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| 19 | .shape {behavior:url(#default#VML);} |
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| 22 | <o:DocumentProperties> |
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| 23 | <o:Author>B Toby</o:Author> |
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| 24 | <o:LastAuthor>Von Dreele</o:LastAuthor> |
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| 25 | <o:Revision>2</o:Revision> |
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| 26 | <o:TotalTime>984</o:TotalTime> |
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| 27 | <o:Created>2014-07-22T21:21:00Z</o:Created> |
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| 28 | <o:LastSaved>2014-07-22T21:21:00Z</o:LastSaved> |
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| 30 | <o:Words>1641</o:Words> |
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| 31 | <o:Characters>9358</o:Characters> |
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| 32 | <o:Company>Argonne National Laboratory</o:Company> |
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| 307 | <w:LsdException Locked="false" Priority="62" SemiHidden="false" |
|---|
| 308 | UnhideWhenUsed="false" Name="Light Grid Accent 6"/> |
|---|
| 309 | <w:LsdException Locked="false" Priority="63" SemiHidden="false" |
|---|
| 310 | UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/> |
|---|
| 311 | <w:LsdException Locked="false" Priority="64" SemiHidden="false" |
|---|
| 312 | UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/> |
|---|
| 313 | <w:LsdException Locked="false" Priority="65" SemiHidden="false" |
|---|
| 314 | UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/> |
|---|
| 315 | <w:LsdException Locked="false" Priority="66" SemiHidden="false" |
|---|
| 316 | UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/> |
|---|
| 317 | <w:LsdException Locked="false" Priority="67" SemiHidden="false" |
|---|
| 318 | UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/> |
|---|
| 319 | <w:LsdException Locked="false" Priority="68" SemiHidden="false" |
|---|
| 320 | UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/> |
|---|
| 321 | <w:LsdException Locked="false" Priority="69" SemiHidden="false" |
|---|
| 322 | UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/> |
|---|
| 323 | <w:LsdException Locked="false" Priority="70" SemiHidden="false" |
|---|
| 324 | UnhideWhenUsed="false" Name="Dark List Accent 6"/> |
|---|
| 325 | <w:LsdException Locked="false" Priority="71" SemiHidden="false" |
|---|
| 326 | UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/> |
|---|
| 327 | <w:LsdException Locked="false" Priority="72" SemiHidden="false" |
|---|
| 328 | UnhideWhenUsed="false" Name="Colorful List Accent 6"/> |
|---|
| 329 | <w:LsdException Locked="false" Priority="73" SemiHidden="false" |
|---|
| 330 | UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/> |
|---|
| 331 | <w:LsdException Locked="false" Priority="19" SemiHidden="false" |
|---|
| 332 | UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/> |
|---|
| 333 | <w:LsdException Locked="false" Priority="21" SemiHidden="false" |
|---|
| 334 | UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/> |
|---|
| 335 | <w:LsdException Locked="false" Priority="31" SemiHidden="false" |
|---|
| 336 | UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/> |
|---|
| 337 | <w:LsdException Locked="false" Priority="32" SemiHidden="false" |
|---|
| 338 | UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/> |
|---|
| 339 | <w:LsdException Locked="false" Priority="33" SemiHidden="false" |
|---|
| 340 | UnhideWhenUsed="false" QFormat="true" Name="Book Title"/> |
|---|
| 341 | <w:LsdException Locked="false" Priority="37" Name="Bibliography"/> |
|---|
| 342 | <w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/> |
|---|
| 343 | </w:LatentStyles> |
|---|
| 344 | </xml><![endif]--> |
|---|
| 345 | <style> |
|---|
| 346 | <!-- |
|---|
| 347 | /* Font Definitions */ |
|---|
| 348 | @font-face |
|---|
| 349 | {font-family:Courier; |
|---|
| 350 | panose-1:2 7 4 9 2 2 5 2 4 4; |
|---|
| 351 | mso-font-alt:"Courier New"; |
|---|
| 352 | mso-font-charset:0; |
|---|
| 353 | mso-generic-font-family:modern; |
|---|
| 354 | mso-font-format:other; |
|---|
| 355 | mso-font-pitch:fixed; |
|---|
| 356 | mso-font-signature:3 0 0 0 1 0;} |
|---|
| 357 | @font-face |
|---|
| 358 | {font-family:Courier; |
|---|
| 359 | panose-1:2 7 4 9 2 2 5 2 4 4; |
|---|
| 360 | mso-font-alt:"Courier New"; |
|---|
| 361 | mso-font-charset:0; |
|---|
| 362 | mso-generic-font-family:modern; |
|---|
| 363 | mso-font-format:other; |
|---|
| 364 | mso-font-pitch:fixed; |
|---|
| 365 | mso-font-signature:3 0 0 0 1 0;} |
|---|
| 366 | @font-face |
|---|
| 367 | {font-family:Cambria; |
|---|
| 368 | panose-1:2 4 5 3 5 4 6 3 2 4; |
|---|
| 369 | mso-font-charset:0; |
|---|
| 370 | mso-generic-font-family:roman; |
|---|
| 371 | mso-font-pitch:variable; |
|---|
| 372 | mso-font-signature:-536870145 1073743103 0 0 415 0;} |
|---|
| 373 | @font-face |
|---|
| 374 | {font-family:Calibri; |
|---|
| 375 | panose-1:2 15 5 2 2 2 4 3 2 4; |
|---|
| 376 | mso-font-charset:0; |
|---|
| 377 | mso-generic-font-family:swiss; |
|---|
| 378 | mso-font-pitch:variable; |
|---|
| 379 | mso-font-signature:-536870145 1073786111 1 0 415 0;} |
|---|
| 380 | @font-face |
|---|
| 381 | {font-family:"Lucida Grande"; |
|---|
| 382 | mso-font-alt:"Times New Roman"; |
|---|
| 383 | mso-font-charset:0; |
|---|
| 384 | mso-generic-font-family:auto; |
|---|
| 385 | mso-font-pitch:variable; |
|---|
| 386 | mso-font-signature:0 1342218751 0 0 447 0;} |
|---|
| 387 | @font-face |
|---|
| 388 | {font-family:Consolas; |
|---|
| 389 | panose-1:2 11 6 9 2 2 4 3 2 4; |
|---|
| 390 | mso-font-charset:0; |
|---|
| 391 | mso-generic-font-family:modern; |
|---|
| 392 | mso-font-pitch:fixed; |
|---|
| 393 | mso-font-signature:-520092929 1073806591 9 0 415 0;} |
|---|
| 394 | /* Style Definitions */ |
|---|
| 395 | p.MsoNormal, li.MsoNormal, div.MsoNormal |
|---|
| 396 | {mso-style-unhide:no; |
|---|
| 397 | mso-style-qformat:yes; |
|---|
| 398 | mso-style-parent:""; |
|---|
| 399 | margin:0in; |
|---|
| 400 | margin-bottom:.0001pt; |
|---|
| 401 | mso-pagination:widow-orphan; |
|---|
| 402 | font-size:12.0pt; |
|---|
| 403 | mso-bidi-font-size:10.0pt; |
|---|
| 404 | font-family:"Times New Roman","serif"; |
|---|
| 405 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 406 | mso-fareast-theme-font:minor-fareast; |
|---|
| 407 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 408 | mso-bidi-theme-font:minor-bidi; |
|---|
| 409 | mso-fareast-language:JA;} |
|---|
| 410 | h1 |
|---|
| 411 | {mso-style-priority:9; |
|---|
| 412 | mso-style-unhide:no; |
|---|
| 413 | mso-style-qformat:yes; |
|---|
| 414 | mso-style-link:"Heading 1 Char"; |
|---|
| 415 | mso-style-next:Normal; |
|---|
| 416 | margin-top:24.0pt; |
|---|
| 417 | margin-right:0in; |
|---|
| 418 | margin-bottom:0in; |
|---|
| 419 | margin-left:0in; |
|---|
| 420 | margin-bottom:.0001pt; |
|---|
| 421 | mso-pagination:widow-orphan lines-together; |
|---|
| 422 | page-break-after:avoid; |
|---|
| 423 | mso-outline-level:1; |
|---|
| 424 | font-size:18.0pt; |
|---|
| 425 | mso-bidi-font-size:16.0pt; |
|---|
| 426 | font-family:"Times New Roman","serif"; |
|---|
| 427 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 428 | mso-fareast-theme-font:major-fareast; |
|---|
| 429 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 430 | mso-bidi-theme-font:major-bidi; |
|---|
| 431 | mso-font-kerning:0pt; |
|---|
| 432 | mso-fareast-language:JA;} |
|---|
| 433 | h2 |
|---|
| 434 | {mso-style-noshow:yes; |
|---|
| 435 | mso-style-priority:9; |
|---|
| 436 | mso-style-qformat:yes; |
|---|
| 437 | mso-style-link:"Heading 2 Char"; |
|---|
| 438 | mso-style-next:Normal; |
|---|
| 439 | margin-top:10.0pt; |
|---|
| 440 | margin-right:0in; |
|---|
| 441 | margin-bottom:0in; |
|---|
| 442 | margin-left:0in; |
|---|
| 443 | margin-bottom:.0001pt; |
|---|
| 444 | mso-pagination:widow-orphan lines-together; |
|---|
| 445 | page-break-after:avoid; |
|---|
| 446 | mso-outline-level:2; |
|---|
| 447 | font-size:13.0pt; |
|---|
| 448 | font-family:"Calibri","sans-serif"; |
|---|
| 449 | mso-ascii-font-family:Calibri; |
|---|
| 450 | mso-ascii-theme-font:major-latin; |
|---|
| 451 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 452 | mso-fareast-theme-font:major-fareast; |
|---|
| 453 | mso-hansi-font-family:Calibri; |
|---|
| 454 | mso-hansi-theme-font:major-latin; |
|---|
| 455 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 456 | mso-bidi-theme-font:major-bidi; |
|---|
| 457 | color:#4F81BD; |
|---|
| 458 | mso-themecolor:accent1; |
|---|
| 459 | mso-fareast-language:JA;} |
|---|
| 460 | a:link, span.MsoHyperlink |
|---|
| 461 | {mso-style-noshow:yes; |
|---|
| 462 | mso-style-priority:99; |
|---|
| 463 | color:blue; |
|---|
| 464 | mso-themecolor:hyperlink; |
|---|
| 465 | text-decoration:underline; |
|---|
| 466 | text-underline:single;} |
|---|
| 467 | a:visited, span.MsoHyperlinkFollowed |
|---|
| 468 | {mso-style-noshow:yes; |
|---|
| 469 | mso-style-priority:99; |
|---|
| 470 | color:purple; |
|---|
| 471 | mso-themecolor:followedhyperlink; |
|---|
| 472 | text-decoration:underline; |
|---|
| 473 | text-underline:single;} |
|---|
| 474 | pre |
|---|
| 475 | {mso-style-noshow:yes; |
|---|
| 476 | mso-style-priority:99; |
|---|
| 477 | mso-style-link:"HTML Preformatted Char"; |
|---|
| 478 | margin:0in; |
|---|
| 479 | margin-bottom:.0001pt; |
|---|
| 480 | mso-pagination:widow-orphan; |
|---|
| 481 | font-size:10.0pt; |
|---|
| 482 | font-family:"Courier New"; |
|---|
| 483 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 484 | mso-fareast-theme-font:minor-fareast;} |
|---|
| 485 | p.MsoAcetate, li.MsoAcetate, div.MsoAcetate |
|---|
| 486 | {mso-style-noshow:yes; |
|---|
| 487 | mso-style-priority:99; |
|---|
| 488 | mso-style-link:"Balloon Text Char"; |
|---|
| 489 | margin:0in; |
|---|
| 490 | margin-bottom:.0001pt; |
|---|
| 491 | mso-pagination:widow-orphan; |
|---|
| 492 | font-size:9.0pt; |
|---|
| 493 | font-family:"Lucida Grande"; |
|---|
| 494 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 495 | mso-fareast-theme-font:minor-fareast; |
|---|
| 496 | mso-fareast-language:JA;} |
|---|
| 497 | p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph |
|---|
| 498 | {mso-style-priority:34; |
|---|
| 499 | mso-style-unhide:no; |
|---|
| 500 | mso-style-qformat:yes; |
|---|
| 501 | margin-top:0in; |
|---|
| 502 | margin-right:0in; |
|---|
| 503 | margin-bottom:0in; |
|---|
| 504 | margin-left:.5in; |
|---|
| 505 | margin-bottom:.0001pt; |
|---|
| 506 | mso-add-space:auto; |
|---|
| 507 | mso-pagination:widow-orphan; |
|---|
| 508 | font-size:12.0pt; |
|---|
| 509 | mso-bidi-font-size:10.0pt; |
|---|
| 510 | font-family:"Times New Roman","serif"; |
|---|
| 511 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 512 | mso-fareast-theme-font:minor-fareast; |
|---|
| 513 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 514 | mso-bidi-theme-font:minor-bidi; |
|---|
| 515 | mso-fareast-language:JA;} |
|---|
| 516 | p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst |
|---|
| 517 | {mso-style-priority:34; |
|---|
| 518 | mso-style-unhide:no; |
|---|
| 519 | mso-style-qformat:yes; |
|---|
| 520 | mso-style-type:export-only; |
|---|
| 521 | margin-top:0in; |
|---|
| 522 | margin-right:0in; |
|---|
| 523 | margin-bottom:0in; |
|---|
| 524 | margin-left:.5in; |
|---|
| 525 | margin-bottom:.0001pt; |
|---|
| 526 | mso-add-space:auto; |
|---|
| 527 | mso-pagination:widow-orphan; |
|---|
| 528 | font-size:12.0pt; |
|---|
| 529 | mso-bidi-font-size:10.0pt; |
|---|
| 530 | font-family:"Times New Roman","serif"; |
|---|
| 531 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 532 | mso-fareast-theme-font:minor-fareast; |
|---|
| 533 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 534 | mso-bidi-theme-font:minor-bidi; |
|---|
| 535 | mso-fareast-language:JA;} |
|---|
| 536 | p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle |
|---|
| 537 | {mso-style-priority:34; |
|---|
| 538 | mso-style-unhide:no; |
|---|
| 539 | mso-style-qformat:yes; |
|---|
| 540 | mso-style-type:export-only; |
|---|
| 541 | margin-top:0in; |
