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19 | o\:* {behavior:url(#default#VML);} |
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20 | w\:* {behavior:url(#default#VML);} |
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21 | .shape {behavior:url(#default#VML);} |
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22 | </style> |
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24 | <o:DocumentProperties> |
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25 | <o:Author>Von Dreele</o:Author> |
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26 | <o:LastAuthor>Von Dreele</o:LastAuthor> |
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27 | <o:Revision>9</o:Revision> |
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28 | <o:TotalTime>2142</o:TotalTime> |
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29 | <o:Created>2015-05-14T17:06:00Z</o:Created> |
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30 | <o:LastSaved>2015-05-14T17:39:00Z</o:LastSaved> |
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31 | <o:Pages>1</o:Pages> |
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32 | <o:Words>4340</o:Words> |
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33 | <o:Characters>24741</o:Characters> |
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34 | <o:Company>Argonne National Laboratory</o:Company> |
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35 | <o:Lines>206</o:Lines> |
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36 | <o:Paragraphs>58</o:Paragraphs> |
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37 | <o:CharactersWithSpaces>29023</o:CharactersWithSpaces> |
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38 | <o:Version>15.00</o:Version> |
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192 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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196 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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198 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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200 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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206 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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208 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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210 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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212 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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213 | Name="List Number 2"/> |
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214 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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215 | Name="List Number 3"/> |
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216 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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218 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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219 | Name="List Number 5"/> |
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220 | <w:LsdException Locked="false" Priority="10" QFormat="true" Name="Title"/> |
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221 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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222 | Name="Closing"/> |
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223 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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229 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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230 | Name="Body Text Indent"/> |
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231 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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232 | Name="List Continue"/> |
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233 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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235 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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236 | Name="List Continue 3"/> |
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237 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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238 | Name="List Continue 4"/> |
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239 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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240 | Name="List Continue 5"/> |
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241 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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242 | Name="Message Header"/> |
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243 | <w:LsdException Locked="false" Priority="11" QFormat="true" Name="Subtitle"/> |
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244 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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245 | Name="Salutation"/> |
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246 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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247 | Name="Date"/> |
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248 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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249 | Name="Body Text First Indent"/> |
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250 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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251 | Name="Body Text First Indent 2"/> |
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252 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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253 | Name="Note Heading"/> |
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254 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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255 | Name="Body Text 2"/> |
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256 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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257 | Name="Body Text 3"/> |
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258 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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259 | Name="Body Text Indent 2"/> |
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260 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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261 | Name="Body Text Indent 3"/> |
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262 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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263 | Name="Block Text"/> |
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264 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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265 | Name="Hyperlink"/> |
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266 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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267 | Name="FollowedHyperlink"/> |
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268 | <w:LsdException Locked="false" Priority="22" QFormat="true" Name="Strong"/> |
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269 | <w:LsdException Locked="false" Priority="20" QFormat="true" Name="Emphasis"/> |
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270 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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271 | Name="Document Map"/> |
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272 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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273 | Name="Plain Text"/> |
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274 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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275 | Name="E-mail Signature"/> |
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276 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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277 | Name="HTML Top of Form"/> |
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278 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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279 | Name="HTML Bottom of Form"/> |
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280 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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281 | Name="Normal (Web)"/> |
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282 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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283 | Name="HTML Acronym"/> |
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284 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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285 | Name="HTML Address"/> |
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286 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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287 | Name="HTML Cite"/> |
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288 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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289 | Name="HTML Code"/> |
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290 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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291 | Name="HTML Definition"/> |
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292 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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293 | Name="HTML Keyboard"/> |
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294 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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295 | Name="HTML Preformatted"/> |
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296 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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297 | Name="HTML Sample"/> |
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298 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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299 | Name="HTML Typewriter"/> |
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300 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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301 | Name="HTML Variable"/> |
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302 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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303 | Name="Normal Table"/> |
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304 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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305 | Name="annotation subject"/> |
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306 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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307 | Name="No List"/> |
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308 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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309 | Name="Outline List 1"/> |
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310 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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311 | Name="Outline List 2"/> |
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312 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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313 | Name="Outline List 3"/> |
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314 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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315 | Name="Table Simple 1"/> |
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316 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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317 | Name="Table Simple 2"/> |
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318 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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319 | Name="Table Simple 3"/> |
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320 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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321 | Name="Table Classic 1"/> |
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322 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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323 | Name="Table Classic 2"/> |
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324 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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325 | Name="Table Classic 3"/> |
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326 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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327 | Name="Table Classic 4"/> |
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328 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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329 | Name="Table Colorful 1"/> |
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330 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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331 | Name="Table Colorful 2"/> |
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332 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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333 | Name="Table Colorful 3"/> |
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334 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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335 | Name="Table Columns 1"/> |
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336 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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337 | Name="Table Columns 2"/> |
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338 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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339 | Name="Table Columns 3"/> |
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340 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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341 | Name="Table Columns 4"/> |
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342 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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343 | Name="Table Columns 5"/> |
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344 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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345 | Name="Table Grid 1"/> |
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346 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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347 | Name="Table Grid 2"/> |
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348 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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349 | Name="Table Grid 3"/> |
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350 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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351 | Name="Table Grid 4"/> |
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352 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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353 | Name="Table Grid 5"/> |
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354 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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355 | Name="Table Grid 6"/> |
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356 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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357 | Name="Table Grid 7"/> |
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358 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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359 | Name="Table Grid 8"/> |
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360 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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361 | Name="Table List 1"/> |
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362 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
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363 | Name="Table List 2"/> |
---|
364 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
365 | Name="Table List 3"/> |
---|
366 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
367 | Name="Table List 4"/> |
---|
368 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
369 | Name="Table List 5"/> |
---|
370 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
371 | Name="Table List 6"/> |
---|
372 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
373 | Name="Table List 7"/> |
---|
374 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
375 | Name="Table List 8"/> |
---|
376 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
377 | Name="Table 3D effects 1"/> |
---|
378 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
379 | Name="Table 3D effects 2"/> |
---|
380 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
381 | Name="Table 3D effects 3"/> |
---|
382 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
383 | Name="Table Contemporary"/> |
---|
384 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
385 | Name="Table Elegant"/> |
---|
386 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
387 | Name="Table Professional"/> |
---|
388 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
389 | Name="Table Subtle 1"/> |
---|
390 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
391 | Name="Table Subtle 2"/> |
---|
392 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
393 | Name="Table Web 1"/> |
---|
394 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
395 | Name="Table Web 2"/> |
---|
396 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
397 | Name="Table Web 3"/> |
---|
398 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
399 | Name="Balloon Text"/> |
---|
400 | <w:LsdException Locked="false" Priority="59" Name="Table Grid"/> |
---|
401 | <w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true" |
---|
402 | Name="Table Theme"/> |
---|
403 | <w:LsdException Locked="false" SemiHidden="true" Name="Placeholder Text"/> |
---|
404 | <w:LsdException Locked="false" Priority="1" QFormat="true" Name="No Spacing"/> |
---|
405 | <w:LsdException Locked="false" Priority="60" Name="Light Shading"/> |
---|
406 | <w:LsdException Locked="false" Priority="61" Name="Light List"/> |
---|
407 | <w:LsdException Locked="false" Priority="62" Name="Light Grid"/> |
---|
408 | <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/> |
---|
409 | <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2"/> |
---|
410 | <w:LsdException Locked="false" Priority="65" Name="Medium List 1"/> |
---|
411 | <w:LsdException Locked="false" Priority="66" Name="Medium List 2"/> |
---|
412 | <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/> |
---|
413 | <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2"/> |
---|
414 | <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/> |
---|
415 | <w:LsdException Locked="false" Priority="70" Name="Dark List"/> |
---|
416 | <w:LsdException Locked="false" Priority="71" Name="Colorful Shading"/> |
---|
417 | <w:LsdException Locked="false" Priority="72" Name="Colorful List"/> |
---|
418 | <w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/> |
---|
419 | <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/> |
---|
420 | <w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/> |
---|
421 | <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/> |
---|
422 | <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/> |
---|
423 | <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/> |
---|
424 | <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/> |
---|
425 | <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/> |
---|
426 | <w:LsdException Locked="false" Priority="34" QFormat="true" |
---|
427 | Name="List Paragraph"/> |
---|
428 | <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/> |
---|
429 | <w:LsdException Locked="false" Priority="30" QFormat="true" |
---|
430 | Name="Intense Quote"/> |
---|
431 | <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/> |
---|
432 | <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/> |
---|
433 | <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/> |
---|
434 | <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/> |
---|
435 | <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/> |
---|
436 | <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/> |
---|
437 | <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/> |
---|
438 | <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/> |
---|
439 | <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/> |
---|
440 | <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/> |
---|
441 | <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/> |
---|
442 | <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/> |
---|
443 | <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/> |
---|
444 | <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/> |
---|
445 | <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/> |
---|
446 | <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/> |
---|
447 | <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/> |
---|
448 | <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/> |
---|
449 | <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/> |
---|
450 | <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/> |
---|
451 | <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/> |
---|
452 | <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/> |
---|
453 | <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/> |
---|
454 | <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/> |
---|
455 | <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/> |
---|
456 | <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/> |
---|
457 | <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/> |
---|
458 | <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/> |
---|
459 | <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/> |
---|
460 | <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/> |
---|
461 | <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/> |
---|
462 | <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/> |
---|
463 | <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/> |
---|
464 | <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/> |
---|
465 | <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/> |
---|
466 | <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/> |
---|
467 | <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/> |
---|
468 | <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/> |
---|
469 | <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/> |
---|
470 | <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/> |
---|
471 | <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/> |
---|
472 | <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/> |
---|
473 | <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/> |
---|
474 | <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/> |
---|
475 | <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/> |
---|
476 | <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/> |
---|
477 | <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/> |
---|
478 | <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/> |
---|
479 | <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/> |
---|
480 | <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/> |
---|
481 | <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/> |
---|
482 | <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/> |
---|
483 | <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/> |
---|
484 | <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/> |
---|
485 | <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/> |
---|
486 | <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/> |
---|
487 | <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/> |
---|
488 | <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/> |
---|
489 | <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/> |
---|
490 | <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/> |
---|
491 | <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/> |
---|
492 | <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/> |
---|
493 | <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/> |
---|
494 | <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/> |
---|
495 | <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/> |
---|
496 | <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/> |
---|
497 | <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/> |
---|
498 | <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/> |
---|
499 | <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/> |
---|
500 | <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/> |
---|
501 | <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/> |
---|
502 | <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/> |
---|
503 | <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/> |
---|
504 | <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/> |
---|
505 | <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/> |
---|
506 | <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/> |
---|
507 | <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/> |
---|
508 | <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/> |
---|
509 | <w:LsdException Locked="false" Priority="19" QFormat="true" |
---|
510 | Name="Subtle Emphasis"/> |
---|
511 | <w:LsdException Locked="false" Priority="21" QFormat="true" |
---|
512 | Name="Intense Emphasis"/> |
---|
513 | <w:LsdException Locked="false" Priority="31" QFormat="true" |
---|
514 | Name="Subtle Reference"/> |
---|
515 | <w:LsdException Locked="false" Priority="32" QFormat="true" |
---|
516 | Name="Intense Reference"/> |
---|
517 | <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/> |
---|
518 | <w:LsdException Locked="false" Priority="37" SemiHidden="true" |
---|
519 | UnhideWhenUsed="true" Name="Bibliography"/> |
---|
520 | <w:LsdException Locked="false" Priority="39" SemiHidden="true" |
---|
521 | UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/> |
---|
522 | <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/> |
---|
523 | <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/> |
---|
524 | <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/> |
---|
525 | <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/> |
---|
526 | <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/> |
---|
527 | <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/> |
---|
528 | <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/> |
---|
529 | <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/> |
---|
530 | <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/> |
---|
531 | <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/> |
---|
532 | <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/> |
---|
533 | <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/> |
---|
534 | <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/> |
---|
535 | <w:LsdException Locked="false" Priority="46" |
---|
536 | Name="Grid Table 1 Light Accent 1"/> |
---|
537 | <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/> |
---|
538 | <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/> |
---|
539 | <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/> |
---|
540 | <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/> |
---|
541 | <w:LsdException Locked="false" Priority="51" |
---|
542 | Name="Grid Table 6 Colorful Accent 1"/> |
---|
543 | <w:LsdException Locked="false" Priority="52" |
---|
544 | Name="Grid Table 7 Colorful Accent 1"/> |
---|
545 | <w:LsdException Locked="false" Priority="46" |
---|
546 | Name="Grid Table 1 Light Accent 2"/> |
---|
547 | <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/> |
---|
548 | <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/> |
---|
549 | <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/> |
---|
550 | <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/> |
---|
551 | <w:LsdException Locked="false" Priority="51" |
---|
552 | Name="Grid Table 6 Colorful Accent 2"/> |
---|
553 | <w:LsdException Locked="false" Priority="52" |
---|
554 | Name="Grid Table 7 Colorful Accent 2"/> |
---|
555 | <w:LsdException Locked="false" Priority="46" |
---|
556 | Name="Grid Table 1 Light Accent 3"/> |
---|
557 | <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/> |
---|
558 | <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/> |
---|
559 | <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/> |
---|
560 | <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/> |
