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| 25 | <o:Author>Von Dreele</o:Author> |
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| 26 | <o:LastAuthor>Von Dreele</o:LastAuthor> |
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| 27 | <o:Revision>9</o:Revision> |
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| 29 | <o:Created>2014-03-20T16:54:00Z</o:Created> |
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| 308 | <w:LsdException Locked="false" Priority="62" SemiHidden="false" |
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| 309 | UnhideWhenUsed="false" Name="Light Grid Accent 6"/> |
|---|
| 310 | <w:LsdException Locked="false" Priority="63" SemiHidden="false" |
|---|
| 311 | UnhideWhenUsed="false" Name="Medium Shading 1 Accent 6"/> |
|---|
| 312 | <w:LsdException Locked="false" Priority="64" SemiHidden="false" |
|---|
| 313 | UnhideWhenUsed="false" Name="Medium Shading 2 Accent 6"/> |
|---|
| 314 | <w:LsdException Locked="false" Priority="65" SemiHidden="false" |
|---|
| 315 | UnhideWhenUsed="false" Name="Medium List 1 Accent 6"/> |
|---|
| 316 | <w:LsdException Locked="false" Priority="66" SemiHidden="false" |
|---|
| 317 | UnhideWhenUsed="false" Name="Medium List 2 Accent 6"/> |
|---|
| 318 | <w:LsdException Locked="false" Priority="67" SemiHidden="false" |
|---|
| 319 | UnhideWhenUsed="false" Name="Medium Grid 1 Accent 6"/> |
|---|
| 320 | <w:LsdException Locked="false" Priority="68" SemiHidden="false" |
|---|
| 321 | UnhideWhenUsed="false" Name="Medium Grid 2 Accent 6"/> |
|---|
| 322 | <w:LsdException Locked="false" Priority="69" SemiHidden="false" |
|---|
| 323 | UnhideWhenUsed="false" Name="Medium Grid 3 Accent 6"/> |
|---|
| 324 | <w:LsdException Locked="false" Priority="70" SemiHidden="false" |
|---|
| 325 | UnhideWhenUsed="false" Name="Dark List Accent 6"/> |
|---|
| 326 | <w:LsdException Locked="false" Priority="71" SemiHidden="false" |
|---|
| 327 | UnhideWhenUsed="false" Name="Colorful Shading Accent 6"/> |
|---|
| 328 | <w:LsdException Locked="false" Priority="72" SemiHidden="false" |
|---|
| 329 | UnhideWhenUsed="false" Name="Colorful List Accent 6"/> |
|---|
| 330 | <w:LsdException Locked="false" Priority="73" SemiHidden="false" |
|---|
| 331 | UnhideWhenUsed="false" Name="Colorful Grid Accent 6"/> |
|---|
| 332 | <w:LsdException Locked="false" Priority="19" SemiHidden="false" |
|---|
| 333 | UnhideWhenUsed="false" QFormat="true" Name="Subtle Emphasis"/> |
|---|
| 334 | <w:LsdException Locked="false" Priority="21" SemiHidden="false" |
|---|
| 335 | UnhideWhenUsed="false" QFormat="true" Name="Intense Emphasis"/> |
|---|
| 336 | <w:LsdException Locked="false" Priority="31" SemiHidden="false" |
|---|
| 337 | UnhideWhenUsed="false" QFormat="true" Name="Subtle Reference"/> |
|---|
| 338 | <w:LsdException Locked="false" Priority="32" SemiHidden="false" |
|---|
| 339 | UnhideWhenUsed="false" QFormat="true" Name="Intense Reference"/> |
|---|
| 340 | <w:LsdException Locked="false" Priority="33" SemiHidden="false" |
|---|
| 341 | UnhideWhenUsed="false" QFormat="true" Name="Book Title"/> |
|---|
| 342 | <w:LsdException Locked="false" Priority="37" Name="Bibliography"/> |
|---|
| 343 | <w:LsdException Locked="false" Priority="39" QFormat="true" Name="TOC Heading"/> |
|---|
| 344 | </w:LatentStyles> |
|---|
| 345 | </xml><![endif]--> |
|---|
| 346 | <style> |
|---|
| 347 | <!-- |
|---|
| 348 | /* Font Definitions */ |
|---|
| 349 | @font-face |
|---|
| 350 | {font-family:Calibri; |
|---|
| 351 | panose-1:2 15 5 2 2 2 4 3 2 4; |
|---|
| 352 | mso-font-charset:0; |
|---|
| 353 | mso-generic-font-family:swiss; |
|---|
| 354 | mso-font-pitch:variable; |
|---|
| 355 | mso-font-signature:-536870145 1073786111 1 0 415 0;} |
|---|
| 356 | @font-face |
|---|
| 357 | {font-family:Tahoma; |
|---|
| 358 | panose-1:2 11 6 4 3 5 4 4 2 4; |
|---|
| 359 | mso-font-charset:0; |
|---|
| 360 | mso-generic-font-family:swiss; |
|---|
| 361 | mso-font-pitch:variable; |
|---|
| 362 | mso-font-signature:-520081665 -1073717157 41 0 66047 0;} |
|---|
| 363 | /* Style Definitions */ |
|---|
| 364 | p.MsoNormal, li.MsoNormal, div.MsoNormal |
|---|
| 365 | {mso-style-unhide:no; |
|---|
| 366 | mso-style-qformat:yes; |
|---|
| 367 | mso-style-parent:""; |
|---|
| 368 | margin:0in; |
|---|
| 369 | margin-bottom:.0001pt; |
|---|
| 370 | mso-pagination:widow-orphan; |
|---|
| 371 | font-size:12.0pt; |
|---|
| 372 | font-family:"Times New Roman","serif"; |
|---|
| 373 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 374 | mso-fareast-theme-font:minor-fareast;} |
|---|
| 375 | h1 |
|---|
| 376 | {mso-style-priority:9; |
|---|
| 377 | mso-style-unhide:no; |
|---|
| 378 | mso-style-qformat:yes; |
|---|
| 379 | mso-style-link:"Heading 1 Char"; |
|---|
| 380 | mso-margin-top-alt:auto; |
|---|
| 381 | margin-right:0in; |
|---|
| 382 | mso-margin-bottom-alt:auto; |
|---|
| 383 | margin-left:0in; |
|---|
| 384 | mso-pagination:widow-orphan; |
|---|
| 385 | mso-outline-level:1; |
|---|
| 386 | font-size:24.0pt; |
|---|
| 387 | font-family:"Times New Roman","serif"; |
|---|
| 388 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 389 | mso-fareast-theme-font:minor-fareast; |
|---|
| 390 | font-weight:bold;} |
|---|
| 391 | h2 |
|---|
| 392 | {mso-style-noshow:yes; |
|---|
| 393 | mso-style-priority:9; |
|---|
| 394 | mso-style-qformat:yes; |
|---|
| 395 | mso-style-link:"Heading 2 Char"; |
|---|
| 396 | mso-margin-top-alt:auto; |
|---|
| 397 | margin-right:0in; |
|---|
| 398 | mso-margin-bottom-alt:auto; |
|---|
| 399 | margin-left:0in; |
|---|
| 400 | mso-pagination:widow-orphan; |
|---|
| 401 | mso-outline-level:2; |
|---|
| 402 | font-size:18.0pt; |
|---|
| 403 | font-family:"Times New Roman","serif"; |
|---|
| 404 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 405 | mso-fareast-theme-font:minor-fareast; |
|---|
| 406 | font-weight:bold;} |
|---|
| 407 | h3 |
|---|
| 408 | {mso-style-noshow:yes; |
|---|
| 409 | mso-style-priority:9; |
|---|
| 410 | mso-style-qformat:yes; |
|---|
| 411 | mso-style-link:"Heading 3 Char"; |
|---|
| 412 | mso-margin-top-alt:auto; |
|---|
| 413 | margin-right:0in; |
|---|
| 414 | mso-margin-bottom-alt:auto; |
|---|
| 415 | margin-left:0in; |
|---|
| 416 | mso-pagination:widow-orphan; |
|---|