|---|
| 542 | margin-right:0in; |
|---|
| 543 | margin-bottom:0in; |
|---|
| 544 | margin-left:.5in; |
|---|
| 545 | margin-bottom:.0001pt; |
|---|
| 546 | mso-add-space:auto; |
|---|
| 547 | mso-pagination:widow-orphan; |
|---|
| 548 | font-size:12.0pt; |
|---|
| 549 | mso-bidi-font-size:10.0pt; |
|---|
| 550 | font-family:"Times New Roman","serif"; |
|---|
| 551 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 552 | mso-fareast-theme-font:minor-fareast; |
|---|
| 553 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 554 | mso-bidi-theme-font:minor-bidi; |
|---|
| 555 | mso-fareast-language:JA;} |
|---|
| 556 | p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast |
|---|
| 557 | {mso-style-priority:34; |
|---|
| 558 | mso-style-unhide:no; |
|---|
| 559 | mso-style-qformat:yes; |
|---|
| 560 | mso-style-type:export-only; |
|---|
| 561 | margin-top:0in; |
|---|
| 562 | margin-right:0in; |
|---|
| 563 | margin-bottom:0in; |
|---|
| 564 | margin-left:.5in; |
|---|
| 565 | margin-bottom:.0001pt; |
|---|
| 566 | mso-add-space:auto; |
|---|
| 567 | mso-pagination:widow-orphan; |
|---|
| 568 | font-size:12.0pt; |
|---|
| 569 | mso-bidi-font-size:10.0pt; |
|---|
| 570 | font-family:"Times New Roman","serif"; |
|---|
| 571 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 572 | mso-fareast-theme-font:minor-fareast; |
|---|
| 573 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 574 | mso-bidi-theme-font:minor-bidi; |
|---|
| 575 | mso-fareast-language:JA;} |
|---|
| 576 | span.Heading1Char |
|---|
| 577 | {mso-style-name:"Heading 1 Char"; |
|---|
| 578 | mso-style-priority:9; |
|---|
| 579 | mso-style-unhide:no; |
|---|
| 580 | mso-style-locked:yes; |
|---|
| 581 | mso-style-link:"Heading 1"; |
|---|
| 582 | mso-ansi-font-size:18.0pt; |
|---|
| 583 | mso-bidi-font-size:16.0pt; |
|---|
| 584 | font-family:"Times New Roman","serif"; |
|---|
| 585 | mso-ascii-font-family:"Times New Roman"; |
|---|
| 586 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 587 | mso-fareast-theme-font:major-fareast; |
|---|
| 588 | mso-hansi-font-family:"Times New Roman"; |
|---|
| 589 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 590 | mso-bidi-theme-font:major-bidi; |
|---|
| 591 | font-weight:bold;} |
|---|
| 592 | span.Heading2Char |
|---|
| 593 | {mso-style-name:"Heading 2 Char"; |
|---|
| 594 | mso-style-noshow:yes; |
|---|
| 595 | mso-style-priority:9; |
|---|
| 596 | mso-style-unhide:no; |
|---|
| 597 | mso-style-locked:yes; |
|---|
| 598 | mso-style-link:"Heading 2"; |
|---|
| 599 | mso-ansi-font-size:13.0pt; |
|---|
| 600 | mso-bidi-font-size:13.0pt; |
|---|
| 601 | font-family:"Calibri","sans-serif"; |
|---|
| 602 | mso-ascii-font-family:Calibri; |
|---|
| 603 | mso-ascii-theme-font:major-latin; |
|---|
| 604 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 605 | mso-fareast-theme-font:major-fareast; |
|---|
| 606 | mso-hansi-font-family:Calibri; |
|---|
| 607 | mso-hansi-theme-font:major-latin; |
|---|
| 608 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 609 | mso-bidi-theme-font:major-bidi; |
|---|
| 610 | color:#4F81BD; |
|---|
| 611 | mso-themecolor:accent1; |
|---|
| 612 | font-weight:bold;} |
|---|
| 613 | span.HTMLPreformattedChar |
|---|
| 614 | {mso-style-name:"HTML Preformatted Char"; |
|---|
| 615 | mso-style-noshow:yes; |
|---|
| 616 | mso-style-priority:99; |
|---|
| 617 | mso-style-unhide:no; |
|---|
| 618 | mso-style-locked:yes; |
|---|
| 619 | mso-style-link:"HTML Preformatted"; |
|---|
| 620 | font-family:Consolas; |
|---|
| 621 | mso-ascii-font-family:Consolas; |
|---|
| 622 | mso-hansi-font-family:Consolas; |
|---|
| 623 | mso-bidi-font-family:Consolas;} |
|---|
| 624 | span.BalloonTextChar |
|---|
| 625 | {mso-style-name:"Balloon Text Char"; |
|---|
| 626 | mso-style-noshow:yes; |
|---|
| 627 | mso-style-priority:99; |
|---|
| 628 | mso-style-unhide:no; |
|---|
| 629 | mso-style-locked:yes; |
|---|
| 630 | mso-style-link:"Balloon Text"; |
|---|
| 631 | mso-ansi-font-size:9.0pt; |
|---|
| 632 | mso-bidi-font-size:9.0pt; |
|---|
| 633 | font-family:"Lucida Grande"; |
|---|
| 634 | mso-ascii-font-family:"Lucida Grande"; |
|---|
| 635 | mso-hansi-font-family:"Lucida Grande"; |
|---|
| 636 | mso-bidi-font-family:"Lucida Grande";} |
|---|
| 637 | .MsoChpDefault |
|---|
| 638 | {mso-style-type:export-only; |
|---|
| 639 | mso-default-props:yes; |
|---|
| 640 | font-size:10.0pt; |
|---|
| 641 | mso-ansi-font-size:10.0pt; |
|---|
| 642 | mso-bidi-font-size:10.0pt; |
|---|
| 643 | font-family:"Cambria","serif"; |
|---|
| 644 | mso-ascii-font-family:Cambria; |
|---|
| 645 | mso-ascii-theme-font:minor-latin; |
|---|
| 646 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 647 | mso-fareast-theme-font:minor-fareast; |
|---|
| 648 | mso-hansi-font-family:Cambria; |
|---|
| 649 | mso-hansi-theme-font:minor-latin; |
|---|
| 650 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 651 | mso-bidi-theme-font:minor-bidi; |
|---|
| 652 | mso-fareast-language:JA;} |
|---|
| 653 | @page WordSection1 |
|---|
| 654 | {size:8.5in 11.0in; |
|---|
| 655 | margin:1.0in 1.25in 1.0in 1.25in; |
|---|
| 656 | mso-header-margin:.5in; |
|---|
| 657 | mso-footer-margin:.5in; |
|---|
| 658 | mso-paper-source:0;} |
|---|
| 659 | div.WordSection1 |
|---|
| 660 | {page:WordSection1;} |
|---|
| 661 | /* List Definitions */ |
|---|
| 662 | @list l0 |
|---|
| 663 | {mso-list-id:109671306; |
|---|
| 664 | mso-list-type:hybrid; |
|---|
| 665 | mso-list-template-ids:129770836 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;} |
|---|
| 666 | @list l0:level1 |
|---|
| 667 | {mso-level-tab-stop:none; |
|---|
| 668 | mso-level-number-position:left; |
|---|
| 669 | text-indent:-.25in;} |
|---|
| 670 | @list l0:level2 |
|---|
| 671 | {mso-level-number-format:alpha-lower; |
|---|
| 672 | mso-level-tab-stop:none; |
|---|
| 673 | mso-level-number-position:left; |
|---|
| 674 | text-indent:-.25in;} |
|---|
| 675 | @list l0:level3 |
|---|
| 676 | {mso-level-number-format:roman-lower; |
|---|
| 677 | mso-level-tab-stop:none; |
|---|
| 678 | mso-level-number-position:right; |
|---|
| 679 | text-indent:-9.0pt;} |
|---|
| 680 | @list l0:level4 |
|---|
| 681 | {mso-level-tab-stop:none; |
|---|
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| 930 | |
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| 931 | <body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'> |
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| 932 | |
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| 933 | <div class=WordSection1> |
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| 934 | |
|---|
| 935 | <h1>Parametric Fitting and Pseudo Variables for Sequential Fits</h1> |
|---|
| 936 | |
|---|
| 937 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 938 | |
|---|
| 939 | <p class=MsoNormal>Once a sequential fit has been performed, any function of |
|---|
| 940 | the fit parameters from the fit and <i style='mso-bidi-font-style:normal'>their |
|---|
| 941 | estimated uncertainty</i> (s.u.) can be computed by defining one or more |
|---|
| 942 | "pseudo-variables". Note that the covariance matrix from the fit is |
|---|
| 943 | used to provide appropriate treatment of the correlation in parameters with |
|---|
| 944 | respect to uncertainty estimation.<span style='mso-spacerun:yes'> </span>In |
|---|
| 945 | addition, parametric equations in terms of sample parameters such as |
|---|
| 946 | temperature and pressure, etc. can be fit to either the parameters from the fit |
|---|
| 947 | or the pseudo-variables. </p> |
|---|
| 948 | |
|---|
| 949 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 950 | |
|---|
| 951 | <p class=MsoNormal>This tutorial assumes that the steps in the <span |
|---|
| 952 | style='mso-bidi-font-family:"Times New Roman"'><a href="SequentialTutorial.htm">Sequential |
|---|
| 953 | refinement of multiple datasets</a> tutorial have already been performed. </span>If |
|---|
| 954 | you have not done so already, <a href="Starting%20GSAS.htm">start GSAS-II</a>. |
|---|
| 955 | Some of the pictures in this tutorial are from a Mac OSX machine; these |
|---|
| 956 | illustrate the differences in menu location from Windows/Linux machines.</p> |
|---|
| 957 | |
|---|
| 958 | <h1>Step 1. Open the previous Sequential Fit</h1> |
|---|
| 959 | |
|---|
| 960 | <p class=MsoNormal><o:p> </o:p></p> |
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| 961 | |
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| 962 | <p class=MsoListParagraphCxSpFirst style='margin-bottom:6.0pt;mso-add-space: |
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| 963 | auto;text-indent:-.25in;mso-list:l4 level1 lfo2'><![if !supportLists]><span |
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| 964 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
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| 965 | style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 966 | </span></span></span><![endif]>Select the<b style='mso-bidi-font-weight:normal'> |
|---|
| 967 | </b><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 968 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>File/Open |
|---|
| 969 | Project</span></b> menu item to load file named <b style='mso-bidi-font-weight: |
|---|
| 970 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 971 | major-latin;mso-hansi-theme-font:major-latin'>SeqTut.gpx</span></b>. </p> |
|---|
| 972 | |
|---|
| 973 | <p class=MsoListParagraphCxSpMiddle style='margin-bottom:6.0pt;mso-add-space: |
|---|
| 974 | auto;text-indent:-.25in;mso-list:l4 level1 lfo2'><![if !supportLists]><span |
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| 975 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 976 | style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 977 | </span></span></span><![endif]>Select the <b style='mso-bidi-font-weight:normal'><span |
|---|
| 978 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 979 | mso-hansi-theme-font:major-latin'>Sequential results</span></b> item in the |
|---|
| 980 | data tree. The sequential refinement results data table is displayed, as below. |
|---|
| 981 | </p> |
|---|
| 982 | |
|---|
| 983 | <p class=MsoListParagraphCxSpLast style='margin-bottom:6.0pt;mso-add-space: |
|---|
| 984 | auto'><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype |
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| 1000 | <v:f eqn="sum @10 21600 0"/> |
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| 1001 | </v:formulas> |
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| 1003 | <o:lock v:ext="edit" aspectratio="t"/> |
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| 1006 | <v:imagedata src="ParametricFitting_files/image001.png" o:title=""/> |
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| 1007 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=350 |
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| 1008 | src="ParametricFitting_files/image001.png" v:shapes="Picture_x0020_36"><![endif]></span></p> |
|---|
| 1009 | |
|---|
| 1010 | <h1>Step 2. Create a Pseudo Variable</h1> |
|---|
| 1011 | |
|---|
| 1012 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1013 | |
|---|
| 1014 | <p class=MsoNormal>Pseudo-variables allow computation of an arbitrarily defined |
|---|
| 1015 | function of combinations of the variables that are displayed in the sequential |
|---|
| 1016 | refinement table. Any valid Python language expression can be used to define |
|---|
| 1017 | this. While one can plot <i style='mso-bidi-font-style:normal'>a</i>, <i |
|---|
| 1018 | style='mso-bidi-font-style:normal'>b</i> and <i style='mso-bidi-font-style: |
|---|
| 1019 | normal'>c</i> axis lengths by clicking on the appropriate column of the table, |
|---|
| 1020 | to compare them one might want to scale them. Alternately, as will be done |
|---|
| 1021 | here, we will plot the ratio of <i style='mso-bidi-font-style:normal'>b</i> and |
|---|
| 1022 | <i style='mso-bidi-font-style:normal'>c</i>.</p> |
|---|
| 1023 | |
|---|
| 1024 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1025 | |
|---|
| 1026 | <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span |
|---|
| 1027 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1028 | style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1029 | </span></span></span><![endif]>Click on the <b style='mso-bidi-font-weight: |
