source: trunk/help/Small Angle Size Distribution.htm @ 1323

Last change on this file since 1323 was 1323, checked in by vondreele, 8 years ago

resolve conflicts in G2grid, fix displat of Seq refinement of SASD data results (a couple more 'gets' needed). Small revisions to SASD tutorials.
Start implementation of SASD smearing correction.

  • Property svn:mime-type set to text/html
File size: 63.6 KB
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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;}
391h2
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;}
407h3
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;}
423h4
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;}
451h5
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;}
468a:link, span.MsoHyperlink
469        {mso-style-noshow:yes;
470        mso-style-priority:99;
471        color:blue;
472        text-decoration:underline;
473        text-underline:single;}
474a:visited, span.MsoHyperlinkFollowed
475        {mso-style-noshow:yes;
476        mso-style-priority:99;
477        color:purple;
478        text-decoration:underline;
479        text-underline:single;}
480p.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;}
491p
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;}
503pre
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";}
514p.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;}
525span.MsoPlaceholderText
526        {mso-style-noshow:yes;
527        mso-style-priority:99;
528        mso-style-unhide:no;
529        color:gray;}
530p.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;}
543p.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;}
559p.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;}
576p.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;}
593p.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;}
610span.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;}
621span.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;}
637span.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;}
653span.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;}
669span.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;
687        color:#4F81BD;
688        mso-themecolor:accent1;
689        font-weight:bold;
690        font-style:italic;}
691span.Heading5Char
692        {mso-style-name:"Heading 5 Char";
693        mso-style-noshow:yes;
694        mso-style-priority:9;
695        mso-style-unhide:no;
696        mso-style-locked:yes;
697        mso-style-link:"Heading 5";
698        mso-ansi-font-size:12.0pt;
699        mso-bidi-font-size:12.0pt;
700        font-family:"Times New Roman","serif";
701        mso-ascii-font-family:"Times New Roman";
702        mso-fareast-font-family:"Times New Roman";
703        mso-fareast-theme-font:minor-fareast;
704        mso-hansi-font-family:"Times New Roman";
705        mso-bidi-font-family:"Times New Roman";
706        color:#4F4FFF;
707        font-weight:bold;}
708span.HTMLPreformattedChar
709        {mso-style-name:"HTML Preformatted Char";
710        mso-style-noshow:yes;
711        mso-style-priority:99;
712        mso-style-unhide:no;
713        mso-style-locked:yes;
714        mso-style-link:"HTML Preformatted";
715        font-family:"Courier New";
716        mso-ascii-font-family:"Courier New";
717        mso-fareast-font-family:"Times New Roman";
718        mso-hansi-font-family:"Courier New";
719        mso-bidi-font-family:"Courier New";}
720span.DocumentMapChar
721        {mso-style-name:"Document Map Char";
722        mso-style-noshow:yes;
723        mso-style-priority:99;
724        mso-style-unhide:no;
725        mso-style-locked:yes;
726        mso-style-link:"Document Map";
727        mso-ansi-font-size:8.0pt;
728        mso-bidi-font-size:8.0pt;
729        font-family:"Tahoma","sans-serif";
730        mso-ascii-font-family:Tahoma;
731        mso-fareast-font-family:"Times New Roman";
732        mso-fareast-theme-font:minor-fareast;
733        mso-hansi-font-family:Tahoma;
734        mso-bidi-font-family:Tahoma;}
735span.BalloonTextChar
736        {mso-style-name:"Balloon Text Char";
737        mso-style-noshow:yes;
738        mso-style-priority:99;
739        mso-style-unhide:no;
740        mso-style-locked:yes;
741        mso-style-link:"Balloon Text";
742        mso-ansi-font-size:8.0pt;