| 417 | mso-outline-level:3; |
|---|
| 418 | font-size:13.5pt; |
|---|
| 419 | font-family:"Times New Roman","serif"; |
|---|
| 420 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 421 | mso-fareast-theme-font:minor-fareast; |
|---|
| 422 | font-weight:bold;} |
|---|
| 423 | h4 |
|---|
| 424 | {mso-style-noshow:yes; |
|---|
| 425 | mso-style-priority:9; |
|---|
| 426 | mso-style-qformat:yes; |
|---|
| 427 | mso-style-link:"Heading 4 Char"; |
|---|
| 428 | mso-style-next:Normal; |
|---|
| 429 | margin-top:10.0pt; |
|---|
| 430 | margin-right:0in; |
|---|
| 431 | margin-bottom:0in; |
|---|
| 432 | margin-left:0in; |
|---|
| 433 | margin-bottom:.0001pt; |
|---|
| 434 | mso-pagination:widow-orphan lines-together; |
|---|
| 435 | page-break-after:avoid; |
|---|
| 436 | mso-outline-level:4; |
|---|
| 437 | font-size:13.0pt; |
|---|
| 438 | font-family:"Cambria","serif"; |
|---|
| 439 | mso-ascii-font-family:Cambria; |
|---|
| 440 | mso-ascii-theme-font:major-latin; |
|---|
| 441 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 442 | mso-fareast-theme-font:major-fareast; |
|---|
| 443 | mso-hansi-font-family:Cambria; |
|---|
| 444 | mso-hansi-theme-font:major-latin; |
|---|
| 445 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 446 | mso-bidi-theme-font:major-bidi; |
|---|
| 447 | color:#4F81BD; |
|---|
| 448 | mso-themecolor:accent1; |
|---|
| 449 | font-weight:bold; |
|---|
| 450 | font-style:italic;} |
|---|
| 451 | h5 |
|---|
| 452 | {mso-style-noshow:yes; |
|---|
| 453 | mso-style-priority:9; |
|---|
| 454 | mso-style-qformat:yes; |
|---|
| 455 | mso-style-link:"Heading 5 Char"; |
|---|
| 456 | mso-margin-top-alt:auto; |
|---|
| 457 | margin-right:0in; |
|---|
| 458 | mso-margin-bottom-alt:auto; |
|---|
| 459 | margin-left:0in; |
|---|
| 460 | mso-pagination:widow-orphan; |
|---|
| 461 | mso-outline-level:5; |
|---|
| 462 | font-size:12.0pt; |
|---|
| 463 | font-family:"Times New Roman","serif"; |
|---|
| 464 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 465 | mso-fareast-theme-font:minor-fareast; |
|---|
| 466 | color:#4F4FFF; |
|---|
| 467 | font-weight:bold;} |
|---|
| 468 | a:link, span.MsoHyperlink |
|---|
| 469 | {mso-style-noshow:yes; |
|---|
| 470 | mso-style-priority:99; |
|---|
| 471 | color:blue; |
|---|
| 472 | text-decoration:underline; |
|---|
| 473 | text-underline:single;} |
|---|
| 474 | a:visited, span.MsoHyperlinkFollowed |
|---|
| 475 | {mso-style-noshow:yes; |
|---|
| 476 | mso-style-priority:99; |
|---|
| 477 | color:purple; |
|---|
| 478 | text-decoration:underline; |
|---|
| 479 | text-underline:single;} |
|---|
| 480 | p.MsoDocumentMap, li.MsoDocumentMap, div.MsoDocumentMap |
|---|
| 481 | {mso-style-noshow:yes; |
|---|
| 482 | mso-style-priority:99; |
|---|
| 483 | mso-style-link:"Document Map Char"; |
|---|
| 484 | margin:0in; |
|---|
| 485 | margin-bottom:.0001pt; |
|---|
| 486 | mso-pagination:widow-orphan; |
|---|
| 487 | font-size:8.0pt; |
|---|
| 488 | font-family:"Tahoma","sans-serif"; |
|---|
| 489 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 490 | mso-fareast-theme-font:minor-fareast;} |
|---|
| 491 | p |
|---|
| 492 | {mso-style-noshow:yes; |
|---|
| 493 | mso-style-priority:99; |
|---|
| 494 | mso-margin-top-alt:auto; |
|---|
| 495 | margin-right:0in; |
|---|
| 496 | mso-margin-bottom-alt:auto; |
|---|
| 497 | margin-left:0in; |
|---|
| 498 | mso-pagination:widow-orphan; |
|---|
| 499 | font-size:12.0pt; |
|---|
| 500 | font-family:"Times New Roman","serif"; |
|---|
| 501 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 502 | mso-fareast-theme-font:minor-fareast;} |
|---|
| 503 | pre |
|---|
| 504 | {mso-style-noshow:yes; |
|---|
| 505 | mso-style-priority:99; |
|---|
| 506 | mso-style-link:"HTML Preformatted Char"; |
|---|
| 507 | margin:0in; |
|---|
| 508 | margin-bottom:.0001pt; |
|---|
| 509 | mso-pagination:widow-orphan; |
|---|
| 510 | tab-stops:45.8pt 91.6pt 137.4pt 183.2pt 229.0pt 274.8pt 320.6pt 366.4pt 412.2pt 458.0pt 503.8pt 549.6pt 595.4pt 641.2pt 687.0pt 732.8pt; |
|---|
| 511 | font-size:10.0pt; |
|---|
| 512 | font-family:"Courier New"; |
|---|
| 513 | mso-fareast-font-family:"Times New Roman";} |
|---|
| 514 | p.MsoAcetate, li.MsoAcetate, div.MsoAcetate |
|---|
| 515 | {mso-style-noshow:yes; |
|---|
| 516 | mso-style-priority:99; |
|---|
| 517 | mso-style-link:"Balloon Text Char"; |
|---|
| 518 | margin:0in; |
|---|
| 519 | margin-bottom:.0001pt; |
|---|
| 520 | mso-pagination:widow-orphan; |
|---|
| 521 | font-size:8.0pt; |
|---|
| 522 | font-family:"Tahoma","sans-serif"; |
|---|
| 523 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 524 | mso-fareast-theme-font:minor-fareast;} |
|---|
| 525 | span.MsoPlaceholderText |
|---|
| 526 | {mso-style-noshow:yes; |
|---|
| 527 | mso-style-priority:99; |
|---|
| 528 | mso-style-unhide:no; |
|---|
| 529 | color:gray;} |
|---|
| 530 | p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing |
|---|
| 531 | {mso-style-noshow:yes; |
|---|
| 532 | mso-style-priority:1; |
|---|
| 533 | mso-style-unhide:no; |
|---|
| 534 | mso-style-qformat:yes; |
|---|
| 535 | mso-style-parent:""; |
|---|
| 536 | margin:0in; |
|---|
| 537 | margin-bottom:.0001pt; |
|---|
| 538 | mso-pagination:widow-orphan; |
|---|
| 539 | font-size:12.0pt; |
|---|
| 540 | font-family:"Times New Roman","serif"; |
|---|
| 541 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 542 | mso-fareast-theme-font:minor-fareast;} |
|---|
| 543 | p.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph |
|---|
| 544 | {mso-style-noshow:yes; |
|---|
| 545 | mso-style-priority:34; |
|---|
| 546 | mso-style-unhide:no; |
|---|
| 547 | mso-style-qformat:yes; |
|---|
| 548 | margin-top:0in; |
|---|
| 549 | margin-right:0in; |
|---|
| 550 | margin-bottom:0in; |
|---|
| 551 | margin-left:.5in; |
|---|
| 552 | margin-bottom:.0001pt; |
|---|
| 553 | mso-add-space:auto; |
|---|
| 554 | mso-pagination:widow-orphan; |
|---|
| 555 | font-size:12.0pt; |
|---|
| 556 | font-family:"Times New Roman","serif"; |
|---|
| 557 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 558 | mso-fareast-theme-font:minor-fareast;} |
|---|
| 559 | p.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst |
|---|
| 560 | {mso-style-noshow:yes; |
|---|
| 561 | mso-style-priority:34; |
