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227 | <body lang=EN-US link=blue vlink=purple> |
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229 | <div class=WordSection1> |
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230 | |
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231 | <h1>Stacking Fault Simulations I</h1> |
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232 | |
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233 | <p class=MsoNormal>In this exercise you will use GSAS-II to simulate the |
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234 | diffraction patterns from faulted diamond. Diamond most commonly has the |
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235 | well-known cubic structure with the space group Fd3m and a=3.5668A. The C-atom |
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236 | is at 1/8,1/8,1/8 and can be viewed as a cubic stacking of ruffled hexagonal |
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237 | nets along the cubic cell 111 diagonal. </p> |
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238 | |
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239 | <p class=MsoNormal><img width=482 height=361 id="Picture 1" |
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240 | src="Stacking%20Faults-I_files/image001.jpg"></p> |
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241 | |
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242 | <p class=MsoNormal>The structure of lonsdaleite has those layers stacked |
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243 | hexagonally and thus a faulted diamond structure may occasionally have |
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244 | hexagonal stacked layers instead of all cubic ones. From geometric |
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245 | considerations, these planar stacking faults must extend across the entire |
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246 | crystal. If there are only a few such faults in a crystal then the diffraction |
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247 | pattern will show two cubic diamond patterns in a twin law relationship. |
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248 | Otherwise, if there are many such faults then the diffraction pattern will show |
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249 | streaks. To simulate the streaks one must first develop a model for the |
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250 | hexagonal net of C-atoms and then show how they stack in either the cubic or hexagonal |
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251 | forms. GSAS-II uses a suite of subroutines from the DIFFaX program (M.M.J. |
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252 | Treacy, J.M. Newsam & M.W. Deem, (1991), Proc. Roy. Soc. Lond. 433A, |
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253 | 499-520) to calculate the diffraction pattern via a general recursion algorithm |
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254 | and a randomized set of stacked layers. NB: this calculation can be quite time |
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255 | consuming particularly if unreasonable demands are made on it. </p> |
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256 | |
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257 | <p class=MsoNormal>If you have not done so already, start GSAS-II.</p> |
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258 | |
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259 | <h2>Simulation 1. Selected area diffraction for random faults in diamond</h2> |
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260 | |
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261 | <p class=MsoNormal>To begin we must have a phase to work with. In the main |
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262 | GSAS-II data tree menu do <b><span style='font-family:"Calibri",sans-serif'>Data/Add |
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263 | new phase</span></b>; a popup window will appear inviting you to name the |
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264 | phase. I entered <b><span style='font-family:"Calibri",sans-serif'>random |
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265 | faults</span></b>. Then find this phase in the data tree under phases and |
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266 | select it; the data window will display the default for the General tab.</p> |
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267 | |
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268 | <p class=MsoNormal><img width=620 height=334 id="Picture 2" |
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269 | src="Stacking%20Faults-I_files/image002.gif"></p> |
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270 | |
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271 | <p class=MsoNormal>Change the phase type to <b><span style='font-family:"Calibri",sans-serif'>faulted</span></b>; |
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272 | the window will be redrawn and a new tab (<b><span style='font-family:"Calibri",sans-serif'>Layers</span></b>) |
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273 | will appear. Select it. Then save the project; I called it <b><span |
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274 | style='font-family:"Calibri",sans-serif'>diamond</span></b>.</p> |
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275 | |