|---|
| 1030 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1031 | major-latin;mso-hansi-theme-font:major-latin'>Pseudo Vars/Add</span></b> menu |
|---|
| 1032 | item to create a new pseudo-variable.</p> |
|---|
| 1033 | |
|---|
| 1034 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1035 | |
|---|
| 1036 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1037 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_2" o:spid="_x0000_i1052" |
|---|
| 1038 | type="#_x0000_t75" style='width:159pt;height:45.75pt;visibility:visible; |
|---|
| 1039 | mso-wrap-style:square'> |
|---|
| 1040 | <v:imagedata src="ParametricFitting_files/image002.png" o:title=""/> |
|---|
| 1041 | </v:shape><![endif]--><![if !vml]><img border=0 width=212 height=61 |
|---|
| 1042 | src="ParametricFitting_files/image003.jpg" v:shapes="Picture_x0020_2"><![endif]></span></p> |
|---|
| 1043 | |
|---|
| 1044 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1045 | |
|---|
| 1046 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span |
|---|
| 1047 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1048 | style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1049 | </span></span></span><![endif]>A window opens to define a formula</p> |
|---|
| 1050 | |
|---|
| 1051 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1052 | |
|---|
| 1053 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1054 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_3" o:spid="_x0000_i1051" |
|---|
| 1055 | type="#_x0000_t75" style='width:309.75pt;height:152.25pt;visibility:visible; |
|---|
| 1056 | mso-wrap-style:square'> |
|---|
| 1057 | <v:imagedata src="ParametricFitting_files/image004.png" o:title="" croptop="4214f" |
|---|
| 1058 | cropbottom="8982f" cropleft="3852f" cropright="3654f"/> |
|---|
| 1059 | </v:shape><![endif]--><![if !vml]><img border=0 width=413 height=203 |
|---|
| 1060 | src="ParametricFitting_files/image005.png" v:shapes="Picture_x0020_3"><![endif]></span></p> |
|---|
| 1061 | |
|---|
| 1062 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1063 | |
|---|
| 1064 | <p class=MsoListParagraphCxSpMiddle><!--[if gte vml 1]><v:shape id="Picture_x0020_4" |
|---|
| 1065 | o:spid="_x0000_s1031" type="#_x0000_t75" style='position:absolute;left:0; |
|---|
| 1066 | text-align:left;margin-left:178.3pt;margin-top:846.2pt;width:229.5pt;height:86.5pt; |
|---|
| 1067 | z-index:251658240;visibility:visible;mso-wrap-style:square; |
|---|
| 1068 | mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; |
|---|
| 1069 | mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; |
|---|
| 1070 | mso-wrap-distance-bottom:0;mso-position-horizontal:right; |
|---|
| 1071 | mso-position-horizontal-relative:margin;mso-position-vertical:absolute; |
|---|
| 1072 | mso-position-vertical-relative:margin;mso-width-percent:0; |
|---|
| 1073 | mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'> |
|---|
| 1074 | <v:imagedata src="ParametricFitting_files/image006.png" o:title=""/> |
|---|
| 1075 | <w:wrap type="square" anchorx="margin" anchory="margin"/> |
|---|
| 1076 | </v:shape><![endif]--><![if !vml]><img width=306 height=115 |
|---|
| 1077 | src="ParametricFitting_files/image007.jpg" align=right hspace=12 v:shapes="Picture_x0020_4"><![endif]>In |
|---|
| 1078 | this window, type a Python expression<b style='mso-bidi-font-weight:normal'>, </b><span |
|---|
| 1079 | style='mso-bidi-font-family:"Times New Roman"'>"</span><b |
|---|
| 1080 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1081 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin;mso-bidi-font-family: |
|---|
| 1082 | "Times New Roman"'>b/c</span></b><span style='mso-bidi-font-family:"Times New Roman"'>",</span> |
|---|
| 1083 | but note that the variables <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1084 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1085 | mso-hansi-theme-font:major-latin'>c</span></b> and <b style='mso-bidi-font-weight: |
|---|
| 1086 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1087 | major-latin;mso-hansi-theme-font:major-latin'>b</span></b> here are arbitrary |
|---|
| 1088 | labels. After entering the formula, press the <b style='mso-bidi-font-weight: |
|---|
| 1089 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1090 | major-latin;mso-hansi-theme-font:major-latin'>Validate</span></b> button or |
|---|
| 1091 | wait a few seconds and the validation will be tested automatically. Note that if |
|---|
| 1092 | you pause too long, while typing, an error message may be displayed as the |
|---|
| 1093 | incomplete formula is found to be invalid. If so, make corrections or keep |
|---|
| 1094 | typing until the entire expression is entered.<span style='mso-spacerun:yes'> |
|---|
| 1095 | </span>The error message will sometimes show where error is encountered, though |
|---|
| 1096 | not in this case. </p> |
|---|
| 1097 | |
|---|
| 1098 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1099 | |
|---|
| 1100 | <p class=MsoListParagraphCxSpMiddle>When the expression is complete, a new |
|---|
| 1101 | table appears where the arbitrary <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1102 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1103 | mso-hansi-theme-font:major-latin'>c</span></b> and <b style='mso-bidi-font-weight: |
|---|
| 1104 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1105 | major-latin;mso-hansi-theme-font:major-latin'>b</span></b> labels will be |
|---|
| 1106 | assigned.</p> |
|---|
| 1107 | |
|---|
| 1108 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1109 | |
|---|
| 1110 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1111 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5" o:spid="_x0000_i1050" |
|---|
| 1112 | type="#_x0000_t75" style='width:309.75pt;height:152.25pt;visibility:visible; |
|---|
| 1113 | mso-wrap-style:square'> |
|---|
| 1114 | <v:imagedata src="ParametricFitting_files/image008.png" o:title="" croptop="4435f" |
|---|
| 1115 | cropbottom="8537f" cropleft="3852f" cropright="3650f"/> |
|---|
| 1116 | </v:shape><![endif]--><![if !vml]><img border=0 width=413 height=203 |
|---|
| 1117 | src="ParametricFitting_files/image009.png" v:shapes="Picture_x0020_5"><![endif]></span></p> |
|---|
| 1118 | |
|---|
| 1119 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1120 | |
|---|
| 1121 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l2 level1 lfo4'><![if !supportLists]><span |
|---|
| 1122 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1123 | style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1124 | </span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_6" |
|---|
| 1125 | o:spid="_x0000_s1030" type="#_x0000_t75" style='position:absolute;left:0; |
|---|
| 1126 | text-align:left;margin-left:37.3pt;margin-top:1143.2pt;width:88.5pt;height:65.5pt; |
|---|
| 1127 | z-index:251659264;visibility:visible;mso-wrap-style:square; |
|---|
| 1128 | mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; |
|---|
| 1129 | mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; |
|---|
| 1130 | mso-wrap-distance-bottom:0;mso-position-horizontal:right; |
|---|
| 1131 | mso-position-horizontal-relative:margin;mso-position-vertical:absolute; |
|---|
| 1132 | mso-position-vertical-relative:margin;mso-width-percent:0; |
|---|
| 1133 | mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'> |
|---|
| 1134 | <v:imagedata src="ParametricFitting_files/image010.png" o:title=""/> |
|---|
| 1135 | <w:wrap type="square" anchorx="margin" anchory="margin"/> |
|---|
| 1136 | </v:shape><![endif]--><![if !vml]><img width=118 height=87 |
|---|
| 1137 | src="ParametricFitting_files/image011.jpg" align=right hspace=12 v:shapes="Picture_x0020_6"><![endif]>Assign |
|---|
| 1138 | the label for the numerator by clicking on the menu button next to label <b |
|---|
| 1139 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1140 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>; |
|---|
| 1141 | this will bring up a list of variable types, from this select <b |
|---|
| 1142 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1143 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Phase</span></b> |
|---|
| 1144 | to bring up a list of phase variables, from that list select variable <b |
|---|
| 1145 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1146 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>0::b</span></b>, |
|---|
| 1147 | which is the <i style='mso-bidi-font-style:normal'>b</i> lattice parameter for |
|---|
| 1148 | phase 0 (CuCr<sub>2</sub>O<sub>4</sub>). Repeat this process to select assign |
|---|
| 1149 | to label <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1150 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>c</span></b> |
|---|
| 1151 | variable <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1152 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>0::b</span></b>.</p> |
|---|
| 1153 | |
|---|
| 1154 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1155 | |
|---|
| 1156 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1157 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8" o:spid="_x0000_i1049" |
|---|
| 1158 | type="#_x0000_t75" style='width:315.75pt;height:129pt;visibility:visible; |
|---|
| 1159 | mso-wrap-style:square'> |
|---|
| 1160 | <v:imagedata src="ParametricFitting_files/image012.png" o:title="" croptop="4597f" |
|---|
| 1161 | cropbottom="9873f" cropleft="3348f" cropright="3506f"/> |
|---|
| 1162 | </v:shape><![endif]--><![if !vml]><img border=0 width=421 height=172 |
|---|
| 1163 | src="ParametricFitting_files/image013.png" v:shapes="Picture_x0020_8"><![endif]></span></p> |
|---|
| 1164 | |
|---|
| 1165 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1166 | |
|---|
| 1167 | <p class=MsoListParagraphCxSpMiddle>As each variable is set, the window shows |
|---|
| 1168 | the value for each variable from the first refinement and when the expression |
|---|
| 1169 | can be evaluated, the value for the expression, evaluated for that first |
|---|
| 1170 | refinement. Only when the expression can be evaluated can the <b |
|---|
| 1171 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1172 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>OK</span></b> |
|---|
| 1173 | button be pressed. </p> |
|---|
| 1174 | |
|---|
| 1175 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1176 | |
|---|
| 1177 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1178 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9" o:spid="_x0000_i1048" |
|---|
| 1179 | type="#_x0000_t75" style='width:314.25pt;height:153.75pt;visibility:visible; |
|---|
| 1180 | mso-wrap-style:square'> |
|---|
| 1181 | <v:imagedata src="ParametricFitting_files/image014.png" o:title="" croptop="3770f" |
|---|
| 1182 | cropbottom="8549f" cropleft="3371f" cropright="3424f"/> |
|---|
| 1183 | </v:shape><![endif]--><![if !vml]><img border=0 width=419 height=205 |
|---|
| 1184 | src="ParametricFitting_files/image015.png" v:shapes="Picture_x0020_9"><![endif]></span></p> |
|---|
| 1185 | |
|---|
| 1186 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1187 | |
|---|
| 1188 | <p class=MsoListParagraphCxSpMiddle>Press<b style='mso-bidi-font-weight:normal'> |
|---|
| 1189 | </b><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1190 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>OK</span></b> |
|---|
| 1191 | to close the window and add the pseudo-variable. Note that a new column appears |
|---|
| 1192 | at the end of the sequential refinement data table. </p> |
|---|
| 1193 | |
|---|
| 1194 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1195 | |
|---|
| 1196 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1197 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10" o:spid="_x0000_i1047" |
|---|
| 1198 | type="#_x0000_t75" style='width:354pt;height:180.75pt;visibility:visible; |
|---|
| 1199 | mso-wrap-style:square'> |
|---|
| 1200 | <v:imagedata src="ParametricFitting_files/image016.png" o:title=""/> |
|---|
| 1201 | </v:shape><![endif]--><![if !vml]><img border=0 width=472 height=241 |
|---|
| 1202 | src="ParametricFitting_files/image016.png" v:shapes="Picture_x0020_10"><![endif]></span></p> |
|---|
| 1203 | |
|---|