|---|
| 562 | mso-style-unhide:no; |
|---|
| 563 | mso-style-qformat:yes; |
|---|
| 564 | mso-style-type:export-only; |
|---|
| 565 | margin-top:0in; |
|---|
| 566 | margin-right:0in; |
|---|
| 567 | margin-bottom:0in; |
|---|
| 568 | margin-left:.5in; |
|---|
| 569 | margin-bottom:.0001pt; |
|---|
| 570 | mso-add-space:auto; |
|---|
| 571 | mso-pagination:widow-orphan; |
|---|
| 572 | font-size:12.0pt; |
|---|
| 573 | font-family:"Times New Roman","serif"; |
|---|
| 574 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 575 | mso-fareast-theme-font:minor-fareast;} |
|---|
| 576 | p.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle |
|---|
| 577 | {mso-style-noshow:yes; |
|---|
| 578 | mso-style-priority:34; |
|---|
| 579 | mso-style-unhide:no; |
|---|
| 580 | mso-style-qformat:yes; |
|---|
| 581 | mso-style-type:export-only; |
|---|
| 582 | margin-top:0in; |
|---|
| 583 | margin-right:0in; |
|---|
| 584 | margin-bottom:0in; |
|---|
| 585 | margin-left:.5in; |
|---|
| 586 | margin-bottom:.0001pt; |
|---|
| 587 | mso-add-space:auto; |
|---|
| 588 | mso-pagination:widow-orphan; |
|---|
| 589 | font-size:12.0pt; |
|---|
| 590 | font-family:"Times New Roman","serif"; |
|---|
| 591 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 592 | mso-fareast-theme-font:minor-fareast;} |
|---|
| 593 | p.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast |
|---|
| 594 | {mso-style-noshow:yes; |
|---|
| 595 | mso-style-priority:34; |
|---|
| 596 | mso-style-unhide:no; |
|---|
| 597 | mso-style-qformat:yes; |
|---|
| 598 | mso-style-type:export-only; |
|---|
| 599 | margin-top:0in; |
|---|
| 600 | margin-right:0in; |
|---|
| 601 | margin-bottom:0in; |
|---|
| 602 | margin-left:.5in; |
|---|
| 603 | margin-bottom:.0001pt; |
|---|
| 604 | mso-add-space:auto; |
|---|
| 605 | mso-pagination:widow-orphan; |
|---|
| 606 | font-size:12.0pt; |
|---|
| 607 | font-family:"Times New Roman","serif"; |
|---|
| 608 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 609 | mso-fareast-theme-font:minor-fareast;} |
|---|
| 610 | span.MsoIntenseReference |
|---|
| 611 | {mso-style-priority:32; |
|---|
| 612 | mso-style-unhide:no; |
|---|
| 613 | mso-style-qformat:yes; |
|---|
| 614 | font-variant:small-caps; |
|---|
| 615 | color:#C0504D; |
|---|
| 616 | mso-themecolor:accent2; |
|---|
| 617 | letter-spacing:.25pt; |
|---|
| 618 | font-weight:bold; |
|---|
| 619 | text-decoration:underline; |
|---|
| 620 | text-underline:single;} |
|---|
| 621 | span.Heading1Char |
|---|
| 622 | {mso-style-name:"Heading 1 Char"; |
|---|
| 623 | mso-style-priority:9; |
|---|
| 624 | mso-style-unhide:no; |
|---|
| 625 | mso-style-locked:yes; |
|---|
| 626 | mso-style-link:"Heading 1"; |
|---|
| 627 | mso-ansi-font-size:24.0pt; |
|---|
| 628 | mso-bidi-font-size:24.0pt; |
|---|
| 629 | font-family:"Times New Roman","serif"; |
|---|
| 630 | mso-ascii-font-family:"Times New Roman"; |
|---|
| 631 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 632 | mso-fareast-theme-font:minor-fareast; |
|---|
| 633 | mso-hansi-font-family:"Times New Roman"; |
|---|
| 634 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 635 | mso-font-kerning:18.0pt; |
|---|
| 636 | font-weight:bold;} |
|---|
| 637 | span.Heading2Char |
|---|
| 638 | {mso-style-name:"Heading 2 Char"; |
|---|
| 639 | mso-style-noshow:yes; |
|---|
| 640 | mso-style-priority:9; |
|---|
| 641 | mso-style-unhide:no; |
|---|
| 642 | mso-style-locked:yes; |
|---|
| 643 | mso-style-link:"Heading 2"; |
|---|
| 644 | mso-ansi-font-size:18.0pt; |
|---|
| 645 | mso-bidi-font-size:18.0pt; |
|---|
| 646 | font-family:"Times New Roman","serif"; |
|---|
| 647 | mso-ascii-font-family:"Times New Roman"; |
|---|
| 648 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 649 | mso-fareast-theme-font:minor-fareast; |
|---|
| 650 | mso-hansi-font-family:"Times New Roman"; |
|---|
| 651 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 652 | font-weight:bold;} |
|---|
| 653 | span.Heading3Char |
|---|
| 654 | {mso-style-name:"Heading 3 Char"; |
|---|
| 655 | mso-style-noshow:yes; |
|---|
| 656 | mso-style-priority:9; |
|---|
| 657 | mso-style-unhide:no; |
|---|
| 658 | mso-style-locked:yes; |
|---|
| 659 | mso-style-link:"Heading 3"; |
|---|
| 660 | mso-ansi-font-size:13.5pt; |
|---|
| 661 | mso-bidi-font-size:13.5pt; |
|---|
| 662 | font-family:"Times New Roman","serif"; |
|---|
| 663 | mso-ascii-font-family:"Times New Roman"; |
|---|
| 664 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 665 | mso-fareast-theme-font:minor-fareast; |
|---|
| 666 | mso-hansi-font-family:"Times New Roman"; |
|---|
| 667 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 668 | font-weight:bold;} |
|---|
| 669 | span.Heading4Char |
|---|
| 670 | {mso-style-name:"Heading 4 Char"; |
|---|
| 671 | mso-style-noshow:yes; |
|---|
| 672 | mso-style-priority:9; |
|---|
| 673 | mso-style-unhide:no; |
|---|
| 674 | mso-style-locked:yes; |
|---|
| 675 | mso-style-link:"Heading 4"; |
|---|
| 676 | mso-ansi-font-size:13.0pt; |
|---|
| 677 | mso-bidi-font-size:13.0pt; |
|---|
| 678 | font-family:"Cambria","serif"; |
|---|
| 679 | mso-ascii-font-family:Cambria; |
|---|
| 680 | mso-ascii-theme-font:major-latin; |
|---|
| 681 | mso-fareast-font-family:"Times New Roman"; |
|---|
| 682 | mso-fareast-theme-font:major-fareast; |
|---|
| 683 | mso-hansi-font-family:Cambria; |
|---|
| 684 | mso-hansi-theme-font:major-latin; |
|---|
| 685 | mso-bidi-font-family:"Times New Roman"; |
|---|
| 686 | mso-bidi-theme-font:major-bidi; |
|---|
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| 885 | <h1><strong><span style='mso-bidi-font-weight:normal'>Small Angle X-Ray Data |
|---|
| 886 | Size Distribution in Alumina Powder</span><o:p></o:p></strong></h1> |
|---|
| 887 | |
|---|
| 888 | <p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'>In |
|---|
| 889 | this tutorial you will determine the size distribution of particles in an |
|---|
| 890 | alumina polishing powder using data from a constant wavelength synchrotron |
|---|
| 891 | X-ray USAXS instrument. You will use both Maximum Entropy (<span class=SpellE>MaxEnt</span>) |
|---|
| 892 | and Total Non-Negative Least Squares (TNNLS) methods assuming spherical |
|---|
| 893 | particles. The data were collected from <span style='mso-fareast-font-family: |