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276 | <p class=MsoNormal><img width=624 height=370 id="Picture 3" |
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277 | src="Stacking%20Faults-I_files/image003.gif"></p> |
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278 | |
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279 | <p class=MsoNormal>First you need to describe the reference unit cell for the |
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280 | stacking model. The cubic/hexagonal stacking in diamond is with layers |
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281 | perpendicular to the 111 axis. This will become the new c-axis. The a- & |
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282 | b-axes are for the hexagonal net of C-atoms that are stacked in this structure. |
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283 | One can also anticipate that the resulting diffraction pattern will have |
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284 | hexagonal <b><span style='font-family:"Calibri",sans-serif'>6/mmm</span></b> |
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285 | symmetry so first select this from the pull down box neat the top of the page; |
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286 | the window will be redrawn.</p> |
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287 | |
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288 | <p class=MsoNormal><img width=624 height=464 id="Picture 4" |
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289 | src="Stacking%20Faults-I_files/image004.gif"></p> |
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290 | |
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291 | <p class=MsoNormal>The a cell parameter for diamond stacking can be assumed to |
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292 | be a<span style='font-size:12.0pt;font-family:"Times New Roman",serif; |
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293 | position:relative;top:3.0pt'><img width=27 height=21 |
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294 | src="Stacking%20Faults-I_files/image005.gif"></span> = <b><span |
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295 | style='font-family:"Calibri",sans-serif'>2.522</span></b> and the c cell |
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296 | parameter is a<span style='font-size:12.0pt;font-family:"Times New Roman",serif; |
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297 | position:relative;top:3.0pt'><img width=27 height=21 |
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298 | src="Stacking%20Faults-I_files/image006.gif"></span> = <b><span |
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299 | style='font-family:"Calibri",sans-serif'>2.059</span></b> since there are 3 |
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300 | layers along the 111 diamond cell diagonal. Enter these in the appropriate |
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301 | places; the cell volume will be revised.</p> |
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302 | |
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303 | <p class=MsoNormal>Now we have to describe the two hexagonal nets that will be |
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304 | stacked for either cubic or hexagonal stacking. Select <b><span |
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305 | style='font-family:"Calibri",sans-serif'>Add new layer?</span></b> the window |
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306 | will be redrawn.</p> |
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307 | |
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308 | <p class=MsoNormal><img width=624 height=479 id="Picture 5" |
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309 | src="Stacking%20Faults-I_files/image007.gif"></p> |
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310 | |
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311 | <p class=MsoNormal>Name the layer (I chose <b><span style='font-family:"Calibri",sans-serif'>layer |
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312 | 1</span></b>) and choose <b><span style='font-family:"Calibri",sans-serif'>-1</span></b> |
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313 | for the layer symmetry. The window will be redrawn after changing the name. |
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314 | Next, select <b><span style='font-family:"Calibri",sans-serif'>Add atom?</span></b> |
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315 | and the window will be redrawn with one line in the layer table.</p> |
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316 | |
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317 | <p class=MsoNormal><img width=624 height=479 id="Picture 6" |
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318 | src="Stacking%20Faults-I_files/image008.gif"></p> |
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319 | |
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320 | <p class=MsoNormal>To make this a C-atom select the <b><span style='font-family: |
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321 | "Calibri",sans-serif'>Unk</span></b> under Type with a double click; a |
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322 | Periodic table will popup. Select <b><span style='font-family:"Calibri",sans-serif'>C</span></b>; |
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323 | the popup will disappear and the window will be redrawn. The coordinates of |
