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| 220 | <div class=WordSection1> |
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| 221 | |
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| 222 | <h1>Stacking Fault Simulations II</h1> |
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| 223 | |
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| 224 | <p class=MsoNormal>In this exercise you will simulate some diffraction patterns |
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| 225 | from kaolinite clays. Kaolinite, Al<sub>2</sub>Si<sub>2</sub>O<sub>5</sub>(OH)<sub>4</sub>, |
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| 226 | is a 1:1 layer silicate with a single unique sheet with AlO<sub>6</sub> |
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| 227 | octahedra on one side and SiO<sub>4</sub> tetrahedra on the other. The layers |
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| 228 | stack with an offset to ideally form a triclinic C1 lattice (Bish & Von |
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| 229 | Dreele, 1989, Clay & Clay Min. 37, 289-296) for a sample of the most |
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| 230 | ordered form of kaolinite from Keokuk, Iowa. Kaolinites from other locations evidently |
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| 231 | have stacking faults so that the peaks are displaced, have peculiar shapes and |
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| 232 | are above a varying background. For the exercise we provide a laboratory |
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| 233 | Bragg-Brentano pattern of Keokuk kaolinite and a less ordered one from |
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| 234 | Washington County, Georgia (Clay Minerals Society Standard KGa-1b) collected |
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| 235 | with CuKa radiation on a Bruker instrument and thus in the Bruker RAW file |
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| 236 | format. The KGa-1b sample contains a small amount of anatase (TiO<sub>2</sub>) |
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| 237 | and the Keokuk kaolinite has some dickite (different ordered stacking of |
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| 238 | kaolinite layers).</p> |
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| 239 | |
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| 240 | <p class=MsoNormal>If you have not done so already, start GSAS-II.</p> |
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| 241 | |
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| 242 | <h2>Part 1. Creating kaolinite layer</h2> |
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| 243 | |
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| 244 | <p class=MsoNormal>In this initial step we will load in from a cif file the |
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| 245 | structure of kaolinite, draw it to see the layer structure and then transform |
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| 246 | it into forms suitable for stacking simulations. To begin do <b><span |
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| 247 | style='font-family:"Calibri",sans-serif'>Import/Phase/from CIF file</span></b>; |
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| 248 | from the file dialog select <b><span style='font-family:"Calibri",sans-serif'>kaolinite.cif</span></b>. |
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| 249 | After the are you sure popup, there will be another warning you that 4 atom |
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| 250 | types (O-H) were not recognized chemical element symbols and they were |
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| 251 | substituted by Xe to make them obvious in the atom list. Press <b><span |
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| 252 | style='font-family:"Calibri",sans-serif'>Ok</span></b>; you are offered a |
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| 253 | chance to change the phase name, I used <b><span style='font-family:"Calibri",sans-serif'>kaolinite</span></b>. |
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| 254 | The General tab is displayed (notice the presence of Xe in the element table).</p> |
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| 255 | |
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| 256 | <p class=MsoNormal><img width=930 height=500 |
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| 257 | src="Stacking%20faults%20II_files/image001.gif"></p> |
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| 258 | |
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| 259 | <p class=MsoNormal>To fix the Xe atoms (they should be O), select <b><span |
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| 260 | style='font-family:"Calibri",sans-serif'>Atoms</span></b> and then double click |
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| 261 | the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b> column |
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| 262 | heading; a small popup will appear. Select <b><span style='font-family:"Calibri",sans-serif'>Xe</span></b> |
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| 263 | & press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; |
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| 264 | the Xe atoms at the bottom of the atom table will be highlighted. Next select <b><span |
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| 265 | style='font-family:"Calibri",sans-serif'>Edit/Modify atom parameters</span></b> |
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| 266 | from the Phase Data menu; a new popup will appear.</p> |
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| 267 | |
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| 268 | <p class=MsoNormal><img width=228 height=268 |
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| 269 | src="Stacking%20faults%20II_files/image002.gif"></p> |
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| 270 | |
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| 271 | <p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>Type</span></b> |
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| 272 | & press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; a |
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| 273 | periodic table of the element will appear. Select <b><span style='font-family: |
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| 274 | "Calibri",sans-serif'>O</span></b> from the O-atom pulldown; the structure will |
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| 275 | be drawn with Al, Si & O atoms only.</p> |
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| 276 | |
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| 277 | <p class=MsoNormal><img width=479 height=358 |
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| 278 | src="Stacking%20faults%20II_files/image003.jpg"></p> |
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| 279 | |