743        mso-bidi-font-size:8.0pt;
744        font-family:"Tahoma","sans-serif";
745        mso-ascii-font-family:Tahoma;
746        mso-fareast-font-family:"Times New Roman";
747        mso-fareast-theme-font:minor-fareast;
748        mso-hansi-font-family:Tahoma;
749        mso-bidi-font-family:Tahoma;}
750span.SpellE
751        {mso-style-name:"";
752        mso-spl-e:yes;}
753span.GramE
754        {mso-style-name:"";
755        mso-gram-e:yes;}
756.MsoChpDefault
757        {mso-style-type:export-only;
758        mso-default-props:yes;
759        font-size:10.0pt;
760        mso-ansi-font-size:10.0pt;
761        mso-bidi-font-size:10.0pt;
762        font-family:"Calibri","sans-serif";
763        mso-ascii-font-family:Calibri;
764        mso-ascii-theme-font:minor-latin;
765        mso-fareast-font-family:Calibri;
766        mso-fareast-theme-font:minor-latin;
767        mso-hansi-font-family:Calibri;
768        mso-hansi-theme-font:minor-latin;
769        mso-bidi-font-family:"Times New Roman";
770        mso-bidi-theme-font:minor-bidi;}
771@page WordSection1
772        {size:8.5in 11.0in;
773        margin:1.0in 1.0in 1.0in 1.0in;
774        mso-header-margin:.5in;
775        mso-footer-margin:.5in;
776        mso-paper-source:0;}
777div.WordSection1
778        {page:WordSection1;}
779 /* List Definitions */
780 @list l0
781        {mso-list-id:608973138;
782        mso-list-type:hybrid;
783        mso-list-template-ids:-1449999034 67698703 67698713 67698715 67698703 67698713 67698715 67698703 67698713 67698715;}
784@list l0:level1
785        {mso-level-tab-stop:none;
786        mso-level-number-position:left;
787        text-indent:-.25in;}
788@list l0:level2
789        {mso-level-number-format:alpha-lower;
790        mso-level-tab-stop:none;
791        mso-level-number-position:left;
792        text-indent:-.25in;}
793@list l0:level3
794        {mso-level-number-format:roman-lower;
795        mso-level-tab-stop:none;
796        mso-level-number-position:right;
797        text-indent:-9.0pt;}
798@list l0:level4
799        {mso-level-tab-stop:none;
800        mso-level-number-position:left;
801        text-indent:-.25in;}
802@list l0:level5
803        {mso-level-number-format:alpha-lower;
804        mso-level-tab-stop:none;
805        mso-level-number-position:left;
806        text-indent:-.25in;}
807@list l0:level6
808        {mso-level-number-format:roman-lower;
809        mso-level-tab-stop:none;
810        mso-level-number-position:right;
811        text-indent:-9.0pt;}
812@list l0:level7
813        {mso-level-tab-stop:none;
814        mso-level-number-position:left;
815        text-indent:-.25in;}
816@list l0:level8
817        {mso-level-number-format:alpha-lower;
818        mso-level-tab-stop:none;
819        mso-level-number-position:left;
820        text-indent:-.25in;}
821@list l0:level9
822        {mso-level-number-format:roman-lower;
823        mso-level-tab-stop:none;
824        mso-level-number-position:right;
825        text-indent:-9.0pt;}
826ol
827        {margin-bottom:0in;}
828ul
829        {margin-bottom:0in;}
830-->
831</style>
832<!--[if gte mso 10]>
833<style>
834 /* Style Definitions */
835 table.MsoNormalTable
836        {mso-style-name:"Table Normal";
837        mso-tstyle-rowband-size:0;
838        mso-tstyle-colband-size:0;
839        mso-style-noshow:yes;
840        mso-style-priority:99;
841        mso-style-parent:"";
842        mso-padding-alt:0in 5.4pt 0in 5.4pt;
843        mso-para-margin:0in;
844        mso-para-margin-bottom:.0001pt;
845        mso-pagination:widow-orphan;
846        font-size:10.0pt;
847        font-family:"Calibri","sans-serif";
848        mso-ascii-font-family:Calibri;
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879</head>
880
881<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
882
883<div class=WordSection1>
884
885<h1><strong><span style='mso-bidi-font-weight:normal'>Small Angle X-Ray Data –
886Size 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
889this tutorial you will determine the size distribution of particles in an
890alumina polishing powder using data from a constant wavelength synchrotron X-ray
891USAXS instrument. You will use both Maximum Entropy (<span class=SpellE>MaxEnt</span>)
892and Total Non-Negative Least Squares (TNNLS) methods assuming spherical