---|
561 | <w:LsdException Locked="false" Priority="51" |
---|
562 | Name="Grid Table 6 Colorful Accent 3"/> |
---|
563 | <w:LsdException Locked="false" Priority="52" |
---|
564 | Name="Grid Table 7 Colorful Accent 3"/> |
---|
565 | <w:LsdException Locked="false" Priority="46" |
---|
566 | Name="Grid Table 1 Light Accent 4"/> |
---|
567 | <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/> |
---|
568 | <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/> |
---|
569 | <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/> |
---|
570 | <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/> |
---|
571 | <w:LsdException Locked="false" Priority="51" |
---|
572 | Name="Grid Table 6 Colorful Accent 4"/> |
---|
573 | <w:LsdException Locked="false" Priority="52" |
---|
574 | Name="Grid Table 7 Colorful Accent 4"/> |
---|
575 | <w:LsdException Locked="false" Priority="46" |
---|
576 | Name="Grid Table 1 Light Accent 5"/> |
---|
577 | <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/> |
---|
578 | <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/> |
---|
579 | <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/> |
---|
580 | <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/> |
---|
581 | <w:LsdException Locked="false" Priority="51" |
---|
582 | Name="Grid Table 6 Colorful Accent 5"/> |
---|
583 | <w:LsdException Locked="false" Priority="52" |
---|
584 | Name="Grid Table 7 Colorful Accent 5"/> |
---|
585 | <w:LsdException Locked="false" Priority="46" |
---|
586 | Name="Grid Table 1 Light Accent 6"/> |
---|
587 | <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/> |
---|
588 | <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/> |
---|
589 | <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/> |
---|
590 | <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/> |
---|
591 | <w:LsdException Locked="false" Priority="51" |
---|
592 | Name="Grid Table 6 Colorful Accent 6"/> |
---|
593 | <w:LsdException Locked="false" Priority="52" |
---|
594 | Name="Grid Table 7 Colorful Accent 6"/> |
---|
595 | <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/> |
---|
596 | <w:LsdException Locked="false" Priority="47" Name="List Table 2"/> |
---|
597 | <w:LsdException Locked="false" Priority="48" Name="List Table 3"/> |
---|
598 | <w:LsdException Locked="false" Priority="49" Name="List Table 4"/> |
---|
599 | <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/> |
---|
600 | <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/> |
---|
601 | <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/> |
---|
602 | <w:LsdException Locked="false" Priority="46" |
---|
603 | Name="List Table 1 Light Accent 1"/> |
---|
604 | <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/> |
---|
605 | <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/> |
---|
606 | <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/> |
---|
607 | <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/> |
---|
608 | <w:LsdException Locked="false" Priority="51" |
---|
609 | Name="List Table 6 Colorful Accent 1"/> |
---|
610 | <w:LsdException Locked="false" Priority="52" |
---|
611 | Name="List Table 7 Colorful Accent 1"/> |
---|
612 | <w:LsdException Locked="false" Priority="46" |
---|
613 | Name="List Table 1 Light Accent 2"/> |
---|
614 | <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/> |
---|
615 | <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/> |
---|
616 | <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/> |
---|
617 | <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/> |
---|
618 | <w:LsdException Locked="false" Priority="51" |
---|
619 | Name="List Table 6 Colorful Accent 2"/> |
---|
620 | <w:LsdException Locked="false" Priority="52" |
---|
621 | Name="List Table 7 Colorful Accent 2"/> |
---|
622 | <w:LsdException Locked="false" Priority="46" |
---|
623 | Name="List Table 1 Light Accent 3"/> |
---|
624 | <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/> |
---|
625 | <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/> |
---|
626 | <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/> |
---|
627 | <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/> |
---|
628 | <w:LsdException Locked="false" Priority="51" |
---|
629 | Name="List Table 6 Colorful Accent 3"/> |
---|
630 | <w:LsdException Locked="false" Priority="52" |
---|
631 | Name="List Table 7 Colorful Accent 3"/> |
---|
632 | <w:LsdException Locked="false" Priority="46" |
---|
633 | Name="List Table 1 Light Accent 4"/> |
---|
634 | <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/> |
---|
635 | <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/> |
---|
636 | <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/> |
---|
637 | <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/> |
---|
638 | <w:LsdException Locked="false" Priority="51" |
---|
639 | Name="List Table 6 Colorful Accent 4"/> |
---|
640 | <w:LsdException Locked="false" Priority="52" |
---|
641 | Name="List Table 7 Colorful Accent 4"/> |
---|
642 | <w:LsdException Locked="false" Priority="46" |
---|
643 | Name="List Table 1 Light Accent 5"/> |
---|
644 | <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/> |
---|
645 | <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/> |
---|
646 | <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/> |
---|
647 | <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/> |
---|
648 | <w:LsdException Locked="false" Priority="51" |
---|
649 | Name="List Table 6 Colorful Accent 5"/> |
---|
650 | <w:LsdException Locked="false" Priority="52" |
---|
651 | Name="List Table 7 Colorful Accent 5"/> |
---|
652 | <w:LsdException Locked="false" Priority="46" |
---|
653 | Name="List Table 1 Light Accent 6"/> |
---|
654 | <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/> |
---|
655 | <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/> |
---|
656 | <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/> |
---|
657 | <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/> |
---|
658 | <w:LsdException Locked="false" Priority="51" |
---|
659 | Name="List Table 6 Colorful Accent 6"/> |
---|
660 | <w:LsdException Locked="false" Priority="52" |
---|
661 | Name="List Table 7 Colorful Accent 6"/> |
---|
662 | </w:LatentStyles> |
---|
663 | </xml><![endif]--> |
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664 | <style> |
---|
665 | <!-- |
---|
666 | /* Font Definitions */ |
---|
667 | @font-face |
---|
668 | {font-family:"Cambria Math"; |
---|
669 | panose-1:2 4 5 3 5 4 6 3 2 4; |
---|
670 | mso-font-charset:0; |
---|
671 | mso-generic-font-family:roman; |
---|
672 | mso-font-pitch:variable; |
---|
673 | mso-font-signature:-536870145 1107305727 0 0 415 0;} |
---|
674 | @font-face |
---|
675 | {font-family:Calibri; |
---|
676 | panose-1:2 15 5 2 2 2 4 3 2 4; |
---|
677 | mso-font-charset:0; |
---|
678 | mso-generic-font-family:swiss; |
---|
679 | mso-font-pitch:variable; |
---|
680 | mso-font-signature:-536870145 1073786111 1 0 415 0;} |
---|
681 | @font-face |
---|
682 | {font-family:Tahoma; |
---|
683 | panose-1:2 11 6 4 3 5 4 4 2 4; |
---|
684 | mso-font-charset:0; |
---|
685 | mso-generic-font-family:swiss; |
---|
686 | mso-font-pitch:variable; |
---|
687 | mso-font-signature:-520081665 -1073717157 41 0 66047 0;} |
---|
688 | /* Style Definitions */ |
---|
689 | p.MsoNormal, li.MsoNormal, div.MsoNormal |
---|
690 | {mso-style-unhide:no; |
---|
691 | mso-style-qformat:yes; |
---|
692 | mso-style-parent:""; |
---|
693 | margin-top:0in; |
---|
694 | margin-right:0in; |
---|
695 | margin-bottom:4.0pt; |
---|
696 | margin-left:0in; |
---|
697 | mso-pagination:widow-orphan; |
---|
698 | font-size:12.0pt; |
---|
699 | font-family:"Times New Roman",serif; |
---|
700 | mso-fareast-font-family:"Times New Roman"; |
---|
701 | mso-fareast-theme-font:minor-fareast;} |
---|
702 | h1 |
---|
703 | {mso-style-priority:9; |
---|
704 | mso-style-unhide:no; |
---|
705 | mso-style-qformat:yes; |
---|
706 | mso-style-link:"Heading 1 Char"; |
---|
707 | mso-margin-top-alt:auto; |
---|
708 | margin-right:0in; |
---|
709 | mso-margin-bottom-alt:auto; |
---|
710 | margin-left:0in; |
---|
711 | mso-pagination:widow-orphan; |
---|
712 | mso-outline-level:1; |
---|
713 | font-size:24.0pt; |
---|
714 | font-family:"Times New Roman",serif; |
---|
715 | mso-fareast-font-family:"Times New Roman"; |
---|
716 | mso-fareast-theme-font:minor-fareast; |
---|
717 | font-weight:bold;} |
---|
718 | h2 |
---|
719 | {mso-style-noshow:yes; |
---|
720 | mso-style-priority:9; |
---|
721 | mso-style-qformat:yes; |
---|
722 | mso-style-link:"Heading 2 Char"; |
---|
723 | mso-margin-top-alt:auto; |
---|
724 | margin-right:0in; |
---|
725 | mso-margin-bottom-alt:auto; |
---|
726 | margin-left:0in; |
---|
727 | mso-pagination:widow-orphan; |
---|
728 | mso-outline-level:2; |
---|
729 | font-size:18.0pt; |
---|
730 | font-family:"Times New Roman",serif; |
---|
731 | mso-fareast-font-family:"Times New Roman"; |
---|
732 | mso-fareast-theme-font:minor-fareast; |
---|
733 | font-weight:bold;} |
---|
734 | h3 |
---|
735 | {mso-style-noshow:yes; |
---|
736 | mso-style-priority:9; |
---|
737 | mso-style-qformat:yes; |
---|
738 | mso-style-link:"Heading 3 Char"; |
---|
739 | mso-margin-top-alt:auto; |
---|
740 | margin-right:0in; |
---|
741 | mso-margin-bottom-alt:auto; |
---|
742 | margin-left:0in; |
---|
743 | mso-pagination:widow-orphan; |
---|
744 | mso-outline-level:3; |
---|
745 | font-size:13.5pt; |
---|
746 | font-family:"Times New Roman",serif; |
---|
747 | mso-fareast-font-family:"Times New Roman"; |
---|
748 | mso-fareast-theme-font:minor-fareast; |
---|
749 | font-weight:bold;} |
---|
750 | h4 |
---|
751 | {mso-style-noshow:yes; |
---|
752 | mso-style-priority:9; |
---|
753 | mso-style-qformat:yes; |
---|
754 | mso-style-link:"Heading 4 Char"; |
---|
755 | mso-style-next:Normal; |
---|
756 | margin-top:10.0pt; |
---|
757 | margin-right:0in; |
---|
758 | margin-bottom:4.0pt; |
---|
759 | margin-left:0in; |
---|
760 | mso-pagination:widow-orphan lines-together; |
---|
761 | page-break-after:avoid; |
---|
762 | mso-outline-level:4; |
---|
763 | font-size:13.0pt; |
---|
764 | font-family:"Cambria",serif; |
---|
765 | mso-ascii-font-family:Cambria; |
---|
766 | mso-ascii-theme-font:major-latin; |
---|
767 | mso-fareast-font-family:"Times New Roman"; |
---|
768 | mso-fareast-theme-font:major-fareast; |
---|
769 | mso-hansi-font-family:Cambria; |
---|
770 | mso-hansi-theme-font:major-latin; |
---|
771 | mso-bidi-font-family:"Times New Roman"; |
---|
772 | mso-bidi-theme-font:major-bidi; |
---|
773 | color:#4F81BD; |
---|
774 | mso-themecolor:accent1; |
---|
775 | font-weight:bold; |
---|
776 | font-style:italic;} |
---|
777 | h5 |
---|
778 | {mso-style-noshow:yes; |
---|
779 | mso-style-priority:9; |
---|
780 | mso-style-qformat:yes; |
---|
781 | mso-style-link:"Heading 5 Char"; |
---|
782 | mso-margin-top-alt:auto; |
---|
783 | margin-right:0in; |
---|
784 | mso-margin-bottom-alt:auto; |
---|
785 | margin-left:0in; |
---|
786 | mso-pagination:widow-orphan; |
---|
787 | mso-outline-level:5; |
---|
788 | font-size:12.0pt; |
---|
789 | font-family:"Times New Roman",serif; |
---|
790 | mso-fareast-font-family:"Times New Roman"; |
---|
791 | mso-fareast-theme-font:minor-fareast; |
---|
792 | color:#4F4FFF; |
---|
793 | font-weight:bold;} |
---|
794 | p.MsoTitle, li.MsoTitle, div.MsoTitle |
---|
795 | {mso-style-noshow:yes; |
---|
796 | mso-style-priority:10; |
---|
797 | mso-style-unhide:no; |
---|
798 | mso-style-qformat:yes; |
---|
799 | mso-style-link:"Title Char"; |
---|
800 | mso-style-next:Normal; |
---|
801 | margin-top:0in; |
---|
802 | margin-right:0in; |
---|
803 | margin-bottom:15.0pt; |
---|
804 | margin-left:0in; |
---|
805 | mso-add-space:auto; |
---|
806 | mso-pagination:widow-orphan; |
---|
807 | border:none; |
---|
808 | mso-border-bottom-alt:solid #4F81BD 1.0pt; |
---|
809 | mso-border-bottom-themecolor:accent1; |
---|
810 | padding:0in; |
---|
811 | mso-padding-alt:0in 0in 4.0pt 0in; |
---|
812 | font-size:26.0pt; |
---|
813 | font-family:"Cambria",serif; |
---|
814 | mso-ascii-font-family:Cambria; |
---|
815 | mso-ascii-theme-font:major-latin; |
---|
816 | mso-fareast-font-family:"Times New Roman"; |
---|
817 | mso-fareast-theme-font:major-fareast; |
---|
818 | mso-hansi-font-family:Cambria; |
---|
819 | mso-hansi-theme-font:major-latin; |
---|
820 | mso-bidi-font-family:"Times New Roman"; |
---|
821 | mso-bidi-theme-font:major-bidi; |
---|
822 | color:#17365D; |
---|
823 | mso-themecolor:text2; |
---|
824 | mso-themeshade:191; |
---|
825 | letter-spacing:.25pt; |
---|
826 | mso-font-kerning:14.0pt;} |
---|
827 | p.MsoTitleCxSpFirst, li.MsoTitleCxSpFirst, div.MsoTitleCxSpFirst |
---|
828 | {mso-style-noshow:yes; |
---|
829 | mso-style-priority:10; |
---|
830 | mso-style-unhide:no; |
---|
831 | mso-style-qformat:yes; |
---|
832 | mso-style-link:"Title Char"; |
---|
833 | mso-style-next:Normal; |
---|
834 | mso-style-type:export-only; |
---|
835 | margin:0in; |
---|
836 | margin-bottom:.0001pt; |
---|
837 | mso-add-space:auto; |
---|
838 | mso-pagination:widow-orphan; |
---|
839 | border:none; |
---|
840 | mso-border-bottom-alt:solid #4F81BD 1.0pt; |
---|
841 | mso-border-bottom-themecolor:accent1; |
---|
842 | padding:0in; |
---|
843 | mso-padding-alt:0in 0in 4.0pt 0in; |
---|
844 | font-size:26.0pt; |
---|
845 | font-family:"Cambria",serif; |
---|
846 | mso-ascii-font-family:Cambria; |
---|
847 | mso-ascii-theme-font:major-latin; |
---|
848 | mso-fareast-font-family:"Times New Roman"; |
---|
849 | mso-fareast-theme-font:major-fareast; |
---|
850 | mso-hansi-font-family:Cambria; |
---|
851 | mso-hansi-theme-font:major-latin; |
---|
852 | mso-bidi-font-family:"Times New Roman"; |
---|
853 | mso-bidi-theme-font:major-bidi; |
---|
854 | color:#17365D; |
---|
855 | mso-themecolor:text2; |
---|
856 | mso-themeshade:191; |
---|
857 | letter-spacing:.25pt; |
---|
858 | mso-font-kerning:14.0pt;} |
---|
859 | p.MsoTitleCxSpMiddle, li.MsoTitleCxSpMiddle, div.MsoTitleCxSpMiddle |
---|
860 | {mso-style-noshow:yes; |
---|
861 | mso-style-priority:10; |
---|
862 | mso-style-unhide:no; |
---|
863 | mso-style-qformat:yes; |
---|
864 | mso-style-link:"Title Char"; |
---|
865 | mso-style-next:Normal; |
---|
866 | mso-style-type:export-only; |
---|
867 | margin:0in; |
---|
868 | margin-bottom:.0001pt; |
---|
869 | mso-add-space:auto; |
---|
870 | mso-pagination:widow-orphan; |
---|
871 | border:none; |
---|
872 | mso-border-bottom-alt:solid #4F81BD 1.0pt; |
---|
873 | mso-border-bottom-themecolor:accent1; |
---|
874 | padding:0in; |
---|
875 | mso-padding-alt:0in 0in 4.0pt 0in; |
---|
876 | font-size:26.0pt; |
---|
877 | font-family:"Cambria",serif; |
---|
878 | mso-ascii-font-family:Cambria; |
---|
879 | mso-ascii-theme-font:major-latin; |
---|
880 | mso-fareast-font-family:"Times New Roman"; |
---|
881 | mso-fareast-theme-font:major-fareast; |
---|
882 | mso-hansi-font-family:Cambria; |
---|
883 | mso-hansi-theme-font:major-latin; |
---|
884 | mso-bidi-font-family:"Times New Roman"; |
---|
885 | mso-bidi-theme-font:major-bidi; |
---|
886 | color:#17365D; |
---|
887 | mso-themecolor:text2; |
---|
888 | mso-themeshade:191; |
---|
889 | letter-spacing:.25pt; |
---|
890 | mso-font-kerning:14.0pt;} |
---|
891 | p.MsoTitleCxSpLast, li.MsoTitleCxSpLast, div.MsoTitleCxSpLast |
---|
892 | {mso-style-noshow:yes; |
---|
893 | mso-style-priority:10; |
---|
894 | mso-style-unhide:no; |
---|
895 | mso-style-qformat:yes; |
---|
896 | mso-style-link:"Title Char"; |
---|
897 | mso-style-next:Normal; |
---|
898 | mso-style-type:export-only; |
---|
899 | margin-top:0in; |
---|
900 | margin-right:0in; |
---|
901 | margin-bottom:15.0pt; |
---|
902 | margin-left:0in; |
---|
903 | mso-add-space:auto; |
---|
904 | mso-pagination:widow-orphan; |
---|
905 | border:none; |
---|
906 | mso-border-bottom-alt:solid #4F81BD 1.0pt; |
---|
907 | mso-border-bottom-themecolor:accent1; |
---|
908 | padding:0in; |
---|
909 | mso-padding-alt:0in 0in 4.0pt 0in; |
---|
910 | font-size:26.0pt; |
---|
911 | font-family:"Cambria",serif; |
---|
912 | mso-ascii-font-family:Cambria; |
---|
913 | mso-ascii-theme-font:major-latin; |
---|
914 | mso-fareast-font-family:"Times New Roman"; |
---|
915 | mso-fareast-theme-font:major-fareast; |
---|
916 | mso-hansi-font-family:Cambria; |
---|
917 | mso-hansi-theme-font:major-latin; |
---|
918 | mso-bidi-font-family:"Times New Roman"; |
---|
919 | mso-bidi-theme-font:major-bidi; |
---|
920 | color:#17365D; |
---|
921 | mso-themecolor:text2; |
---|
922 | mso-themeshade:191; |
---|
923 | letter-spacing:.25pt; |
---|
924 | mso-font-kerning:14.0pt;} |
---|
925 | a:link, span.MsoHyperlink |
---|
926 | {mso-style-noshow:yes; |
---|
927 | mso-style-priority:99; |
---|
928 | color:blue; |
---|
929 | text-decoration:underline; |
---|
930 | text-underline:single;} |
---|
931 | a:visited, span.MsoHyperlinkFollowed |
---|
932 | {mso-style-noshow:yes; |
---|
933 | mso-style-priority:99; |
---|
934 | color:purple; |
---|
935 | text-decoration:underline; |
---|
936 | text-underline:single;} |
---|
937 | p.MsoDocumentMap, li.MsoDocumentMap, div.MsoDocumentMap |
---|
938 | {mso-style-noshow:yes; |
---|
939 | mso-style-priority:99; |
---|
940 | mso-style-link:"Document Map Char"; |
---|
941 | margin-top:0in; |
---|
942 | margin-right:0in; |
---|
943 | margin-bottom:4.0pt; |
---|
944 | margin-left:0in; |
---|
945 | mso-pagination:widow-orphan; |
---|
946 | font-size:8.0pt; |
---|
947 | font-family:"Tahoma",sans-serif; |
---|
948 | mso-fareast-font-family:"Times New Roman"; |
---|
949 | mso-fareast-theme-font:minor-fareast;} |
---|
950 | p |
---|
951 | {mso-style-noshow:yes; |
---|
952 | mso-style-priority:99; |
---|
953 | mso-margin-top-alt:auto; |
---|
954 | margin-right:0in; |
---|
955 | mso-margin-bottom-alt:auto; |
---|
956 | margin-left:0in; |
---|
957 | mso-pagination:widow-orphan; |
---|
958 | font-size:12.0pt; |
---|
959 | font-family:"Times New Roman",serif; |
---|
960 | mso-fareast-font-family:"Times New Roman"; |
---|
961 | mso-fareast-theme-font:minor-fareast;} |
---|
962 | pre |
---|
963 | {mso-style-noshow:yes; |
---|
964 | mso-style-priority:99; |
---|
965 | mso-style-link:"HTML Preformatted Char"; |
---|
966 | margin-top:0in; |
---|
967 | margin-right:0in; |
---|
968 | margin-bottom:4.0pt; |
---|
969 | margin-left:0in; |
---|
970 | mso-pagination:widow-orphan; |
---|
971 | tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; |
---|
972 | font-size:10.0pt; |
---|
973 | font-family:"Courier New"; |
---|
974 | mso-fareast-font-family:"Times New Roman";} |
---|
975 | p.MsoAcetate, li.MsoAcetate, div.MsoAcetate |
---|
976 | {mso-style-noshow:yes; |
---|
977 | mso-style-priority:99; |
---|
978 | mso-style-link:"Balloon Text Char"; |
---|
979 | margin-top:0in; |
---|
980 | margin-right:0in; |
---|
981 | margin-bottom:4.0pt; |
---|
982 | margin-left:0in; |
---|
983 | mso-pagination:widow-orphan; |
---|
984 | font-size:8.0pt; |
---|
985 | font-family:"Tahoma",sans-serif; |
---|
986 | mso-fareast-font-family:"Times New Roman"; |
---|
987 | mso-fareast-theme-font:minor-fareast;} |
---|
988 | span.MsoPlaceholderText |
---|
989 | {mso-style-noshow:yes; |
---|
990 | mso-style-priority:99; |
---|
991 | mso-style-unhide:no; |
---|
992 | color:gray;} |
---|
993 | p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing |
---|
994 | {mso-style-noshow:yes; |
---|
995 | mso-style-priority:1; |
---|
996 | mso-style-unhide:no; |
---|
997 | mso-style-qformat:yes; |
---|
998 | mso-style-parent:""; |
---|
999 | margin-top:0in; |
---|
1000 | margin-right:0in; |
---|
1001 | margin-bottom:4.0pt; |
---|
1002 | margin-left:0in; |
---|
1003 | mso-pagination:widow-orphan; |
---|
1004 | font-size:12.0pt; |
---|
1005 | font-family:"Times New Roman",serif; |
---|
1006 | mso-fareast-font-family:"Times New Roman"; |
---|
1007 | mso-fareast-theme-font:minor-fareast;} |
---|
1008 | p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph |
---|
1009 | {mso-style-noshow:yes; |
---|
1010 | mso-style-priority:34; |
---|
1011 | mso-style-unhide:no; |
---|
1012 | mso-style-qformat:yes; |
---|
1013 | margin-top:0in; |
---|
1014 | margin-right:0in; |
---|
1015 | margin-bottom:4.0pt; |
---|
1016 | margin-left:.5in; |
---|
1017 | mso-add-space:auto; |
---|
1018 | mso-pagination:widow-orphan; |
---|
1019 | font-size:12.0pt; |
---|
1020 | font-family:"Times New Roman",serif; |
---|
1021 | mso-fareast-font-family:"Times New Roman"; |
---|
1022 | mso-fareast-theme-font:minor-fareast;} |
---|
1023 | p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst |
---|
1024 | {mso-style-noshow:yes; |
---|
1025 | mso-style-priority:34; |
---|
1026 | mso-style-unhide:no; |
---|
1027 | mso-style-qformat:yes; |
---|
1028 | mso-style-type:export-only; |
---|
1029 | margin-top:0in; |
---|
1030 | margin-right:0in; |
---|
1031 | margin-bottom:0in; |
---|
1032 | margin-left:.5in; |
---|
1033 | margin-bottom:.0001pt; |
---|
1034 | mso-add-space:auto; |
---|
1035 | mso-pagination:widow-orphan; |
---|
1036 | font-size:12.0pt; |
---|
1037 | font-family:"Times New Roman",serif; |
---|
1038 | mso-fareast-font-family:"Times New Roman"; |
---|
1039 | mso-fareast-theme-font:minor-fareast;} |
---|
1040 | p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle |
---|
1041 | {mso-style-noshow:yes; |
---|
1042 | mso-style-priority:34; |
---|
1043 | mso-style-unhide:no; |
---|
1044 | mso-style-qformat:yes; |
---|
1045 | mso-style-type:export-only; |
---|
1046 | margin-top:0in; |
---|
1047 | margin-right:0in; |
---|
1048 | margin-bottom:0in; |
---|
1049 | margin-left:.5in; |
---|
1050 | margin-bottom:.0001pt; |
---|
1051 | mso-add-space:auto; |
---|
1052 | mso-pagination:widow-orphan; |
---|
1053 | font-size:12.0pt; |
---|
1054 | font-family:"Times New Roman",serif; |
---|
1055 | mso-fareast-font-family:"Times New Roman"; |
---|
1056 | mso-fareast-theme-font:minor-fareast;} |
---|
1057 | p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast |
---|
1058 | {mso-style-noshow:yes; |
---|
1059 | mso-style-priority:34; |
---|
1060 | mso-style-unhide:no; |
---|
1061 | mso-style-qformat:yes; |
---|
1062 | mso-style-type:export-only; |
---|
1063 | margin-top:0in; |
---|
1064 | margin-right:0in; |
---|
1065 | margin-bottom:4.0pt; |
---|
1066 | margin-left:.5in; |
---|
1067 | mso-add-space:auto; |
---|
1068 | mso-pagination:widow-orphan; |
---|
1069 | font-size:12.0pt; |
---|
1070 | font-family:"Times New Roman",serif; |
---|
1071 | mso-fareast-font-family:"Times New Roman"; |
---|
1072 | mso-fareast-theme-font:minor-fareast;} |
---|
1073 | span.MsoIntenseReference |
---|
1074 | {mso-style-priority:32; |
---|
1075 | mso-style-unhide:no; |
---|
1076 | mso-style-qformat:yes; |
---|
1077 | font-variant:small-caps; |
---|
1078 | color:#C0504D; |
---|
1079 | mso-themecolor:accent2; |
---|
1080 | letter-spacing:.25pt; |
---|
1081 | font-weight:bold; |
---|
1082 | text-decoration:underline; |
---|
1083 | text-underline:single;} |
---|
1084 | span.Heading1Char |
---|
1085 | {mso-style-name:"Heading 1 Char"; |
---|
1086 | mso-style-priority:9; |
---|
1087 | mso-style-unhide:no; |
---|
1088 | mso-style-locked:yes; |
---|
1089 | mso-style-link:"Heading 1"; |
---|
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1410 | |
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1412 | |
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1413 | <div class=WordSection1> |
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1414 | |
---|
1415 | <h1 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
1416 | 0in;line-height:115%'>Texture analysis of 2D data in GSAS-II</h1> |
---|
1417 | |
---|
1418 | <h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
1419 | 0in;line-height:115%'>Introduction</h2> |
---|
1420 | |
---|
1421 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Texture |
---|
1422 | analysis using GSAS-II employs spherical harmonics modeling, as described by |
---|
1423 | Bunge, "Texture Analysis in Materials Science" (1982), and |
---|
1424 | implemented by Von Dreele, J. Appl. <span class=SpellE>Cryst</span>., <b |
---|
1425 | style='mso-bidi-font-weight:normal'>30</b>, 517-525 (1997) in GSAS. The even |
---|
1426 | part of the orientation distribution function (ODF) via the general axis |
---|
1427 | equation</p> |
---|
1428 | |
---|
1429 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc |
---|
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---|
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---|
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---|
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---|
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---|
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---|
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---|
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---|
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---|
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1453 | "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-fareast-font-family: |
---|
1454 | "Times New Roman";mso-hansi-font-family:"Cambria Math";font-style:italic; |
---|
1455 | mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i |
---|
1456 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1457 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:nary><m:naryPr><m:chr |
---|
1458 | m:val="∑"/><m:limLoc m:val="undOvr"/><span style='font-family: |
---|
1459 | "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-fareast-font-family: |
---|
1460 | "Times New Roman";mso-hansi-font-family:"Cambria Math";font-style:italic; |
---|
1461 | mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i |
---|
1462 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1463 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span |
---|
1464 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1465 | mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math"; |
---|
1466 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i |
---|
1467 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i |
---|
1468 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1469 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary></m:e></m:nary><m:sSubSup><m:sSubSupPr><span |
---|
1470 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1471 | mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math"; |
---|
1472 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i |
---|
1473 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1474 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1475 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><i |
---|
1476 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(h)</m:r></span></i><m:sSubSup><m:sSubSupPr><span |
---|
1477 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1478 | mso-fareast-font-family:"Times New Roman";mso-hansi-font-family:"Cambria Math"; |
---|
1479 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i |
---|
1480 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1481 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1482 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i |
---|
1483 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span |
---|
1484 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1485 | "Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US; |
---|
1486 | mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shapetype |
---|
1487 | id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" |
---|
1488 | path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> |
---|
1489 | <v:stroke joinstyle="miter"/> |
---|
1490 | <v:formulas> |
---|
1491 | <v:f eqn="if lineDrawn pixelLineWidth 0"/> |
---|
1492 | <v:f eqn="sum @0 1 0"/> |
---|
1493 | <v:f eqn="sum 0 0 @1"/> |
---|
1494 | <v:f eqn="prod @2 1 2"/> |
---|
1495 | <v:f eqn="prod @3 21600 pixelWidth"/> |
---|
1496 | <v:f eqn="prod @3 21600 pixelHeight"/> |
---|
1497 | <v:f eqn="sum @0 0 1"/> |
---|
1498 | <v:f eqn="prod @6 1 2"/> |
---|
1499 | <v:f eqn="prod @7 21600 pixelWidth"/> |
---|
1500 | <v:f eqn="sum @8 21600 0"/> |
---|
1501 | <v:f eqn="prod @7 21600 pixelHeight"/> |
---|
1502 | <v:f eqn="sum @10 21600 0"/> |
---|
1503 | </v:formulas> |
---|
1504 | <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> |
---|
1505 | <o:lock v:ext="edit" aspectratio="t"/> |
---|
1506 | </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:267.75pt; |
---|
1507 | height:42pt'> |
---|
1508 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image001.png" |
---|
1509 | o:title="" chromakey="white"/> |
---|
1510 | </v:shape><![endif]--><![if !vml]><img width=357 height=56 |
---|
1511 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image002.png" |
---|
1512 | v:shapes="_x0000_i1025"><![endif]></span><![endif]></p> |
---|
1513 | |
---|
1514 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
1515 | margin-left:0in;line-height:115%'><span class=GramE>is</span> used to give the |
---|
1516 | intensity corrections due to texture. The two harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
1517 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1518 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1519 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
1520 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1521 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1522 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span |
---|
1523 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1524 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1525 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style: |