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| 280 | <p class=MsoNormal>To better visualize the stacking layer, select the <b><span |
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| 281 | style='font-family:"Calibri",sans-serif'>Draw Atoms</span></b> tab and then |
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| 282 | double click the empty upper left corner box of the table. All atoms will turn |
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| 283 | green. Then do <b><span style='font-family:"Calibri",sans-serif'>Edit/Fill unit |
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| 284 | cell</span></b>; the structure will be redrawn with all atoms that belong in |
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| 285 | the unit cell. Finally, double click on the <b><span style='font-family:"Calibri",sans-serif'>Type</span></b> |
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| 286 | column heading, select <b><span style='font-family:"Calibri",sans-serif'>Al</span></b> |
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| 287 | & <b><span style='font-family:"Calibri",sans-serif'>Si</span></b> (they |
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| 288 | will turn green) and then do <b><span style='font-family:"Calibri",sans-serif'>Edit/Fill |
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| 289 | CN sphere</span></b>. After a bit of rotating the structure around, the |
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| 290 | layering along the c-axis (blue line) will be evident.</p> |
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| 291 | |
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| 292 | <p class=MsoNormal><img width=480 height=359 |
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| 293 | src="Stacking%20faults%20II_files/image004.jpg"></p> |
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| 294 | |
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| 295 | <p class=MsoNormal>One can easily see the layer of SiO<sub>4</sub> tetrahedra |
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| 296 | and AlO<sub>6</sub> octahedra. Also notice that the next layer (represented by |
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| 297 | the 4 O atoms at the bottom of the above drawing are offset giving a triclinic |
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| 298 | lattice.</p> |
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| 299 | |
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| 300 | <p class=MsoNormal>The stacking fault simulation calculation via DIFFaX |
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| 301 | routines requires that the stacking layers be defined in a coordinate system |
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| 302 | that has the stacking direction perpendicular to the stacking plane defined as |
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| 303 | the c-axis. This requires transformation of the unit cell and atom coordinates; |
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| 304 | a suitable tool exists in GSAS-II to do this. Select the <b><span |
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| 305 | style='font-family:"Calibri",sans-serif'>General</span></b> tab and do <b><span |
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| 306 | style='font-family:"Calibri",sans-serif'>Compute/Transform</span></b>; a popup |
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| 307 | window will appear.</p> |
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| 308 | |
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| 309 | <p class=MsoNormal><img width=350 height=339 |
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| 310 | src="Stacking%20faults%20II_files/image005.gif"></p> |
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| 311 | |
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| 312 | <p class=MsoNormal>Note that this allows one to transform the structure |
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| 313 | according to a matrix and then shift the resultant positions along some vector |
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| 314 | and then select those that are unique according to a selected space group. The |
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| 315 | pulldown gives a selection of commonly used transformations; we want the last |
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| 316 | one, <b><span style='font-family:"Calibri",sans-serif'>abc*</span></b>, which |
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| 317 | satisfies the stacking fault requirement. Select it; notice that the space |
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| 318 | group is changed to P1. Leave this as the kaolinite layer has no symmetry; in |
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| 319 | other circumstances the layer may have an inversion center in which P-1 should |
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| 320 | be used. If you press <b><span style='font-family:"Calibri",sans-serif'>Test</span></b>, |
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| 321 | the new lattice parameters will be shown.</p> |
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| 322 | |
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| 323 | <p class=MsoNormal><img width=350 height=339 |
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| 324 | src="Stacking%20faults%20II_files/image006.gif"></p> |
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| 325 | |
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| 326 | <p class=MsoNormal>The a & b axes stay the same, but c is now smaller (the |
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| 327 | interlayer distance in kaolinite) and <span style='font-family:Symbol'>a</span> |
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| 328 | & <span style='font-family:Symbol'>b</span> = 90 (<span style='font-family: |
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| 329 | Symbol'>g</span> is unchanged). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; |
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| 330 | a new phase (kaolinite abc*) will be made. Select it from the GSAS-II data tree |
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| 331 | and then select the <b><span style='font-family:"Calibri",sans-serif'>Draw |
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| 332 | Atoms</span></b> tab to see the result.</p> |
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| 333 | |
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| 334 | <p class=MsoNormal><img width=475 height=355 |
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| 335 | src="Stacking%20faults%20II_files/image007.jpg"></p> |
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| 336 | |
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| 337 | </div> |
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| 338 | |
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| 339 | </body> |
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| 340 | |
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| 341 | </html> |
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