|---|
| 894 | Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold; |
|---|
| 895 | mso-bidi-font-style:italic'>powders spread onto sticky tape and covered with |
|---|
| 896 | another layer of the same tape. The data were corrected for background from |
|---|
| 897 | data collected from two layers of sticky tape. However, the sample thickness is |
|---|
| 898 | not</span> accurately known <span style='mso-fareast-font-family:Calibri; |
|---|
| 899 | mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold;mso-bidi-font-style: |
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| 900 | italic'>so the data are not calibrated on an absolute scale.<o:p></o:p></span></p> |
|---|
| 901 | |
|---|
| 902 | <p class=MsoNormal>If you have not done so already, <a |
|---|
| 903 | href="Starting%20GSAS.htm">start GSAS-II</a>.</p> |
|---|
| 904 | |
|---|
| 905 | <h2>Step 1: read in the data file</h2> |
|---|
| 906 | |
|---|
| 907 | <p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span |
|---|
| 908 | style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span |
|---|
| 909 | style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]>Use |
|---|
| 910 | the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 911 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family: |
|---|
| 912 | Calibri;mso-bidi-theme-font:minor-latin'>Import/Small Angle Data/from a q step |
|---|
| 913 | QIE data file</span></b> menu item to read the data file into GSAS-II. This |
|---|
| 914 | read option is set to read three column small angle scattering data (SASD) as |
|---|
| 915 | Q, intensity and estimated standard deviation in intensity; there may be a |
|---|
| 916 | header with metadata information in the front of this file.<span |
|---|
| 917 | style='mso-spacerun:yes'> </span>Change the file directory to <b |
|---|
| 918 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 919 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family: |
|---|
| 920 | Calibri;mso-bidi-theme-font:minor-latin'>Exercises/Small angle</span></b><span |
|---|
| 921 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 922 | mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font: |
|---|
| 923 | minor-latin'> to find the file.</span></p> |
|---|
| 924 | |
|---|
| 925 | <p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span |
|---|
| 926 | style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span |
|---|
| 927 | style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]>Select |
|---|
| 928 | the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 929 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family: |
|---|
| 930 | Calibri;mso-bidi-theme-font:minor-latin'>alumina data.dat</span></b><span |
|---|
| 931 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 932 | mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font: |
|---|
| 933 | minor-latin'> data</span> file in the first dialog and press <b |
|---|
| 934 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 935 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family: |
|---|
| 936 | Calibri;mso-bidi-theme-font:minor-latin'>Open</span></b>. There will be a |
|---|
| 937 | Dialog box asking <span class=GramE><b style='mso-bidi-font-weight:normal'><span |
|---|
| 938 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 939 | mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font: |
|---|
| 940 | minor-latin'>Is</span></b></span><b style='mso-bidi-font-weight:normal'><span |
|---|
| 941 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 942 | mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font: |
|---|
| 943 | minor-latin'> this the file you want?</span></b> Press <span class=GramE><b |
|---|
| 944 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 945 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family: |
|---|
| 946 | Calibri;mso-bidi-theme-font:minor-latin'>Yes</span></b></span> button to |
|---|
| 947 | proceed.</p> |
|---|
| 948 | |
|---|
| 949 | <p class=MsoNormal>At this point the <b style='mso-bidi-font-weight:normal'><span |
|---|
| 950 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 951 | mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font: |
|---|
| 952 | minor-latin'>GSAS-II data tree</span></b> window will have several entries and |
|---|
| 953 | the plot window will show the SASD pattern as a log-log plot of intensity vs. Q</p> |
|---|
| 954 | |
|---|
| 955 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype |
|---|
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|---|
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|---|
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|---|
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|---|
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|---|
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|---|
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|---|
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|---|
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|---|
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| 976 | style='width:525pt;height:450pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 977 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image001.png" |
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| 978 | o:title=""/> |
|---|
| 979 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
|---|
| 980 | src="Small%20Angle%20Size%20Distribution_files/image001.png" v:shapes="Picture_x0020_6"><![endif]></span></p> |
|---|
| 981 | |
|---|
| 982 | <h2>Step 2: Set Limits</h2> |
|---|
| 983 | |
|---|
| 984 | <p class=MsoNormal>For this step we will reposition the limits to enclose only |
|---|
| 985 | that part of the SASD pattern suitable for size distribution analysis. |
|---|
| 986 | Typically this covers 10<sup>-3</sup> < Q < 10<sup>-1</sup>; below this |
|---|
| 987 | range scattering is from very large objects not readily described by the size |
|---|
| 988 | distribution analysis and above the scattering is mostly background. Select <b |
|---|
| 989 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 990 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Limits</span></b> |
|---|