---|
1526 | normal'><span style='font-family:"Cambria Math",serif'><m:r>h</m:r></span></i></m:e></m:d></m:oMath><![endif]--><![if !msEquation]><span |
---|
1527 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1528 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
1529 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
1530 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
1531 | type="#_x0000_t75" style='width:32.25pt;height:26.25pt'> |
---|
1532 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image003.png" |
---|
1533 | o:title="" chromakey="white"/> |
---|
1534 | </v:shape><![endif]--><![if !vml]><img width=43 height=35 |
---|
1535 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image004.png" |
---|
1536 | v:shapes="_x0000_i1025"><![endif]></span><![endif]><span |
---|
1537 | style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
1538 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1539 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1540 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
1541 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1542 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1543 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i |
---|
1544 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
1545 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1546 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
1547 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
1548 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
1549 | type="#_x0000_t75" style='width:30pt;height:26.25pt'> |
---|
1550 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png" |
---|
1551 | o:title="" chromakey="white"/> |
---|
1552 | </v:shape><![endif]--><![if !vml]><img width=40 height=35 |
---|
1553 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png" |
---|
1554 | v:shapes="_x0000_i1025"><![endif]></span><![endif]>, take on values according |
---|
1555 | to the crystal and sample symmetries, respectively, and thus the two inner |
---|
1556 | summations are over only the resulting unique, nonzero harmonic terms. These |
---|
1557 | unique terms are automatically selected by <span style='mso-bidi-font-weight: |
---|
1558 | bold'>GSAS-II</span> according to the space group symmetry and the user chosen |
---|
1559 | sample symmetry. The available sample symmetries are cylindrical symmetry, 2/m, |
---|
1560 | mmm and no symmetry. The choice of sample symmetry profoundly affects the |
---|
1561 | selection of harmonic coefficients. For example, in the case of cylindrical |
---|
1562 | sample symmetry (fiber texture) only <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
1563 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1564 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1565 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
1566 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1567 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1568 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:sup></m:sSubSup><i |
---|
1569 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
1570 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1571 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
1572 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
1573 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
1574 | type="#_x0000_t75" style='width:29.25pt;height:26.25pt'> |
---|
1575 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image007.png" |
---|
1576 | o:title="" chromakey="white"/> |
---|
1577 | </v:shape><![endif]--><![if !vml]><img width=39 height=35 |
---|
1578 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image008.png" |
---|
1579 | v:shapes="_x0000_i1025"><![endif]></span><![endif]><span |
---|
1580 | style='mso-spacerun:yes'> </span>terms are nonzero so the rest are excluded |
---|
1581 | from the <span class=GramE>summations</span> and the set of <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
1582 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1583 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1584 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
1585 | normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i |
---|
1586 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1587 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>0</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span |
---|
1588 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1589 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
1590 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
1591 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
1592 | type="#_x0000_t75" style='width:21pt;height:26.25pt'> |
---|
1593 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image009.png" |
---|
1594 | o:title="" chromakey="white"/> |
---|
1595 | </v:shape><![endif]--><![if !vml]><img width=28 height=35 |
---|
1596 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image010.png" |
---|
1597 | v:shapes="_x0000_i1025"><![endif]></span><![endif]>coefficients is sufficient |
---|
1598 | to describe the effect on the diffraction patterns due to texture. The crystal |
---|
1599 | harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
1600 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1601 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1602 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
1603 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1604 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1605 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i |
---|
1606 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(h)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
1607 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1608 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
1609 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
1610 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
1611 | type="#_x0000_t75" style='width:32.25pt;height:26.25pt'> |
---|
1612 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image011.png" |
---|
1613 | o:title="" chromakey="white"/> |
---|
1614 | </v:shape><![endif]--><![if !vml]><img width=43 height=35 |
---|
1615 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image012.png" |
---|
1616 | v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined for each |
---|
1617 | reflection, h, <i>via</i> polar and azimuthal coordinates (<span |
---|
1618 | style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>) |
---|
1619 | of a unit vector coincident with h relative to the reciprocal lattice. For most |
---|
1620 | crystal symmetries, <span style='font-family:Symbol'>f</span> is the angle |
---|
1621 | between h and the n-<span class=SpellE>th</span> order major rotation axis of |
---|
1622 | the space group (usually the c-axis) and <span style='font-family:Symbol'>b</span> |
---|
1623 | is the angle between the projections of h and any secondary axis (usually the |
---|
1624 | a-axis) onto the normal plane.<span style='mso-spacerun:yes'> </span>In a |
---|
1625 | similar way the sample harmonic factor, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
1626 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1627 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1628 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
1629 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1630 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1631 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i |
---|
1632 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>y</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
1633 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1634 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
1635 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
1636 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
1637 | type="#_x0000_t75" style='width:30pt;height:26.25pt'> |
---|
1638 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image005.png" |
---|
1639 | o:title="" chromakey="white"/> |
---|
1640 | </v:shape><![endif]--><![if !vml]><img width=40 height=35 |
---|
1641 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image006.png" |
---|
1642 | v:shapes="_x0000_i1025"><![endif]></span><![endif]>, is defined according to |
---|
1643 | polar and azimuthal coordinates (<span style='font-family:Symbol'>y</span>, <span |
---|
1644 | style='font-family:Symbol'>g</span>) of a unit vector coincident with the |
---|
1645 | diffraction vector relative to a coordinate system attached to the external |
---|
1646 | form of the sample. For example, in the case of a rolled steel plate having mmm |
---|
1647 | symmetry, the polar angle, <span style='font-family:Symbol'>y</span>, is |
---|
1648 | frequently measured from the normal direction (ND) and <span style='font-family: |
---|
1649 | Symbol'>g</span> is then measured from the rolling direction (RD) in the TD |
---|
1650 | (transverse direction) - RD plane.<span style='mso-spacerun:yes'> </span>Thus, |
---|
1651 | the general axis equation becomes</p> |
---|
1652 | |
---|
1653 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
1654 | margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc |
---|
1655 | m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span |
---|
1656 | style='font-family:"Cambria Math",serif'><m:r>A</m:r></span></i><m:d><m:dPr><span |
---|
1657 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1658 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1659 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style: |
---|
1660 | normal'><span style='font-family:"Cambria Math",serif'><m:r>ϕ</m:r><m:r>,</m:r><m:r>β</m:r><m:r>,</m:r><m:r>ψ</m:r><m:r>,</m:r><m:r>γ</m:r></span></i></m:e></m:d><i |
---|
1661 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=1+</m:r></span></i><m:nary><m:naryPr><m:chr |
---|
1662 | m:val="∑"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif; |
---|
1663 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
1664 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i |
---|
1665 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>=2</m:r></span></i></m:sub><m:sup><m:sSub><m:sSubPr><span |
---|
1666 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1667 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1668 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style: |
---|
1669 | normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i |
---|
1670 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub></m:sSub></m:sup><m:e><m:f><m:fPr><span |
---|
1671 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1672 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1673 | normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style: |
---|
1674 | normal'><span style='font-family:"Cambria Math",serif'><m:r>4</m:r><m:r>π</m:r></span></i></m:num><m:den><i |
---|
1675 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>L</m:r><m:r>+1</m:r></span></i></m:den></m:f></m:e></m:nary><m:nary><m:naryPr><m:chr |
---|
1676 | m:val="∑"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif; |
---|
1677 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
1678 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i |
---|
1679 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1680 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:nary><m:naryPr><m:chr |
---|
1681 | m:val="∑"/><m:limLoc m:val="undOvr"/><span style='font-family: |
---|
1682 | "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family: |
---|
1683 | "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i |
---|
1684 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1685 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span |
---|
1686 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1687 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1688 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i |
---|
1689 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i |
---|
1690 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1691 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:sSubSup><m:sSubSupPr><span |
---|
1692 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1693 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1694 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i |
---|
1695 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1696 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1697 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span |
---|
1698 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1699 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1700 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style: |
---|
1701 | normal'><span style='font-family:"Cambria Math",serif'><m:r>φ</m:r><m:r>,</m:r><m:r>β</m:r></span></i></m:e></m:d></m:e></m:nary><m:sSubSup><m:sSubSupPr><span |
---|
1702 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1703 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1704 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
1705 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1706 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1707 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i |
---|
1708 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>ψ</m:r><m:r>,</m:r><m:r>γ</m:r><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span |
---|
1709 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1710 | "Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US; |
---|
1711 | mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape |
---|
1712 | id="_x0000_i1025" type="#_x0000_t75" style='width:321pt;height:54pt'> |
---|
1713 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image013.png" |
---|
1714 | o:title="" chromakey="white"/> |
---|
1715 | </v:shape><![endif]--><![if !vml]><img width=428 height=72 |
---|
1716 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image014.png" |
---|
1717 | v:shapes="_x0000_i1025"><![endif]></span><![endif]><br style='mso-special-character: |
---|
1718 | line-break'> |
---|
1719 | <![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'> |
---|
1720 | <![endif]></p> |
---|
1721 | |
---|
1722 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In a |
---|
1723 | diffraction experiment the crystal reflection coordinates (<span |
---|
1724 | style='font-family:Symbol'>f</span>, <span style='font-family:Symbol'>b</span>) |
---|
1725 | are determined by the choice of reflection index (<span class=SpellE>hkl</span>) |
---|
1726 | while the sample coordinates (<span style='font-family:Symbol'>y</span>, <span |
---|
1727 | style='font-family:Symbol'>g</span>) are determined by the sample orientation |
---|
1728 | on the diffractometer.</p> |
---|
1729 | |
---|
1730 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
1731 | margin-left:0in;line-height:115%'>To define the sample coordinates (<span |
---|
1732 | style='font-family:Symbol'>y</span>, <span style='font-family:Symbol'>g</span>), |
---|
1733 | we have defined an instrument coordinate system (I, J, K) such that K is normal |
---|
1734 | to the diffraction plane and J is coincident with the direction of the incident |
---|
1735 | radiation beam toward the source. We further define a standard set of |
---|
1736 | right-handed goniometer <span class=SpellE>eulerian</span> angles (<span |
---|
1737 | style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>, |
---|
1738 | <span style='font-family:Symbol'>F</span>) so that <span style='font-family: |
---|
1739 | Symbol'>W</span> and <span style='font-family:Symbol'>F</span> are rotations |
---|
1740 | about K and <span style='font-family:Symbol'>C</span> is a rotation about J |
---|
1741 | when <span style='font-family:Symbol'>W</span> <span style='font-family:Symbol'><span |
---|
1742 | style='mso-spacerun:yes'> </span></span>= 0.<span style='mso-spacerun:yes'> |
---|
1743 | </span>Finally, as the sample may be mounted so that the sample coordinate |
---|
1744 | system (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>) |
---|
1745 | does not coincide with the instrument coordinate system (I, J, K), we define |
---|
1746 | three <span class=SpellE>eulerian</span> sample rotation offset angles (<span |
---|
1747 | style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>, |
---|
1748 | <span style='font-family:Symbol'>F</span><sub>s</sub>) that describe the |
---|
1749 | rotation from (I<sub>s</sub>, <span class=SpellE>J<sub>s</sub></span>, K<sub>s</sub>) |
---|
1750 | to (I, J, K).<span style='mso-spacerun:yes'> </span>The sample rotation angles |
---|
1751 | are defined so that with the goniometer angles at zero <span style='font-family: |
---|
1752 | Symbol'>W</span><sub>s</sub> and <span style='font-family:Symbol'>F</span><sub>s</sub> |
---|
1753 | are rotations about I and <span style='font-family:Symbol'>C</span><sub>s</sub> |
---|
1754 | is a rotation about J.<span style='mso-spacerun:yes'> </span>The zeros of |
---|
1755 | these three sample rotation angles can be refined as part of the Rietveld |
---|
1756 | analysis to accommodate any angular offset in sample mounting. After including |
---|
1757 | the diffraction angle, <span style='font-family:Symbol'>Q</span>, and a |
---|
1758 | detector azimuthal angle, A, the full rotation matrix, <b style='mso-bidi-font-weight: |
---|
1759 | normal'>M</b>, is </p> |
---|
1760 | |
---|
1761 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
1762 | margin-left:0in;line-height:115%'><b style='mso-bidi-font-weight:normal'>M = -</b><b |
---|
1763 | style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>Q</span>A</b><b |
---|
1764 | style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>W<span |
---|
1765 | class=GramE>C<span style='font-family:"Times New Roman",serif'>(</span></span>F</span>+</b><b |
---|
1766 | style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>F</span><sub>s</sub>)</b><b |
---|
1767 | style='mso-bidi-font-weight:normal'><span style='font-family:Symbol'>C</span><span |
---|
1768 | class=SpellE><sub>s</sub><span style='font-family:Symbol'>W</span><sub>s</sub></span><o:p></o:p></b></p> |
---|
1769 | |
---|
1770 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
1771 | margin-left:0in;line-height:115%'>By transformation of unit Cartesian vectors |
---|
1772 | (100, 010 and 001) with this rotation matrix, the sample orientation |
---|
1773 | coordinates (<span style='font-family:Symbol'>y</span>, <span style='font-family: |
---|
1774 | Symbol'>g</span>) are given by</p> |
---|
1775 | |
---|
1776 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
1777 | margin-left:0in;line-height:115%'><span class=GramE><i>cos</i>(</span><span |
---|
1778 | style='font-family:Symbol'>y</span>) = <!--[if gte msEquation 12]><m:oMath><i |
---|
1779 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span |
---|
1780 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1781 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1782 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count |
---|
1783 | m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span |
---|
1784 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1785 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1786 | normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i |
---|
1787 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i |
---|
1788 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i |
---|
1789 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:oMath><![endif]--><![if !msEquation]><span |
---|
1790 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1791 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
1792 | top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
1793 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
1794 | type="#_x0000_t75" style='width:33.75pt;height:50.25pt'> |
---|
1795 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image015.png" |
---|
1796 | o:title="" chromakey="white"/> |
---|
1797 | </v:shape><![endif]--><![if !vml]><img width=45 height=67 |
---|
1798 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image016.png" |
---|
1799 | v:shapes="_x0000_i1025"><![endif]></span><![endif]><span |
---|
1800 | style='mso-spacerun:yes'> </span>and<span style='mso-spacerun:yes'> </span><i>tan</i>(<span |
---|
1801 | style='font-family:Symbol'>g</span>) = <!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:type |
---|
1802 | m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family: |
---|
1803 | "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic; |
---|
1804 | mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i |
---|
1805 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span |
---|
1806 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1807 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1808 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count |
---|
1809 | m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span |
---|
1810 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1811 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1812 | normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i |
---|
1813 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i |
---|
1814 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr><m:mr><m:e><i |
---|
1815 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:num><m:den><i |
---|
1816 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>M</m:r></span></i><m:d><m:dPr><span |
---|
1817 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1818 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1819 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:m><m:mPr><m:mcs><m:mc><m:mcPr><m:count |
---|
1820 | m:val="1"/><m:mcJc m:val="center"/></m:mcPr></m:mc></m:mcs><span |
---|
1821 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1822 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1823 | normal'><m:ctrlPr></m:ctrlPr></span></m:mPr><m:mr><m:e><i |
---|
1824 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:e></m:mr><m:mr><m:e><i |
---|
1825 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr><m:mr><m:e><i |
---|
1826 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:e></m:mr></m:m></m:e></m:d></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span |
---|
1827 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1828 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
1829 | top:15.0pt;mso-text-raise:-15.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
1830 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
1831 | type="#_x0000_t75" style='width:80.25pt;height:50.25pt'> |
---|
1832 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image017.png" |
---|
1833 | o:title="" chromakey="white"/> |
---|
1834 | </v:shape><![endif]--><![if !vml]><img width=107 height=67 |
---|
1835 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image018.png" |
---|
1836 | v:shapes="_x0000_i1025"><![endif]></span><![endif]></p> |
---|
1837 | |
---|
1838 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
1839 | margin-left:0in;line-height:115%'>The harmonic terms, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
1840 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1841 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1842 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
1843 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1844 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1845 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i |
---|
1846 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>φ</m:r><m:r>,</m:r><m:r>β</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
1847 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1848 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
1849 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
1850 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
1851 | type="#_x0000_t75" style='width:46.5pt;height:26.25pt'> |
---|
1852 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image019.png" |
---|
1853 | o:title="" chromakey="white"/> |
---|
1854 | </v:shape><![endif]--><![if !vml]><img width=62 height=35 |
---|
1855 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image020.png" |
---|
1856 | v:shapes="_x0000_i1025"><![endif]></span><![endif]><span |
---|
1857 | style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
1858 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1859 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1860 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
1861 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1862 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1863 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSubSup><i |
---|
1864 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>ψ</m:r><m:r>,</m:r><m:r>γ</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
1865 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1866 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
1867 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
1868 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
1869 | type="#_x0000_t75" style='width:42.75pt;height:26.25pt'> |
---|
1870 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image021.png" |
---|
1871 | o:title="" chromakey="white"/> |
---|
1872 | </v:shape><![endif]--><![if !vml]><img width=57 height=35 |
---|
1873 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image022.png" |
---|
1874 | v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are developed from</p> |
---|
1875 | |
---|
1876 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
1877 | margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc |
---|
1878 | m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
1879 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1880 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1881 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
1882 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
1883 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1884 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span |
---|
1885 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1886 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1887 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style: |
---|
1888 | normal'><span style='font-family:"Cambria Math",serif'><m:r>φ</m:r><m:r>,</m:r><m:r>β</m:r></span></i></m:e></m:d><i |
---|
1889 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:f><m:fPr><span |
---|
1890 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1891 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1892 | normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style: |
---|
1893 | normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:num><m:den><m:rad><m:radPr><m:degHide |
---|
1894 | m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family: |
---|
1895 | "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic; |
---|
1896 | mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><i |
---|
1897 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>π</m:r></span></i></m:e></m:rad></m:den></m:f><m:sSup><m:sSupPr><span |
---|
1898 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1899 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1900 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style: |
---|
1901 | normal'><span style='font-family:"Cambria Math",serif'><m:r>e</m:r></span></i></m:e><m:sup><i |
---|
1902 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>imβ</m:r></span></i></m:sup></m:sSup><m:sSubSup><m:sSubSupPr><span |
---|
1903 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1904 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1905 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr |
---|
1906 | m:val="̅"/><span style='font-family:"Cambria Math",serif; |
---|
1907 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
1908 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i |
---|
1909 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i |
---|
1910 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1911 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
1912 | </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style: |
---|
1913 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span |
---|
1914 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1915 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1916 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
1917 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
1918 | m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
1919 | normal'><span style='font-family:"Cambria Math",serif'><m:r>φ</m:r></span></i></m:e></m:func><i |
---|
1920 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span |
---|
1921 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1922 | "Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US; |
---|
1923 | mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape |
---|
1924 | id="_x0000_i1025" type="#_x0000_t75" style='width:165pt;height:42pt'> |
---|
1925 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image023.png" |
---|
1926 | o:title="" chromakey="white"/> |
---|
1927 | </v:shape><![endif]--><![if !vml]><img width=220 height=56 |
---|
1928 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image024.png" |
---|
1929 | v:shapes="_x0000_i1025"><![endif]></span><![endif]></p> |