| 1204 | <p class=MsoListParagraphCxSpMiddle><!--[if gte vml 1]><v:shape id="Picture_x0020_11" |
|---|
| 1205 | o:spid="_x0000_s1029" type="#_x0000_t75" style='position:absolute;left:0; |
|---|
| 1206 | text-align:left;margin-left:42.3pt;margin-top:666.2pt;width:93.5pt;height:39pt; |
|---|
| 1207 | z-index:251660288;visibility:visible;mso-wrap-style:square; |
|---|
| 1208 | mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; |
|---|
| 1209 | mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; |
|---|
| 1210 | mso-wrap-distance-bottom:0;mso-position-horizontal:right; |
|---|
| 1211 | mso-position-horizontal-relative:margin;mso-position-vertical:absolute; |
|---|
| 1212 | mso-position-vertical-relative:margin;mso-width-percent:0; |
|---|
| 1213 | mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'> |
|---|
| 1214 | <v:imagedata src="ParametricFitting_files/image018.png" o:title=""/> |
|---|
| 1215 | <w:wrap type="square" anchorx="margin" anchory="margin"/> |
|---|
| 1216 | </v:shape><![endif]--><![if !vml]><img width=125 height=52 |
|---|
| 1217 | src="ParametricFitting_files/image019.jpg" align=right hspace=12 v:shapes="Picture_x0020_11"><![endif]>Also |
|---|
| 1218 | note that positioning the mouse above any cell in the table and waiting for a |
|---|
| 1219 | few seconds causes the s.u. to be shown as a tooltip. </p> |
|---|
| 1220 | |
|---|
| 1221 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1222 | |
|---|
| 1223 | <p class=MsoListParagraphCxSpMiddle>Double clicking on the <b style='mso-bidi-font-weight: |
|---|
| 1224 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1225 | major-latin;mso-hansi-theme-font:major-latin'>b/c</span></b> column will cause |
|---|
| 1226 | the pseudo-variable to be plotted:</p> |
|---|
| 1227 | |
|---|
| 1228 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1229 | |
|---|
| 1230 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1231 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_12" o:spid="_x0000_i1046" |
|---|
| 1232 | type="#_x0000_t75" style='width:351.75pt;height:303pt;visibility:visible; |
|---|
| 1233 | mso-wrap-style:square'> |
|---|
| 1234 | <v:imagedata src="ParametricFitting_files/image020.png" o:title=""/> |
|---|
| 1235 | </v:shape><![endif]--><![if !vml]><img border=0 width=469 height=404 |
|---|
| 1236 | src="ParametricFitting_files/image020.png" v:shapes="Picture_x0020_12"><![endif]></span></p> |
|---|
| 1237 | |
|---|
| 1238 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1239 | |
|---|
| 1240 | <p class=MsoListParagraphCxSpMiddle>Press the "<b style='mso-bidi-font-weight: |
|---|
| 1241 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1242 | major-latin;mso-hansi-theme-font:major-latin'>s</span></b>" key inside the |
|---|
| 1243 | plot to select<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight: |
|---|
| 1244 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1245 | major-latin;mso-hansi-theme-font:major-latin'>Temperature</span></b> as the |
|---|
| 1246 | x-axis. </p> |
|---|
| 1247 | |
|---|
| 1248 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1249 | |
|---|
| 1250 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1251 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_13" o:spid="_x0000_i1045" |
|---|
| 1252 | type="#_x0000_t75" style='width:162.75pt;height:156pt;visibility:visible; |
|---|
| 1253 | mso-wrap-style:square'> |
|---|
| 1254 | <v:imagedata src="ParametricFitting_files/image022.png" o:title="" croptop="4105f" |
|---|
| 1255 | cropbottom="8920f" cropleft="6109f" cropright="5911f"/> |
|---|
| 1256 | </v:shape><![endif]--><![if !vml]><img border=0 width=217 height=208 |
|---|
| 1257 | src="ParametricFitting_files/image023.png" v:shapes="Picture_x0020_13"><![endif]></span></p> |
|---|
| 1258 | |
|---|
| 1259 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1260 | |
|---|
| 1261 | <p class=MsoListParagraphCxSpMiddle>The plot will then appear as below:</p> |
|---|
| 1262 | |
|---|
| 1263 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1264 | |
|---|
| 1265 | <p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US; |
|---|
| 1266 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_14" o:spid="_x0000_i1044" |
|---|
| 1267 | type="#_x0000_t75" style='width:353.25pt;height:303.75pt;visibility:visible; |
|---|
| 1268 | mso-wrap-style:square'> |
|---|
| 1269 | <v:imagedata src="ParametricFitting_files/image024.png" o:title=""/> |
|---|
| 1270 | </v:shape><![endif]--><![if !vml]><img border=0 width=471 height=405 |
|---|
| 1271 | src="ParametricFitting_files/image024.png" v:shapes="Picture_x0020_14"><![endif]></span></p> |
|---|
| 1272 | |
|---|
| 1273 | <h1>Step 3: Fitting a simple parametric equation to the unit cell volume</h1> |
|---|
| 1274 | |
|---|
| 1275 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1276 | |
|---|
| 1277 | <p class=MsoNormal>In the next few steps we will fit increasingly sophisticated |
|---|
| 1278 | equations of state to different parameters. As a simple example, we can |
|---|
| 1279 | double-click on<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight: |
|---|
| 1280 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1281 | major-latin;mso-hansi-theme-font:major-latin'>0::Vol</span></b>, to plot the |
|---|
| 1282 | unit volume for the first phase vs. T, and fit this to a straight line.<span |
|---|
| 1283 | style='mso-spacerun:yes'> </span></p> |
|---|
| 1284 | |
|---|
| 1285 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1286 | |
|---|
| 1287 | <p class=MsoListParagraphCxSpFirst><span style='mso-fareast-language:EN-US; |
|---|
| 1288 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_15" o:spid="_x0000_i1043" |
|---|
| 1289 | type="#_x0000_t75" style='width:356.25pt;height:305.25pt;visibility:visible; |
|---|
| 1290 | mso-wrap-style:square'> |
|---|
| 1291 | <v:imagedata src="ParametricFitting_files/image026.png" o:title=""/> |
|---|
| 1292 | </v:shape><![endif]--><![if !vml]><img border=0 width=475 height=407 |
|---|
| 1293 | src="ParametricFitting_files/image026.png" v:shapes="Picture_x0020_15"><![endif]></span></p> |
|---|
| 1294 | |
|---|
| 1295 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span |
|---|
| 1296 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1297 | style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1298 | </span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_16" |
|---|
| 1299 | o:spid="_x0000_s1028" type="#_x0000_t75" style='position:absolute;left:0; |
|---|
| 1300 | text-align:left;margin-left:21.8pt;margin-top:891.2pt;width:73pt;height:53pt; |
|---|
| 1301 | z-index:251661312;visibility:visible;mso-wrap-style:square; |
|---|
| 1302 | mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; |
|---|
| 1303 | mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; |
|---|
| 1304 | mso-wrap-distance-bottom:0;mso-position-horizontal:right; |
|---|
| 1305 | mso-position-horizontal-relative:margin;mso-position-vertical:absolute; |
|---|
| 1306 | mso-position-vertical-relative:margin;mso-width-percent:0; |
|---|
| 1307 | mso-height-percent:0;mso-width-relative:margin;mso-height-relative:margin'> |
|---|
| 1308 | <v:imagedata src="ParametricFitting_files/image028.png" o:title=""/> |
|---|
| 1309 | <w:wrap type="square" anchorx="margin" anchory="margin"/> |
|---|
| 1310 | </v:shape><![endif]--><![if !vml]><img width=97 height=71 |
|---|
| 1311 | src="ParametricFitting_files/image029.jpg" align=right hspace=12 v:shapes="Picture_x0020_16"><![endif]>Click |
|---|
| 1312 | on the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1313 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Parametric |
|---|
| 1314 | Fit/Add</span></b><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1315 | major-latin;mso-hansi-theme-font:major-latin'> <b style='mso-bidi-font-weight: |
|---|
| 1316 | normal'>equation</b></span> menu item, which opens a window similar to what was |
|---|
| 1317 | used before to create a pseudo-variable, except that here an equation is |
|---|
| 1318 | defined.<span style='mso-spacerun:yes'> </span></p> |
|---|
| 1319 | |
|---|
| 1320 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1321 | |
|---|
| 1322 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1323 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_17" o:spid="_x0000_i1042" |
|---|
| 1324 | type="#_x0000_t75" style='width:311.25pt;height:152.25pt;visibility:visible; |
|---|
| 1325 | mso-wrap-style:square'> |
|---|
| 1326 | <v:imagedata src="ParametricFitting_files/image030.png" o:title="" croptop="4213f" |
|---|
| 1327 | cropbottom="8982f" cropleft="3490f" cropright="3653f"/> |
|---|
| 1328 | </v:shape><![endif]--><![if !vml]><img border=0 width=415 height=203 |
|---|
| 1329 | src="ParametricFitting_files/image031.png" v:shapes="Picture_x0020_17"><![endif]></span></p> |
|---|
| 1330 | |
|---|
| 1331 | <p class=MsoListParagraphCxSpLast><o:p> </o:p></p> |
|---|
| 1332 | |
|---|
| 1333 | <p class=MsoNormal>We will want to fit the unit cell volume to an equation of |
|---|
| 1334 | form <i style='mso-bidi-font-style:normal'>y = mx+b</i>, where y will be the |
|---|
| 1335 | volume and x temperature and m and b will be best fit. </p> |
|---|
| 1336 | |
|---|
| 1337 | <p class=MsoNormal><b style='mso-bidi-font-weight:normal'><o:p> </o:p></b></p> |
|---|
| 1338 | |
|---|
| 1339 | <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><b |
|---|
| 1340 | style='mso-bidi-font-weight:normal'><span style='mso-fareast-font-family:"Times New Roman"; |
|---|
| 1341 | mso-bidi-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span |
|---|
| 1342 | style='font:7.0pt "Times New Roman"'> </span></span></span></b><![endif]>Click |
|---|
| 1343 | the<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight: |
|---|
| 1344 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1345 | major-latin;mso-hansi-theme-font:major-latin'>↕ </span></b>button to select |
|---|
| 1346 | a dependent variable for "y". From the phase list, select the unit |
|---|
| 1347 | cell volume for the CuCr<sub>2</sub>O<sub>4</sub> phase, select<b |
|---|
| 1348 | style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1349 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1350 | mso-hansi-theme-font:major-latin'>0::Vol</span></b> and then press<b |
|---|
| 1351 | style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1352 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1353 | mso-hansi-theme-font:major-latin'>OK</span>.<o:p></o:p></b></p> |
|---|
| 1354 | |
|---|
| 1355 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1356 | |
|---|
| 1357 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1358 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_19" o:spid="_x0000_i1041" |
|---|
| 1359 | type="#_x0000_t75" style='width:314.25pt;height:132pt;visibility:visible; |
|---|
| 1360 | mso-wrap-style:square'> |
|---|
| 1361 | <v:imagedata src="ParametricFitting_files/image032.png" o:title="" croptop="3830f" |
|---|
| 1362 | cropbottom="9359f" cropleft="3705f" cropright="3502f"/> |
|---|
| 1363 | </v:shape><![endif]--><![if !vml]><img border=0 width=419 height=176 |
|---|
| 1364 | src="ParametricFitting_files/image033.png" v:shapes="Picture_x0020_19"><![endif]></span></p> |
|---|
| 1365 | |
|---|
| 1366 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1367 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_20" o:spid="_x0000_i1040" |
|---|
| 1368 | type="#_x0000_t75" style='width:311.25pt;height:155.25pt;visibility:visible; |
|---|
| 1369 | mso-wrap-style:square'> |
|---|
| 1370 | <v:imagedata src="ParametricFitting_files/image034.png" o:title="" croptop="3548f" |
|---|
| 1371 | cropbottom="8549f" cropleft="3611f" cropright="3665f"/> |
|---|
| 1372 | </v:shape><![endif]--><![if !vml]><img border=0 width=415 height=207 |
|---|
| 1373 | src="ParametricFitting_files/image035.png" v:shapes="Picture_x0020_20"><![endif]></span></p> |
|---|
| 1374 | |
|---|
| 1375 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1376 | |
|---|
| 1377 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span |
|---|
| 1378 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1379 | style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1380 | </span></span></span><![endif]>Now we enter the equation using Python syntax, |
