src="Stacking%20Faults-I_files/image041.png" o:title=""/> 1534 </v:shape><![endif]--><![if !vml]><img width=624 height=535 1535 src="Stacking%20Faults-I_files/image042.gif" v:shapes="Picture_x0020_51"><![endif]></span></p> 508 1536 509 1537 <p class=MsoNormal>The blue line is a simulated observed pattern with imposed … … 514 1542 pattern unless you reset the dummy profile as noted above.</p> 515 1543 516 <h2>Simulation 3. Sequential parameter change</h2> 1544 <h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 3. 1545 Sequential parameter change<o:p></o:p></span></h2> 517 1546 518 1547 <p class=MsoNormal>A perhaps useful means of exploring the effects of changing … … 521 1550 simulations</span></b> from the Layers menu; a popup will appear</p> 522 1551 523 <p class=MsoNormal><img width=279 height=191 524 src="Stacking%20Faults-I_files/image023.gif"></p> 1552 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1553 id="Picture_x0020_52" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:209.25pt; 1554 height:2in;visibility:visible;mso-wrap-style:square'> 1555 <v:imagedata src="Stacking%20Faults-I_files/image043.png" o:title=""/> 1556 </v:shape><![endif]--><![if !vml]><img width=279 height=192 1557 src="Stacking%20Faults-I_files/image044.gif" v:shapes="Picture_x0020_52"><![endif]></span></p> 525 1558 526 1559 <p class=MsoNormal>Here you select the parameter, range and number of steps 527 1560 (both ends will be used). From the <b><span style='font-family:"Calibri",sans-serif'>Select 528 parameter</span></b> pulldown choose <b><span style='font-family:"Calibri",sans-serif'>TransP ;0;0</span></b>;529 this is the layer 1 to layer 1 transition probability. Then change the no. 530 steps to <b><span style='font-family:"Calibri",sans-serif'>10</span></b> (11 will 531 be calculated). We have the same choices for instrument broadening as above; 532 use the default. Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>;1561 parameter</span></b> pulldown choose <b><span style='font-family:"Calibri",sans-serif'>TransP<span 1562 class=GramE>;0</span>;0</span></b>; this is the layer 1 to layer 1 transition 1563 probability. Then change the no. steps to <b><span style='font-family:"Calibri",sans-serif'>10</span></b> 1564 (11 will be calculated). We have the same choices for instrument broadening as 1565 above; use the default. Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; 533 1566 the next popup allows selection of a powder pattern (e.g. for comparison and 534 1567 the range for the calculation). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> … … 536 1569 progress and the transition matrix for each step. A popup will appear when the 537 1570 sequence is finished after several seconds. Notice that the matrix is not 538 symmetric so that layer1 to layer 1 probability is not the same as layer 2 to 539 layer 2 at each step in the simulation. We can force this by selecting <b><span 540 style='font-family:"Calibri",sans-serif'>Symmetric probabilities?</span></b> on 541 the Layers page. Do this and repeat the sequential simulation as above. Now the 542 matrices are symmetric as one could expect. When the simulation is finished, 543 select the <b><span style='font-family:"Calibri",sans-serif'>Plot sequential 544 result?</span></b> box; a new plot will appear.</p> 545 546 <p class=MsoNormal><img width=624 height=535 547 src="Stacking%20Faults-I_files/image024.gif"></p> 1571 symmetric (see console) so that layer1 to layer 1 probability is not the same 1572 as layer 2 to layer 2 at each step in the simulation. We can force this by 1573 selecting <b><span style='font-family:"Calibri",sans-serif'>Symmetric 1574 probabilities?</span></b> <span class=GramE>on</span> the Layers page. Do this 1575 and repeat the sequential simulation as above. Now the matrices are symmetric 1576 as one could expect. When the simulation is finished, select the <b><span 1577 style='font-family:"Calibri",sans-serif'>Plot sequential result?</span></b> <span 1578 class=GramE>box</span>; a new plot will appear.</p> 1579 1580 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1581 id="Picture_x0020_61" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt; 1582 height:401.25pt;visibility:visible;mso-wrap-style:square'> 1583 <v:imagedata src="Stacking%20Faults-I_files/image046.png" o:title=""/> 1584 </v:shape><![endif]--><![if !vml]><img width=624 height=535 1585 src="Stacking%20Faults-I_files/image048.gif" v:shapes="Picture_x0020_61"><![endif]></span></p> 548 1586 549 1587 <p class=MsoNormal>This is a multiline plot; you can shift the lines with the <b><span 550 style='font-family:"Calibri",sans-serif'>U,D,L,R</span></b> keys (<b><span 551 style='font-family:"Calibri",sans-serif'>O</span></b> resets offsets to zero). 