---|
1930 | |
---|
1931 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
1932 | margin-left:0in;line-height:115%'><span class=GramE>where</span> the normalized |
---|
1933 | associated Legendre functions, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
1934 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1935 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1936 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr |
---|
1937 | m:val="̅"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family: |
---|
1938 | "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic; |
---|
1939 | mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i |
---|
1940 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i |
---|
1941 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1942 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><i |
---|
1943 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>x</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
1944 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1945 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
1946 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
1947 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
1948 | type="#_x0000_t75" style='width:33pt;height:26.25pt'> |
---|
1949 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image025.png" |
---|
1950 | o:title="" chromakey="white"/> |
---|
1951 | </v:shape><![endif]--><![if !vml]><img width=44 height=35 |
---|
1952 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image026.png" |
---|
1953 | v:shapes="_x0000_i1025"><![endif]></span><![endif]>, are defined via a Fourier |
---|
1954 | expansion as</p> |
---|
1955 | |
---|
1956 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
1957 | margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc |
---|
1958 | m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
1959 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1960 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1961 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr |
---|
1962 | m:val="̅"/><span style='font-family:"Cambria Math",serif; |
---|
1963 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
1964 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i |
---|
1965 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i |
---|
1966 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1967 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
1968 | </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span |
---|
1969 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1970 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1971 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span |
---|
1972 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1973 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1974 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
1975 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
1976 | m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
1977 | normal'><span style='font-family:"Cambria Math",serif'><m:r>φ</m:r></span></i></m:e></m:func></m:e></m:d><i |
---|
1978 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:nary><m:naryPr><m:chr |
---|
1979 | m:val="∑"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif; |
---|
1980 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
1981 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i |
---|
1982 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>s</m:r><m:r>=0</m:r></span></i></m:sub><m:sup><i |
---|
1983 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span |
---|
1984 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1985 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1986 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i |
---|
1987 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i |
---|
1988 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
1989 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
1990 | </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span |
---|
1991 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
1992 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
1993 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
1994 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
1995 | m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
1996 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>sφ</m:r><m:r>)</m:r></span></i></m:e></m:func></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span |
---|
1997 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
1998 | "Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US; |
---|
1999 | mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape |
---|
2000 | id="_x0000_i1025" type="#_x0000_t75" style='width:154.5pt;height:52.5pt'> |
---|
2001 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image027.png" |
---|
2002 | o:title="" chromakey="white"/> |
---|
2003 | </v:shape><![endif]--><![if !vml]><img width=206 height=70 |
---|
2004 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image028.png" |
---|
2005 | v:shapes="_x0000_i1025"><![endif]></span><![endif]></p> |
---|
2006 | |
---|
2007 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2008 | margin-left:0in;line-height:115%'><span class=GramE>for</span> m even and</p> |
---|
2009 | |
---|
2010 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2011 | margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc |
---|
2012 | m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
2013 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2014 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2015 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr |
---|
2016 | m:val="̅"/><span style='font-family:"Cambria Math",serif; |
---|
2017 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
2018 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i |
---|
2019 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i |
---|
2020 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2021 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
2022 | </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span |
---|
2023 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2024 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2025 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span |
---|
2026 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2027 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2028 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
2029 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
2030 | m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
2031 | normal'><span style='font-family:"Cambria Math",serif'><m:r>φ</m:r></span></i></m:e></m:func></m:e></m:d><i |
---|
2032 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:nary><m:naryPr><m:chr |
---|
2033 | m:val="∑"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif; |
---|
2034 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
2035 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i |
---|
2036 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>s</m:r><m:r>=1</m:r></span></i></m:sub><m:sup><i |
---|
2037 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span |
---|
2038 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2039 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2040 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i |
---|
2041 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i |
---|
2042 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2043 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
2044 | </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:func><m:funcPr><span |
---|
2045 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2046 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2047 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
2048 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
2049 | m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
2050 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>sφ</m:r><m:r>)</m:r></span></i></m:e></m:func></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span |
---|
2051 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2052 | "Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US; |
---|
2053 | mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape |
---|
2054 | id="_x0000_i1025" type="#_x0000_t75" style='width:158.25pt;height:52.5pt'> |
---|
2055 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image029.png" |
---|
2056 | o:title="" chromakey="white"/> |
---|
2057 | </v:shape><![endif]--><![if !vml]><img width=211 height=70 |
---|
2058 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image030.png" |
---|
2059 | v:shapes="_x0000_i1025"><![endif]></span><![endif]></p> |
---|
2060 | |
---|
2061 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2062 | margin-left:0in;line-height:115%'><span class=GramE>for</span> m odd.<span |
---|
2063 | style='mso-spacerun:yes'> </span>Each sum is only over either the even or odd |
---|
2064 | values of s, respectively, because of the properties of the Fourier |
---|
2065 | coefficients<span class=GramE>, </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
2066 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2067 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2068 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
2069 | normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r><m:r>'</m:r></span></i></m:e><m:sub><i |
---|
2070 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2071 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
2072 | </m:r><m:r>ms</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span |
---|
2073 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2074 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
2075 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
2076 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
2077 | type="#_x0000_t75" style='width:24.75pt;height:26.25pt'> |
---|
2078 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image031.png" |
---|
2079 | o:title="" chromakey="white"/> |
---|
2080 | </v:shape><![endif]--><![if !vml]><img width=33 height=35 |
---|
2081 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image032.png" |
---|
2082 | v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span |
---|
2083 | style='mso-spacerun:yes'> </span>These Fourier coefficients are determined so |
---|
2084 | that the definition</p> |
---|
2085 | |
---|
2086 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2087 | margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc |
---|
2088 | m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
2089 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2090 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2091 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr |
---|
2092 | m:val="̅"/><span style='font-family:"Cambria Math",serif; |
---|
2093 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
2094 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i |
---|
2095 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i |
---|
2096 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2097 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
2098 | </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span |
---|
2099 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2100 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2101 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:func><m:funcPr><span |
---|
2102 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2103 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2104 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
2105 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
2106 | m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
2107 | normal'><span style='font-family:"Cambria Math",serif'><m:r>φ</m:r></span></i></m:e></m:func></m:e></m:d><i |
---|
2108 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:sSubSup><m:sSubSupPr><span |
---|
2109 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2110 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2111 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr |
---|
2112 | m:val="̅"/><span style='font-family:"Cambria Math",serif; |
---|
2113 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
2114 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i |
---|
2115 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i |
---|
2116 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2117 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
2118 | </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span |
---|
2119 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2120 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2121 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style: |
---|
2122 | normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e></m:d><i |
---|
2123 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:rad><m:radPr><m:degHide |
---|
2124 | m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family: |
---|
2125 | "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic; |
---|
2126 | mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span |
---|
2127 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2128 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2129 | normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:d><m:dPr><span |
---|
2130 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2131 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2132 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style: |
---|
2133 | normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>+</m:r><m:r>m</m:r></span></i></m:e></m:d><i |
---|
2134 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>!</m:r></span></i></m:num><m:den><m:d><m:dPr><span |
---|
2135 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2136 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2137 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style: |
---|
2138 | normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:e></m:d><i |
---|
2139 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>!</m:r></span></i></m:den></m:f></m:e></m:rad><m:rad><m:radPr><m:degHide |
---|
2140 | m:val="on"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family: |
---|
2141 | "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic; |
---|
2142 | mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:radPr><m:deg></m:deg><m:e><m:f><m:fPr><span |
---|
2143 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2144 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2145 | normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style: |
---|
2146 | normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>L</m:r><m:r>+1</m:r></span></i></m:num><m:den><i |
---|
2147 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:den></m:f></m:e></m:rad><m:f><m:fPr><span |
---|
2148 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2149 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2150 | normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span |
---|
2151 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2152 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2153 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style: |
---|
2154 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(-1)</m:r></span></i></m:e><m:sup><i |
---|
2155 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span |
---|
2156 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2157 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2158 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style: |
---|
2159 | normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:e><m:sup><i |
---|
2160 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup></m:sSup><i |
---|
2161 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>!</m:r></span></i></m:den></m:f><m:sSup><m:sSupPr><span |
---|
2162 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2163 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2164 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style: |
---|
2165 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><span |
---|
2166 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2167 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2168 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style: |
---|
2169 | normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i |
---|
2170 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i |
---|
2171 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:e><m:sup><m:f><m:fPr><m:type |
---|
2172 | m:val="lin"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family: |
---|
2173 | "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic; |
---|
2174 | mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i |
---|
2175 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>m</m:r></span></i></m:num><m:den><i |
---|
2176 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:den></m:f></m:sup></m:sSup><m:f><m:fPr><span |
---|
2177 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2178 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2179 | normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span |
---|
2180 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2181 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2182 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style: |
---|
2183 | normal'><span style='font-family:"Cambria Math",serif'><m:r>d</m:r></span></i></m:e><m:sup><i |
---|
2184 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span |
---|
2185 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2186 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2187 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style: |
---|
2188 | normal'><span style='font-family:"Cambria Math",serif'><m:r>dx</m:r></span></i></m:e><m:sup><i |
---|
2189 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>-</m:r><m:r>m</m:r></span></i></m:sup></m:sSup></m:den></m:f><m:sSup><m:sSupPr><span |
---|
2190 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2191 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2192 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style: |
---|
2193 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(1-</m:r></span></i><m:sSup><m:sSupPr><span |
---|
2194 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2195 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2196 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style: |
---|
2197 | normal'><span style='font-family:"Cambria Math",serif'><m:r>x</m:r></span></i></m:e><m:sup><i |
---|
2198 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup><i |
---|
2199 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:e><m:sup><i |
---|
2200 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup></m:sSup></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span |
---|
2201 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2202 | "Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US; |
---|
2203 | mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape |
---|
2204 | id="_x0000_i1025" type="#_x0000_t75" style='width:423.75pt;height:55.5pt'> |
---|
2205 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image033.png" |
---|
2206 | o:title="" chromakey="white"/> |
---|
2207 | </v:shape><![endif]--><![if !vml]><img width=565 height=74 |
---|
2208 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image034.png" |
---|
2209 | v:shapes="_x0000_i1025"><![endif]></span><![endif]></p> |
---|
2210 | |
---|
2211 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2212 | margin-left:0in;line-height:115%'><span class=GramE>is</span> satisfied.<span |
---|
2213 | style='mso-spacerun:yes'> </span>Terms of the form <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span |
---|
2214 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2215 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2216 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
2217 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
2218 | m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
2219 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>mβ</m:r><m:r>)</m:r></span></i></m:e></m:func><m:sSubSup><m:sSubSupPr><span |
---|
2220 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2221 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2222 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr |
---|
2223 | m:val="̅"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family: |
---|
2224 | "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic; |
---|
2225 | mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i |
---|
2226 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i |
---|
2227 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2228 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
2229 | </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style: |
---|
2230 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span |
---|
2231 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2232 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2233 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
2234 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
2235 | m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
2236 | normal'><span style='font-family:"Cambria Math",serif'><m:r>mβ</m:r></span></i></m:e></m:func><i |
---|
2237 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
2238 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2239 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
2240 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
2241 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
2242 | type="#_x0000_t75" style='width:111pt;height:26.25pt'> |
---|
2243 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image035.png" |
---|
2244 | o:title="" chromakey="white"/> |
---|
2245 | </v:shape><![endif]--><![if !vml]><img width=148 height=35 |
---|
2246 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image036.png" |
---|
2247 | v:shapes="_x0000_i1025"><![endif]></span><![endif]><span |
---|
2248 | style='mso-spacerun:yes'> </span>and <!--[if gte msEquation 12]><m:oMath><m:func><m:funcPr><span |
---|
2249 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2250 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2251 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
2252 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
2253 | m:val="p"/></m:rPr>sin</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
2254 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>mβ</m:r><m:r>)</m:r></span></i></m:e></m:func><m:sSubSup><m:sSubSupPr><span |
---|
2255 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2256 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2257 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr |
---|
2258 | m:val="̅"/><span style='font-family:"Cambria Math",serif;mso-ascii-font-family: |
---|
2259 | "Cambria Math";mso-hansi-font-family:"Cambria Math";font-style:italic; |
---|
2260 | mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i |
---|
2261 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i |
---|
2262 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2263 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
2264 | </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style: |
---|
2265 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span |
---|
2266 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2267 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2268 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
2269 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
2270 | m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
2271 | normal'><span style='font-family:"Cambria Math",serif'><m:r>φ</m:r></span></i></m:e></m:func><i |
---|
2272 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
2273 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2274 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
2275 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
2276 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
2277 | type="#_x0000_t75" style='width:100.5pt;height:26.25pt'> |
---|
2278 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image037.png" |
---|
2279 | o:title="" chromakey="white"/> |
---|
2280 | </v:shape><![endif]--><![if !vml]><img width=134 height=35 |
---|
2281 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image038.png" |
---|
2282 | v:shapes="_x0000_i1025"><![endif]></span><![endif]><span |
---|
2283 | style='mso-spacerun:yes'> </span>are combined depending on the symmetry and the |
---|
2284 | value of m along with appropriate normalization coefficients to give the |
---|
2285 | harmonic terms <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
2286 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2287 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2288 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
2289 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
2290 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2291 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
2292 | </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style: |
---|
2293 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>φ</m:r><m:r>,</m:r><m:r>β</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
2294 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2295 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
2296 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
2297 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
2298 | type="#_x0000_t75" style='width:48pt;height:26.25pt'> |
---|
2299 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png" |
---|
2300 | o:title="" chromakey="white"/> |
---|
2301 | </v:shape><![endif]--><![if !vml]><img width=64 height=35 |
---|
2302 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png" |
---|
2303 | v:shapes="_x0000_i1025"><![endif]></span><![endif]><span |
---|
2304 | style='mso-spacerun:yes'> </span><span class=GramE>and </span><!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
2305 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2306 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2307 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
2308 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
2309 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2310 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
2311 | </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style: |
---|
2312 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>ψ</m:r><m:r>,</m:r><m:r>γ</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
2313 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2314 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
2315 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
2316 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
2317 | type="#_x0000_t75" style='width:45pt;height:26.25pt'> |
---|
2318 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image041.png" |
---|
2319 | o:title="" chromakey="white"/> |
---|
2320 | </v:shape><![endif]--><![if !vml]><img width=60 height=35 |
---|
2321 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image042.png" |
---|
2322 | v:shapes="_x0000_i1025"><![endif]></span><![endif]>.<span |
---|
2323 | style='mso-spacerun:yes'> </span>For cubic crystal symmetry, the term <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
2324 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2325 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2326 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
2327 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
2328 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2329 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
2330 | </m:r><m:r>m</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style: |
---|
2331 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r><m:r>φ</m:r><m:r>,</m:r><m:r>β</m:r><m:r>)</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span |
---|
2332 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2333 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
2334 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
2335 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
2336 | type="#_x0000_t75" style='width:48pt;height:26.25pt'> |
---|
2337 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image039.png" |
---|
2338 | o:title="" chromakey="white"/> |
---|
2339 | </v:shape><![endif]--><![if !vml]><img width=64 height=35 |
---|
2340 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image040.png" |
---|
2341 | v:shapes="_x0000_i1025"><![endif]></span><![endif]><span |
---|
2342 | style='mso-spacerun:yes'> </span>is obtained directly from the Fourier |
---|
2343 | expansion</p> |
---|
2344 | |
---|
2345 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2346 | margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc |
---|
2347 | m:val="left"/></m:oMathParaPr><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
2348 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2349 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2350 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
2351 | normal'><span style='font-family:"Cambria Math",serif'><m:r>k</m:r></span></i></m:e><m:sub><i |