|---|
| 1381 | which is simply "<b style='mso-bidi-font-weight:normal'><span |
|---|
| 1382 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1383 | mso-hansi-theme-font:major-latin'>m*x + b</span></b>", note that the use |
|---|
| 1384 | of spaces and the choice of labels is arbitrary. If one were to accidentally |
|---|
| 1385 | leave out the "<span style='font-family:Courier'>*</span>" and typed |
|---|
| 1386 | "<span style='font-family:Courier'>mx</span>" then that would be considered |
|---|
| 1387 | a label, if "<span style='font-family:Courier'>m x</span>" were |
|---|
| 1388 | typed, an error message would be displayed. </p> |
|---|
| 1389 | |
|---|
| 1390 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1391 | |
|---|
| 1392 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1393 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_21" o:spid="_x0000_i1039" |
|---|
| 1394 | type="#_x0000_t75" style='width:315.75pt;height:155.25pt;visibility:visible; |
|---|
| 1395 | mso-wrap-style:square'> |
|---|
| 1396 | <v:imagedata src="ParametricFitting_files/image036.png" o:title="" croptop="3326f" |
|---|
| 1397 | cropbottom="8766f" cropleft="3010f" cropright="3419f"/> |
|---|
| 1398 | </v:shape><![endif]--><![if !vml]><img border=0 width=421 height=207 |
|---|
| 1399 | src="ParametricFitting_files/image037.png" v:shapes="Picture_x0020_21"><![endif]></span></p> |
|---|
| 1400 | |
|---|
| 1401 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1402 | |
|---|
| 1403 | <p class=MsoListParagraphCxSpMiddle>Then press <b style='mso-bidi-font-weight: |
|---|
| 1404 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1405 | major-latin;mso-hansi-theme-font:major-latin'>Validate</span></b> or wait a few |
|---|
| 1406 | seconds and a window changes, as above, allowing assignment of the three new |
|---|
| 1407 | labels (<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1408 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b>, |
|---|
| 1409 | <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1410 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x</span></b>, |
|---|
| 1411 | and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1412 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>). |
|---|
| 1413 | </p> |
|---|
| 1414 | |
|---|
| 1415 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1416 | |
|---|
| 1417 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span |
|---|
| 1418 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1419 | style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1420 | </span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_22" |
|---|
| 1421 | o:spid="_x0000_s1027" type="#_x0000_t75" style='position:absolute;left:0; |
|---|
| 1422 | text-align:left;margin-left:43.8pt;margin-top:603.2pt;width:95pt;height:35pt; |
|---|
| 1423 | z-index:251662336;visibility:visible;mso-wrap-style:square; |
|---|
| 1424 | mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; |
|---|
| 1425 | mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; |
|---|
| 1426 | mso-wrap-distance-bottom:0;mso-position-horizontal:right; |
|---|
| 1427 | mso-position-horizontal-relative:margin;mso-position-vertical:absolute; |
|---|
| 1428 | mso-position-vertical-relative:margin;mso-width-percent:0; |
|---|
| 1429 | mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'> |
|---|
| 1430 | <v:imagedata src="ParametricFitting_files/image038.png" o:title=""/> |
|---|
| 1431 | <w:wrap type="square" anchorx="margin" anchory="margin"/> |
|---|
| 1432 | </v:shape><![endif]--><![if !vml]><img width=127 height=47 |
|---|
| 1433 | src="ParametricFitting_files/image039.jpg" align=right hspace=12 v:shapes="Picture_x0020_22"><![endif]>Assign |
|---|
| 1434 | <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1435 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b> |
|---|
| 1436 | and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1437 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b> |
|---|
| 1438 | as refinable free parameters: Click on the <b style='mso-bidi-font-weight: |
|---|
| 1439 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1440 | major-latin;mso-hansi-theme-font:major-latin'>↕</span></b><span |
|---|
| 1441 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1442 | mso-hansi-theme-font:major-latin'> </span>button next to b and select<b |
|---|
| 1443 | style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1444 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1445 | mso-hansi-theme-font:major-latin'>Free</span></b>. Then repeat this for<b |
|---|
| 1446 | style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1447 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1448 | mso-hansi-theme-font:major-latin'>m</span></b>. </p> |
|---|
| 1449 | |
|---|
| 1450 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1451 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_23" o:spid="_x0000_i1038" |
|---|
| 1452 | type="#_x0000_t75" style='width:314.25pt;height:153pt;visibility:visible; |
|---|
| 1453 | mso-wrap-style:square'> |
|---|
| 1454 | <v:imagedata src="ParametricFitting_files/image040.png" o:title="" croptop="3992f" |
|---|
| 1455 | cropbottom="8541f" cropleft="3250f" cropright="3415f"/> |
|---|
| 1456 | </v:shape><![endif]--><![if !vml]><img border=0 width=419 height=204 |
|---|
| 1457 | src="ParametricFitting_files/image041.png" v:shapes="Picture_x0020_23"><![endif]></span></p> |
|---|
| 1458 | |
|---|
| 1459 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1460 | |
|---|
| 1461 | <p class=MsoListParagraphCxSpMiddle>It is not necessary to change the default |
|---|
| 1462 | variable names, the initial values, or the refine flag. </p> |
|---|
| 1463 | |
|---|
| 1464 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1465 | |
|---|
| 1466 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span |
|---|
| 1467 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1468 | style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1469 | </span></span></span><![endif]><!--[if gte vml 1]><v:shape id="Picture_x0020_24" |
|---|
| 1470 | o:spid="_x0000_s1026" type="#_x0000_t75" style='position:absolute;left:0; |
|---|
| 1471 | text-align:left;margin-left:24.3pt;margin-top:837.2pt;width:75.5pt;height:26pt; |
|---|
| 1472 | z-index:251663360;visibility:visible;mso-wrap-style:square; |
|---|
| 1473 | mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt; |
|---|
| 1474 | mso-wrap-distance-top:0;mso-wrap-distance-right:9pt; |
|---|
| 1475 | mso-wrap-distance-bottom:0;mso-position-horizontal:right; |
|---|
| 1476 | mso-position-horizontal-relative:margin;mso-position-vertical:absolute; |
|---|
| 1477 | mso-position-vertical-relative:margin;mso-width-percent:0; |
|---|
| 1478 | mso-height-percent:0;mso-width-relative:page;mso-height-relative:page'> |
|---|
| 1479 | <v:imagedata src="ParametricFitting_files/image042.png" o:title=""/> |
|---|
| 1480 | <w:wrap type="square" anchorx="margin" anchory="margin"/> |
|---|
| 1481 | </v:shape><![endif]--><![if !vml]><img width=101 height=35 |
|---|
| 1482 | src="ParametricFitting_files/image043.jpg" align=right hspace=12 v:shapes="Picture_x0020_24"><![endif]>To |
|---|
| 1483 | set <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1484 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x</span></b> |
|---|
| 1485 | as the temperature, click on the <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1486 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1487 | mso-hansi-theme-font:major-latin'>↕</span></b><span style='font-family: |
|---|
| 1488 | "Calibri","sans-serif";mso-ascii-theme-font:major-latin;mso-hansi-theme-font: |
|---|
| 1489 | major-latin'> </span>button next to <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1490 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1491 | mso-hansi-theme-font:major-latin'>x</span></b>, select<b style='mso-bidi-font-weight: |
|---|
| 1492 | normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family: |
|---|
| 1493 | "Calibri","sans-serif";mso-ascii-theme-font:major-latin;mso-hansi-theme-font: |
|---|
| 1494 | major-latin'>Global</span>,</b> and then select<b style='mso-bidi-font-weight: |
|---|
| 1495 | normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family: |
|---|
| 1496 | "Calibri","sans-serif";mso-ascii-theme-font:major-latin;mso-hansi-theme-font: |
|---|
| 1497 | major-latin'>Temperature</span></b> from the list and click on<b |
|---|
| 1498 | style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1499 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1500 | mso-hansi-theme-font:major-latin'>OK</span></b>.</p> |
|---|
| 1501 | |
|---|
| 1502 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1503 | |
|---|
| 1504 | <p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span |
|---|
| 1505 | style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1506 | id="Picture_x0020_25" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:245.25pt; |
|---|
| 1507 | height:108.75pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1508 | <v:imagedata src="ParametricFitting_files/image044.png" o:title="" croptop="5483f" |
|---|
| 1509 | cropbottom="10984f" cropleft="4191f" cropright="4159f"/> |
|---|
| 1510 | </v:shape><![endif]--><![if !vml]><img border=0 width=327 height=145 |
|---|
| 1511 | src="ParametricFitting_files/image045.png" v:shapes="Picture_x0020_25"><![endif]></span></p> |
|---|
| 1512 | |
|---|
| 1513 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1514 | |
|---|
| 1515 | <p class=MsoListParagraphCxSpMiddle>The window then changes, showing the values |
|---|
| 1516 | of the dependent variable and the expression for the first refinement, as |
|---|
| 1517 | below. <span style='mso-spacerun:yes'> </span>Optionally, the values for <b |
|---|
| 1518 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1519 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b> |
|---|
| 1520 | and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1521 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b> |
|---|
| 1522 | could be changed manually and the displayed value will be updated when <b |
|---|
| 1523 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1524 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>Validate</span></b> |
|---|
| 1525 | is pressed or after a short delay.</p> |
|---|
| 1526 | |
|---|
| 1527 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1528 | |
|---|
| 1529 | <p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US; |
|---|
| 1530 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_26" o:spid="_x0000_i1036" |
|---|
| 1531 | type="#_x0000_t75" style='width:314.25pt;height:153pt;visibility:visible; |
|---|
| 1532 | mso-wrap-style:square'> |
|---|
| 1533 | <v:imagedata src="ParametricFitting_files/image046.png" o:title="" croptop="3992f" |
|---|
| 1534 | cropbottom="8541f" cropleft="3490f" cropright="3294f"/> |
|---|
| 1535 | </v:shape><![endif]--><![if !vml]><img border=0 width=419 height=204 |
|---|
| 1536 | src="ParametricFitting_files/image047.png" v:shapes="Picture_x0020_26"><![endif]></span></p> |
|---|
| 1537 | |
|---|
| 1538 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1539 | |
|---|
| 1540 | <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span |
|---|
| 1541 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1542 | style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1543 | </span></span></span><![endif]>Press the <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1544 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1545 | mso-hansi-theme-font:major-latin'>OK</span></b> button to save this parametric |
|---|
| 1546 | fit. The <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1547 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b> |
|---|
| 1548 | and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1549 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>m</span></b> |
|---|
| 1550 | values are then refined and the console shows the results:</p> |
|---|
| 1551 | |
|---|
| 1552 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo6'><![if !supportLists]><span |
|---|
| 1553 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1554 | style='mso-list:Ignore'>7.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1555 | </span></span></span><![endif]><o:p> </o:p></p> |