552 Ive done this for the next plot.</p> 553 554 <p class=MsoNormal><img width=624 height=535 555 src="Stacking%20Faults-I_files/image025.gif"></p> 556 557 <p class=MsoNormal>The first blue line is for pure hexagonal londsdaleite stacking 558 and the last magenta line is for pure cubic diamond stacking. You can see how 559 some lines quickly vanish with the introduction of stacking faults while other 560 persist across the entire sequence. This is a good place to save your project 561 file; the sequential result will be included.</p> 562 563 <h2>Simulation 4. Modelling clustering in diamond</h2> 1588 style='font-family:"Calibri",sans-serif'>U<span class=GramE>,D,L,R</span></span></b> 1589 keys (<b><span style='font-family:"Calibri",sans-serif'>O</span></b> resets 1590 offsets to zero). Ive done this for the next plot.</p> 1591 1592 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1593 id="Picture_x0020_62" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt; 1594 height:401.25pt;visibility:visible;mso-wrap-style:square'> 1595 <v:imagedata src="Stacking%20Faults-I_files/image083.png" o:title=""/> 1596 </v:shape><![endif]--><![if !vml]><img width=624 height=535 1597 src="Stacking%20Faults-I_files/image084.gif" v:shapes="Picture_x0020_62"><![endif]></span></p> 1598 1599 <p class=MsoNormal>The first blue line is for pure hexagonal <span 1600 class=SpellE>londsdaleite</span> stacking and the last magenta line is for pure 1601 cubic diamond stacking. You can see how some lines quickly vanish with the 1602 introduction of stacking faults while other persist across the entire sequence. 1603 This is a good place to save your project file; the sequential result will be 1604 included.</p> 1605 1606 <h2><span style='mso-fareast-font-family:"Times New Roman"'>Simulation 4. 1607 Modelling clustering in diamond<o:p></o:p></span></h2> 564 1608 565 1609 <p class=MsoNormal>In this simulation we will explore the possibility that the 566 1610 stacking history affects the probability of a fault. In the case of diamond, a 567 fault to form londsdaleite could be followed by similar layers until a lower 568 probability fault converts the structure back to diamond. The crystal then has 569 blocks of diamond structure interleaved with blocks of londsdaleite. This is 570 best done in a new phase so we dont mess up the above simulations, but most of 571 the data in the current phase is useful for the cluster model. The easiest way 572 is to import the new phase from the current project. <b><span style='font-family: 573 "Calibri",sans-serif'>Do Import/Phase/from GSAS-II gpx file</span></b> from the 574 main GSAS-II data tree menu. A file selection dialog box will appear; select 575 the current project file (<b><span style='font-family:"Calibri",sans-serif'>diamond.gpx</span></b>) 576 and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>. A 577 small popup will appear confirming your choice; press <b><span 578 style='font-family:"Calibri",sans-serif'>Yes</span></b>. The next popup offers 579 the change to name the phase, I chose <b><span style='font-family:"Calibri",sans-serif'>clustered</span></b> 1611 fault to form <span class=SpellE>londsdaleite</span> could be followed by 1612 similar layers until a lower probability fault converts the structure back to 1613 diamond. The crystal then has blocks of diamond structure interleaved with 1614 blocks of <span class=SpellE>londsdaleite</span>. This is best done in a new 1615 phase so we dont mess up the above simulations, but most of the data in the 1616 current phase is useful for the cluster model. The easiest way is to import the 1617 new phase from the current project. <b><span style='font-family:"Calibri",sans-serif'>Do 1618 Import/Phase/from GSAS-II <span class=SpellE>gpx</span> file</span></b> from 1619 the main GSAS-II data tree <span class=GramE>menu.