893particles. The data were collected from <span style='mso-fareast-font-family:
894Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold;
895mso-bidi-font-style:italic'>powders spread onto sticky tape and covered with
896another layer of the same tape. The data were corrected for background from
897data collected from two layers of sticky tape. However, the sample thickness is
898not</span> accurately known <span style='mso-fareast-font-family:Calibri;
899mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold;mso-bidi-font-style:
900italic'>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
903href="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
908style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
909style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
910the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
911mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
912Calibri;mso-bidi-theme-font:minor-latin'>Import/Small Angle Data/from a q step
913QIE data file</span></b> menu item to read the data file into GSAS-II. This
914read option is set to read three column small angle scattering data (SASD) as Q
915in Å<sup>-1</sup>, intensity and estimated standard deviation in intensity;
916there may be a header with metadata information in the front of this file.<span
917style='mso-spacerun:yes'>  </span>Change the file directory to <b
918style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
919mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
920Calibri;mso-bidi-theme-font:minor-latin'>Exercises/Small angle</span></b><span
921style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
922mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
923minor-latin'> to find the file</span>; you will have to select the ‘<b
924style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
925mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file
926(*.*)</span></b>’ filter to see it.</p>
927
928<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
929style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
930style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
931the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
932mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
933Calibri;mso-bidi-theme-font:minor-latin'>alumina data.dat</span></b><span
934style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
935mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
936minor-latin'> data</span> file in the first dialog and press <b
937style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
938mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
939Calibri;mso-bidi-theme-font:minor-latin'>Open</span></b>. There will be a
940Dialog box asking <span class=GramE><b style='mso-bidi-font-weight:normal'><span
941style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
942mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
943minor-latin'>Is</span></b></span><b style='mso-bidi-font-weight:normal'><span
944style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
945mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
946minor-latin'> this the file you want?</span></b> Press <span class=GramE><b
947style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
948mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
949Calibri;mso-bidi-theme-font:minor-latin'>Yes</span></b></span> button to
950proceed.</p>
951
952<p class=MsoNormal>At this point the <b style='mso-bidi-font-weight:normal'><span
953style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
954mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
955minor-latin'>GSAS-II data tree</span></b> window will have several entries and
956the plot window will show the SASD pattern as a log-log plot of intensity vs. Q</p>
957
958<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
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980 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image001.png"
981  o:title=""/>
982</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
983src="Small%20Angle%20Size%20Distribution_files/image001.png" v:shapes="Picture_x0020_6"><![endif]></span></p>
984
985<h2>Step 2: Set Limits</h2>
986
987<p class=MsoNormal>For this step we will reposition the limits to enclose only
988that part of the SASD pattern suitable for size distribution analysis.