---|
2352 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2353 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSubSup><m:d><m:dPr><span |
---|
2354 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2355 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2356 | normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style: |
---|
2357 | normal'><span style='font-family:"Cambria Math",serif'><m:r>φ</m:r><m:r>,</m:r><m:r>β</m:r></span></i></m:e></m:d><i |
---|
2358 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:nary><m:naryPr><m:chr |
---|
2359 | m:val="∑"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif; |
---|
2360 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
2361 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i |
---|
2362 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>=0</m:r></span></i></m:sub><m:sup><i |
---|
2363 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSubSup><m:sSubSupPr><span |
---|
2364 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2365 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2366 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i |
---|
2367 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>B</m:r></span></i></m:e><m:sub><i |
---|
2368 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2369 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>nm</m:r></span></i></m:sup></m:sSubSup></m:e></m:nary><m:sSubSup><m:sSubSupPr><span |
---|
2370 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2371 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2372 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><m:acc><m:accPr><m:chr |
---|
2373 | m:val="̅"/><span style='font-family:"Cambria Math",serif; |
---|
2374 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
2375 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:accPr><m:e><i |
---|
2376 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>P</m:r></span></i></m:e></m:acc></m:e><m:sub><i |
---|
2377 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2378 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r> |
---|
2379 | </m:r><m:r>n</m:r></span></i></m:sup></m:sSubSup><i style='mso-bidi-font-style: |
---|
2380 | normal'><span style='font-family:"Cambria Math",serif'><m:r>(</m:r></span></i><m:func><m:funcPr><span |
---|
2381 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2382 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2383 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
2384 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
2385 | m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
2386 | normal'><span style='font-family:"Cambria Math",serif'><m:r>φ</m:r></span></i></m:e></m:func><i |
---|
2387 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>)</m:r></span></i><m:func><m:funcPr><span |
---|
2388 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2389 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2390 | normal'><m:ctrlPr></m:ctrlPr></span></m:funcPr><m:fName><span |
---|
2391 | style='font-family:"Cambria Math",serif'><m:r><m:rPr><m:scr m:val="roman"/><m:sty |
---|
2392 | m:val="p"/></m:rPr>cos</m:r></span></m:fName><m:e><i style='mso-bidi-font-style: |
---|
2393 | normal'><span style='font-family:"Cambria Math",serif'><m:r>nβ</m:r></span></i></m:e></m:func></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span |
---|
2394 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2395 | "Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US; |
---|
2396 | mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape |
---|
2397 | id="_x0000_i1025" type="#_x0000_t75" style='width:193.5pt;height:52.5pt'> |
---|
2398 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image043.png" |
---|
2399 | o:title="" chromakey="white"/> |
---|
2400 | </v:shape><![endif]--><![if !vml]><img width=258 height=70 |
---|
2401 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image044.png" |
---|
2402 | v:shapes="_x0000_i1025"><![endif]></span><![endif]></p> |
---|
2403 | |
---|
2404 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2405 | margin-left:0in;line-height:115%'><span class=GramE>using</span> the |
---|
2406 | coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
2407 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2408 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2409 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
2410 | normal'><span style='font-family:"Cambria Math",serif'><m:r>B</m:r></span></i></m:e><m:sub><i |
---|
2411 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2412 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>nm</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span |
---|
2413 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2414 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
2415 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
2416 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
2417 | type="#_x0000_t75" style='width:22.5pt;height:26.25pt'> |
---|
2418 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image045.png" |
---|
2419 | o:title="" chromakey="white"/> |
---|
2420 | </v:shape><![endif]--><![if !vml]><img width=30 height=35 |
---|
2421 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image046.png" |
---|
2422 | v:shapes="_x0000_i1025"><![endif]></span><![endif]>, as tabulated by Bunge |
---|
2423 | (1982). </p> |
---|
2424 | |
---|
2425 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2426 | margin-left:0in;line-height:115%'>The Rietveld refinement of texture then |
---|
2427 | proceeds by constructing derivatives of the profile intensities with respect to |
---|
2428 | the allowed harmonic coefficients, <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
2429 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2430 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2431 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
2432 | normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i |
---|
2433 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2434 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span |
---|
2435 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2436 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
2437 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
2438 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
2439 | type="#_x0000_t75" style='width:21.75pt;height:26.25pt'> |
---|
2440 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png" |
---|
2441 | o:title="" chromakey="white"/> |
---|
2442 | </v:shape><![endif]--><![if !vml]><img width=29 height=35 |
---|
2443 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png" |
---|
2444 | v:shapes="_x0000_i1025"><![endif]></span><![endif]>, and the three sample |
---|
2445 | orientation angles, <span style='font-family:Symbol'>W</span><sub>s</sub>, <span |
---|
2446 | style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family:Symbol'>F</span><sub>s</sub>, |
---|
2447 | all of which can be adjustable parameters of the refinement. Once the |
---|
2448 | refinement is complete, pole figures for any reflection may be constructed by |
---|
2449 | use of the general axis equation, the refined values for <!--[if gte msEquation 12]><m:oMath><m:sSubSup><m:sSubSupPr><span |
---|
2450 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2451 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2452 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i style='mso-bidi-font-style: |
---|
2453 | normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i |
---|
2454 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2455 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:oMath><![endif]--><![if !msEquation]><span |
---|
2456 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2457 | "Times New Roman";mso-fareast-theme-font:minor-fareast;position:relative; |
---|
2458 | top:3.0pt;mso-text-raise:-3.0pt;mso-ansi-language:EN-US;mso-fareast-language: |
---|
2459 | EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape id="_x0000_i1025" |
---|
2460 | type="#_x0000_t75" style='width:21.75pt;height:26.25pt'> |
---|
2461 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image047.png" |
---|
2462 | o:title="" chromakey="white"/> |
---|
2463 | </v:shape><![endif]--><![if !vml]><img width=29 height=35 |
---|
2464 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image048.png" |
---|
2465 | v:shapes="_x0000_i1025"><![endif]></span><![endif]><span |
---|
2466 | style='mso-spacerun:yes'> </span>and the sample orientation angles <span |
---|
2467 | style='font-family:Symbol'>W</span><sub>s</sub>, <span style='font-family:Symbol'>C</span><sub>s</sub>, |
---|
2468 | <span class=GramE><span style='font-family:Symbol'>F</span></span><sub>s</sub>. |
---|
2469 | </p> |
---|
2470 | |
---|
2471 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2472 | margin-left:0in;line-height:115%'>The magnitude of the texture is evaluated |
---|
2473 | from the texture index by</p> |
---|
2474 | |
---|
2475 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2476 | margin-left:0in;line-height:115%'><!--[if gte msEquation 12]><m:oMathPara><m:oMathParaPr><m:jc |
---|
2477 | m:val="left"/></m:oMathParaPr><m:oMath><i style='mso-bidi-font-style:normal'><span |
---|
2478 | style='font-family:"Cambria Math",serif'><m:r>J</m:r><m:r>=1+</m:r></span></i><m:nary><m:naryPr><m:chr |
---|
2479 | m:val="∑"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif; |
---|
2480 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
2481 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i |
---|
2482 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r><m:r>=2</m:r></span></i></m:sub><m:sup><m:sSub><m:sSubPr><span |
---|
2483 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2484 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2485 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubPr><m:e><i style='mso-bidi-font-style: |
---|
2486 | normal'><span style='font-family:"Cambria Math",serif'><m:r>N</m:r></span></i></m:e><m:sub><i |
---|
2487 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub></m:sSub></m:sup><m:e><m:f><m:fPr><span |
---|
2488 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2489 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2490 | normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style: |
---|
2491 | normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:num><m:den><i |
---|
2492 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r><m:r>L</m:r><m:r>+1</m:r></span></i></m:den></m:f></m:e></m:nary><m:nary><m:naryPr><m:chr |
---|
2493 | m:val="∑"/><m:limLoc m:val="undOvr"/><span style='font-family:"Cambria Math",serif; |
---|
2494 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
2495 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i |
---|
2496 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2497 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:nary><m:naryPr><m:chr |
---|
2498 | m:val="∑"/><m:limLoc m:val="undOvr"/><span style='font-family: |
---|
2499 | "Cambria Math",serif;mso-ascii-font-family:"Cambria Math";mso-hansi-font-family: |
---|
2500 | "Cambria Math";font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:naryPr><m:sub><i |
---|
2501 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>=-</m:r><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2502 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sup><m:e><m:sSup><m:sSupPr><span |
---|
2503 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2504 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2505 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><m:begChr |
---|
2506 | m:val="|"/><m:endChr m:val="|"/><span style='font-family:"Cambria Math",serif; |
---|
2507 | mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; |
---|
2508 | font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:sSubSup><m:sSubSupPr><span |
---|
2509 | style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math"; |
---|
2510 | mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style: |
---|
2511 | normal'><m:ctrlPr></m:ctrlPr></span></m:sSubSupPr><m:e><i |
---|
2512 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>C</m:r></span></i></m:e><m:sub><i |
---|
2513 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>L</m:r></span></i></m:sub><m:sup><i |
---|
2514 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>mn</m:r></span></i></m:sup></m:sSubSup></m:e></m:d></m:e><m:sup><i |
---|
2515 | style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>2</m:r></span></i></m:sup></m:sSup></m:e></m:nary></m:e></m:nary></m:oMath></m:oMathPara><![endif]--><![if !msEquation]><span |
---|
2516 | style='font-size:12.0pt;font-family:"Times New Roman",serif;mso-fareast-font-family: |
---|
2517 | "Times New Roman";mso-fareast-theme-font:minor-fareast;mso-ansi-language:EN-US; |
---|
2518 | mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape |
---|
2519 | id="_x0000_i1025" type="#_x0000_t75" style='width:180.75pt;height:54pt'> |
---|
2520 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image049.png" |
---|
2521 | o:title="" chromakey="white"/> |
---|
2522 | </v:shape><![endif]--><![if !vml]><img width=241 height=72 |
---|
2523 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image050.png" |
---|
2524 | v:shapes="_x0000_i1025"><![endif]></span><![endif]></p> |
---|
2525 | |
---|
2526 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2527 | margin-left:0in;line-height:115%'>If the texture is random then J = 1, |
---|
2528 | otherwise J > 1; for a single crystal J = <span style='font-family:Symbol'>¥.</span> |
---|
2529 | </p> |
---|
2530 | |
---|
2531 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2532 | margin-left:0in;line-height:115%'>In GSAS-II the texture is defined in two ways |
---|
2533 | to accommodate the two possible uses of this correction. In one a suite of |
---|
2534 | spherical harmonics coefficients is defined for the texture of a phase in the |
---|
2535 | sample; this can have any of the possible sample symmetries and is the usual |
---|
2536 | result desired for texture analysis. The other is the suite of spherical |
---|
2537 | harmonics terms for cylindrical sample symmetry for each phase in each powder |
---|
2538 | pattern (histogram) and is usually used to accommodate preferred orientation |
---|
2539 | effects in a Rietveld refinement. The former description allows refinement of |
---|
2540 | the sample orientation zeros, <span style='font-family:Symbol'>W</span><sub>s</sub>, |
---|
2541 | <span style='font-family:Symbol'>C</span><sub>s</sub>, <span style='font-family: |
---|
2542 | Symbol'>F</span><sub>s</sub>, but the latter description does not (they are |
---|
2543 | assumed to be zero and not refinable). The sample orientation angles, (<span |
---|
2544 | style='font-family:Symbol'>W</span>, <span style='font-family:Symbol'>C</span>, |
---|
2545 | <span style='font-family:Symbol'>F) </span>are specified in the Sample |
---|
2546 | Parameters table in the GSAS-II data tree structure and are applied for either |
---|
2547 | description.</p> |
---|
2548 | |
---|
2549 | <p class=gsastext style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
2550 | margin-left:0in;line-height:115%'>In this tutorial we will use both of these |
---|
2551 | descriptions to determine the texture of the two phases in a <span |
---|
2552 | class=SpellE>NiTi</span> shape memory alloy sample with cylindrical symmetry |
---|
2553 | (wire texture) as collected at APS on beam line 1ID-C (data kindly provided by |
---|
2554 | Paul Paradise & Aaron <span class=SpellE>Stebner</span> of Colo. School of |
---|
2555 | Mines). Thus, there are three ways within GSAS-II that can be used for this |
---|
2556 | texture analysis all beginning with the same 2D area detector image. Each will |
---|
2557 | be described in turn after the initial setup of the GSAS-II project, image |
---|
2558 | input & integration.</p> |
---|
2559 | |
---|
2560 | <h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
2561 | 0in;line-height:115%'>Step 1. Image input & integration</h2> |
---|
2562 | |
---|
2563 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you have |
---|
2564 | not done so already, <u><span style='color:#0070C0'><a |
---|
2565 | href="Starting%20GSAS.htm"><span style='color:windowtext;text-decoration:none; |
---|
2566 | text-underline:none'>start GSAS-II</span></a></span></u>. Note that menu |
---|
2567 | entries are listed in <b style='mso-bidi-font-weight:normal'><span |
---|
2568 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2569 | mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font: |
---|
2570 | minor-latin'>bold face</span></b> below as <b style='mso-bidi-font-weight:normal'><span |
---|
2571 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2572 | mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font: |
---|
2573 | minor-latin'>Help/About GSAS-II</span></b>, which lists first the name of the |
---|
2574 | menu (here <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
2575 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
2576 | minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'>Help</span></b>) |
---|
2577 | and second the name of the entry in the menu (here <b style='mso-bidi-font-weight: |
---|
2578 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2579 | minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri; |
---|
2580 | mso-bidi-theme-font:minor-latin'>About GSAS-II</span></b>). </p> |
---|
2581 | |
---|
2582 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Use the <b |
---|
2583 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2584 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Read |
---|
2585 | image data</span></b> menu item to read the data file into the current GSAS-II |
---|
2586 | project. A file selection dialog will be shown; its appearance will depend on |
---|
2587 | your OS. Change the search directory to <b style='mso-bidi-font-weight:normal'><span |
---|
2588 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2589 | mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font: |
---|
2590 | minor-latin'>/exercises/2DTexture </span></b>and then select the file <b |
---|
2591 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2592 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NDC5_01588_1.ge2</span></b>. |
---|
2593 | A (faint) image will appear</p> |
---|
2594 | |
---|
2595 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2596 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_29" |
---|
2597 | o:spid="_x0000_i1081" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
2598 | visibility:visible;mso-wrap-style:square'> |
---|
2599 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png" |
---|
2600 | o:title=""/> |
---|
2601 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
2602 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image051.png" |
---|
2603 | v:shapes="Picture_x0020_29"><![endif]></span></p> |
---|
2604 | |
---|
2605 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2606 | class=GramE>and</span> the <b style='mso-bidi-font-weight:normal'><span |
---|
2607 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2608 | mso-hansi-theme-font:minor-latin'>Image Controls</span></b> data page will show</p> |
---|
2609 | |
---|
2610 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2611 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_30" |
---|
2612 | o:spid="_x0000_i1080" type="#_x0000_t75" style='width:472.5pt;height:388.5pt; |
---|
2613 | visibility:visible;mso-wrap-style:square'> |
---|
2614 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png" |
---|
2615 | o:title=""/> |
---|
2616 | </v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518 |
---|
2617 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image052.png" |
---|
2618 | v:shapes="Picture_x0020_30"><![endif]></span></p> |
---|
2619 | |
---|
2620 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detector |
---|
2621 | was previously calibrated and the coefficients are stored in a file found by |
---|
2622 | doing <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2623 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Operations/Load |
---|
2624 | Controls</span></b> from the <b style='mso-bidi-font-weight:normal'><span |
---|
2625 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2626 | mso-hansi-theme-font:minor-latin'>Image Controls</span></b> menu. A file |
---|
2627 | selection popup will appear showing <b style='mso-bidi-font-weight:normal'><span |
---|
2628 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2629 | mso-hansi-theme-font:minor-latin'>NDC5.imctrl</span></b>; select it and press <b |
---|
2630 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2631 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Open</span></b>. |
---|
2632 | The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2633 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image |
---|
2634 | Controls</span></b> window will be repainted with the new values (do a reselect |
---|
2635 | of the image from the tree and then <b style='mso-bidi-font-weight:normal'><span |
---|
2636 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2637 | mso-hansi-theme-font:minor-latin'>Image Controls</span></b> to make sure the |
---|
2638 | image is up to date.)</p> |
---|
2639 | |
---|
2640 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2641 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_31" |
---|
2642 | o:spid="_x0000_i1079" type="#_x0000_t75" style='width:472.5pt;height:388.5pt; |
---|
2643 | visibility:visible;mso-wrap-style:square'> |
---|
2644 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png" |
---|
2645 | o:title=""/> |
---|
2646 | </v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518 |
---|
2647 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image053.png" |
---|
2648 | v:shapes="Picture_x0020_31"><![endif]></span></p> |
---|
2649 | |
---|
2650 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The detail in |
---|
2651 | the image can be enhanced by lowering the <b style='mso-bidi-font-weight:normal'><span |
---|
2652 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2653 | mso-hansi-theme-font:minor-latin'>Max intensity</span></b> (<b |
---|
2654 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2655 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>15000</span></b> |
---|
2656 | is suitable) and shows that the diffraction rings show the effect of texture |
---|
2657 | and that the image has a fairly high background. Placing the cursor in the |
---|
2658 | corners or inside the inner ring shows a background >1700. This can be suppressed |
---|
2659 | by adjusting the <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
2660 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
2661 | minor-latin'>Flat <span class=SpellE>Bkg</span></span></b> (I chose <b |
---|
2662 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2663 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>1700</span></b> |
---|
2664 | for this). The image will now show the rings much more clearly.</p> |
---|
2665 | |
---|
2666 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2667 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32" |
---|
2668 | o:spid="_x0000_i1078" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
2669 | visibility:visible;mso-wrap-style:square'> |
---|
2670 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png" |
---|
2671 | o:title=""/> |
---|
2672 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
2673 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image054.png" |
---|
2674 | v:shapes="Picture_x0020_32"><![endif]></span></p> |
---|
2675 | |
---|
2676 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For texture |
---|
2677 | analysis we will need to integrate the image into a number of slices sampling |
---|
2678 | the changing ring intensity with azimuthal angle. Also note that the image |
---|
2679 | seems to have <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
2680 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
2681 | minor-latin'>mm</span></b> symmetry so that the unique part of this intensity |
---|
2682 | variation covers 0-90° of azimuth. In addition the ring intensity variation is |
---|
2683 | such that using 10° slices will capture it reasonably well. However, we want to |
---|
2684 | include both 0° and 90° as slice centers. Thus there will be 10 slices |
---|
2685 | beginning at -5° and ending at 95°. Check the <b style='mso-bidi-font-weight: |
---|
2686 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2687 | minor-latin;mso-hansi-theme-font:minor-latin'>Show integration limits?</span></b> |
---|
2688 | <span class=GramE>box</span> and uncheck the <b style='mso-bidi-font-weight: |
---|
2689 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2690 | minor-latin;mso-hansi-theme-font:minor-latin'>Do full integration? </span></b><span |
---|
2691 | class=GramE>box</span>, enter <b style='mso-bidi-font-weight:normal'><span |
---|
2692 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2693 | mso-hansi-theme-font:minor-latin'>10</span></b> in the <b style='mso-bidi-font-weight: |
---|
2694 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2695 | minor-latin;mso-hansi-theme-font:minor-latin'>No. azimuth bins</span></b>, |
---|
2696 | enter <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2697 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-5</span></b> |
---|
2698 | in the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2699 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Start |
---|
2700 | azimuth</span></b> box (it will change to 355) and enter <b style='mso-bidi-font-weight: |
---|
2701 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2702 | minor-latin;mso-hansi-theme-font:minor-latin'>455</span></b> in the <b |
---|
2703 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2704 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>End azimuth</span></b> |
---|
2705 | box. In addition, recall that the sample was mounted vertically and thus is |
---|
2706 | aligned with the defined laboratory I axis. Thus, the sample coordinate system |
---|
2707 | needs to be rotated by 90° to match the sample axis with the K axis; this can |
---|
2708 | be done by making the <b style='mso-bidi-font-weight:normal'><span |
---|
2709 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2710 | mso-hansi-theme-font:minor-latin'>Sample goniometer axis Chi</span></b> = <b |
---|
2711 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2712 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>90</span></b>. |
---|
2713 | The plot will change with each entry and at the end should look like</p> |
---|
2714 | |
---|
2715 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2716 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_33" |
---|
2717 | o:spid="_x0000_i1077" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
2718 | visibility:visible;mso-wrap-style:square'> |
---|
2719 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png" |
---|
2720 | o:title=""/> |
---|
2721 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
2722 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image055.png" |
---|
2723 | v:shapes="Picture_x0020_33"><![endif]></span></p> |
---|
2724 | |
---|
2725 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The <b |
---|
2726 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2727 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image |
---|
2728 | Controls</span></b> should be</p> |
---|
2729 | |
---|
2730 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2731 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_34" |
---|
2732 | o:spid="_x0000_i1076" type="#_x0000_t75" style='width:472.5pt;height:388.5pt; |
---|
2733 | visibility:visible;mso-wrap-style:square'> |
---|
2734 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png" |
---|
2735 | o:title=""/> |
---|
2736 | </v:shape><![endif]--><![if !vml]><img border=0 width=630 height=518 |
---|
2737 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image056.png" |
---|
2738 | v:shapes="Picture_x0020_34"><![endif]></span></p> |
---|
2739 | |
---|
2740 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It turns out |
---|
2741 | that the image contains a number of picked bits (very high count zingers); |
---|
2742 | these can be mostly eliminated by setting the upper threshold in Masks. Select <b |
---|
2743 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2744 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Masks</span></b> |
---|
2745 | and the following should appear</p> |
---|
2746 | |
---|
2747 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2748 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35" |
---|
2749 | o:spid="_x0000_i1075" type="#_x0000_t75" style='width:297.75pt;height:99.75pt; |
---|
2750 | visibility:visible;mso-wrap-style:square'> |
---|
2751 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png" |
---|
2752 | o:title=""/> |
---|
2753 | </v:shape><![endif]--><![if !vml]><img border=0 width=397 height=133 |
---|
2754 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image057.png" |
---|
2755 | v:shapes="Picture_x0020_35"><![endif]></span></p> |
---|
2756 | |
---|
2757 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the <b |
---|