|---|
| 1556 | |
|---|
| 1557 | <p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space: |
|---|
| 1558 | auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'>Fit |
|---|
| 1559 | Results<o:p></o:p></span></b></p> |
|---|
| 1560 | |
|---|
| 1561 | <p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space: |
|---|
| 1562 | auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span |
|---|
| 1563 | style='mso-spacerun:yes'> </span>0::Vol = m*x +b<o:p></o:p></span></b></p> |
|---|
| 1564 | |
|---|
| 1565 | <p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space: |
|---|
| 1566 | auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span |
|---|
| 1567 | style='mso-spacerun:yes'> </span>x<span style='mso-spacerun:yes'> </span>= |
|---|
| 1568 | Temperature<o:p></o:p></span></b></p> |
|---|
| 1569 | |
|---|
| 1570 | <p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space: |
|---|
| 1571 | auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span |
|---|
| 1572 | style='mso-spacerun:yes'> </span>b<span style='mso-spacerun:yes'> </span>= |
|---|
| 1573 | 561.7722(26)<o:p></o:p></span></b></p> |
|---|
| 1574 | |
|---|
| 1575 | <p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space: |
|---|
| 1576 | auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:Courier'><span |
|---|
| 1577 | style='mso-spacerun:yes'> </span>m<span style='mso-spacerun:yes'> </span>= |
|---|
| 1578 | 0.014833(14)<o:p></o:p></span></b></p> |
|---|
| 1579 | |
|---|
| 1580 | |
|---|
| 1581 | <p class=MsoListParagraphCxSpMiddle style='margin-left:1.5in;mso-add-space: |
|---|
| 1582 | auto'><span style='font-family:Courier'><o:p> </o:p></span></p> |
|---|
| 1583 | |
|---|
| 1584 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1585 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_27" o:spid="_x0000_i1035" |
|---|
| 1586 | type="#_x0000_t75" style='width:350.25pt;height:302.25pt;visibility:visible; |
|---|
| 1587 | mso-wrap-style:square'> |
|---|
| 1588 | <v:imagedata src="ParametricFitting_files/image048.png" o:title=""/> |
|---|
| 1589 | </v:shape><![endif]--><![if !vml]><img border=0 width=467 height=403 |
|---|
| 1590 | src="ParametricFitting_files/image048.png" v:shapes="Picture_x0020_27"><![endif]></span><span |
|---|
| 1591 | style='font-family:"Cambria","serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1592 | mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> |
|---|
| 1593 | |
|---|
| 1594 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1595 | |
|---|
| 1596 | <p class=MsoListParagraphCxSpMiddle>Also, the plot shows the actual values and |
|---|
| 1597 | the fit. Note that while the values are close to a straight line, the |
|---|
| 1598 | deviations are huge compared to the estimated uncertainty values for the unit |
|---|
| 1599 | cell volume (shown as very small error bars, unless the plot is |
|---|
| 1600 | magnified).<span style='mso-spacerun:yes'> </span>If a linear relationship had |
|---|
| 1601 | been defined as a constraint (as can be done with other software packages) <i>the |
|---|
| 1602 | unit cell parameters would have been forced onto this line with no obvious |
|---|
| 1603 | indication that this was not a correct result.</i> </p> |
|---|
| 1604 | |
|---|
| 1605 | <p class=MsoListParagraphCxSpLast><span style='mso-spacerun:yes'> </span></p> |
|---|
| 1606 | |
|---|
| 1607 | <h1>Step 4: Examples of more complex fitt<span class=Heading1Char><span |
|---|
| 1608 | style='font-weight:normal'>i</span></span>ng equations</h1> |
|---|
| 1609 | |
|---|
| 1610 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1611 | |
|---|
| 1612 | <p class=MsoNormal>Here we will look at how more sophisticated Python |
|---|
| 1613 | capabilities can be used to fit more complex behavior.<span |
|---|
| 1614 | style='mso-spacerun:yes'> </span></p> |
|---|
| 1615 | |
|---|
| 1616 | <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span |
|---|
| 1617 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1618 | style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1619 | </span></span></span><![endif]>Optionally Double-click on the<b |
|---|
| 1620 | style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1621 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1622 | mso-hansi-theme-font:major-latin'>0::c</span> </b>column. Note the changes in |
|---|
| 1623 | the <i style='mso-bidi-font-style:normal'>c</i> unit cell parameter as a |
|---|
| 1624 | function of temperature, as shown below. </p> |
|---|
| 1625 | |
|---|
| 1626 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1627 | |
|---|
| 1628 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1629 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_28" o:spid="_x0000_i1034" |
|---|
| 1630 | type="#_x0000_t75" style='width:350.25pt;height:303pt;visibility:visible; |
|---|
| 1631 | mso-wrap-style:square'> |
|---|
| 1632 | <v:imagedata src="ParametricFitting_files/image050.png" o:title=""/> |
|---|
| 1633 | </v:shape><![endif]--><![if !vml]><img border=0 width=467 height=404 |
|---|
| 1634 | src="ParametricFitting_files/image050.png" v:shapes="Picture_x0020_28"><![endif]></span></p> |
|---|
| 1635 | |
|---|
| 1636 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1637 | |
|---|
| 1638 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span |
|---|
| 1639 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1640 | style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1641 | </span></span></span><![endif]>We will now fit <i style='mso-bidi-font-style: |
|---|
| 1642 | normal'>c</i> as a function of form 1/(1 + exp[k(t-t<sub>0</sub>)]). Select the<b |
|---|
| 1643 | style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1644 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1645 | mso-hansi-theme-font:major-latin'>Parametric Fit/Add</span></b><span |
|---|
| 1646 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1647 | mso-hansi-theme-font:major-latin'> <b style='mso-bidi-font-weight:normal'>equation</b></span> |
|---|
| 1648 | menu item (as before). For the dependent variable, click on<b style='mso-bidi-font-weight: |
|---|
| 1649 | normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family: |
|---|
| 1650 | "Calibri","sans-serif";mso-ascii-theme-font:major-latin;mso-hansi-theme-font: |
|---|
| 1651 | major-latin'>Phase</span></b> and then select<b style='mso-bidi-font-weight: |
|---|
| 1652 | normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family: |
|---|
| 1653 | "Calibri","sans-serif";mso-ascii-theme-font:major-latin;mso-hansi-theme-font: |
|---|
| 1654 | major-latin'>0::c</span></b>.<span style='mso-spacerun:yes'> </span></p> |
|---|
| 1655 | |
|---|
| 1656 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1657 | |
|---|
| 1658 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span |
|---|
| 1659 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1660 | style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1661 | </span></span></span><![endif]>We then enter expression</p> |
|---|
| 1662 | |
|---|
| 1663 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1664 | |
|---|
| 1665 | <p class=MsoListParagraphCxSpMiddle style='text-indent:.5in'><b |
|---|
| 1666 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1667 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b + c / |
|---|
| 1668 | (1+math.exp(k*(t-t0)))<o:p></o:p></span></b></p> |
|---|
| 1669 | |
|---|
| 1670 | <p class=MsoListParagraphCxSpMiddle><span style='font-family:"Cambria","serif"; |
|---|
| 1671 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p> </o:p></span></p> |
|---|
| 1672 | |
|---|
| 1673 | <p class=MsoListParagraphCxSpLast>Note that use of spaces here is arbitrary, |
|---|
| 1674 | but all parentheses are required. Also note that the exponential function |
|---|
| 1675 | [exp(x) or e<sup>x</sup>] is supplied in Python in the math and numpy modules |
|---|
| 1676 | as math.exp(), numpy.exp(). Either of these can be used as well as the |
|---|
| 1677 | convenience abbreviation of np.exp(). Further, there are also a small number of |
|---|
| 1678 | common functions that are defined without the prefix for convenience [these |
|---|
| 1679 | include pi, exp(), sqrt(), sind(), cosd(), tand() where d indicates an argument |
|---|
| 1680 | in degrees.]</p> |
|---|
| 1681 | |
|---|
| 1682 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1683 | |
|---|
| 1684 | <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span |
|---|
| 1685 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1686 | style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1687 | </span></span></span><![endif]>Assign free variables to<b style='mso-bidi-font-weight: |
|---|
| 1688 | normal'> </b><b style='mso-bidi-font-weight:normal'><span style='font-family: |
|---|
| 1689 | "Calibri","sans-serif";mso-ascii-theme-font:major-latin;mso-hansi-theme-font: |
|---|
| 1690 | major-latin'>b</span>, </b><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1691 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1692 | mso-hansi-theme-font:major-latin'>c</span>, </b><b style='mso-bidi-font-weight: |
|---|
| 1693 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1694 | major-latin;mso-hansi-theme-font:major-latin'>k</span> </b>and<b |
|---|
| 1695 | style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1696 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1697 | mso-hansi-theme-font:major-latin'>t0</span></b>, similar as to what was done |
|---|
| 1698 | before. Note that the<b style='mso-bidi-font-weight:normal'> </b>variable name |
|---|
| 1699 | for the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1700 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b> |
|---|
| 1701 | label was set automatically to <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1702 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1703 | mso-hansi-theme-font:major-latin'>b_1</span></b>. If the same variable name (<b |
|---|
| 1704 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1705 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b>) |
|---|
| 1706 | was used again here, the same value would be used to fit both equations, which |
|---|
| 1707 | is certainly not what we want here.<span style='mso-spacerun:yes'> </span>Finally, |
|---|
| 1708 | since this equation is too complex to fit without some reasonable starting |
|---|
| 1709 | values, specify an approximate value, <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1710 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1711 | mso-hansi-theme-font:major-latin'>120</span></b>, for the vicinity of where the <i |
|---|
| 1712 | style='mso-bidi-font-style:normal'>c</i> lattice parameter starts to |
|---|
| 1713 | change (<b style='mso-bidi-font-weight: |
|---|
| 1714 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1715 | major-latin;mso-hansi-theme-font:major-latin'>t0</span></b>) and |
|---|
| 1716 | non-zero values for variables <B>c</B> and <B>k</B>.</p> |
|---|
| 1717 | |
|---|
| 1718 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1719 | |
|---|
| 1720 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1721 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_40" o:spid="_x0000_i1033" |
|---|
| 1722 | type="#_x0000_t75" style='width:317.25pt;height:171pt;visibility:visible; |
|---|
| 1723 | mso-wrap-style:square'> |
|---|
| 1724 | <v:imagedata src="ParametricFitting_files/image052.png" o:title=""/> |
|---|
| 1725 | </v:shape><![endif]--><![if !vml]><img border=0 width=423 height=228 |
|---|
| 1726 | src="ParametricFitting_files/image052.png" v:shapes="Picture_x0020_40"><![endif]></span></p> |
|---|
| 1727 | |
|---|
| 1728 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1729 | |
|---|
| 1730 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span |
|---|
| 1731 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1732 | style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1733 | </span></span></span><![endif]>Optionally, press the <b style='mso-bidi-font-weight: |
|---|
| 1734 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1735 | major-latin;mso-hansi-theme-font:major-latin'>Fit</span></b> button to see if |
|---|