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324 | 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>; |
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325 | you may enter these as fractions. Select a table item to complete the entry; |
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326 | the window should show the new position.</p> |
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327 | |
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328 | <p class=MsoNormal><img width=624 height=479 id="Picture 8" |
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329 | src="Stacking%20Faults-I_files/image009.gif"></p> |
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330 | |
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331 | <p class=MsoNormal>You can draw the layer to see what it looks like; select <b><span |
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332 | style='font-family:"Calibri",sans-serif'>Draw layer?</span></b> and the drawing |
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333 | will appear. </p> |
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334 | |
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335 | <p class=MsoNormal><img width=486 height=363 id="Picture 10" |
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336 | src="Stacking%20Faults-I_files/image010.jpg"></p> |
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337 | |
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338 | <p class=MsoNormal>A unit cell box is drawn with a 5x5 suite of unit cells; the |
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339 | ruffled hexagonal net perpendicular to the c-axis (blue line) is clear.</p> |
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340 | |
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341 | <p class=MsoNormal>Now we need a second layer; repeat the steps for making a |
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342 | layer using <b><span style='font-family:"Calibri",sans-serif'>1/3,1/6,-1/8</span></b> |
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343 | for the C-atom position with <b><span style='font-family:"Calibri",sans-serif'>-1</span></b> |
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344 | for the layer symmetry. The window should look like this when done.</p> |
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345 | |
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346 | <p class=MsoNormal><img width=624 height=624 id="Picture 11" |
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347 | src="Stacking%20Faults-I_files/image011.gif"></p> |
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348 | |
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349 | <p class=MsoNormal>Ive stretched it a bit to show the Layer-Layer transition |
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350 | probabilities. Change <b><span style='font-family:"Calibri",sans-serif'>Dz</span></b> |
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351 | for each entry to <b><span style='font-family:"Calibri",sans-serif'>1.0</span></b> |
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352 | to properly space out the stacked layers. If you select the first box in the |
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353 | plot column for layer 1 you will see the two layers stacked but in a way |
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354 | reminiscent of how carbon sheets stack in graphite. </p> |
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355 | |
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356 | <p class=MsoNormal><img width=479 height=358 id="Picture 12" |
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357 | src="Stacking%20Faults-I_files/image012.jpg"></p> |
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358 | |
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359 | <p class=MsoNormal>Clearly not diamond stacking. The table defines how the next |
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360 | layer is displaced relative to the reference layer. You can shift this layer by |
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361 | using the <b><span style='font-family:"Calibri",sans-serif'>X,Y,Z</span></b> |
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362 | & <b><span style='font-family:"Calibri",sans-serif'>shift-X,Y,Z</span></b> |
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363 | keys; the plot will be redrawn and the table entry updated each time you shift |
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364 | the layer. When you get to the right offset for diamond additional bonds will |
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365 | appear connecting the layers together. The correct shift is <b><span |
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366 | style='font-family:"Calibri",sans-serif'>Dx=2/3</span></b>, <b><span |
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367 | style='font-family:"Calibri",sans-serif'>Dy=1/3</span></b> and <b><span |
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368 | style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b> for the layer 1 to |
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369 | layer 1 transition and for layer 2 to layer 2 the shifts are <b><span |
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370 | style='font-family:"Calibri",sans-serif'>Dx=-2/3</span></b>, <b><span |
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371 | style='font-family:"Calibri",sans-serif'>Dy=-1/3</span></b> and <b><span |