| 991 | under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 992 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina |
|---|
| 993 | data.dat</span></b> from the GSAS-II tree. Then set <b style='mso-bidi-font-weight: |
|---|
| 994 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 995 | minor-latin;mso-hansi-theme-font:minor-latin'>changed</span></b> to <b |
|---|
| 996 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 997 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.001</span></b> |
|---|
| 998 | for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span |
|---|
| 999 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1000 | mso-hansi-theme-font:minor-latin'>Tmin</span></b></span> and <b |
|---|
| 1001 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1002 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.1</span></b> |
|---|
| 1003 | for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1004 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1005 | mso-hansi-theme-font:minor-latin'>Tmax</span></b></span>. You can also set the |
|---|
| 1006 | limits using the cursor on the plot by either picking a point on the curve with |
|---|
| 1007 | the left or right mouse button or by dragging the green and red vertical lines |
|---|
| 1008 | to the desired positions. The limits window should look like</p> |
|---|
| 1009 | |
|---|
| 1010 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1011 | id="Picture_x0020_22" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:225pt; |
|---|
| 1012 | height:195pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1013 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image002.png" |
|---|
| 1014 | o:title=""/> |
|---|
| 1015 | </v:shape><![endif]--><![if !vml]><img border=0 width=300 height=260 |
|---|
| 1016 | src="Small%20Angle%20Size%20Distribution_files/image002.png" v:shapes="Picture_x0020_22"><![endif]></span><span |
|---|
| 1017 | style='mso-spacerun:yes'> </span></p> |
|---|
| 1018 | |
|---|
| 1019 | <h2>Step 3 Select the scattering substances for your sample</h2> |
|---|
| 1020 | |
|---|
| 1021 | <p class=MsoNormal><span style='mso-no-proof:yes'>Two scsttering substances |
|---|
| 1022 | need to be defined for your sample to give the anticipated scattering contrast; |
|---|
| 1023 | in this case one is alumina and the other is vacuum (really air). Parameters |
|---|
| 1024 | for a number of substances are defined in the file </span><b style='mso-bidi-font-weight: |
|---|
| 1025 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1026 | minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span |
|---|
| 1027 | style='mso-no-proof:yes'>. You can add your own substances to this or better |
|---|
| 1028 | put them in </span><b style='mso-bidi-font-weight:normal'><span |
|---|
| 1029 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1030 | mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>UserSubstances.py</span></b><span |
|---|
| 1031 | style='mso-no-proof:yes'>; this is read after Substances.py when you load |
|---|
| 1032 | substances for your selection. </span>Select <b style='mso-bidi-font-weight: |
|---|
| 1033 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1034 | minor-latin;mso-hansi-theme-font:minor-latin'>Substances</span></b> under <b |
|---|
| 1035 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1036 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina |
|---|
| 1037 | data.dat</span></b> from the GSAS-II tree. Then do <b style='mso-bidi-font-weight: |
|---|
| 1038 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1039 | minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Load</span></b> substance |
|---|
| 1040 | from the menu; a popup window will appear with possible selections</p> |
|---|
| 1041 | |
|---|
| 1042 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1043 | id="Picture_x0020_23" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:259.5pt; |
|---|
| 1044 | height:252pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1045 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image003.png" |
|---|
| 1046 | o:title=""/> |
|---|
| 1047 | </v:shape><![endif]--><![if !vml]><img border=0 width=346 height=336 |
|---|
| 1048 | src="Small%20Angle%20Size%20Distribution_files/image003.png" v:shapes="Picture_x0020_23"><![endif]><o:p></o:p></span></p> |
|---|
| 1049 | |
|---|
| 1050 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1051 | |
|---|
| 1052 | <p class=MsoNormal>Select <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1053 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1054 | mso-hansi-theme-font:minor-latin'>Alumina</span></b> and press <b |
|---|
| 1055 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1056 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>; |
|---|
| 1057 | the relevant data for alumina (and vacuum) are displayed next</p> |
|---|
| 1058 | |
|---|
| 1059 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1060 | id="Picture_x0020_24" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:259.5pt; |
|---|
| 1061 | height:195pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1062 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image004.png" |
|---|
| 1063 | o:title=""/> |
|---|
| 1064 | </v:shape><![endif]--><![if !vml]><img border=0 width=346 height=260 |
|---|
| 1065 | src="Small%20Angle%20Size%20Distribution_files/image004.png" v:shapes="Picture_x0020_24"><![endif]></span><span |
|---|
| 1066 | style='mso-spacerun:yes'> </span></p> |
|---|
| 1067 | |
|---|
| 1068 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1069 | |
|---|
| 1070 | <p class=MsoNormal>If desired you can load/add as many substances as you desire |
|---|
| 1071 | into this list; you can also delete any of them (except vacuum). The |
|---|
| 1072 | composition, volume occupied by the atoms in the composition and the density |
|---|
| 1073 | are given for each substance. These can each be edited; the other values will |
|---|
| 1074 | change accordingly. If your substance isnt in the list, you can <b |
|---|
| 1075 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1076 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add |
|---|
| 1077 | substance</span></b> to create a new one (you will be asked for a name and the |