989Typically this covers 10<sup>-3</sup> &lt; Q &lt; 10<sup>-1</sup>; below this
990range scattering is from very large objects not readily described by the size
991distribution analysis and above the scattering is mostly background. Select <b
992style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
993mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Limits</span></b>
994under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
995mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
996data.dat</span></b> from the GSAS-II tree. Then set <b style='mso-bidi-font-weight:
997normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
998minor-latin;mso-hansi-theme-font:minor-latin'>changed</span></b> to <b
999style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1000mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.001</span></b>
1001for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1002style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
1003mso-hansi-theme-font:minor-latin'>Tmin</span></b></span> and <b
1004style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1005mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.1</span></b>
1006for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1007style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
1008mso-hansi-theme-font:minor-latin'>Tmax</span></b></span>. You can also set the
1009limits using the cursor on the plot by either picking a point on the curve with
1010the left or right mouse button or by dragging the green and red vertical lines
1011to the desired positions. The limits window should look like</p>
1012
1013<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1014 id="Picture_x0020_22" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:225pt;
1015 height:195pt;visibility:visible;mso-wrap-style:square'>
1016 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image002.png"
1017  o:title=""/>
1018</v:shape><![endif]--><![if !vml]><img border=0 width=300 height=260
1019src="Small%20Angle%20Size%20Distribution_files/image002.png" v:shapes="Picture_x0020_22"><![endif]></span><span
1020style='mso-spacerun:yes'> </span></p>
1021
1022<h2>Step 3 Select the scattering substances for your sample</h2>
1023
1024<p class=MsoNormal><span style='mso-no-proof:yes'>Two scsttering substances
1025need to be defined for your sample to give the anticipated scattering contrast;
1026in this case one is alumina and the other is “vacuum” (really air). Parameters
1027for a number of substances are defined in the file </span><b style='mso-bidi-font-weight:
1028normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1029minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1030style='mso-no-proof:yes'>. You can add your own substances to this or better put
1031them in </span><b style='mso-bidi-font-weight:normal'><span style='font-family:
1032"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1033minor-latin;mso-no-proof:yes'>UserSubstances.py</span></b><span
1034style='mso-no-proof:yes'>; this is read after </span><b style='mso-bidi-font-weight:
1035normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1036minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1037style='mso-no-proof:yes'> when you load substances for your selection. </span>Select
1038<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1039mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Substances</span></b>
1040under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1041mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1042data.dat</span></b> from the GSAS-II tree. Then do <b style='mso-bidi-font-weight:
1043normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1044minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Load</span></b> substance
1045from the menu; a popup window will appear with possible selections</p>
1046
1047<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1048 id="Picture_x0020_23" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:259.5pt;
1049 height:252pt;visibility:visible;mso-wrap-style:square'>
1050 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image003.png"
1051  o:title=""/>
1052</v:shape><![endif]--><![if !vml]><img border=0 width=346 height=336
1053src="Small%20Angle%20Size%20Distribution_files/image003.png" v:shapes="Picture_x0020_23"><![endif]><o:p></o:p></span></p>
1054
1055<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1056
1057<p class=MsoNormal>Select <b style='mso-bidi-font-weight:normal'><span
1058style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
1059mso-hansi-theme-font:minor-latin'>Alumina</span></b> and press <b
1060style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1061mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>;
1062the relevant data for alumina (and vacuum) are displayed next</p>
1063
1064<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1065 id="Picture_x0020_24" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:259.5pt;
1066 height:195pt;visibility:visible;mso-wrap-style:square'>
1067 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image004.png"
1068  o:title=""/>
1069</v:shape><![endif]--><![if !vml]><img border=0 width=346 height=260
1070src="Small%20Angle%20Size%20Distribution_files/image004.png" v:shapes="Picture_x0020_24"><![endif]></span><span
1071style='mso-spacerun:yes'> </span></p>
1072
1073<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1074
1075<p class=MsoNormal>If desired you can load/add as many substances as you desire
1076into this list; you can also delete any of them (except vacuum). The
1077composition, volume occupied by the atoms in the composition and the density
1078are given for each substance. These can each be edited; the other values will
1079change accordingly. If your substance isn’t in the list, you can <b
1080style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1081mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add
1082substance</span></b> to create a new one (you will be asked for a name and the
1083set of elements in two successive popup windows). From this information the
1084scattering density and that as affected by resonant scattering for the listed
1085wavelength is displayed (the wavelength can be changed in the <b
1086style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1087mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Instrument
1088Parameters</span></b> GSAS-II tree item if needed). The resonant scattering
1089value is used for contrast calculations.</p>
1090
1091<h2>Step 4: Set Sample parameters </h2>
1092
1093<p class=MsoNormal>Two of the substances you have loaded into GSAS-II next need