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372 | style='font-family:"Calibri",sans-serif'>Dz=1.0</span></b>. For the remaining |
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373 | layer 1-layer 2 and <i>vice versa</i> transitions <b><span style='font-family: |
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374 | "Calibri",sans-serif'>Dx=Dy=0</span></b>. Layer 1 to layer 1 stacking looks |
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375 | like.</p> |
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376 | |
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377 | <p class=MsoNormal><img width=477 height=357 id="Picture 13" |
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378 | src="Stacking%20Faults-I_files/image013.jpg"></p> |
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379 | |
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380 | <p class=MsoNormal>You can explore the result of various stacking sequences in |
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381 | the next block of commands; enter <b><span style='font-family:"Calibri",sans-serif'>1 |
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382 | 1 1 1 2 2 2 2</span></b> into the box and press <b><span style='font-family: |
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383 | "Calibri",sans-serif'>Enter</span></b>. A plot showing the result of a single |
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384 | twin fault will be shown.</p> |
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385 | |
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386 | <p class=MsoNormal><img width=483 height=361 id="Picture 14" |
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387 | src="Stacking%20Faults-I_files/image014.jpg"></p> |
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388 | |
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389 | <p class=MsoNormal>If you enter 1 2 1 2 1 2 1 2 then the structure of |
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390 | lonsdaleite will be shown; 1 1 1 1 1 1 or 2 2 2 2 2 2 gives the diamond |
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391 | structure. </p> |
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392 | |
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393 | <p class=MsoNormal>Finally we must select transition probabilities; they should |
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394 | sum to 1.0 for each block. Use <b><span style='font-family:"Calibri",sans-serif'>0.7</span></b> |
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395 | for layer 1 to layer 1 and layer 2 to layer 2; the cross terms are then <b><span |
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396 | style='font-family:"Calibri",sans-serif'>0.3</span></b> to give</p> |
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397 | |
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398 | <p class=MsoNormal><img width=624 height=448 |
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399 | src="Stacking%20Faults-I_files/image015.gif"></p> |
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400 | |
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401 | <p class=MsoNormal>We are now ready to do a single crystal simulation; select <b><span |
---|
402 | style='font-family:"Calibri",sans-serif'>Operations/Simulate pattern</span></b> |
---|
403 | from the Phase data window menu. A small popup will appear</p> |
---|
404 | |
---|
405 | <p class=MsoNormal><img width=279 height=136 |
---|
406 | src="Stacking%20Faults-I_files/image016.gif"></p> |
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407 | |
---|
408 | <p class=MsoNormal>Select <b><span style='font-family:"Calibri",sans-serif'>selected |
---|
409 | area</span></b> for the calculation type; the popup will be redrawn with new |
---|
410 | options.</p> |
---|
411 | |
---|
412 | <p class=MsoNormal><img width=242 height=136 id="Picture 15" |
---|
413 | src="Stacking%20Faults-I_files/image017.gif"></p> |
---|
414 | |
---|
415 | <p class=MsoNormal>To make it interesting select <b><span style='font-family: |
---|
416 | "Calibri",sans-serif'>Max. l index</span></b> of <b><span style='font-family: |
---|
417 | "Calibri",sans-serif'>6</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>. |
---|
418 | Very quickly a new popup will appear letting you know the simulation is |
---|
419 | finished; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>. |
---|
420 | The data window will be redrawn</p> |
---|
421 | |
---|
422 | <p class=MsoNormal><img width=624 height=474 id="Picture 16" |
---|
423 | src="Stacking%20Faults-I_files/image018.gif"></p> |
---|
424 | |
---|
425 | <p class=MsoNormal>At the top is a new item <b><span style='font-family:"Calibri",sans-serif'>Plot |
---|
426 | selected area diffraction?</span></b> Select it and a new plot will appear. The |
---|
427 | intensity scale is adjusted by pressing <b><span style='font-family:"Calibri",sans-serif'>D</span></b> |
---|
428 | (or <b><span style='font-family:"Calibri",sans-serif'>U</span></b>); I got</p> |
---|
429 | |
---|
430 | <p class=MsoNormal><img width=484 height=455 id="Picture 17" |
---|
431 | src="Stacking%20Faults-I_files/image019.gif"></p> |
---|
432 | |
---|
433 | <p class=MsoNormal>The streaking intermixed with sharp spots is clearly obvious |
---|
434 | in this plot. Save this project; youll need it for the next simulation.</p> |
---|
435 | |
---|
436 | <h2>Simulation 2. Laboratory powder diffraction simulation for random faults in |
---|
437 | diamond</h2> |
---|
438 | |