2758 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2759 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Upper |
---|
2760 | threshold</span></b> to <b style='mso-bidi-font-weight:normal'><span |
---|
2761 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2762 | mso-hansi-theme-font:minor-latin'>2500</span></b>; the image will be redrawn |
---|
2763 | reflecting this mask. By zooming in you may see isolated red pixels; these are |
---|
2764 | excluded points. Make sure the diffraction rings do not have any excluded |
---|
2765 | points. For example with the level set to 2200 the plot shows</p> |
---|
2766 | |
---|
2767 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2768 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_36" |
---|
2769 | o:spid="_x0000_i1074" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
2770 | visibility:visible;mso-wrap-style:square'> |
---|
2771 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png" |
---|
2772 | o:title=""/> |
---|
2773 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
2774 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image058.png" |
---|
2775 | v:shapes="Picture_x0020_36"><![endif]></span></p> |
---|
2776 | |
---|
2777 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2778 | class=GramE>for</span> one ring. This level is too low. Return to the <b |
---|
2779 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2780 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image |
---|
2781 | Controls</span></b> item in the data tree.</p> |
---|
2782 | |
---|
2783 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now |
---|
2784 | ready to integrate the image; do <b style='mso-bidi-font-weight:normal'><span |
---|
2785 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2786 | mso-hansi-theme-font:minor-latin'>Operations/Integrate</span></b> from the <b |
---|
2787 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2788 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Image |
---|
2789 | Controls</span></b> menu. When done the last powder pattern in the tree will be |
---|
2790 | displayed</p> |
---|
2791 | |
---|
2792 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2793 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_37" |
---|
2794 | o:spid="_x0000_i1073" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
2795 | visibility:visible;mso-wrap-style:square'> |
---|
2796 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png" |
---|
2797 | o:title=""/> |
---|
2798 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
2799 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image059.png" |
---|
2800 | v:shapes="Picture_x0020_37"><![endif]></span></p> |
---|
2801 | |
---|
2802 | <h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
2803 | 0in;line-height:115%'>Step 2. Enter <span class=SpellE>NiTi</span> phases</h2> |
---|
2804 | |
---|
2805 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This <span |
---|
2806 | class=SpellE>NiTi</span> alloy consists of two phases, cubic B2 and monoclinic |
---|
2807 | B19. Their parameters are<span class=GramE>:</span><br> |
---|
2808 | B2: <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2809 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>P m 3 m</span></b>, |
---|
2810 | a=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2811 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>3.0240</span></b>, |
---|
2812 | Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2813 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0,0,0</span></b>, |
---|
2814 | <span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span |
---|
2815 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2816 | mso-hansi-theme-font:minor-latin'>œ,œ,œ</span></b>, <span class=SpellE>U<sub>iso</sub></span>=<b |
---|
2817 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2818 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.005 </span></b>for |
---|
2819 | both.<br> |
---|
2820 | B19:<span style='mso-spacerun:yes'> </span><b style='mso-bidi-font-weight: |
---|
2821 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2822 | minor-latin;mso-hansi-theme-font:minor-latin'>P 1 1 21/m</span></b>, a=<b |
---|
2823 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2824 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.8853</span></b>, |
---|
2825 | b=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2826 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.6353</span></b>, |
---|
2827 | c=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2828 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>4.1368</span></b>, |
---|
2829 | γ=<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2830 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>96.821</span></b>, |
---|
2831 | <span class=SpellE>Ti</span> <b style='mso-bidi-font-weight:normal'><span |
---|
2832 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2833 | mso-hansi-theme-font:minor-latin'>0.5787<span class=GramE>,0.2841,Œ</span></span></b>, |
---|
2834 | Ni <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2835 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.9700,0.8209,Œ</span></b>, |
---|
2836 | <span class=SpellE>U<sub>iso</sub></span>=<b style='mso-bidi-font-weight:normal'><span |
---|
2837 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2838 | mso-hansi-theme-font:minor-latin'>0.005</span></b> for both.<br> |
---|
2839 | Use the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2840 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data/Add |
---|
2841 | phase</span></b> to enter the <b style='mso-bidi-font-weight:normal'><span |
---|
2842 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2843 | mso-hansi-theme-font:minor-latin'>B2</span></b> and <b style='mso-bidi-font-weight: |
---|
2844 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2845 | minor-latin;mso-hansi-theme-font:minor-latin'>B19</span></b> phases; then for |
---|
2846 | each enter the information given above on their respective <b style='mso-bidi-font-weight: |
---|
2847 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2848 | minor-latin;mso-hansi-theme-font:minor-latin'>General</span></b> and <b |
---|
2849 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2850 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Atoms</span></b> |
---|
2851 | tabs. Dont forget the spaces between the axial fields for the space group |
---|
2852 | symbols. On the <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
2853 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
2854 | minor-latin'>Atoms</span></b> tab begin by doing <b style='mso-bidi-font-weight: |
---|
2855 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2856 | minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Append atom</span></b> twice |
---|
2857 | then fill in the <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
2858 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
2859 | minor-latin'>Type</span></b> and coordinates boxes. A double click of the <b |
---|
2860 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2861 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Type</span></b> |
---|
2862 | entry will show a popup of the Periodic Table; select the element as |
---|
2863 | appropriate. NB: GSAS-II happily takes 1/2 & 1/4 for coordinate values; |
---|
2864 | these get converted to their decimal equivalent upon entry. Note the use of a |
---|
2865 | nonstandard space group designation for B19. When done the B2 Atoms table |
---|
2866 | should look like</p> |
---|
2867 | |
---|
2868 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2869 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_38" |
---|
2870 | o:spid="_x0000_i1072" type="#_x0000_t75" style='width:525pt;height:166.5pt; |
---|
2871 | visibility:visible;mso-wrap-style:square'> |
---|
2872 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png" |
---|
2873 | o:title=""/> |
---|
2874 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=222 |
---|
2875 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image060.png" |
---|
2876 | v:shapes="Picture_x0020_38"><![endif]></span></p> |
---|
2877 | |
---|
2878 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2879 | class=GramE>and</span> the B19 Atoms table should be</p> |
---|
2880 | |
---|
2881 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2882 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_39" |
---|
2883 | o:spid="_x0000_i1071" type="#_x0000_t75" style='width:525pt;height:163.5pt; |
---|
2884 | visibility:visible;mso-wrap-style:square'> |
---|
2885 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png" |
---|
2886 | o:title=""/> |
---|
2887 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=218 |
---|
2888 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image061.png" |
---|
2889 | v:shapes="Picture_x0020_39"><![endif]></span></p> |
---|
2890 | |
---|
2891 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the |
---|
2892 | <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2893 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b> |
---|
2894 | tab for each phase; there will be a message indicating the lack of data for |
---|
2895 | each. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2896 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add |
---|
2897 | powder histograms</span></b>, do <b style='mso-bidi-font-weight:normal'><span |
---|
2898 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2899 | mso-hansi-theme-font:minor-latin'>Set All</span></b> on the popup selection |
---|
2900 | window and press <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
2901 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
2902 | minor-latin'>OK</span></b>. The window for B2 will change to</p> |
---|
2903 | |
---|
2904 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2905 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40" |
---|
2906 | o:spid="_x0000_i1070" type="#_x0000_t75" style='width:342.75pt;height:375pt; |
---|
2907 | visibility:visible;mso-wrap-style:square'> |
---|
2908 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png" |
---|
2909 | o:title=""/> |
---|
2910 | </v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500 |
---|
2911 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png" |
---|
2912 | v:shapes="Picture_x0020_40"><![endif]></span></p> |
---|
2913 | |
---|
2914 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2915 | class=GramE>and</span> that for B19 will be</p> |
---|
2916 | |
---|
2917 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2918 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_41" |
---|
2919 | o:spid="_x0000_i1069" type="#_x0000_t75" style='width:370.5pt;height:375pt; |
---|
2920 | visibility:visible;mso-wrap-style:square'> |
---|
2921 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png" |
---|
2922 | o:title=""/> |
---|
2923 | </v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500 |
---|
2924 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image063.png" |
---|
2925 | v:shapes="Picture_x0020_41"><![endif]></span></p> |
---|
2926 | |
---|
2927 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You should now |
---|
2928 | save the project file (I used <span class=SpellE><b style='mso-bidi-font-weight: |
---|
2929 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2930 | minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span> for a |
---|
2931 | name); we will use this as a starting point for three different texture |
---|
2932 | determinations. Do a <b style='mso-bidi-font-weight:normal'><span |
---|
2933 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2934 | mso-hansi-theme-font:minor-latin'>File/Save project as
</span></b> and give it |
---|
2935 | a new name (I used <span class=SpellE><b style='mso-bidi-font-weight:normal'><span |
---|
2936 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2937 | mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight: |
---|
2938 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2939 | minor-latin;mso-hansi-theme-font:minor-latin'>-A</span></b>); this will become |
---|
2940 | the new project name for the next part of this tutorial.</p> |
---|
2941 | |
---|
2942 | <h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
2943 | 0in;line-height:115%'>Method A. Full refinement</h2> |
---|
2944 | |
---|
2945 | <h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
2946 | 0in;line-height:115%'>Introduction</h3> |
---|
2947 | |
---|
2948 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In this method |
---|
2949 | we will do a full Rietveld refinement of the texture, profile parameters, peak |
---|
2950 | position variables and crystal structure parameters. This is suitable in this |
---|
2951 | case because of the relatively small number of histograms (10 in this case) |
---|
2952 | needed for the texture determination; do recall that each phase in each |
---|
2953 | histogram has a set of parameters (e.g. phase fraction, size, <span |
---|
2954 | class=SpellE>mustrain</span> & hydrostatic strain) in addition to the ones |
---|
2955 | for each histogram (e.g. background & scale factor). Consequently the total |
---|
2956 | number of parameters can build up very quickly in this method of analysis. The |
---|
2957 | other two methods seek to reduce this problem by splitting the fitting into a |
---|
2958 | sequential refinement (histogram by histogram) step followed by a texture |
---|
2959 | fitting step.</p> |
---|
2960 | |
---|
2961 | <h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
2962 | 0in;line-height:115%'>Step 1. Initial refinement</h3> |
---|
2963 | |
---|
2964 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In the initial |
---|
2965 | refinement we need to vary the phase fraction for each phase/histogram and the |
---|
2966 | background in each histogram. To start select any <b style='mso-bidi-font-weight: |
---|
2967 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2968 | minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b> entry from the |
---|
2969 | GSAS-II data tree and select <b style='mso-bidi-font-weight:normal'><span |
---|
2970 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
2971 | mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b> for it. Note |
---|
2972 | that Goniometer chi is set to 90; that came from the same entry in the Image |
---|
2973 | Controls during integration. Also, if you chose other than the 1<sup>st</sup> |
---|
2974 | PWDR data set the Detector azimuth will be some nonzero value; that is also |
---|
2975 | reflected in the name assigned to the histogram (e.g. <b style='mso-bidi-font-weight: |
---|
2976 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2977 | minor-latin;mso-hansi-theme-font:minor-latin'>PWDR NDC5_01588_1.ge2 <span |
---|
2978 | class=SpellE>Azm</span>= 40.00</span></b>). Uncheck the <b style='mso-bidi-font-weight: |
---|
2979 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2980 | minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b> |
---|
2981 | box and then do <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
2982 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
2983 | minor-latin'>Command/Copy flags</span></b>; select <b style='mso-bidi-font-weight: |
---|
2984 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
2985 | minor-latin;mso-hansi-theme-font:minor-latin'>Set All</span></b> and then press |
---|
2986 | <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
2987 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>. |
---|
2988 | That will clear the scale factor refinement flag for all histograms; we will be |
---|
2989 | varying the phase fractions instead.</p> |
---|
2990 | |
---|
2991 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select |
---|
2992 | the B2 phase and pick the Data tab; you will see</p> |
---|
2993 | |
---|
2994 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
2995 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42" |
---|
2996 | o:spid="_x0000_i1068" type="#_x0000_t75" style='width:342.75pt;height:375pt; |
---|
2997 | visibility:visible;mso-wrap-style:square'> |
---|
2998 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png" |
---|
2999 | o:title=""/> |
---|
3000 | </v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500 |
---|
3001 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image062.png" |
---|
3002 | v:shapes="Picture_x0020_42"><![endif]></span></p> |
---|
3003 | |
---|
3004 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Select the <b |
---|
3005 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3006 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase |
---|
3007 | fraction</span></b> box. Then do <b style='mso-bidi-font-weight:normal'><span |
---|
3008 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3009 | mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b>, select <b |
---|
3010 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3011 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Set <span |
---|
3012 | class=GramE>All</span></span></b> & press <b style='mso-bidi-font-weight: |
---|
3013 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3014 | minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to copy these to |
---|
3015 | the other histograms. Next select the <b style='mso-bidi-font-weight:normal'><span |
---|
3016 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3017 | mso-hansi-theme-font:minor-latin'>B19</span></b> phase and repeat this process. |
---|
3018 | We are now ready for the first refinement; do <b style='mso-bidi-font-weight: |
---|
3019 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3020 | minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> from |
---|
3021 | the main GSAS-II data tree window. A progress bar popup will appear and when |
---|
3022 | done a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3023 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refinement |
---|
3024 | results</span></b> popup will show with Rw~32%. Press <b style='mso-bidi-font-weight: |
---|
3025 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3026 | minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to load this |
---|
3027 | result; GSAS-II will return you to the last window you were using and display |
---|
3028 | the 1<sup>st</sup> powder pattern showing you the fit</p> |
---|
3029 | |
---|
3030 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3031 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_43" |
---|
3032 | o:spid="_x0000_i1067" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
3033 | visibility:visible;mso-wrap-style:square'> |
---|
3034 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png" |
---|
3035 | o:title=""/> |
---|
3036 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
3037 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image064.png" |
---|
3038 | v:shapes="Picture_x0020_43"><![endif]></span></p> |
---|
3039 | |
---|
3040 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is quite |
---|
3041 | poor. You can survey the fit successively by 1<sup>st</sup> selecting say the 1<sup>st</sup> |
---|
3042 | PWDR entry from the tree and then using the up/down arrow keys to step to the |
---|
3043 | next one; the plot will redraw at each step (NB: at full scale) and the data |
---|
3044 | window will show statistics of the fit. There is a substantial intensity |
---|
3045 | discrepancy; this is due to the texture. It is also evident that some of the |
---|
3046 | peaks are out of place relative to the reflection markers; this is due to |
---|
3047 | macroscopic strain in the drawn wire. For the <span style='font-family:"Calibri",sans-serif; |
---|
3048 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span> |
---|
3049 | phase select the <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3050 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3051 | minor-latin'>Texture</span></b> tab; it should look like</p> |
---|
3052 | |
---|
3053 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3054 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44" |
---|
3055 | o:spid="_x0000_i1066" type="#_x0000_t75" style='width:456pt;height:217.5pt; |
---|
3056 | visibility:visible;mso-wrap-style:square'> |
---|
3057 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png" |
---|
3058 | o:title=""/> |
---|
3059 | </v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290 |
---|
3060 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png" |
---|
3061 | v:shapes="Picture_x0020_44"><![endif]></span></p> |
---|
3062 | |
---|
3063 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The texture |
---|
3064 | model is <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3065 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>cylindrical</span></b> |
---|
3066 | by default; that is what we want. Change the <b style='mso-bidi-font-weight: |
---|
3067 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3068 | minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to <b |
---|
3069 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3070 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>8</span></b> |
---|
3071 | and check both <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3072 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3073 | minor-latin'>Refine texture</span></b> and <b style='mso-bidi-font-weight:normal'><span |
---|
3074 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3075 | mso-hansi-theme-font:minor-latin'>Show <span class=SpellE>coeff</span></span></b>. |
---|
3076 | The window should look like</p> |
---|
3077 | |
---|
3078 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3079 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45" |
---|
3080 | o:spid="_x0000_i1065" type="#_x0000_t75" style='width:456pt;height:250.5pt; |
---|
3081 | visibility:visible;mso-wrap-style:square'> |
---|
3082 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png" |
---|
3083 | o:title=""/> |
---|
3084 | </v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334 |
---|
3085 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png" |
---|
3086 | v:shapes="Picture_x0020_45"><![endif]></span></p> |
---|
3087 | |
---|
3088 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the |
---|
3089 | <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3090 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b> |
---|
3091 | tab, select <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3092 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3093 | minor-latin'>D11</span></b>; the <b style='mso-bidi-font-weight:normal'><span |
---|
3094 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3095 | mso-hansi-theme-font:minor-latin'>Data</span></b> window should look like (any |
---|
3096 | PWDR item will do)</p> |
---|
3097 | |
---|
3098 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3099 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_46" |
---|
3100 | o:spid="_x0000_i1064" type="#_x0000_t75" style='width:342.75pt;height:375pt; |
---|
3101 | visibility:visible;mso-wrap-style:square'> |
---|
3102 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png" |
---|
3103 | o:title=""/> |
---|
3104 | </v:shape><![endif]--><![if !vml]><img border=0 width=457 height=500 |
---|
3105 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image067.png" |
---|
3106 | v:shapes="Picture_x0020_46"><![endif]></span></p> |
---|
3107 | |
---|
3108 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then do <b |
---|
3109 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3110 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy |
---|
3111 | flags</span></b> to have <b style='mso-bidi-font-weight:normal'><span |
---|
3112 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3113 | mso-hansi-theme-font:minor-latin'>D11</span></b> refined for all PWDR data |
---|
3114 | sets.</p> |
---|
3115 | |
---|
3116 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next select |
---|
3117 | the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3118 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19</span></b> |
---|
3119 | phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3120 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b> |
---|
3121 | tab. Then select <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3122 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3123 | minor-latin'>6</span></b> for the <b style='mso-bidi-font-weight:normal'><span |
---|
3124 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3125 | mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> and check the two |
---|
3126 | boxes as before.</p> |
---|
3127 | |
---|
3128 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3129 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_47" |
---|
3130 | o:spid="_x0000_i1063" type="#_x0000_t75" style='width:478.5pt;height:302.25pt; |
---|
3131 | visibility:visible;mso-wrap-style:square'> |
---|
3132 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png" |
---|
3133 | o:title=""/> |
---|
3134 | </v:shape><![endif]--><![if !vml]><img border=0 width=638 height=403 |
---|
3135 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image068.png" |
---|
3136 | v:shapes="Picture_x0020_47"><![endif]></span></p> |
---|
3137 | |
---|
3138 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Then go to the |
---|
3139 | <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3140 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b> |
---|
3141 | tab for the <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3142 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3143 | minor-latin'>B19</span></b> phase and check all 4 of the <span class=SpellE><b |
---|
3144 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3145 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dij</span></b></span> |
---|
3146 | boxes and do <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3147 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3148 | minor-latin'>Edit/Copy flags</span></b> as before. The tab will look like</p> |
---|
3149 | |
---|
3150 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3151 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48" |
---|
3152 | o:spid="_x0000_i1062" type="#_x0000_t75" style='width:370.5pt;height:375pt; |
---|
3153 | visibility:visible;mso-wrap-style:square'> |
---|
3154 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png" |
---|
3155 | o:title=""/> |
---|
3156 | </v:shape><![endif]--><![if !vml]><img border=0 width=494 height=500 |
---|
3157 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image069.png" |
---|
3158 | v:shapes="Picture_x0020_48"><![endif]></span></p> |
---|
3159 | |
---|
3160 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do <b |
---|
3161 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3162 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> |
---|
3163 | from the main menu. The refinement will finish with <span class=SpellE>Rw</span> |
---|
3164 | ~27%; the 1<sup>st</sup> PWDR pattern looks like</p> |
---|
3165 | |
---|
3166 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3167 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_49" |
---|
3168 | o:spid="_x0000_i1061" type="#_x0000_t75" style='width:525pt;height:413.25pt; |
---|
3169 | visibility:visible;mso-wrap-style:square'> |
---|
3170 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png" |
---|
3171 | o:title=""/> |
---|
3172 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551 |
---|
3173 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image070.png" |
---|
3174 | v:shapes="Picture_x0020_49"><![endif]></span></p> |
---|
3175 | |
---|
3176 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The calculated |
---|
3177 | peaks for both phases are too sharp. It is likely that this is a <span |
---|
3178 | class=SpellE>microstrain</span> effect. Select <b style='mso-bidi-font-weight: |
---|
3179 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3180 | minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b> for the <b |
---|
3181 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3182 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2 </span></b>phase |
---|
3183 | and select the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span |
---|
3184 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3185 | mso-hansi-theme-font:minor-latin'>microstrain</span></b></span> box. Then do <b |
---|
3186 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3187 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy |
---|
3188 | flags</span></b> to set it for the other PWDR data sets. Do the same for the <b |
---|
3189 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3190 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19</span></b> |
---|
3191 | phase. Then do <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3192 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3193 | minor-latin'>Calculate/Refine</span></b> from the main menu. The fit will be |
---|
3194 | substantially improved with <span class=SpellE>Rw</span> ~9.2%.</p> |
---|
3195 | |
---|
3196 | <h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
3197 | 0in;line-height:115%'>Step 2. Finish refinement and examine texture</h3> |
---|
3198 | |
---|
3199 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Looking at the |
---|