1094to be selected for this size distribution analysis; Select <b style='mso-bidi-font-weight:
1095normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1096minor-latin;mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b>
1097under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1098mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1099data.dat</span></b> from the GSAS-II tree. Near the bottom of the window will
1100be two rows marked “<b style='mso-bidi-font-weight:normal'><span
1101style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
1102mso-hansi-theme-font:minor-latin'>Material</span></b>”; select <b
1103style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1104mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Alumina</span></b>
1105from one of the pull downs (leave the other as <b style='mso-bidi-font-weight:
1106normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1107minor-latin;mso-hansi-theme-font:minor-latin'>vacuum</span></b>). The window
1108will show at the bottom the computed contrast between alumina and vacuum
1109without and with consideration of resonant scattering effects; the latter is used
1110in subsequent calculations.</p>
1111
1112<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1113 id="Picture_x0020_25" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:305.25pt;
1114 height:369pt;visibility:visible;mso-wrap-style:square'>
1115 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image005.png"
1116  o:title=""/>
1117</v:shape><![endif]--><![if !vml]><img border=0 width=407 height=492
1118src="Small%20Angle%20Size%20Distribution_files/image005.png" v:shapes="Picture_x0020_25"><![endif]></span></p>
1119
1120<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1121
1122<p class=MsoNormal>For experiments for which you know the transmission and the
1123sample thickness, you can manipulate the <b style='mso-bidi-font-weight:normal'><span
1124style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
1125mso-hansi-theme-font:minor-latin'>volume fractions</span></b> to make the
1126calculated transmission match the observed one. Additionally, if you have
1127absolute scaling information, you can rescale the data by adjusting the <b
1128style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1129mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>histogram
1130scale factor</span></b>; multiple data sets can be scaled together via the <b
1131style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1132mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Command/Set
1133scale</span></b> menu item.</p>
1134
1135<h2>Step 5 Size distribution via Maximum Entropy</h2>
1136
1137<p class=MsoNormal>You are now ready to attempt a size distribution analysis
1138using the maximum entropy method. Select <b style='mso-bidi-font-weight:normal'><span
1139style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
1140mso-hansi-theme-font:minor-latin'>Models</span></b> under <b style='mso-bidi-font-weight:
1141normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1142minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina data.dat</span></b>
1143from the GSAS-II tree; the window will display</p>
1144
1145<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1146 id="Picture_x0020_15" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:355.5pt;
1147 height:191.25pt;visibility:visible;mso-wrap-style:square'>
1148 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image006.png"
1149  o:title=""/>
1150</v:shape><![endif]--><![if !vml]><img border=0 width=474 height=255
1151src="Small%20Angle%20Size%20Distribution_files/image006.png" v:shapes="Picture_x0020_15"><![endif]></span></p>
1152
1153<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1154
1155<p class=MsoNormal>Many selections are made by default for this analysis;
1156however it is important that an appropriate value is selected for the
1157background. From the high Q end of the data plot</p>
1158
1159<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1160 id="Picture_x0020_27" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt;
1161 height:450pt;visibility:visible;mso-wrap-style:square'>
1162 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image007.png"
1163  o:title=""/>
1164</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1165src="Small%20Angle%20Size%20Distribution_files/image007.png" v:shapes="Picture_x0020_27"><![endif]></span><span
1166style='mso-spacerun:yes'> </span></p>
1167
1168<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1169
1170<p class=MsoNormal>It is clear that the intensity levels off at an apparent
1171background level of ~<b style='mso-bidi-font-weight:normal'><span
1172style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
1173mso-hansi-theme-font:minor-latin'>0.12</span></b>; enter that into the
1174appropriate place in the data window. The plot will be redrawn showing a horizontal
1175red line for the background. All the other parameters seem reasonable for a 1<sup>st</sup>
1176attempt at a <span class=SpellE>MaxEnt</span> solution. Do <b style='mso-bidi-font-weight:
1177normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1178minor-latin;mso-hansi-theme-font:minor-latin'>Models/Fit</span></b>; the
1179console window will show that the calculation did not converge and the <b
1180style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1181mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Size
1182Distribution</span></b> plot has a “choppy” appearance.</p>
1183
1184<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1185 id="Picture_x0020_28" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:525pt;
1186 height:450pt;visibility:visible;mso-wrap-style:square'>
1187 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image008.png"
1188  o:title=""/>
1189</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1190src="Small%20Angle%20Size%20Distribution_files/image008.png" v:shapes="Picture_x0020_28"><![endif]></span></p>
1191
1192<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1193
1194<p class=MsoNormal>This is not a satisfactory result, but the suggestion given
1195in the console window is worth trying. Change the <b style='mso-bidi-font-weight:
1196normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1197minor-latin;mso-hansi-theme-font:minor-latin'>Error multiplier</span></b> to <b
1198style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1199mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>5</span></b>
1200(notice the increased error bars on the data plot) and repeat <b
1201style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1202mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Model/Fit</span></b>.