---|
439 | <p class=MsoNormal>The setup for a powder pattern simulation is the same as |
---|
440 | above for selected are diffraction with one crucial difference. We need a dummy |
---|
441 | powder pattern to define the simulation limits. Using the same project as |
---|
442 | above, do <b><span style='font-family:"Calibri",sans-serif'>Import/Powder |
---|
443 | data/Simulate a data set</span></b> from the main GSAS-II data tree window. A |
---|
444 | popup will appear requesting the selection of an instrument parameter file; |
---|
445 | here we will use one of the built in defaults. Press <b><span style='font-family: |
---|
446 | "Calibri",sans-serif'>Cancel</span></b> and a new popup will appear offering |
---|
447 | some choices.</p> |
---|
448 | |
---|
449 | <p class=MsoNormal><img width=322 height=268 id="Picture 18" |
---|
450 | src="Stacking%20Faults-I_files/image020.gif"></p> |
---|
451 | |
---|
452 | <p class=MsoNormal>Use the first one for <b><span style='font-family:"Calibri",sans-serif'>CuKa |
---|
453 | lab data</span></b>; a new popup will appear</p> |
---|
454 | |
---|
455 | <p class=MsoNormal><img width=318 height=342 id="Picture 19" |
---|
456 | src="Stacking%20Faults-I_files/image021.gif"></p> |
---|
457 | |
---|
458 | <p class=MsoNormal>Change the end angle to <b><span style='font-family:"Calibri",sans-serif'>150</span></b> |
---|
459 | and the step size to <b><span style='font-family:"Calibri",sans-serif'>0.02</span></b>; |
---|
460 | press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and |
---|
461 | choose <b><span style='font-family:"Calibri",sans-serif'>random faults </span></b>(your |
---|
462 | phase name). Notice the small data window lets you know that you can clear the |
---|
463 | observed intensities in the simulation by doing an <b><span style='font-family: |
---|
464 | "Calibri",sans-serif'>Edit range</span></b> (no need to change anything). The |
---|
465 | tree will have a new item <b><span style='font-family:"Calibri",sans-serif'>PWDR |
---|
466 | CW x-ray simulation</span></b>. Select <b><span style='font-family:"Calibri",sans-serif'>Background</span></b> |
---|
467 | & enter <b><span style='font-family:"Calibri",sans-serif'>50</span></b> for |
---|
468 | the 1<sup>st</sup> coefficient. Next select <b><span style='font-family:"Calibri",sans-serif'>Sample |
---|
469 | parameters</span></b> and enter <b><span style='font-family:"Calibri",sans-serif'>1000</span></b> |
---|
470 | for the <b><span style='font-family:"Calibri",sans-serif'>Histogram scale |
---|
471 | factor</span></b> and change the <b><span style='font-family:"Calibri",sans-serif'>Diffractometer |
---|
472 | type</span></b> to <b><span style='font-family:"Calibri",sans-serif'>Bragg-Brentano</span></b>. |
---|
473 | Finally, find your phase (<b><span style='font-family:"Calibri",sans-serif'>random |
---|
474 | faults</span></b>) and select it and then the <b><span style='font-family:"Calibri",sans-serif'>Layers</span></b> |
---|
475 | tab. It should be unchanged from when the selected area simulation was |
---|
476 | finished.</p> |
---|
477 | |
---|
478 | <p class=MsoNormal>To do the simulation do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate |
---|
479 | pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> |
---|
480 | from the popup. The calculated pattern will by default be broadened using U, V, |
---|
481 | & W from the Instrument parameters for the chosen powder pattern. Other |
---|
482 | choices use a mean Gaussian broadening (faster) or no broadening (even faster). |
---|
483 | The only choice for the pattern is given in the next popup; press <b><span |
---|
484 | style='font-family:"Calibri",sans-serif'>Ok</span></b> and the simulation will |
---|
485 | proceed. After a few seconds a small popup will appear letting you know it is |
---|
486 | done; press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> and |
---|
487 | the powder pattern will be displayed with the result. On the plot press the <b><span |
---|
488 | style='font-family:"Calibri",sans-serif'>+</span></b> key to suppress the + |
---|
489 | marks. The plot should look like: Ive expanded the scale to show the |
---|
490 | interesting stuff around each peak.</p> |
---|
491 | |
---|
492 | <p class=MsoNormal><img width=624 height=587 id="Picture 20" |
---|
493 | src="Stacking%20Faults-I_files/image022.gif"></p> |
---|
494 | |
---|
495 | <p class=MsoNormal>The blue line is a simulated observed pattern with imposed |
---|
496 | Poisson noise, the red line is the calculated background and the green curve is |
---|
497 | the smooth calculated pattern. A difference curve is also shown. You can play |
---|
498 | with changing the transition probabilities and/or the layer offsets to see what |
---|
499 | effect these have on the pattern; changing these will change the calculated |
---|
500 | pattern unless you reset the dummy profile as noted above.</p> |
---|
501 | |
---|
502 | <h2>Simulation 3. Sequential parameter change</h2> |
---|
503 | |
---|
504 | <p class=MsoNormal>A perhaps useful means of exploring the effects of changing |
---|
505 | stacking parameters is doing a sequence of simulations varying one parameter |
---|
506 | over a range. To try this out do Operations/Sequence simulations from the |
---|
507 | Layers menu; a popup will appear</p> |
---|
508 | |
---|
509 | <p class=MsoNormal><img width=279 height=191 id="Picture 21" |
---|
510 | src="Stacking%20Faults-I_files/image023.gif"></p> |
---|
511 | |
---|
512 | <p class=MsoNormal>Here you select the parameter, range and number of steps |
---|