|---|
| 1078 | set of elements in two successive popup windows). From this information the |
|---|
| 1079 | scattering density and that as affected by resonant scattering for the listed |
|---|
| 1080 | wavelength is displayed (the wavelength can be changed in the <b |
|---|
| 1081 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1082 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Instrument |
|---|
| 1083 | Parameters</span></b> GSAS-II tree item if needed). The resonant scattering |
|---|
| 1084 | value is used for contrast calculations.</p> |
|---|
| 1085 | |
|---|
| 1086 | <h2>Step 4: Set Sample parameters </h2> |
|---|
| 1087 | |
|---|
| 1088 | <p class=MsoNormal>Two of the substances you have loaded into GSAS-II next need |
|---|
| 1089 | to be selected for this experiment; Select <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1090 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1091 | mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b> under <b |
|---|
| 1092 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1093 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina |
|---|
| 1094 | data.dat</span></b> from the GSAS-II tree. Near the bottom of the window will |
|---|
| 1095 | be two rows marked <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1096 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1097 | mso-hansi-theme-font:minor-latin'>Material</span></b>; select <b |
|---|
| 1098 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1099 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Alumina</span></b> |
|---|
| 1100 | from one of the pull downs (leave the other as <b style='mso-bidi-font-weight: |
|---|
| 1101 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1102 | minor-latin;mso-hansi-theme-font:minor-latin'>vacuum</span></b>). The window |
|---|
| 1103 | will show at the bottom the computed contrast between alumina and vacuum |
|---|
| 1104 | without and with consideration of resonant scattering effects; the latter is |
|---|
| 1105 | used in subsequent calculations.</p> |
|---|
| 1106 | |
|---|
| 1107 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1108 | id="Picture_x0020_25" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:305.25pt; |
|---|
| 1109 | height:369pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1110 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image005.png" |
|---|
| 1111 | o:title=""/> |
|---|
| 1112 | </v:shape><![endif]--><![if !vml]><img border=0 width=407 height=492 |
|---|
| 1113 | src="Small%20Angle%20Size%20Distribution_files/image005.png" v:shapes="Picture_x0020_25"><![endif]></span></p> |
|---|
| 1114 | |
|---|
| 1115 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1116 | |
|---|
| 1117 | <p class=MsoNormal>For experiments for which you know the transmission and the |
|---|
| 1118 | sample thickness, you can manipulate the <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1119 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1120 | mso-hansi-theme-font:minor-latin'>volume fractions</span></b> to make the |
|---|
| 1121 | calculated transmission match the observed one. Additionally, if you have |
|---|
| 1122 | absolute scaling information, you can rescale the data by adjusting the <b |
|---|
| 1123 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1124 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>histogram |
|---|
| 1125 | scale factor</span></b>; multiple data sets can be scaled together via the <b |
|---|
| 1126 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1127 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Command/Set |
|---|
| 1128 | scale</span></b> menu item.</p> |
|---|
| 1129 | |
|---|
| 1130 | <h2>Step 5 Size distribution via Maximum Entropy</h2> |
|---|
| 1131 | |
|---|
| 1132 | <p class=MsoNormal>You are now ready to attempt a size distribution analysis |
|---|
| 1133 | using the maximum entropy method. Select <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1134 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1135 | mso-hansi-theme-font:minor-latin'>Models</span></b> under <b style='mso-bidi-font-weight: |
|---|
| 1136 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1137 | minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina data.dat</span></b> |
|---|
| 1138 | from the GSAS-II tree; the window will display</p> |
|---|
| 1139 | |
|---|
| 1140 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1141 | id="Picture_x0020_15" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:355.5pt; |
|---|
| 1142 | height:191.25pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1143 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image006.png" |
|---|
| 1144 | o:title=""/> |
|---|
| 1145 | </v:shape><![endif]--><![if !vml]><img border=0 width=474 height=255 |
|---|
| 1146 | src="Small%20Angle%20Size%20Distribution_files/image006.png" v:shapes="Picture_x0020_15"><![endif]></span></p> |
|---|
| 1147 | |
|---|
| 1148 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1149 | |
|---|
| 1150 | <p class=MsoNormal>Many selections are made by default for this <span |
|---|
| 1151 | class=GramE>analysis,</span> however it is important that an appropriate value |
|---|
| 1152 | is selected for the background. From the high Q end of the data plot</p> |
|---|
| 1153 | |
|---|
| 1154 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1155 | id="Picture_x0020_27" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt; |
|---|
| 1156 | height:450pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1157 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image007.png" |
|---|
| 1158 | o:title=""/> |
|---|
| 1159 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
|---|
| 1160 | src="Small%20Angle%20Size%20Distribution_files/image007.png" v:shapes="Picture_x0020_27"><![endif]></span><span |
|---|
| 1161 | style='mso-spacerun:yes'> </span></p> |
|---|
| 1162 | |
|---|
| 1163 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1164 | |
|---|
| 1165 | <p class=MsoNormal>It is clear that the intensity levels off at an apparent |
|---|
| 1166 | background level of ~0.12; enter that into the appropriate place in the data |
|---|