1203Convergence is now achieved in &lt;10 cycles (see console window for details)
1204and a much smoother size distribution results</p>
1205
1206<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1207 id="Picture_x0020_29" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:525pt;
1208 height:450pt;visibility:visible;mso-wrap-style:square'>
1209 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image009.png"
1210  o:title=""/>
1211</v:shape><![endif]--><![if !vml]><img border=0 width=700 height=600
1212src="Small%20Angle%20Size%20Distribution_files/image009.png" v:shapes="Picture_x0020_29"><![endif]></span></p>
1213
1214<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1215
1216<p class=MsoNormal>This is a good result: clearly the alumina polishing powder
1217has a bimodal distribution with diameters centered about ~1600Å and ~160Å (not
1218500Å and 1µm as advertised by the manufacturer!).</p>
1219
1220<p class=MsoNormal>You may wish to explore the effect of some of the other
1221parameters in the data window. Most are obvious but <b style='mso-bidi-font-weight:
1222normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1223minor-latin;mso-hansi-theme-font:minor-latin'>Log floor factor</span></b> needs
1224a bit of explanation. This is the log of the minimum size distribution (scaled
1225by the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1226mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>histogram
1227scale factor</span></b> and the <b style='mso-bidi-font-weight:normal'><span
1228style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
1229mso-hansi-theme-font:minor-latin'>contrast</span></b>). This size distribution
1230minimum needs to be set within 1-2 orders of magnitude of the optimal value and
1231can differ from the default of 10<sup>-3; </sup>it is worth changing if
1232convergence is poor despite trying different error multipliers. Try changing it
1233to see what effect it has on the result. With the original settings the data
1234fit looks like</p>
1235
1236<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1237 id="Picture_x0020_30" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:621.75pt;
1238 height:450pt;visibility:visible;mso-wrap-style:square'>
1239 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image010.png"
1240  o:title=""/>
1241</v:shape><![endif]--><![if !vml]><img border=0 width=829 height=600
1242src="Small%20Angle%20Size%20Distribution_files/image010.png" v:shapes="Picture_x0020_30"><![endif]></span></p>
1243
1244<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1245
1246<p class=MsoNormal>The green curve is the result calculated from the size
1247distribution. Notice that it is not perfect, there is appreciable misfit around
1248Q=0.003Å<sup>-1</sup>. This may be due to the assumption that the particles are
1249spheres; they could be some other shape (I could get a better fit by setting
1250the Spheroid aspect ratio to 2.0), however this tool is not really the
1251appropriate one to make this determination.</p>
1252
1253<h2>Step 6 Size Distribution <i style='mso-bidi-font-style:normal'>via</i>
1254Total Non-Negative Least Squares (TNNLS)</h2>
1255
1256<p class=MsoNormal>An alternative method for determining size distributions is
1257the TNNLS or Interior-Point Gradient (IPG) method. As the name implies this is
1258a gradient refinement method for the special case of all positive data and
1259parameter values. To try it on this alumina data, select <b style='mso-bidi-font-weight:
1260normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1261minor-latin;mso-hansi-theme-font:minor-latin'>IPG</span></b> from the <b
1262style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1263mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Fitting
1264method</span></b> pull down. The data window will change to give</p>
1265
1266<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1267 id="Picture_x0020_16" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:375.75pt;
1268 height:191.25pt;visibility:visible;mso-wrap-style:square'>
1269 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image011.png"