</span> A file selection 1620 dialog box will appear; select the current project file (<span class=SpellE><b><span 1621 style='font-family:"Calibri",sans-serif'>diamond.gpx</span></b></span>) and 1622 press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>. A 1623 small popup will appear confirming your choice; press <span class=GramE><b><span 1624 style='font-family:"Calibri",sans-serif'>Yes</span></b></span>. The next popup 1625 offers the change to name the phase, I chose <b><span style='font-family:"Calibri",sans-serif'>clustered</span></b> 580 1626 for the name. Next select the PWDR data set to be linked to this phase. The 581 1627 General tab for the new phase will appear.</p> 582 1628 583 <p class=MsoNormal><img width=624 height=336 584 src="Stacking%20Faults-I_files/image026.gif"></p> 1629 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1630 id="Picture_x0020_55" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:468pt; 1631 height:173.25pt;visibility:visible;mso-wrap-style:square'> 1632 <v:imagedata src="Stacking%20Faults-I_files/image073.png" o:title=""/> 1633 </v:shape><![endif]--><![if !vml]><img width=624 height=231 1634 src="Stacking%20Faults-I_files/image085.gif" v:shapes="Picture_x0020_55"><![endif]></span></p> 585 1635 586 1636 <p class=MsoNormal>Notice that the Phase type is faulted and that Layers is one 587 1637 of the tabs; select it.</p> 588 1638 589 <p class=MsoNormal><img width=624 height=474 590 src="Stacking%20Faults-I_files/image027.gif"></p> 1639 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1640 id="Picture_x0020_56" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:468pt; 1641 height:276pt;visibility:visible;mso-wrap-style:square'> 1642 <v:imagedata src="Stacking%20Faults-I_files/image075.png" o:title=""/> 1643 </v:shape><![endif]--><![if !vml]><img width=624 height=368 1644 src="Stacking%20Faults-I_files/image086.gif" v:shapes="Picture_x0020_56"><![endif]></span></p> 591 1645 592 1646 <p class=MsoNormal>This is all the same information as for the random faults 593 1647 phase. To simulate clustering we need two new layers which are the same as 594 these two listed here. Do <b><span style='font-family:"Calibri",sans-serif'>Add 595 new layer?</span></b> twice so two new layers appear. Name them <b><span 1648 these two listed here. Do <span class=GramE><b><span style='font-family:"Calibri",sans-serif'>Add</span></b></span><b><span 1649 style='font-family:"Calibri",sans-serif'> new layer?</span></b> <span 1650 class=GramE>twice</span> so two new layers appear. Name them <b><span 596 1651 style='font-family:"Calibri",sans-serif'>layer 3</span></b> and <b><span 597 style='font-family:"Calibri",sans-serif'>layer 4</span></b>. Make layer 3 <b><span 598 style='font-family:"Calibri",sans-serif'>Same as layer</span></b> 1 (select 599 from the pull down) and layer 4 <b><span style='font-family:"Calibri",sans-serif'>Same 1652 style='font-family:"Calibri",sans-serif'>layer 4</span></b>. Make layer 3 <span 1653 class=GramE><b><span style='font-family:"Calibri",sans-serif'>Same</span></b></span><b><span 1654 style='font-family:"Calibri",sans-serif'> as layer</span></b> 1 (select from 1655 the pull down) and layer 4 <b><span style='font-family:"Calibri",sans-serif'>Same 600 1656 as layer 2</span></b>. Each time the window is redrawn so that the transition 601 1657 probability tables reflect these changes. You should also change the <b><span … … 608 1664 <p class=MsoNormal> </p> 609 1665 610 <p class=MsoNormal><img width=624 height=474 611 src="Stacking%20Faults-I_files/image028.gif"></p> 1666 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1667 id="Picture_x0020_57" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt; 1668 height:276pt;visibility:visible;mso-wrap-style:square'> 1669 <v:imagedata src="Stacking%20Faults-I_files/image077.png" o:title=""/> 1670 </v:shape><![endif]--><![if !vml]><img width=624 height=368 1671 src="Stacking%20Faults-I_files/image087.gif" v:shapes="Picture_x0020_57"><![endif]></span></p> 612 1672 613 1673 <p class=MsoNormal> </p> … … 615 1675 <p class=MsoNormal>The transition vectors for the cluster model are similar to 616 1676 the random faults model, i.e. layer 1-1 and layer 3-1 transitions are <b><span 617 style='font-family:"Calibri",sans-serif'>2/3,1/3,1</span></b> for Dx, Dy & 618 Dz, layer, and layer 2-4 and 4-4 transitions are <b><span style='font-family: 619 "Calibri",sans-serif'>-2/3,-1/3,1</span></b> for Dx, Dy & Dz. All the rest 620 are <b><span style='font-family:"Calibri",sans-serif'>0,0,1</span></b> for 621 Dx,,Dy & Dz. The probabilities can best be seen from the following array</p> 1677 