| 1167 | window. The plot will be redrawn showing a horizontal green line for the |
|---|
| 1168 | background. All the other parameters seem reasonable for a 1<sup>st</sup> |
|---|
| 1169 | attempt at a <span class=SpellE>MaxEnt</span> solution. Do <b style='mso-bidi-font-weight: |
|---|
| 1170 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1171 | minor-latin;mso-hansi-theme-font:minor-latin'>Models/Fit</span></b>; the |
|---|
| 1172 | console window will show that the calculation did not converge and the <b |
|---|
| 1173 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1174 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Size |
|---|
| 1175 | Distribution</span></b> plot has a choppy appearance.</p> |
|---|
| 1176 | |
|---|
| 1177 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1178 | id="Picture_x0020_28" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:525pt; |
|---|
| 1179 | height:450pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1180 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image008.png" |
|---|
| 1181 | o:title=""/> |
|---|
| 1182 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
|---|
| 1183 | src="Small%20Angle%20Size%20Distribution_files/image008.png" v:shapes="Picture_x0020_28"><![endif]></span></p> |
|---|
| 1184 | |
|---|
| 1185 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1186 | |
|---|
| 1187 | <p class=MsoNormal>This is not a satisfactory result, but the suggestion given |
|---|
| 1188 | in the console window is worth trying. Change the <b style='mso-bidi-font-weight: |
|---|
| 1189 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1190 | minor-latin;mso-hansi-theme-font:minor-latin'>Error multiplier</span></b> to <b |
|---|
| 1191 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1192 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>5</span></b> |
|---|
| 1193 | (notice the increased error bars on the data plot) and repeat <b |
|---|
| 1194 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1195 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Model/Fit</span></b>. |
|---|
| 1196 | Convergence is now achieved in <10 cycles (see console window for details) |
|---|
| 1197 | and a much smoother size distribution results</p> |
|---|
| 1198 | |
|---|
| 1199 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1200 | id="Picture_x0020_29" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:525pt; |
|---|
| 1201 | height:450pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1202 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image009.png" |
|---|
| 1203 | o:title=""/> |
|---|
| 1204 | </v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600 |
|---|
| 1205 | src="Small%20Angle%20Size%20Distribution_files/image009.png" v:shapes="Picture_x0020_29"><![endif]></span></p> |
|---|
| 1206 | |
|---|
| 1207 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1208 | |
|---|
| 1209 | <p class=MsoNormal>This is a good result: clearly the alumina polishing powder |
|---|
| 1210 | has a bimodal distribution with diameters centered about ~1600Å and ~160Å (not |
|---|
| 1211 | 500Å and 1µm as advertised by the manufacturer!).</p> |
|---|
| 1212 | |
|---|
| 1213 | <p class=MsoNormal>You may wish to explore the effect of some of the other |
|---|
| 1214 | parameters in the data window. Most are obvious but <b style='mso-bidi-font-weight: |
|---|
| 1215 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1216 | minor-latin;mso-hansi-theme-font:minor-latin'>Log floor factor</span></b> needs |
|---|
| 1217 | a bit of explanation. This is the log of the minimum size distribution (scaled |
|---|
| 1218 | by the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1219 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>histogram |
|---|
| 1220 | scale factor</span></b> and the <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1221 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1222 | mso-hansi-theme-font:minor-latin'>contrast</span></b>). This size distribution |
|---|
| 1223 | minimum needs to be set within 1-2 orders of magnitude of the optimal value and |
|---|
| 1224 | can differ from the default of 10<sup>-3; </sup>it is worth changing if |
|---|
| 1225 | convergence is poor despite trying different error multipliers. Try changing it |
|---|
| 1226 | to see what effect it has on the result. With the original settings the data |
|---|
| 1227 | fit looks like</p> |
|---|
| 1228 | |
|---|
| 1229 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1230 | id="Picture_x0020_30" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:621.75pt; |
|---|
| 1231 | height:450pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1232 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image010.png" |
|---|
| 1233 | o:title=""/> |
|---|
| 1234 | </v:shape><![endif]--><![if !vml]><img border=0 width=829 height=600 |
|---|
| 1235 | src="Small%20Angle%20Size%20Distribution_files/image010.png" v:shapes="Picture_x0020_30"><![endif]></span></p> |
|---|
| 1236 | |
|---|
| 1237 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1238 | |
|---|
| 1239 | <p class=MsoNormal>The green curve is the result calculated from the size |
|---|
| 1240 | distribution. Notice that it is not perfect, there is appreciable misfit around |
|---|
| 1241 | Q=0.03A. This may be due to the assumption that the particles are spheres; they |
|---|
| 1242 | could be some other shape (I could get a better fit by setting the Spheroid |
|---|
| 1243 | aspect ratio to 2.0), however this tool is not really the appropriate one to |
|---|
| 1244 | make this determination.</p> |
|---|
| 1245 | |
|---|
| 1246 | <h2>Step 6 Size Distribution <i style='mso-bidi-font-style:normal'>via</i> |
|---|
| 1247 | Total Non-Negative Least Squares (TNNLS)</h2> |
|---|
| 1248 | |
|---|
| 1249 | <p class=MsoNormal>An alternative method for determining size distributions is |
|---|
| 1250 | the TNNLS or Interior-Point Gradient (IPG) method. As the name implies this is |
|---|
| 1251 | a gradient refinement method for the special case of all positive data and |
|---|
| 1252 | parameter values. To try it on this alumina data, select <b style='mso-bidi-font-weight: |
|---|
| 1253 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1254 | minor-latin;mso-hansi-theme-font:minor-latin'>IPG</span></b> from the <b |