3200 | individual PWDR data sets (e.g. the one for <span class=SpellE>Azm</span>=20.00)</p> |
---|
3201 | |
---|
3202 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3203 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_50" |
---|
3204 | o:spid="_x0000_i1060" type="#_x0000_t75" style='width:525pt;height:413.25pt; |
---|
3205 | visibility:visible;mso-wrap-style:square'> |
---|
3206 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png" |
---|
3207 | o:title=""/> |
---|
3208 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551 |
---|
3209 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image071.png" |
---|
3210 | v:shapes="Picture_x0020_50"><![endif]></span></p> |
---|
3211 | |
---|
3212 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is evident |
---|
3213 | that there remains intensity differences due to texture. We can increase the |
---|
3214 | harmonic order to more closely fit these, however one should only do this |
---|
3215 | carefully. Select the Texture tab for the B2 phase; the Texture tab will show</p> |
---|
3216 | |
---|
3217 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3218 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_18" |
---|
3219 | o:spid="_x0000_i1059" type="#_x0000_t75" style='width:456pt;height:250.5pt; |
---|
3220 | visibility:visible;mso-wrap-style:square'> |
---|
3221 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png" |
---|
3222 | o:title=""/> |
---|
3223 | </v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334 |
---|
3224 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image072.png" |
---|
3225 | v:shapes="Picture_x0020_18"><![endif]></span></p> |
---|
3226 | |
---|
3227 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a drawing |
---|
3228 | of the 001 pole figure will be drawn. This is the very typical bulls eye for |
---|
3229 | cylindrical texture; of much more use is an inverse pole figure. Select that |
---|
3230 | from the Texture plot type; the plot will be redrawn</p> |
---|
3231 | |
---|
3232 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3233 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_52" |
---|
3234 | o:spid="_x0000_i1058" type="#_x0000_t75" style='width:525pt;height:413.25pt; |
---|
3235 | visibility:visible;mso-wrap-style:square'> |
---|
3236 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png" |
---|
3237 | o:title=""/> |
---|
3238 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551 |
---|
3239 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image073.png" |
---|
3240 | v:shapes="Picture_x0020_52"><![endif]></span></p> |
---|
3241 | |
---|
3242 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This shows the |
---|
3243 | probability of reflection vectors coinciding with the sample wire axis the high |
---|
3244 | spots are the 111 family of reflections. We should try the next higher Harmonic |
---|
3245 | order (10). </p> |
---|
3246 | |
---|
3247 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next go to the |
---|
3248 | Texture tab for the B19 phase. Again a <span class=SpellE>bullseye</span> pole |
---|
3249 | figure is drawn; change that to an Inverse pole figure.</p> |
---|
3250 | |
---|
3251 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3252 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_53" |
---|
3253 | o:spid="_x0000_i1057" type="#_x0000_t75" style='width:525pt;height:413.25pt; |
---|
3254 | visibility:visible;mso-wrap-style:square'> |
---|
3255 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png" |
---|
3256 | o:title=""/> |
---|
3257 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551 |
---|
3258 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image074.png" |
---|
3259 | v:shapes="Picture_x0020_53"><![endif]></span></p> |
---|
3260 | |
---|
3261 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This phase is |
---|
3262 | very strongly textured (the cursor shows 12-13 MRD at the peaks) along the -140 |
---|
3263 | direction. Again we want to increment the Harmonic order to the next higher |
---|
3264 | level (8). Again do Calculate/Refine from the main menu; the <span |
---|
3265 | class=SpellE>Rwp</span> has dropped to ~7.9%. One can add the atom <span |
---|
3266 | class=SpellE>Uiso</span> for the Ni and <span class=SpellE>Ti</span> atoms in |
---|
3267 | the B2 phase and the coordinates and <span class=SpellE>Uiso</span> for the |
---|
3268 | B19 phase. The <span class=SpellE>Rw</span> drops a bit further to ~7.4%. |
---|
3269 | Finally, we can increase the harmonic order again for the B19 phase (it is |
---|
3270 | very strongly textured!) to 10 and the B2 phase to 12; the final refinement |
---|
3271 | converged to <span class=SpellE>Rw</span> ~6.8% and the B19 inverse pole |
---|
3272 | figure has peaks at ~18 MRD (Multiple of Random Distribution) and the B2 phase |
---|
3273 | peaks are ~7MRD.</p> |
---|
3274 | |
---|
3275 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B19 |
---|
3276 | coefficients</p> |
---|
3277 | |
---|
3278 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3279 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_54" |
---|
3280 | o:spid="_x0000_i1056" type="#_x0000_t75" style='width:502.5pt;height:375pt; |
---|
3281 | visibility:visible;mso-wrap-style:square'> |
---|
3282 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png" |
---|
3283 | o:title=""/> |
---|
3284 | </v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500 |
---|
3285 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image075.png" |
---|
3286 | v:shapes="Picture_x0020_54"><![endif]></span></p> |
---|
3287 | |
---|
3288 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3289 | class=GramE>and</span> inverse pole figure</p> |
---|
3290 | |
---|
3291 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3292 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_55" |
---|
3293 | o:spid="_x0000_i1055" type="#_x0000_t75" style='width:525pt;height:413.25pt; |
---|
3294 | visibility:visible;mso-wrap-style:square'> |
---|
3295 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png" |
---|
3296 | o:title=""/> |
---|
3297 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551 |
---|
3298 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image076.png" |
---|
3299 | v:shapes="Picture_x0020_55"><![endif]></span></p> |
---|
3300 | |
---|
3301 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The B2 |
---|
3302 | coefficients</p> |
---|
3303 | |
---|
3304 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3305 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_56" |
---|
3306 | o:spid="_x0000_i1054" type="#_x0000_t75" style='width:480pt;height:267.75pt; |
---|
3307 | visibility:visible;mso-wrap-style:square'> |
---|
3308 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png" |
---|
3309 | o:title=""/> |
---|
3310 | </v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357 |
---|
3311 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image077.png" |
---|
3312 | v:shapes="Picture_x0020_56"><![endif]></span></p> |
---|
3313 | |
---|
3314 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3315 | class=GramE>and</span> inverse pole figure</p> |
---|
3316 | |
---|
3317 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3318 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_57" |
---|
3319 | o:spid="_x0000_i1053" type="#_x0000_t75" style='width:525pt;height:413.25pt; |
---|
3320 | visibility:visible;mso-wrap-style:square'> |
---|
3321 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png" |
---|
3322 | o:title=""/> |
---|
3323 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=551 |
---|
3324 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image078.png" |
---|
3325 | v:shapes="Picture_x0020_57"><![endif]></span></p> |
---|
3326 | |
---|
3327 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This completes |
---|
3328 | the tutorial on Method A for doing texture analysis. It is useful for a case |
---|
3329 | like this one where there are very few data sets required for the texture |
---|
3330 | analysis. However, for the case of lower sample symmetry one must several dozen |
---|
3331 | or even a few hundred histograms and then the suite of parameters can easily be |
---|
3332 | > 1000 of which only a few dozen describe the texture. This leads to the |
---|
3333 | next Methods for texture analysis in GSAS-II.</p> |
---|
3334 | |
---|
3335 | <h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
3336 | 0in;line-height:115%'>Method B. Sequential refinement & texture analysis |
---|
3337 | from result</h2> |
---|
3338 | |
---|
3339 | <h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
3340 | 0in;line-height:115%'>Introduction</h3> |
---|
3341 | |
---|
3342 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins |
---|
3343 | the texture analysis in much the same way as Method A except that all the |
---|
3344 | initial refinements are done sequentially, that is refinements are done for |
---|
3345 | the parameters associated with each powder pattern to convergence in a serial |
---|
3346 | fashion. In this case where there are 10 PWDR data sets, there will be 10 |
---|
3347 | refinements done in sequence. Parameters that span all the data (e.g. lattice |
---|
3348 | parameters, atom parameters & texture) are not varied in this sequence |
---|
3349 | refinement. The effect of texture is modeled as a Preferred Orientation |
---|
3350 | correction to each histogram. To begin do <b style='mso-bidi-font-weight:normal'><span |
---|
3351 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3352 | mso-hansi-theme-font:minor-latin'>File/Open project
</span></b> for the <span |
---|
3353 | class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3354 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3355 | minor-latin'>NiTi.gpx</span></b></span> file created in the first step and then |
---|
3356 | do a <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3357 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Save |
---|
3358 | project as
</span></b> to save it as <span class=SpellE><b style='mso-bidi-font-weight: |
---|
3359 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3360 | minor-latin;mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b |
---|
3361 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3362 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>-B</span></b>. |
---|
3363 | This renames the project and it should have one IMG, 10 PWDR entries and two |
---|
3364 | phases of <span class=SpellE>NiTi</span> (B2 and B19).</p> |
---|
3365 | |
---|
3366 | <h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
3367 | 0in;line-height:115%'>Step 1. Initial refinement</h3> |
---|
3368 | |
---|
3369 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This begins |
---|
3370 | the same way as Method A so Ill be brief. Do the following steps:</p> |
---|
3371 | |
---|
3372 | <p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;mso-add-space: |
---|
3373 | auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span |
---|
3374 | style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span |
---|
3375 | style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]>Select |
---|
3376 | any <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3377 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>PWDR</span></b> |
---|
3378 | entry, go to <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3379 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3380 | minor-latin'>Sample Parameters</span></b> and uncheck <b style='mso-bidi-font-weight: |
---|
3381 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3382 | minor-latin;mso-hansi-theme-font:minor-latin'>Histogram scale factor</span></b>. |
---|
3383 | Then copy the flags to the other PWDR entries.</p> |
---|
3384 | |
---|
3385 | <p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;mso-add-space: |
---|
3386 | auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span |
---|
3387 | style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span |
---|
3388 | style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]>Select |
---|
3389 | the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3390 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> |
---|
3391 | phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3392 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b> |
---|
3393 | tab and check the <b style='mso-bidi-font-weight:normal'><span |
---|
3394 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3395 | mso-hansi-theme-font:minor-latin'>Phase fraction</span></b> box and change the <span |
---|
3396 | class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3397 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3398 | minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span |
---|
3399 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3400 | mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b |
---|
3401 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3402 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical |
---|
3403 | harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span |
---|
3404 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3405 | mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the |
---|
3406 | flag and the model to the other PWDR entries.</p> |
---|
3407 | |
---|
3408 | <p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space: |
---|
3409 | auto;text-indent:-.25in;line-height:115%;mso-list:l0 level1 lfo2'><![if !supportLists]><span |
---|
3410 | style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span |
---|
3411 | style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]>Select |
---|
3412 | the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3413 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19</span></b> |
---|
3414 | phase <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3415 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Data</span></b> |
---|
3416 | tab and check the <b style='mso-bidi-font-weight:normal'><span |
---|
3417 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3418 | mso-hansi-theme-font:minor-latin'>Phase fraction box</span></b> and change the <span |
---|
3419 | class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3420 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3421 | minor-latin'>Preferred</span></b></span><b style='mso-bidi-font-weight:normal'><span |
---|
3422 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3423 | mso-hansi-theme-font:minor-latin'> orientation model</span></b> to <b |
---|
3424 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3425 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Spherical |
---|
3426 | harmonics</span></b>. Then do <b style='mso-bidi-font-weight:normal'><span |
---|
3427 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3428 | mso-hansi-theme-font:minor-latin'>Edit/Copy data</span></b> to copy both the |
---|
3429 | flag and the model to the other PWDR entries.</p> |
---|
3430 | |
---|
3431 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select <b |
---|
3432 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3433 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b> |
---|
3434 | from the GSAS-II data tree</p> |
---|
3435 | |
---|
3436 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3437 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_1" |
---|
3438 | o:spid="_x0000_i1052" type="#_x0000_t75" style='width:330.75pt;height:153.75pt; |
---|
3439 | visibility:visible;mso-wrap-style:square'> |
---|
3440 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png" |
---|
3441 | o:title=""/> |
---|
3442 | </v:shape><![endif]--><![if !vml]><img border=0 width=441 height=205 |
---|
3443 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image079.png" |
---|
3444 | v:shapes="Picture_x0020_1"><![endif]></span></p> |
---|
3445 | |
---|
3446 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Press the <b |
---|
3447 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3448 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Select Data</span></b> |
---|
3449 | button for <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3450 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3451 | minor-latin'>Sequential Refinement</span></b>; a file selection popup will |
---|
3452 | appear. Do <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3453 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3454 | minor-latin'>Set All</span></b> and press <b style='mso-bidi-font-weight:normal'><span |
---|
3455 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3456 | mso-hansi-theme-font:minor-latin'>OK</span></b>. The <b style='mso-bidi-font-weight: |
---|
3457 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3458 | minor-latin;mso-hansi-theme-font:minor-latin'>Controls</span></b> page will be |
---|
3459 | repainted indicating that 10 data sets are selected for sequential refinement.</p> |
---|
3460 | |
---|
3461 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3462 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_2" |
---|
3463 | o:spid="_x0000_i1051" type="#_x0000_t75" style='width:330.75pt;height:163.5pt; |
---|
3464 | visibility:visible;mso-wrap-style:square'> |
---|
3465 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png" |
---|
3466 | o:title=""/> |
---|
3467 | </v:shape><![endif]--><![if !vml]><img border=0 width=441 height=218 |
---|
3468 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image080.png" |
---|
3469 | v:shapes="Picture_x0020_2"><![endif]></span></p> |
---|
3470 | |
---|
3471 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>You have the |
---|
3472 | choice of starting at the last one and for copying results from one to the |
---|
3473 | next. We wont do either here. Each refinement will use the other controls |
---|
3474 | (e.g. <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3475 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Max cycles</span></b>) |
---|
3476 | as controls. We are now ready to do the 1<sup>st</sup> sequential refinement. |
---|
3477 | Do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3478 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Sequential |
---|
3479 | refine</span></b> from the main menu. A progress bar popup will appear showing |
---|
3480 | residuals as it processes each of 10 data sets. After a few seconds the <b |
---|
3481 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3482 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refinement |
---|
3483 | results</span></b> popup will appear; press <b style='mso-bidi-font-weight: |
---|
3484 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3485 | minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> to accept them. The |
---|
3486 | data window displays the <b style='mso-bidi-font-weight:normal'><span |
---|
3487 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3488 | mso-hansi-theme-font:minor-latin'>Sequential refinement results</span></b> as a |
---|
3489 | table.</p> |
---|
3490 | |
---|
3491 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3492 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3" |
---|
3493 | o:spid="_x0000_i1050" type="#_x0000_t75" style='width:525pt;height:262.5pt; |
---|
3494 | visibility:visible;mso-wrap-style:square'> |
---|
3495 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png" |
---|
3496 | o:title=""/> |
---|
3497 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350 |
---|
3498 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image081.png" |
---|
3499 | v:shapes="Picture_x0020_3"><![endif]></span></p> |
---|
3500 | |
---|
3501 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>There is a row |
---|
3502 | for each data set and columns for all refined parameters and some derived ones |
---|
3503 | along with residual and convergence indicators. The residuals are not very good |
---|
3504 | (we havent really refined much) but the Δχ<sup>2</sup> column shows |
---|
3505 | that convergence was achieved (NB: poor convergence will be highlighted in |
---|
3506 | yellow or red depending on how bad it is).</p> |
---|
3507 | |
---|
3508 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>If you examine |
---|
3509 | one of the PWDR entries, youll see that just in this point in Method <span |
---|
3510 | class=GramE>A</span> much of the misfit is texture and perhaps peak position.</p> |
---|
3511 | |
---|
3512 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3513 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_4" |
---|
3514 | o:spid="_x0000_i1049" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
3515 | visibility:visible;mso-wrap-style:square'> |
---|
3516 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png" |
---|
3517 | o:title=""/> |
---|
3518 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
3519 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image082.png" |
---|
3520 | v:shapes="Picture_x0020_4"><![endif]></span></p> |
---|
3521 | |
---|
3522 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>To set these |
---|
3523 | parameters, select the Data tab for the B2 phase</p> |
---|
3524 | |
---|
3525 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3526 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5" |
---|
3527 | o:spid="_x0000_i1048" type="#_x0000_t75" style='width:381pt;height:375pt; |
---|
3528 | visibility:visible;mso-wrap-style:square'> |
---|
3529 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png" |
---|
3530 | o:title=""/> |
---|
3531 | </v:shape><![endif]--><![if !vml]><img border=0 width=508 height=500 |
---|
3532 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image083.png" |
---|
3533 | v:shapes="Picture_x0020_5"><![endif]></span></p> |
---|
3534 | |
---|
3535 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Check the D11 |
---|
3536 | box under Hydrostatic/elastic strain, set the Harmonic order to 6 and check the |
---|
3537 | Refine box for it (Preferred orientation). Then in two steps, do Edit/Copy |
---|
3538 | flags and Set All for the file selection. Then do Edit/Copy selected data; that |
---|
3539 | will bring up a new popup</p> |
---|
3540 | |
---|
3541 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3542 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_6" |
---|
3543 | o:spid="_x0000_i1047" type="#_x0000_t75" style='width:240pt;height:232.5pt; |
---|
3544 | visibility:visible;mso-wrap-style:square'> |
---|
3545 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png" |
---|
3546 | o:title=""/> |
---|
3547 | </v:shape><![endif]--><![if !vml]><img border=0 width=320 height=310 |
---|
3548 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image084.png" |
---|
3549 | v:shapes="Picture_x0020_6"><![endif]></span></p> |
---|
3550 | |
---|
3551 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This allows |
---|
3552 | you to select which parameters to copy data and flags. Select Pref. <span |
---|
3553 | class=SpellE>Ori</span>. And press OK; the file selection is next. Do Set <span |
---|
3554 | class=GramE>All</span> and OK to do this copy. That copies the full spherical |
---|
3555 | harmonics model to the other data sets. Select one to check if youd like.</p> |
---|
3556 | |
---|
3557 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Next do the |
---|
3558 | same thing for the B19 phase; here there are 4 <span class=SpellE>Dij</span> |
---|
3559 | parameters to check (do all of them) and use spherical harmonics order 4. When |
---|
3560 | done that Data window will look like</p> |
---|
3561 | |
---|
3562 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3563 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_7" |
---|
3564 | o:spid="_x0000_i1046" type="#_x0000_t75" style='width:381pt;height:467.25pt; |
---|
3565 | visibility:visible;mso-wrap-style:square'> |
---|
3566 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png" |
---|
3567 | o:title=""/> |
---|
3568 | </v:shape><![endif]--><![if !vml]><img border=0 width=508 height=623 |
---|
3569 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image085.png" |
---|
3570 | v:shapes="Picture_x0020_7"><![endif]></span></p> |
---|
3571 | |
---|
3572 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>We are now |
---|
3573 | ready for the next refinement; do Calculate/Sequential refine. Be careful not |
---|
3574 | (by habit say) pick Refine; a warning popup will appear. After it completes the |
---|
3575 | Sequential refinement results shows that the fit is better but convergence |
---|
3576 | wasnt quite complete.</p> |
---|
3577 | |
---|
3578 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3579 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8" |
---|
3580 | o:spid="_x0000_i1045" type="#_x0000_t75" style='width:525pt;height:262.5pt; |
---|
3581 | visibility:visible;mso-wrap-style:square'> |
---|
3582 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png" |
---|
3583 | o:title=""/> |
---|
3584 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350 |
---|
3585 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image086.png" |
---|
3586 | v:shapes="Picture_x0020_8"><![endif]></span></p> |
---|
3587 | |
---|
3588 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>It is probably |
---|
3589 | best to do another round of sequential refinement (I had to do two) to get |
---|
3590 | convergence. A plot of one PWDR entry gives</p> |
---|
3591 | |
---|
3592 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3593 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9" |
---|
3594 | o:spid="_x0000_i1044" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
3595 | visibility:visible;mso-wrap-style:square'> |
---|
3596 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png" |
---|
3597 | o:title=""/> |
---|
3598 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
3599 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image087.png" |
---|
3600 | v:shapes="Picture_x0020_9"><![endif]></span></p> |
---|
3601 | |
---|
3602 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>As our |
---|
3603 | experience in Method A, the calculated peaks are too sharp. We need to vary the |
---|
3604 | <span class=SpellE>mustrain</span> parameters for both phases. Go to the Data |
---|
3605 | tab for each phase, check the <span class=SpellE>microstrain</span> box and do |
---|
3606 | Edit/Copy flags for all the data sets. Then do another Calculate/Sequential |
---|
3607 | refine. My Sequential refinement results showed great improvement but |
---|
3608 | incomplete refinement</p> |
---|
3609 | |
---|
3610 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3611 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10" |
---|
3612 | o:spid="_x0000_i1043" type="#_x0000_t75" style='width:525pt;height:262.5pt; |
---|
3613 | visibility:visible;mso-wrap-style:square'> |
---|
3614 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png" |
---|
3615 | o:title=""/> |
---|
3616 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350 |
---|
3617 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image088.png" |
---|
3618 | v:shapes="Picture_x0020_10"><![endif]></span></p> |
---|
3619 | |
---|
3620 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Repeating the |
---|
3621 | sequential refinement (twice) gave convergence.</p> |
---|
3622 | |
---|
3623 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3624 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_11" |
---|
3625 | o:spid="_x0000_i1042" type="#_x0000_t75" style='width:525pt;height:262.5pt; |
---|
3626 | visibility:visible;mso-wrap-style:square'> |
---|
3627 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png" |
---|
3628 | o:title=""/> |
---|
3629 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350 |
---|
3630 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image089.png" |
---|
3631 | v:shapes="Picture_x0020_11"><![endif]></span></p> |
---|
3632 | |
---|
3633 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Examination of |
---|
3634 | the PWDR data sets showed a fairly good fit but some discrepancies (especially |
---|
3635 | for <span class=SpellE>Azm</span>=20.00)</p> |
---|
3636 | |
---|
3637 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3638 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12" |
---|
3639 | o:spid="_x0000_i1041" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
3640 | visibility:visible;mso-wrap-style:square'> |
---|
3641 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png" |
---|
3642 | o:title=""/> |
---|
3643 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
3644 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image090.png" |
---|
3645 | v:shapes="Picture_x0020_12"><![endif]></span></p> |
---|
3646 | |
---|
3647 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Showing that |
---|
3648 | perhaps the B19 phase needs high order spherical harmonics. Select the Data |
---|
3649 | tab for the B19 phase and change the Harmonic order to 6. Then do Edit/Copy |
---|
3650 | selected data for <span class=SpellE>Pref.Ori</span>. <span class=GramE>to</span> |
---|
3651 | the other data sets. This (after few repeats) gives a further improvement in |
---|
3652 | the fit</p> |
---|
3653 | |
---|
3654 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3655 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13" |
---|
3656 | o:spid="_x0000_i1040" type="#_x0000_t75" style='width:525pt;height:262.5pt; |