| 1736 | the equation can be refined with starting values of zero for the other three |
|---|
| 1737 | parameters.<span style='mso-spacerun:yes'> </span>A fit is obtained and is |
|---|
| 1738 | plotted. </p> |
|---|
| 1739 | |
|---|
| 1740 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1741 | |
|---|
| 1742 | <p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span><span |
|---|
| 1743 | style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1744 | id="Picture_x0020_41" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:317.25pt; |
|---|
| 1745 | height:168.75pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1746 | <v:imagedata src="ParametricFitting_files/image054.png" o:title=""/> |
|---|
| 1747 | </v:shape><![endif]--><![if !vml]><img border=0 width=423 height=225 |
|---|
| 1748 | src="ParametricFitting_files/image054.png" v:shapes="Picture_x0020_41"><![endif]></span></p> |
|---|
| 1749 | |
|---|
| 1750 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1751 | |
|---|
| 1752 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span |
|---|
| 1753 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1754 | style='mso-list:Ignore'>6.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1755 | </span></span></span><![endif]>Press <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1756 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1757 | mso-hansi-theme-font:major-latin'>OK</span></b> to add this equation to the |
|---|
| 1758 | parametric fits and both equations are refit (and if the label for <b |
|---|
| 1759 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1760 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b</span></b> |
|---|
| 1761 | had not been changed, applying the constraint that <b style='mso-bidi-font-weight: |
|---|
| 1762 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1763 | major-latin;mso-hansi-theme-font:major-latin'>b</span></b> must be the same for |
|---|
| 1764 | both equations.) </p> |
|---|
| 1765 | |
|---|
| 1766 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1767 | |
|---|
| 1768 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1769 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_32" o:spid="_x0000_i1031" |
|---|
| 1770 | type="#_x0000_t75" style='width:353.25pt;height:300.75pt;visibility:visible; |
|---|
| 1771 | mso-wrap-style:square'> |
|---|
| 1772 | <v:imagedata src="ParametricFitting_files/image056.png" o:title=""/> |
|---|
| 1773 | </v:shape><![endif]--><![if !vml]><img border=0 width=471 height=401 |
|---|
| 1774 | src="ParametricFitting_files/image056.png" v:shapes="Picture_x0020_32"><![endif]></span></p> |
|---|
| 1775 | |
|---|
| 1776 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1777 | |
|---|
| 1778 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l1 level1 lfo8'><![if !supportLists]><span |
|---|
| 1779 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1780 | style='mso-list:Ignore'>7.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1781 | </span></span></span><![endif]>We will now try a more complex equation for the |
|---|
| 1782 | same data, where we set the value to <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1783 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1784 | mso-hansi-theme-font:major-latin'>b</span></b> for temperatures less than <b |
|---|
| 1785 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1786 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>t0</span></b> |
|---|
| 1787 | and a critical phenomenon formulism [(t-t<sub>0</sub>)<sup>-a</sup>] for |
|---|
| 1788 | temperatures above <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1789 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1790 | mso-hansi-theme-font:major-latin'>t0</span></b>. To do this we use the Python |
|---|
| 1791 | syntax "<b style='mso-bidi-font-weight:normal'><span style='font-family: |
|---|
| 1792 | "Calibri","sans-serif";mso-ascii-theme-font:major-latin;mso-hansi-theme-font: |
|---|
| 1793 | major-latin'>x1 if testexp else x2</span></b>" which is <b |
|---|
| 1794 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1795 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x1</span></b> |
|---|
| 1796 | where the test expression (<b style='mso-bidi-font-weight:normal'><span |
|---|
| 1797 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1798 | mso-hansi-theme-font:major-latin'>testexp</span></b> here) is <b |
|---|
| 1799 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1800 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>True</span></b> |
|---|
| 1801 | and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1802 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>x2</span></b> |
|---|
| 1803 | otherwise. Thus we can use an expression such as:</p> |
|---|
| 1804 | |
|---|
| 1805 | <p class=MsoListParagraphCxSpMiddle><span style='mso-spacerun:yes'> </span></p> |
|---|
| 1806 | |
|---|
| 1807 | <p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space: |
|---|
| 1808 | auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1809 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b if t <= |
|---|
| 1810 | t0 else b + c * (1-(t-t0)**d)<o:p></o:p></span></b></p> |
|---|
| 1811 | |
|---|
| 1812 | <p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space: |
|---|
| 1813 | auto'><span style='font-family:Courier'><o:p> </o:p></span></p> |
|---|
| 1814 | |
|---|
| 1815 | <p class=MsoListParagraphCxSpMiddle>This may be easier to read with the |
|---|
| 1816 | inclusion of extra parentheses (that have no effect on the execution):<span |
|---|
| 1817 | style='font-family:"Cambria","serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1818 | mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> |
|---|
| 1819 | |
|---|
| 1820 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1821 | |
|---|
| 1822 | <p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space: |
|---|
| 1823 | auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1824 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b if (t |
|---|
| 1825 | <= t0) else (b + c * (1-(t-t0)**d))<o:p></o:p></span></b></p> |
|---|
| 1826 | |
|---|
| 1827 | <p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space: |
|---|
| 1828 | auto'><span style='font-family:Courier'><o:p> </o:p></span></p> |
|---|
| 1829 | |
|---|
| 1830 | <p class=MsoListParagraphCxSpMiddle>As before, add an equation (or edit an |
|---|
| 1831 | existing one), set the dependent variable to <b style='mso-bidi-font-weight: |
|---|
| 1832 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1833 | major-latin;mso-hansi-theme-font:major-latin'>0::c</span></b>, enter the |
|---|
| 1834 | expression and assign the free and fixed variables, as before. Set the exponent |
|---|
| 1835 | and the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1836 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>t0</span></b> |
|---|
| 1837 | values to initial values of <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1838 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1839 | mso-hansi-theme-font:major-latin'>-0.025</span></b> and <b style='mso-bidi-font-weight: |
|---|
| 1840 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1841 | major-latin;mso-hansi-theme-font:major-latin'>120</span></b>, respectively, and |
|---|
| 1842 | turn off their refinement flags. Then press <b style='mso-bidi-font-weight: |
|---|
| 1843 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1844 | major-latin;mso-hansi-theme-font:major-latin'>Fit</span></b>.<span |
|---|
| 1845 | style='font-family:"Cambria","serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1846 | mso-hansi-theme-font:minor-latin'><o:p></o:p></span></p> |
|---|
| 1847 | |
|---|
| 1848 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1849 | mso-no-proof:yes'><o:p> </o:p></span></p> |
|---|
| 1850 | |
|---|
| 1851 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1852 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_42" o:spid="_x0000_i1030" |
|---|
| 1853 | type="#_x0000_t75" style='width:315.75pt;height:168.75pt;visibility:visible; |
|---|
| 1854 | mso-wrap-style:square'> |
|---|
| 1855 | <v:imagedata src="ParametricFitting_files/image058.png" o:title=""/> |
|---|
| 1856 | </v:shape><![endif]--><![if !vml]><img border=0 width=421 height=225 |
|---|
| 1857 | src="ParametricFitting_files/image058.png" v:shapes="Picture_x0020_42"><![endif]></span></p> |
|---|
| 1858 | |
|---|
| 1859 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1860 | |
|---|
| 1861 | <p class=MsoListParagraphCxSpMiddle>Then turn refinement of <b |
|---|
| 1862 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1863 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>t0</span></b> |
|---|
| 1864 | back on and press <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1865 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1866 | mso-hansi-theme-font:major-latin'>OK</span></b>. The resulting fit shows the |
|---|
| 1867 | trends quite well: </p> |
|---|
| 1868 | |
|---|
| 1869 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1870 | |
|---|
| 1871 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1872 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35" o:spid="_x0000_i1029" |
|---|
| 1873 | type="#_x0000_t75" style='width:351pt;height:302.25pt;visibility:visible; |
|---|
| 1874 | mso-wrap-style:square'> |
|---|
| 1875 | <v:imagedata src="ParametricFitting_files/image060.png" o:title=""/> |
|---|
| 1876 | </v:shape><![endif]--><![if !vml]><img border=0 width=468 height=403 |
|---|
| 1877 | src="ParametricFitting_files/image060.png" v:shapes="Picture_x0020_35"><![endif]></span></p> |
|---|
| 1878 | |
|---|
| 1879 | <p class=MsoListParagraphCxSpLast><o:p> </o:p></p> |
|---|
| 1880 | |
|---|
| 1881 | <h1>Step 5: Fitting to a Pseudo Variable</h1> |
|---|
| 1882 | |
|---|
| 1883 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1884 | |
|---|
| 1885 | <p class=MsoNormal>One can fit a function to a pseudo variable, just as to a |
|---|
| 1886 | direct variable. If we look at the plot shown in Step 2, it appears there are |
|---|
| 1887 | two regions. We can treat the lower range as a power-law growth, T<sup>k</sup>, |
|---|
| 1888 | and the upper region as linear (m*T + b). </p> |
|---|
| 1889 | |
|---|
| 1890 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1891 | |
|---|
| 1892 | <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span |
|---|
| 1893 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1894 | style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1895 | </span></span></span><![endif]>As before, add an equation<b style='mso-bidi-font-weight: |
|---|
| 1896 | normal'> </b>(or edit an existing one). For the dependent variable, select<b |
|---|
| 1897 | style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1898 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1899 | mso-hansi-theme-font:major-latin'>Global</span></b> to bring up that selection |
|---|
| 1900 | of variables and select<b style='mso-bidi-font-weight:normal'> </b><b |
|---|
| 1901 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1902 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>b/c</span> </b>and |
|---|
| 1903 | press<b style='mso-bidi-font-weight:normal'> </b><b style='mso-bidi-font-weight: |
|---|
| 1904 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1905 | major-latin;mso-hansi-theme-font:major-latin'>OK</span>. </b></p> |
|---|
| 1906 | |
|---|
| 1907 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1908 | |
|---|
| 1909 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span |
|---|
| 1910 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1911 | style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1912 | </span></span></span><![endif]>Then enter the equation as </p> |
|---|
| 1913 | |
|---|
| 1914 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1915 | |
|---|
| 1916 | <p class=MsoListParagraphCxSpMiddle style='margin-left:1.0in;mso-add-space: |
|---|
| 1917 | auto'><b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1918 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin;mso-bidi-font-family: |
|---|
| 1919 | "Lucida Grande";color:black'>(o1 + (a1*T)**k) if T < 120 else (o2 + a2*T</span></b><b |
|---|