|---|
| 1255 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1256 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Fitting |
|---|
| 1257 | method</span></b> pull down. The data window will change to give</p> |
|---|
| 1258 | |
|---|
| 1259 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1260 | id="Picture_x0020_16" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:375.75pt; |
|---|
| 1261 | height:191.25pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1262 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image011.png" |
|---|
| 1263 | o:title=""/> |
|---|
| 1264 | </v:shape><![endif]--><![if !vml]><img border=0 width=501 height=255 |
|---|
| 1265 | src="Small%20Angle%20Size%20Distribution_files/image011.png" v:shapes="Picture_x0020_16"><![endif]></span></p> |
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| 1266 | |
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| 1267 | <p class=MsoNormal><o:p> </o:p></p> |
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| 1268 | |
|---|
| 1269 | <p class=MsoNormal>Reset the Error multiplier back to 1.0 and then do |
|---|
| 1270 | Models/Fit to run the IPG fitting. The IPG algorithm did not converge in 100 |
|---|
| 1271 | cycles and resulting size distribution is a little choppy but has roughly the |
|---|
| 1272 | same bimodal distribution found by <span class=SpellE>MaxEnt</span>.</p> |
|---|
| 1273 | |
|---|
| 1274 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1275 | id="Picture_x0020_289" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:621.75pt; |
|---|
| 1276 | height:450pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1277 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image012.png" |
|---|
| 1278 | o:title=""/> |
|---|
| 1279 | </v:shape><![endif]--><![if !vml]><img border=0 width=829 height=600 |
|---|
| 1280 | src="Small%20Angle%20Size%20Distribution_files/image012.png" v:shapes="Picture_x0020_289"><![endif]></span></p> |
|---|
| 1281 | |
|---|
| 1282 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1283 | |
|---|
| 1284 | <p class=MsoNormal>This can be considerably improved by setting the <b |
|---|
| 1285 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1286 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Error |
|---|
| 1287 | multiplier</span></b> to 2.0; the IPG fit con<span style='mso-no-proof:yes'>verges |
|---|
| 1288 | in <20 cycles and gives a smoother size distribution.<o:p></o:p></span></p> |
|---|
| 1289 | |
|---|
| 1290 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1291 | id="Picture_x0020_291" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:621.75pt; |
|---|
| 1292 | height:450pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1293 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image013.png" |
|---|
| 1294 | o:title=""/> |
|---|
| 1295 | </v:shape><![endif]--><![if !vml]><img border=0 width=829 height=600 |
|---|
| 1296 | src="Small%20Angle%20Size%20Distribution_files/image013.png" v:shapes="Picture_x0020_291"><![endif]></span></p> |
|---|
| 1297 | |
|---|
| 1298 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1299 | |
|---|
| 1300 | <p class=MsoNormal>The bimodal distribution is again quite clear with ~1400A |
|---|
| 1301 | and ~150A diameter particles. This method appears to give a better fit to the |
|---|
| 1302 | data than the <span class=SpellE>MaxEnt</span> method particularly in the |
|---|
| 1303 | Q~0.3A region</p> |
|---|
| 1304 | |
|---|
| 1305 | <p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape |
|---|
| 1306 | id="Picture_x0020_292" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:621.75pt; |
|---|
| 1307 | height:450pt;visibility:visible;mso-wrap-style:square'> |
|---|
| 1308 | <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image014.png" |
|---|
| 1309 | o:title=""/> |
|---|
| 1310 | </v:shape><![endif]--><![if !vml]><img border=0 width=829 height=600 |
|---|
| 1311 | src="Small%20Angle%20Size%20Distribution_files/image014.png" v:shapes="Picture_x0020_292"><![endif]></span></p> |
|---|
| 1312 | |
|---|
| 1313 | <p class=MsoNormal><o:p> </o:p></p> |
|---|
| 1314 | |
|---|
| 1315 | <p class=MsoNormal>You may wish to explore the other parameters for the IPG |
|---|
| 1316 | fitting. If <b style='mso-bidi-font-weight:normal'><span style='font-family: |
|---|
| 1317 | "Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font: |
|---|
| 1318 | minor-latin'>Q power weight</span></b> is set to <b style='mso-bidi-font-weight: |
|---|
| 1319 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1320 | minor-latin;mso-hansi-theme-font:minor-latin'>0-4</span></b>, that changes the |
|---|
| 1321 | data weighting to <span class=SpellE><span class=GramE>Q<sup>p</sup></span></span>. |
|---|
| 1322 | This can change the convergence of the IPG method and yield improved results if |
|---|
| 1323 | one is unsuccessful with the default settings. I got a nice fit with a <b |
|---|
| 1324 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1325 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Q power |
|---|
| 1326 | weight</span></b> of <b style='mso-bidi-font-weight:normal'><span |
|---|
| 1327 | style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin; |
|---|
| 1328 | mso-hansi-theme-font:minor-latin'>3</span></b> and <b style='mso-bidi-font-weight: |
|---|
| 1329 | normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font: |
|---|
| 1330 | minor-latin;mso-hansi-theme-font:minor-latin'>Error multiplier</span></b> of <b |
|---|
| 1331 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1332 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.0</span></b>.</p> |
|---|
| 1333 | |
|---|
| 1334 | <p class=MsoNormal>You should save this GSAS-II project as it will be used in tutorials |
|---|
| 1335 | for fitting small angle scattering data; I used <span class=SpellE><b |
|---|
| 1336 | style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif"; |
|---|
| 1337 | mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>alumina.gpx</span></b></span>.</p> |
|---|
| 1338 | |
|---|
| 1339 | </div> |
|---|
| 1340 | |
|---|
| 1341 | </body> |
|---|
| 1342 | |
|---|
| 1343 | </html> |
|---|