style='font-family:"Calibri",sans-serif'>2/3,1/3,1</span></b> for <span 1678 class=SpellE>Dx</span>, <span class=SpellE>Dy</span> & <span class=SpellE>Dz</span>, 1679 layer, and layer 2-4 and 4-4 transitions are <b><span style='font-family:"Calibri",sans-serif'>-2/3,-1/3,1</span></b> 1680 for <span class=SpellE>Dx</span>, <span class=SpellE>Dy</span> & Dz. All 1681 the rest are <b><span style='font-family:"Calibri",sans-serif'>0<span 1682 class=GramE>,0,1</span></span></b> for <span class=SpellE>Dx</span>,,<span 1683 class=SpellE>Dy</span> & Dz. The probabilities can best be seen from the 1684 following array</p> 622 1685 623 1686 <p class=MsoNormal> </p> 624 1687 625 1688 <table class=MsoNormalTable border=0 cellspacing=0 cellpadding=0 626 style='border-collapse:collapse '>627 <tr style=' height:21.45pt'>1689 style='border-collapse:collapse;mso-yfti-tbllook:1184;mso-padding-alt:0in 0in 0in 0in'> 1690 <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;height:21.45pt'> 628 1691 <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; 629 1692 padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> … … 647 1710 </td> 648 1711 </tr> 649 <tr style=' height:21.45pt'>1712 <tr style='mso-yfti-irow:1;height:21.45pt'> 650 1713 <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; 651 1714 border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> … … 673 1736 </td> 674 1737 </tr> 675 <tr style=' height:21.45pt'>1738 <tr style='mso-yfti-irow:2;height:21.45pt'> 676 1739 <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; 677 1740 border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> … … 699 1762 </td> 700 1763 </tr> 701 <tr style=' height:21.45pt'>1764 <tr style='mso-yfti-irow:3;height:21.45pt'> 702 1765 <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; 703 1766 border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> … … 725 1788 </td> 726 1789 </tr> 727 <tr style=' height:21.45pt'>1790 <tr style='mso-yfti-irow:4;mso-yfti-lastrow:yes;height:21.45pt'> 728 1791 <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; 729 1792 border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> … … 758 1821 style='font-family:"Calibri",sans-serif'>0.1</span></b>, HS = <b><span 759 1822 style='font-family:"Calibri",sans-serif'>0.8</span></b> and HF = <b><span 760 style='font-family:"Calibri",sans-serif'>0.2</span></b>. This will give more 761 and thicker cubic blocks than hexagonal ones. Set these values and the 762 Transition tables should look like</p> 763 764 <p class=MsoNormal><img width=624 height=620 765 src="Stacking%20Faults-I_files/image029.gif"></p> 1823 style='font-family:"Calibri",sans-serif'>0.2</span></b>. This will give more and 1824 thicker cubic blocks than hexagonal ones. Set these values and the Transition 1825 tables should look like</p> 1826 1827 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1828 id="Picture_x0020_59" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:468pt; 1829 height:457.5pt;visibility:visible;mso-wrap-style:square'> 1830 <v:imagedata src="Stacking%20Faults-I_files/image079.png" o:title=""/> 1831 </v:shape><![endif]--><![if !vml]><img width=624 height=610 1832 src="Stacking%20Faults-I_files/image088.gif" v:shapes="Picture_x0020_59"><![endif]></span></p> 766 1833 767 1834 <p class=MsoNormal>Before doing the simulation we need to clear away the old … … 776 1843 will look like</p> 777 1844 778 <p class=MsoNormal><img width=624 height=535 779 src="Stacking%20Faults-I_files/image030.gif"></p> 1845 <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape 1846 id="Picture_x0020_60" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt; 1847 height:401.25pt;visibility:visible;mso-wrap-style:square'> 1848 <v:imagedata src="Stacking%20Faults-I_files/image081.png" o:title=""/> 1849 </v:shape><![endif]--><![if !vml]><img width=624 height=535 1850 src="Stacking%20Faults-I_files/image089.gif" v:shapes="Picture_x0020_60"><![endif]></span></p> 780 1851 781 1852 <p class=MsoNormal>Again, I have used <b><span style='font-family:"Calibri",sans-serif'>+</span></b> … … 790 1861 is checked otherwise youll get nonsense. This ends this stacking fault 791 1862 tutorial; the next one involves using kaolinite layers to simulate diffraction 792 patterns from kaolinite clays.< /p>1863 patterns from kaolinite clays.<o:p></o:p></p> 793 1864 794 1865 </div> 795 1866 1867 </span></span> 796 1868 </body> 797 1869
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