---|
3657 | visibility:visible;mso-wrap-style:square'> |
---|
3658 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png" |
---|
3659 | o:title=""/> |
---|
3660 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350 |
---|
3661 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image091.png" |
---|
3662 | v:shapes="Picture_x0020_13"><![endif]></span></p> |
---|
3663 | |
---|
3664 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This fit is |
---|
3665 | now sufficient for us to proceed to the next step and determine the texture of |
---|
3666 | the two phases.</p> |
---|
3667 | |
---|
3668 | <h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
3669 | 0in;line-height:115%'>Step 2. Texture analysis</h3> |
---|
3670 | |
---|
3671 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>During the |
---|
3672 | sequential refinements done in Step 1, we fitted the profiles allowing strain |
---|
3673 | parameters (<span class=SpellE>Dij</span>) for peak position shifts and <span |
---|
3674 | class=SpellE>microstrain</span> for peak shape. We modeled the intensity |
---|
3675 | variation with a spherical harmonics preferred orientation correction. If you |
---|
3676 | select any PWDR entry from the GSAS-II data tree and pick the Reflection List |
---|
3677 | subentry (at the bottom) you can see the magnitude of this correction for each |
---|
3678 | reflection in each phase.</p> |
---|
3679 | |
---|
3680 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>For the B2 |
---|
3681 | phase we see</p> |
---|
3682 | |
---|
3683 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3684 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14" |
---|
3685 | o:spid="_x0000_i1039" type="#_x0000_t75" style='width:659.25pt;height:262.5pt; |
---|
3686 | visibility:visible;mso-wrap-style:square'> |
---|
3687 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png" |
---|
3688 | o:title=""/> |
---|
3689 | </v:shape><![endif]--><![if !vml]><img border=0 width=879 height=350 |
---|
3690 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image092.png" |
---|
3691 | v:shapes="Picture_x0020_14"><![endif]></span></p> |
---|
3692 | |
---|
3693 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3694 | class=GramE>and</span> for the B19 phase we see</p> |
---|
3695 | |
---|
3696 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3697 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15" |
---|
3698 | o:spid="_x0000_i1038" type="#_x0000_t75" style='width:659.25pt;height:273pt; |
---|
3699 | visibility:visible;mso-wrap-style:square'> |
---|
3700 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png" |
---|
3701 | o:title=""/> |
---|
3702 | </v:shape><![endif]--><![if !vml]><img border=0 width=879 height=364 |
---|
3703 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image093.png" |
---|
3704 | v:shapes="Picture_x0020_15"><![endif]></span></p> |
---|
3705 | |
---|
3706 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>The preferred |
---|
3707 | orientation correction is <span class=SpellE>Prfo</span>; notice a few entries |
---|
3708 | in red. These are nonphysical correction values (the correction cant be |
---|
3709 | negative) but by in large these are small. This next step uses these |
---|
3710 | corrections as input data for a texture refinement. To start select the Texture |
---|
3711 | tab for the B2 phase; youll see</p> |
---|
3712 | |
---|
3713 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3714 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_16" |
---|
3715 | o:spid="_x0000_i1037" type="#_x0000_t75" style='width:456pt;height:217.5pt; |
---|
3716 | visibility:visible;mso-wrap-style:square'> |
---|
3717 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png" |
---|
3718 | o:title=""/> |
---|
3719 | </v:shape><![endif]--><![if !vml]><img border=0 width=608 height=290 |
---|
3720 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image065.png" |
---|
3721 | v:shapes="Picture_x0020_16"><![endif]></span></p> |
---|
3722 | |
---|
3723 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Since this |
---|
3724 | sample has wire texture, well use the default Texture model (cylindrical). |
---|
3725 | Then set the Harmonic order to 12 (what we used earlier) and check the Refine |
---|
3726 | and Show <span class=SpellE>coeff</span> boxes. The data window will be redrawn |
---|
3727 | (and a blank plot will appear).</p> |
---|
3728 | |
---|
3729 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3730 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_17" |
---|
3731 | o:spid="_x0000_i1036" type="#_x0000_t75" style='width:456pt;height:250.5pt; |
---|
3732 | visibility:visible;mso-wrap-style:square'> |
---|
3733 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png" |
---|
3734 | o:title=""/> |
---|
3735 | </v:shape><![endif]--><![if !vml]><img border=0 width=608 height=334 |
---|
3736 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image066.png" |
---|
3737 | v:shapes="Picture_x0020_17"><![endif]></span></p> |
---|
3738 | |
---|
3739 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do |
---|
3740 | Texture/Refine texture from the menu; the window will be repainted and a <span |
---|
3741 | class=SpellE>bullseye</span> pole figure will appear. </p> |
---|
3742 | |
---|
3743 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3744 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20" |
---|
3745 | o:spid="_x0000_i1035" type="#_x0000_t75" style='width:480pt;height:267.75pt; |
---|
3746 | visibility:visible;mso-wrap-style:square'> |
---|
3747 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png" |
---|
3748 | o:title=""/> |
---|
3749 | </v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357 |
---|
3750 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image094.png" |
---|
3751 | v:shapes="Picture_x0020_20"><![endif]></span></p> |
---|
3752 | |
---|
3753 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Change the |
---|
3754 | Texture plot type to Inverse pole figure to get a more useful plot</p> |
---|
3755 | |
---|
3756 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3757 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_19" |
---|
3758 | o:spid="_x0000_i1034" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
3759 | visibility:visible;mso-wrap-style:square'> |
---|
3760 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png" |
---|
3761 | o:title=""/> |
---|
3762 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
3763 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image095.png" |
---|
3764 | v:shapes="Picture_x0020_19"><![endif]></span></p> |
---|
3765 | |
---|
3766 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This is |
---|
3767 | essentially the same as we obtained earlier in Method <span class=GramE>A</span> |
---|
3768 | (maybe not quite as strong here).</p> |
---|
3769 | |
---|
3770 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the |
---|
3771 | Texture tab for the B19 phase and do the same; use Harmonic order 10 as we did |
---|
3772 | earlier in Method A. After setting the two flags and doing Texture/Refine |
---|
3773 | texture we get</p> |
---|
3774 | |
---|
3775 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3776 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21" |
---|
3777 | o:spid="_x0000_i1033" type="#_x0000_t75" style='width:502.5pt;height:375pt; |
---|
3778 | visibility:visible;mso-wrap-style:square'> |
---|
3779 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png" |
---|
3780 | o:title=""/> |
---|
3781 | </v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500 |
---|
3782 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image096.png" |
---|
3783 | v:shapes="Picture_x0020_21"><![endif]></span></p> |
---|
3784 | |
---|
3785 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>And a <span |
---|
3786 | class=SpellE>bullseye</span> pole figure; change that to Inverse pole figure to |
---|
3787 | see the texture</p> |
---|
3788 | |
---|
3789 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
3790 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_22" |
---|
3791 | o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
3792 | visibility:visible;mso-wrap-style:square'> |
---|
3793 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png" |
---|
3794 | o:title=""/> |
---|
3795 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
3796 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image097.png" |
---|
3797 | v:shapes="Picture_x0020_22"><![endif]></span></p> |
---|
3798 | |
---|
3799 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Again this is |
---|
3800 | very similar to what we found in Method A but again not quite as strong (max |
---|
3801 | MRD ~13 instead of ~18).</p> |
---|
3802 | |
---|
3803 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now do a |
---|
3804 | File/Save project from the main menu; this saves the final texture results done |
---|
3805 | in Step 2 (you also will need it for Method C).</p> |
---|
3806 | |
---|
3807 | <h2 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
3808 | 0in;line-height:115%'>Method C. Sequential refinement & full texture |
---|
3809 | refinement</h2> |
---|
3810 | |
---|
3811 | <h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
3812 | 0in;line-height:115%'>Introduction</h3> |
---|
3813 | |
---|
3814 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>This uses the |
---|
3815 | same approach as Method B except that after the sequential refinements are |
---|
3816 | finished we then fix almost all the parameters and then do a final texture |
---|
3817 | refinement with all the data. Thus, this is a replacement for Step 2 in Method |
---|
3818 | B. To begin do <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3819 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3820 | minor-latin'>File/Open project
</span></b> for the <span class=SpellE><b |
---|
3821 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3822 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>NiTi-B.gpx</span></b></span> |
---|
3823 | file created in Method B and then do a <b style='mso-bidi-font-weight:normal'><span |
---|
3824 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3825 | mso-hansi-theme-font:minor-latin'>File/Save project as
</span></b> to save it |
---|
3826 | as <span class=SpellE><b style='mso-bidi-font-weight:normal'><span |
---|
3827 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3828 | mso-hansi-theme-font:minor-latin'>NiTi</span></b></span><b style='mso-bidi-font-weight: |
---|
3829 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3830 | minor-latin;mso-hansi-theme-font:minor-latin'>-C</span></b>. This renames the |
---|
3831 | project and it should have one IMG, 10 PWDR entries and two phases of <span |
---|
3832 | class=SpellE>NiTi</span> (B2 and B19).</p> |
---|
3833 | |
---|
3834 | <h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
3835 | 0in;line-height:115%'>Step 1. Clearing unwanted variables from sequential |
---|
3836 | refinement</h3> |
---|
3837 | |
---|
3838 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Here we want |
---|
3839 | to clear refinement flags for all parameters that need not be varied in a |
---|
3840 | texture analysis refinement. The general rule is to not refine any parameter |
---|
3841 | unless we expect it to affect the peak intensities. These are listed below:</p> |
---|
3842 | |
---|
3843 | <p class=MsoListParagraphCxSpFirst style='margin-bottom:12.0pt;mso-add-space: |
---|
3844 | auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span |
---|
3845 | style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1)<span |
---|
3846 | style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><b |
---|
3847 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3848 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>: |
---|
3849 | as the background was fit during the sequential refinement we should fix it |
---|
3850 | here. Select any <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3851 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3852 | minor-latin'>PWDR</span></b> entry and choose the <b style='mso-bidi-font-weight: |
---|
3853 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3854 | minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b> subentry |
---|
3855 | for it. Clear the <b style='mso-bidi-font-weight:normal'><span |
---|
3856 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3857 | mso-hansi-theme-font:minor-latin'>Refine</span></b> flags and the do <b |
---|
3858 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3859 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Copy |
---|
3860 | flags</span></b> selecting all data sets. This will clear all background |
---|
3861 | refinement flags.</p> |
---|
3862 | |
---|
3863 | <p class=MsoListParagraphCxSpMiddle style='margin-bottom:12.0pt;mso-add-space: |
---|
3864 | auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span |
---|
3865 | style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2)<span |
---|
3866 | style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><b |
---|
3867 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3868 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> |
---|
3869 | phase: we do not want to refine either the <span class=SpellE>microstrain</span>, |
---|
3870 | D<sub>11</sub>, or preferred orientation coefficients. Select the <b |
---|
3871 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3872 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> |
---|
3873 | phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3874 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3875 | minor-latin'>Data</span></b> tab. <span class=GramE>Clear</span> the <span |
---|
3876 | class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3877 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3878 | minor-latin'>microstrain</span></b></span>, <b style='mso-bidi-font-weight: |
---|
3879 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3880 | minor-latin;mso-hansi-theme-font:minor-latin'>D<sub>11</sub></span></b> and <b |
---|
3881 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3882 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred |
---|
3883 | orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span |
---|
3884 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3885 | mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will |
---|
3886 | avoid a lot of nasty (but harmless) messages at the start of the refinement). |
---|
3887 | Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3888 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy |
---|
3889 | flags</span></b> selecting all data to clear all the flags and an <b |
---|
3890 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3891 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy |
---|
3892 | selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight: |
---|
3893 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3894 | minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to |
---|
3895 | copy the zeroed out harmonic coefficients.</p> |
---|
3896 | |
---|
3897 | <p class=MsoListParagraphCxSpLast style='margin-bottom:12.0pt;mso-add-space: |
---|
3898 | auto;text-indent:-.25in;line-height:115%;mso-list:l1 level1 lfo4'><![if !supportLists]><span |
---|
3899 | style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>3)<span |
---|
3900 | style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><b |
---|
3901 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3902 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19</span></b>: |
---|
3903 | we do not want to refine either the <span class=SpellE>microstrain</span>, <span |
---|
3904 | class=SpellE>Dij</span>, or preferred orientation coefficients. Select the <b |
---|
3905 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3906 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19</span></b> |
---|
3907 | phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3908 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3909 | minor-latin'>Data</span></b> tab. Clear the <span class=SpellE><b |
---|
3910 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3911 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>microstrain</span></b></span>, |
---|
3912 | four <span class=SpellE><b style='mso-bidi-font-weight:normal'><span |
---|
3913 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3914 | mso-hansi-theme-font:minor-latin'>Dij</span></b></span> and <b |
---|
3915 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3916 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Preferred |
---|
3917 | orientation</span></b> boxes. Also set the <b style='mso-bidi-font-weight:normal'><span |
---|
3918 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3919 | mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero (this will |
---|
3920 | avoid a lot of nasty (but harmless) messages at the start of the refinement). |
---|
3921 | Then do <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3922 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy |
---|
3923 | flags</span></b> selecting all data to clear all the flags and an <b |
---|
3924 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3925 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Copy |
---|
3926 | selected data</span></b> for <span class=SpellE><b style='mso-bidi-font-weight: |
---|
3927 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3928 | minor-latin;mso-hansi-theme-font:minor-latin'>Pref.Ori</span></b></span> to |
---|
3929 | copy the zeroed out harmonic coefficients.</p> |
---|
3930 | |
---|
3931 | <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
3932 | margin-left:.25in;line-height:115%'><o:p> </o:p></p> |
---|
3933 | |
---|
3934 | <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
3935 | margin-left:.25in;line-height:115%'>Notice that we have allowed refinement of |
---|
3936 | the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3937 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Phase fractions</span></b>; |
---|
3938 | these may change during the texture refinement. Now select the <b |
---|
3939 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3940 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b> |
---|
3941 | tab for the <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
3942 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
3943 | minor-latin'>B2</span></b> phase (it may still have values from the Method B).</p> |
---|
3944 | |
---|
3945 | <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
3946 | margin-left:.25in;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
---|
3947 | id="Picture_x0020_23" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:480pt; |
---|
3948 | height:267.75pt;visibility:visible;mso-wrap-style:square'> |
---|
3949 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png" |
---|
3950 | o:title=""/> |
---|
3951 | </v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357 |
---|
3952 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image098.png" |
---|
3953 | v:shapes="Picture_x0020_23"><![endif]></span></p> |
---|
3954 | |
---|
3955 | <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
3956 | margin-left:.25in;line-height:115%'>You can clear these by setting the <b |
---|
3957 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3958 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Harmonic |
---|
3959 | order</span></b> to zero and then back to <b style='mso-bidi-font-weight:normal'><span |
---|
3960 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3961 | mso-hansi-theme-font:minor-latin'>12</span></b>. Leave the <b style='mso-bidi-font-weight: |
---|
3962 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
3963 | minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b> & <b |
---|
3964 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3965 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b> |
---|
3966 | boxes checked.</p> |
---|
3967 | |
---|
3968 | <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
3969 | margin-left:.25in;line-height:115%'><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
---|
3970 | id="Picture_x0020_24" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:480pt; |
---|
3971 | height:267.75pt;visibility:visible;mso-wrap-style:square'> |
---|
3972 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png" |
---|
3973 | o:title=""/> |
---|
3974 | </v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357 |
---|
3975 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image099.png" |
---|
3976 | v:shapes="Picture_x0020_24"><![endif]></span></p> |
---|
3977 | |
---|
3978 | <p class=MsoNormal style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt; |
---|
3979 | margin-left:.25in;line-height:115%'>Then do the same for the <b |
---|
3980 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3981 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19</span></b> |
---|
3982 | phase. Select the <b style='mso-bidi-font-weight:normal'><span |
---|
3983 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3984 | mso-hansi-theme-font:minor-latin'>B19</span></b> phase and its <b |
---|
3985 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3986 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b> |
---|
3987 | tab. <span class=GramE>Set</span> the <b style='mso-bidi-font-weight:normal'><span |
---|
3988 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
3989 | mso-hansi-theme-font:minor-latin'>Harmonic order</span></b> to zero and then |
---|
3990 | back to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3991 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>10</span></b>. |
---|
3992 | Leave the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3993 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refine</span></b> |
---|
3994 | and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
3995 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Show</span></b> |
---|
3996 | boxes checked. This completes the setup for the full texture refinement.</p> |
---|
3997 | |
---|
3998 | <h3 style='margin-top:0in;margin-right:0in;margin-bottom:12.0pt;margin-left: |
---|
3999 | 0in;line-height:115%'>Step 2. Texture refinement</h3> |
---|
4000 | |
---|
4001 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Do <b |
---|
4002 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
4003 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Calculate/Refine</span></b> |
---|
4004 | from the main menu; you will see the warning message</p> |
---|
4005 | |
---|
4006 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
4007 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_25" |
---|
4008 | o:spid="_x0000_i1029" type="#_x0000_t75" style='width:363pt;height:120.75pt; |
---|
4009 | visibility:visible;mso-wrap-style:square'> |
---|
4010 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png" |
---|
4011 | o:title=""/> |
---|
4012 | </v:shape><![endif]--><![if !vml]><img border=0 width=484 height=161 |
---|
4013 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image100.png" |
---|
4014 | v:shapes="Picture_x0020_25"><![endif]></span></p> |
---|
4015 | |
---|
4016 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>In this case |
---|
4017 | you do want to do a <span class=SpellE>nonsequential</span> full refinement, so |
---|
4018 | press the OK button. A quick look at the console will show that there are 61 |
---|
4019 | variables in this refinement. If yours shows more then you didnt clear all the |
---|
4020 | flags in Step 1. The <b style='mso-bidi-font-weight:normal'><span |
---|
4021 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
4022 | mso-hansi-theme-font:minor-latin'>Sequential results</span></b> entry is |
---|
4023 | deleted from the GSAS-II data tree. A progress bar will show giving the |
---|
4024 | residuals during the refinement. When finished, select the <b style='mso-bidi-font-weight: |
---|
4025 | normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font: |
---|
4026 | minor-latin;mso-hansi-theme-font:minor-latin'>B2</span></b> phase and its <b |
---|
4027 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
4028 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Texture</span></b> |
---|
4029 | tab; if the Texture plot type is still <b style='mso-bidi-font-weight:normal'><span |
---|
4030 | style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin; |
---|
4031 | mso-hansi-theme-font:minor-latin'>Inverse pole figure</span></b> (from Method |
---|
4032 | B) you should see</p> |
---|
4033 | |
---|
4034 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
4035 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26" |
---|
4036 | o:spid="_x0000_i1028" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
4037 | visibility:visible;mso-wrap-style:square'> |
---|
4038 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png" |
---|
4039 | o:title=""/> |
---|
4040 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
4041 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image101.png" |
---|
4042 | v:shapes="Picture_x0020_26"><![endif]></span></p> |
---|
4043 | |
---|
4044 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
4045 | class=GramE>which</span> is almost identical to that from Method A. The |
---|
4046 | coefficients are seen in</p> |
---|
4047 | |
---|
4048 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
4049 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27" |
---|
4050 | o:spid="_x0000_i1027" type="#_x0000_t75" style='width:480pt;height:267.75pt; |
---|
4051 | visibility:visible;mso-wrap-style:square'> |
---|
4052 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png" |
---|
4053 | o:title=""/> |
---|
4054 | </v:shape><![endif]--><![if !vml]><img border=0 width=640 height=357 |
---|
4055 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image102.png" |
---|
4056 | v:shapes="Picture_x0020_27"><![endif]></span></p> |
---|
4057 | |
---|
4058 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>Now select the |
---|
4059 | <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif; |
---|
4060 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>B19</span></b> |
---|
4061 | phase and its <b style='mso-bidi-font-weight:normal'><span style='font-family: |
---|
4062 | "Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
---|
4063 | minor-latin'>Texture</span></b> tab; the inverse pole figure is</p> |
---|
4064 | |
---|
4065 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
4066 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28" |
---|
4067 | o:spid="_x0000_i1026" type="#_x0000_t75" style='width:525pt;height:450pt; |
---|
4068 | visibility:visible;mso-wrap-style:square'> |
---|
4069 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png" |
---|
4070 | o:title=""/> |
---|
4071 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
---|
4072 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image103.png" |
---|
4073 | v:shapes="Picture_x0020_28"><![endif]></span></p> |
---|
4074 | |
---|
4075 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
4076 | class=GramE>and</span> also almost identical to what was obtained in Method A; |
---|
4077 | the coefficients are seen in</p> |
---|
4078 | |
---|
4079 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'><span |
---|
4080 | style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_58" |
---|
4081 | o:spid="_x0000_i1025" type="#_x0000_t75" style='width:502.5pt;height:375pt; |
---|
4082 | visibility:visible;mso-wrap-style:square'> |
---|
4083 | <v:imagedata src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png" |
---|
4084 | o:title=""/> |
---|
4085 | </v:shape><![endif]--><![if !vml]><img border=0 width=670 height=500 |
---|
4086 | src="Texture%20analysis%20of%202D%20data%20in%20GSAS-II_files/image104.png" |
---|
4087 | v:shapes="Picture_x0020_58"><![endif]></span></p> |
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4088 | |
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4089 | <p class=MsoNormal style='margin-bottom:12.0pt;line-height:115%'>With this |
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4090 | Method you can add parameters (atom coordinates & thermal motion |
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4091 | parameters) that could not be refined in method B. It should be clear from this |
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4092 | tutorial that in more complex textures where the data set may consist of slices |
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4093 | obtained from a suite of 2D images collected as the sample is rotated, Method C |
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4094 | will give a relatively fast determination of the texture without resorting to large |
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4095 | matrix least-squares refinements.</p> |
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4096 | |
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4097 | </div> |
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4098 | |
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4099 | </body> |
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4100 | |
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4101 | </html> |
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