513 | (both ends will be used). From the <b><span style='font-family:"Calibri",sans-serif'>Select |
---|
514 | parameter</span></b> pulldown choose <b><span style='font-family:"Calibri",sans-serif'>TransP;0;0</span></b>; |
---|
515 | this is the layer 1 to layer 1 transition probability. Then change the no. |
---|
516 | steps to <b><span style='font-family:"Calibri",sans-serif'>10</span></b> (11 |
---|
517 | will be calculated). We have the same choices for instrument broadening as |
---|
518 | above; use the default. Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; |
---|
519 | the next popup allows selection of a powder pattern (e.g. for comparison and |
---|
520 | the range for the calculation). Press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> |
---|
521 | for this one; the sequential simulation will proceed. The console displays |
---|
522 | progress and the transition matrix for each step. A popup will appear when the |
---|
523 | sequence is finished after several seconds. Notice that the matrix is not |
---|
524 | symmetric so that layer1 to layer 1 probability is not the same as layer 2 to |
---|
525 | layer 2 at each step in the simulation. We can force this by selecting <b><span |
---|
526 | style='font-family:"Calibri",sans-serif'>Symmetric probabilities?</span></b> on |
---|
527 | the Layers page. Do this and repeat the sequential simulation as above. Now the |
---|
528 | matrices are symmetric as one could expect. When the simulation is finished, |
---|
529 | select the <b><span style='font-family:"Calibri",sans-serif'>Plot sequential |
---|
530 | result?</span></b> box; a new plot will appear.</p> |
---|
531 | |
---|
532 | <p class=MsoNormal><img width=624 height=535 id="Picture 22" |
---|
533 | src="Stacking%20Faults-I_files/image024.gif"></p> |
---|
534 | |
---|
535 | <p class=MsoNormal>This is a multiline plot; you can shift the lines with the <b><span |
---|
536 | style='font-family:"Calibri",sans-serif'>U,D,L,R</span></b> keys (<b><span |
---|
537 | style='font-family:"Calibri",sans-serif'>O</span></b> resets offsets to zero). |
---|
538 | Ive done this for the next plot.</p> |
---|
539 | |
---|
540 | <p class=MsoNormal><img width=624 height=535 id="Picture 23" |
---|
541 | src="Stacking%20Faults-I_files/image025.gif"></p> |
---|
542 | |
---|
543 | <p class=MsoNormal>The first blue line is for pure hexagonal lonsdaleite |
---|
544 | stacking and the last magenta line is for pure cubic diamond stacking. You can see |
---|
545 | how some lines quickly vanish with the introduction of stacking faults while |
---|
546 | other persist across the entire sequence. This is a good place to save your |
---|
547 | project file; the sequential result will be included.</p> |
---|
548 | |
---|
549 | <h2>Simulation 4. Modelling clustering in diamond</h2> |
---|
550 | |
---|
551 | <p class=MsoNormal>In this simulation we will explore the possibility that the |
---|
552 | stacking history affects the probability of a fault. In the case of diamond, a |
---|
553 | fault to form lonsdaleite could be followed by similar layers until a lower |
---|
554 | probability fault converts the structure back to diamond. The crystal then has |
---|
555 | blocks of diamond structure interleaved with blocks of lonsdaleite. This is |
---|
556 | best done in a new phase so we dont mess up the above simulations, but most of |
---|
557 | the data in the current phase is useful for the cluster model. The easiest way |
---|
558 | is to import the new phase from the current project. <b><span style='font-family: |
---|
559 | "Calibri",sans-serif'>Do Import/Phase/from GSAS-II gpx file</span></b> from the |
---|
560 | main GSAS-II data tree menu. A file selection dialog box will appear; select |
---|
561 | the current project file (<b><span style='font-family:"Calibri",sans-serif'>diamond.gpx</span></b>) |
---|
562 | and press <b><span style='font-family:"Calibri",sans-serif'>Open</span></b>. A |
---|
563 | small popup will appear confirming your choice; press <b><span |
---|
564 | style='font-family:"Calibri",sans-serif'>Yes</span></b>. The next popup offers |
---|
565 | the change to name the phase, I chose <b><span style='font-family:"Calibri",sans-serif'>clustered</span></b> |
---|
566 | for the name. Next select the PWDR data set to be linked to this phase. The |
---|
567 | General tab for the new phase will appear.</p> |
---|
568 | |
---|
569 | <p class=MsoNormal><img width=624 height=336 id="Picture 24" |
---|
570 | src="Stacking%20Faults-I_files/image026.gif"></p> |
---|
571 | |
---|
572 | <p class=MsoNormal>Notice that the Phase type is faulted and that Layers is one |
---|
573 | of the tabs; select it.</p> |
---|
574 | |
---|
575 | <p class=MsoNormal><img width=624 height=474 id="Picture 26" |
---|
576 | src="Stacking%20Faults-I_files/image027.gif"></p> |
---|
577 | |
---|
578 | <p class=MsoNormal>This is all the same information as for the random faults |
---|
579 | phase. To simulate clustering we need two new layers which are the same as |
---|
580 | these two listed here. Do <b><span style='font-family:"Calibri",sans-serif'>Add |
---|
581 | new layer?</span></b> twice so two new layers appear. Name them <b><span |
---|
582 | style='font-family:"Calibri",sans-serif'>layer 3</span></b> and <b><span |
---|
583 | style='font-family:"Calibri",sans-serif'>layer 4</span></b>. Make layer 3 <b><span |
---|
584 | style='font-family:"Calibri",sans-serif'>Same as layer</span></b> 1 (select |
---|
585 | from the pull down) and layer 4 <b><span style='font-family:"Calibri",sans-serif'>Same |
---|
586 | as layer 2</span></b>. Each time the window is redrawn so that the transition |