| 1920 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1921 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>)<o:p></o:p></span></b></p> |
|---|
| 1922 | |
|---|
| 1923 | <p class=MsoListParagraphCxSpMiddle><span style='font-family:"Cambria","serif"; |
|---|
| 1924 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><o:p> </o:p></span></p> |
|---|
| 1925 | |
|---|
| 1926 | <p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span |
|---|
| 1927 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1928 | style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1929 | </span></span></span><![endif]>Assign the free and fixed variables, as shown |
|---|
| 1930 | below. Note that the exponent (<b style='mso-bidi-font-weight:normal'><span |
|---|
| 1931 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1932 | mso-hansi-theme-font:major-latin'>k</span></b>) and scaling factor (<b |
|---|
| 1933 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1934 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>a1</span></b>), |
|---|
| 1935 | cannot start as zero<b style='mso-bidi-font-weight:normal'>. </b></p> |
|---|
| 1936 | |
|---|
| 1937 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1938 | |
|---|
| 1939 | <p class=MsoListParagraphCxSpLast><span style='mso-fareast-language:EN-US; |
|---|
| 1940 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_44" o:spid="_x0000_i1028" |
|---|
| 1941 | type="#_x0000_t75" style='width:332.25pt;height:186pt;visibility:visible; |
|---|
| 1942 | mso-wrap-style:square'> |
|---|
| 1943 | <v:imagedata src="ParametricFitting_files/image062.png" o:title=""/> |
|---|
| 1944 | </v:shape><![endif]--><![if !vml]><img border=0 width=443 height=248 |
|---|
| 1945 | src="ParametricFitting_files/image062.png" v:shapes="Picture_x0020_44"><![endif]></span></p> |
|---|
| 1946 | |
|---|
| 1947 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1948 | |
|---|
| 1949 | <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l3 level1 lfo10'><![if !supportLists]><span |
|---|
| 1950 | style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><span |
|---|
| 1951 | style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'> |
|---|
| 1952 | </span></span></span><![endif]>Press the <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1953 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
|---|
| 1954 | mso-hansi-theme-font:major-latin'>Fit</span></b> button and note that all the |
|---|
| 1955 | free variables are adjusted </p> |
|---|
| 1956 | |
|---|
| 1957 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1958 | |
|---|
| 1959 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1960 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_45" o:spid="_x0000_i1027" |
|---|
| 1961 | type="#_x0000_t75" style='width:333.75pt;height:189pt;visibility:visible; |
|---|
| 1962 | mso-wrap-style:square'> |
|---|
| 1963 | <v:imagedata src="ParametricFitting_files/image064.png" o:title=""/> |
|---|
| 1964 | </v:shape><![endif]--><![if !vml]><img border=0 width=445 height=252 |
|---|
| 1965 | src="ParametricFitting_files/image064.png" v:shapes="Picture_x0020_45"><![endif]></span><span |
|---|
| 1966 | style='mso-spacerun:yes'> </span></p> |
|---|
| 1967 | |
|---|
| 1968 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1969 | |
|---|
| 1970 | <p class=MsoListParagraphCxSpMiddle>Also, that the plotted result is close to |
|---|
| 1971 | the values from the refinement.</p> |
|---|
| 1972 | |
|---|
| 1973 | <p class=MsoListParagraphCxSpMiddle><o:p> </o:p></p> |
|---|
| 1974 | |
|---|
| 1975 | <p class=MsoListParagraphCxSpMiddle><span style='mso-fareast-language:EN-US; |
|---|
| 1976 | mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_48" o:spid="_x0000_i1026" |
|---|
| 1977 | type="#_x0000_t75" style='width:348.75pt;height:302.25pt;visibility:visible; |
|---|
| 1978 | mso-wrap-style:square'> |
|---|
| 1979 | <v:imagedata src="ParametricFitting_files/image066.png" o:title=""/> |
|---|
| 1980 | </v:shape><![endif]--><![if !vml]><img border=0 width=465 height=403 |
|---|
| 1981 | src="ParametricFitting_files/image066.png" v:shapes="Picture_x0020_48"><![endif]></span></p> |
|---|
| 1982 | |
|---|
| 1983 | <p class=MsoListParagraphCxSpLast><o:p> </o:p></p> |
|---|
| 1984 | |
|---|
| 1985 | <p class=MsoNormal style='margin-left:.25in'><o:p> </o:p></p> |
|---|
| 1986 | |
|---|
| 1987 | <p class=MsoNormal>This completes this tutorial on use of Pseudo Variables and |
|---|
| 1988 | parametric fitting. </p> |
|---|
| 1989 | |
|---|
| 1990 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1991 | |
|---|
| 1992 | <h1>Advanced Use: Externally-Defined Functions</h1> |
|---|
| 1993 | |
|---|
| 1994 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1995 | |
|---|
| 1996 | <p class=MsoNormal>The parametric refinement section of GSAS-II is intended to |
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| 1997 | be quite flexible, but for very complex fitting, a user may wish to define a custom |
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| 1998 | Python function. Such a function can be defined in a separate module that will |
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| 1999 | be accessed with a parametric equation (or pseudo variable).</p> |
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| 2000 | |
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| 2001 | <p class=MsoNormal><o:p> </o:p></p> |
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| 2002 | |
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| 2003 | <p class=MsoNormal>As an example of that, if we create a file called <b |
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| 2004 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
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| 2005 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>fittest.py</span></b> |
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| 2006 | and locate that file in any directory in the Python path (most simply, in the |
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| 2007 | directory where the project file, <b style='mso-bidi-font-weight:normal'><span |
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| 2008 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
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| 2009 | mso-hansi-theme-font:major-latin'>SeqTut.gpx</span></b>, is located) and place |
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| 2010 | a routine <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
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| 2011 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>fitfxn</span></b> |
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| 2012 | in that module:</p> |
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| 2013 | |
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| 2014 | <blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'> |
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| 2015 | |
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| 2016 | <blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><pre><o:p> </o:p></pre><pre><b |
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| 2017 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
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| 2018 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'># file fittest.py<o:p></o:p></span></b></pre><pre><b |
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| 2019 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
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| 2020 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'>def fitfxn(T,o1,o2,a1,a2,k):<o:p></o:p></span></b></pre><pre><b |
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| 2021 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
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| 2022 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'> </span>if T < 120:<o:p></o:p></span></b></pre><pre><b |
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| 2023 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
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| 2024 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'> </span>return o1 + (a1*T)**k<o:p></o:p></span></b></pre><pre><b |
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| 2025 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
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| 2026 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'> </span>else:<o:p></o:p></span></b></pre><pre><b |
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| 2027 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
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| 2028 | mso-ascii-theme-font:major-latin;mso-hansi-theme-font:major-latin'><span style='mso-spacerun:yes'> </span>return o2 + a2*T<o:p></o:p></span></b></pre></blockquote> |
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| 2029 | |
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| 2030 | </blockquote> |
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| 2031 | |
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| 2032 | <p class=MsoNormal>The function <b style='mso-bidi-font-weight:normal'><span |
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| 2033 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
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| 2034 | mso-hansi-theme-font:major-latin'>fittest.fitfxn</span></b> can then be used to |
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| 2035 | duplicate the previous example: </p> |
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| 2036 | |
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| 2037 | <p class=MsoNormal><o:p> </o:p></p> |
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| 2038 | |
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| 2039 | <p class=MsoNormal><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
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| 2040 | id="Picture_x0020_47" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:315pt; |
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| 2041 | height:185.25pt;visibility:visible;mso-wrap-style:square'> |
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| 2042 | <v:imagedata src="ParametricFitting_files/image068.png" o:title="" croptop="3393f" |
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| 2043 | cropbottom="7847f" cropleft="3471f" cropright="3290f"/> |
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| 2044 | </v:shape><![endif]--><![if !vml]><img border=0 width=420 height=247 |
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| 2045 | src="ParametricFitting_files/image069.png" v:shapes="Picture_x0020_47"><![endif]></span></p> |
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| 2046 | |
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| 2047 | <p class=MsoNormal><o:p> </o:p></p> |
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| 2048 | |
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| 2049 | <p class=MsoNormal>Note that module <b style='mso-bidi-font-weight:normal'><span |
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| 2050 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:major-latin; |
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| 2051 | mso-hansi-theme-font:major-latin'>fittest</span></b> is automatically located |
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| 2052 | and loaded, provided it is found in the path. No changes to the standard |
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| 2053 | distributed GSAS-II code are needed. Care to avoid use of a module name already |
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| 2054 | found in GSAS-II or Python is wise.</p> |
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| 2055 | |
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| 2056 | </div> |
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| 2057 | |
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| 2058 | </body> |
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| 2059 | |
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| 2060 | </html> |
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