---|
587 | probability tables reflect these changes. You should also change the <b><span |
---|
588 | style='font-family:"Calibri",sans-serif'>Diffraction Laue symmetry</span></b> |
---|
589 | to <b><span style='font-family:"Calibri",sans-serif'>-3m</span></b>. When you |
---|
590 | are done the upper part of the Layers window should look like.</p> |
---|
591 | |
---|
592 | <p class=MsoNormal> </p> |
---|
593 | |
---|
594 | <p class=MsoNormal> </p> |
---|
595 | |
---|
596 | <p class=MsoNormal><img width=624 height=474 id="Picture 28" |
---|
597 | src="Stacking%20Faults-I_files/image028.gif"></p> |
---|
598 | |
---|
599 | <p class=MsoNormal> </p> |
---|
600 | |
---|
601 | <p class=MsoNormal>The transition vectors for the cluster model are similar to |
---|
602 | the random faults model, i.e. layer 1-1 and layer 3-1 transitions are <b><span |
---|
603 | style='font-family:"Calibri",sans-serif'>2/3,1/3,1</span></b> for Dx, Dy & |
---|
604 | Dz, layer, and layer 2-4 and 4-4 transitions are <b><span style='font-family: |
---|
605 | "Calibri",sans-serif'>-2/3,-1/3,1</span></b> for Dx, Dy & Dz. All the rest |
---|
606 | are <b><span style='font-family:"Calibri",sans-serif'>0,0,1</span></b> for |
---|
607 | Dx,,Dy & Dz. The probabilities can best be seen from the following array</p> |
---|
608 | |
---|
609 | <p class=MsoNormal> </p> |
---|
610 | |
---|
611 | <table class=MsoTableGrid border=1 cellspacing=0 cellpadding=0 |
---|
612 | style='border-collapse:collapse;border:none'> |
---|
613 | <tr style='height:21.45pt'> |
---|
614 | <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; |
---|
615 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
616 | <p class=MsoNormal>Layer</p> |
---|
617 | </td> |
---|
618 | <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; |
---|
619 | border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
620 | <p class=MsoNormal>1</p> |
---|
621 | </td> |
---|
622 | <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; |
---|
623 | border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
624 | <p class=MsoNormal>2</p> |
---|
625 | </td> |
---|
626 | <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; |
---|
627 | border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
628 | <p class=MsoNormal>3</p> |
---|
629 | </td> |
---|
630 | <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; |
---|
631 | border-left:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
632 | <p class=MsoNormal>4</p> |
---|
633 | </td> |
---|
634 | </tr> |
---|
635 | <tr style='height:21.45pt'> |
---|
636 | <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; |
---|
637 | border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
638 | <p class=MsoNormal>1</p> |
---|
639 | </td> |
---|
640 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
641 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
642 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
643 | <p class=MsoNormal>CS</p> |
---|
644 | </td> |
---|
645 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
646 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
647 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
648 | <p class=MsoNormal>CF</p> |
---|
649 | </td> |
---|
650 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
651 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
652 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
653 | <p class=MsoNormal>x</p> |
---|
654 | </td> |
---|
655 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
656 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
657 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
658 | <p class=MsoNormal>x</p> |
---|
659 | </td> |
---|
660 | </tr> |
---|
661 | <tr style='height:21.45pt'> |
---|
662 | <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; |
---|
663 | border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
664 | <p class=MsoNormal>2</p> |
---|
665 | </td> |
---|
666 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
667 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
668 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
669 | <p class=MsoNormal>x</p> |
---|
670 | </td> |
---|
671 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
672 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
673 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
674 | <p class=MsoNormal>x</p> |
---|
675 | </td> |
---|
676 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
677 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
678 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
679 | <p class=MsoNormal>HS</p> |
---|
680 | </td> |
---|
681 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
682 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
683 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
684 | <p class=MsoNormal>HF</p> |
---|
685 | </td> |
---|
686 | </tr> |
---|
687 | <tr style='height:21.45pt'> |
---|
688 | <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; |
---|
689 | border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
690 | <p class=MsoNormal>3</p> |
---|
691 | </td> |
---|
692 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
693 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
694 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
695 | <p class=MsoNormal>HF</p> |
---|
696 | </td> |
---|
697 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
698 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
699 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
700 | <p class=MsoNormal>HS</p> |
---|
701 | </td> |
---|
702 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
703 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
704 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
705 | <p class=MsoNormal>x</p> |
---|
706 | </td> |
---|
707 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
708 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
709 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
710 | <p class=MsoNormal>x</p> |
---|
711 | </td> |
---|
712 | </tr> |
---|
713 | <tr style='height:21.45pt'> |
---|
714 | <td width=72 valign=top style='width:54.05pt;border:solid windowtext 1.0pt; |
---|
715 | border-top:none;padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
716 | <p class=MsoNormal>4</p> |
---|
717 | </td> |
---|
718 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
719 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
720 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
---|
721 | <p class=MsoNormal>x</p> |
---|
722 | </td> |
---|
723 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
724 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
725 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
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726 | <p class=MsoNormal>x</p> |
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727 | </td> |
---|
728 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
729 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
730 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
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731 | <p class=MsoNormal>CF</p> |
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732 | </td> |
---|
733 | <td width=72 valign=top style='width:54.05pt;border-top:none;border-left: |
---|
734 | none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; |
---|
735 | padding:0in 5.4pt 0in 5.4pt;height:21.45pt'> |
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736 | <p class=MsoNormal>CS</p> |
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737 | </td> |
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738 | </tr> |
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739 | </table> |
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740 | |
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741 | <p class=MsoNormal>Where CS cubic stacking, CF cubic fault, HS hexagonal |
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742 | stacking, HF hexagonal fault and x not allowed. A suitable model might be |
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743 | CS = <b><span style='font-family:"Calibri",sans-serif'>0.9</span></b>, CF = <b><span |
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744 | style='font-family:"Calibri",sans-serif'>0.1</span></b>, HS = <b><span |
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745 | style='font-family:"Calibri",sans-serif'>0.8</span></b> and HF = <b><span |
---|
746 | style='font-family:"Calibri",sans-serif'>0.2</span></b>. This will give more |
---|
747 | and thicker cubic blocks than hexagonal ones. Set these values and the |
---|
748 | Transition tables should look like</p> |
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749 | |
---|
750 | <p class=MsoNormal><img width=624 height=620 id="Picture 29" |
---|
751 | src="Stacking%20Faults-I_files/image029.gif"></p> |
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752 | |
---|
753 | <p class=MsoNormal>Before doing the simulation we need to clear away the old |
---|
754 | one; select the <b><span style='font-family:"Calibri",sans-serif'>PWDR</span></b> |
---|
755 | entry from the GSAS-II data tree and then select <b><span style='font-family: |
---|
756 | "Calibri",sans-serif'>Edit range</span></b> from the data window. Dont change |
---|
757 | anything, just press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b>; |
---|
758 | this will clear the previous simulation. Then return to the clustered phase |
---|
759 | Layers tab. Do <b><span style='font-family:"Calibri",sans-serif'>Operations/Simulate |
---|
760 | pattern</span></b> and press <b><span style='font-family:"Calibri",sans-serif'>Ok</span></b> |
---|
761 | twice. The simulation will require some seconds to finish; the powder profile |
---|
762 | will look like</p> |
---|
763 | |
---|
764 | <p class=MsoNormal><img width=624 height=535 id="Picture 30" |
---|
765 | src="Stacking%20Faults-I_files/image030.gif"></p> |
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766 | |
---|
767 | <p class=MsoNormal>Again, I have used <b><span style='font-family:"Calibri",sans-serif'>+</span></b> |
---|
768 | and zoomed in to show the interesting part of the pattern. </p> |
---|
769 | |
---|
770 | <p class=MsoNormal>As additional work you can do sequential simulations to |
---|
771 | explore the effect of changing probabilities. Try varying <b><span |
---|
772 | style='font-family:"Calibri",sans-serif'>TransP;0;0</span></b>, i.e. layer 1 |
---|
773 | layer 1 (CS) transition probability and <b><span style='font-family:"Calibri",sans-serif'>TransP;2;1</span></b>, |
---|
774 | i.e. layer 3 layer 2 (HS) transition probability. Be sure the <b><span |
---|
775 | style='font-family:"Calibri",sans-serif'>Symmetric probabilities</span></b> box |
---|
776 | is checked otherwise youll get nonsense. This ends this stacking fault |
---|
777 | tutorial; the next one involves using kaolinite layers to simulate diffraction |
---|
778 | patterns from kaolinite clays.</p> |
---|
779 | |
---|
780 | </div> |
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781 | |
---|
782 | </body> |
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783 | |
---|
784 | </html> |
---|