1270  o:title=""/>
1271</v:shape><![endif]--><![if !vml]><img border=0 width=501 height=255
1272src="Small%20Angle%20Size%20Distribution_files/image011.png" v:shapes="Picture_x0020_16"><![endif]></span></p>
1273
1274<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1275
1276<p class=MsoNormal>Reset the Error multiplier back to <b style='mso-bidi-font-weight:
1277normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1278minor-latin;mso-hansi-theme-font:minor-latin'>1.0</span></b> and then do <b
1279style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1280mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models/Fit</span></b>
1281to run the IPG fitting. The IPG algorithm did not converge in 100 cycles and
1282resulting size distribution is a little choppy but has roughly the same bimodal
1283distribution found by <span class=SpellE>MaxEnt</span>.</p>
1284
1285<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1286 id="Picture_x0020_289" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:621.75pt;
1287 height:450pt;visibility:visible;mso-wrap-style:square'>
1288 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image012.png"
1289  o:title=""/>
1290</v:shape><![endif]--><![if !vml]><img border=0 width=829 height=600
1291src="Small%20Angle%20Size%20Distribution_files/image012.png" v:shapes="Picture_x0020_289"><![endif]></span></p>
1292
1293<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1294
1295<p class=MsoNormal>This can be considerably improved by setting the <b
1296style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1297mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Error
1298multiplier</span></b> to <b style='mso-bidi-font-weight:normal'><span
1299style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
1300mso-hansi-theme-font:minor-latin'>2.0</span></b>; the IPG fit con<span
1301style='mso-no-proof:yes'>verges in &lt;20 cycles and gives a smoother size
1302distribution.<o:p></o:p></span></p>
1303
1304<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1305 id="Picture_x0020_291" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:621.75pt;
1306 height:450pt;visibility:visible;mso-wrap-style:square'>
1307 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image013.png"
1308  o:title=""/>
1309</v:shape><![endif]--><![if !vml]><img border=0 width=829 height=600
1310src="Small%20Angle%20Size%20Distribution_files/image013.png" v:shapes="Picture_x0020_291"><![endif]></span></p>
1311
1312<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1313
1314<p class=MsoNormal>The bimodal distribution is again quite clear with ~1400Å
1315and ~150Å diameter particles. This method appears to give a better fit to the
1316data than the <span class=SpellE>MaxEnt</span> method particularly in the
1317Q~0.003Å<sup>-1</sup> region’</p>
1318
1319<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1320 id="Picture_x0020_292" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:621.75pt;
1321 height:450pt;visibility:visible;mso-wrap-style:square'>
1322 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image014.png"
1323  o:title=""/>
1324</v:shape><![endif]--><![if !vml]><img border=0 width=829 height=600
1325src="Small%20Angle%20Size%20Distribution_files/image014.png" v:shapes="Picture_x0020_292"><![endif]></span></p>
1326
1327<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1328
1329<p class=MsoNormal>You may wish to explore the other parameters for the IPG
1330fitting. If <b style='mso-bidi-font-weight:normal'><span style='font-family:
1331"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1332minor-latin'>Q power weight</span></b> is set to <b style='mso-bidi-font-weight:
1333normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1334minor-latin;mso-hansi-theme-font:minor-latin'>0-4</span></b>, that changes the
1335data weighting to <span class=SpellE><span class=GramE>Q<sup>p</sup></span></span>.
1336This can change the convergence of the IPG method and yield improved results if
1337one is unsuccessful with the default settings. I got a nice fit with a <b
1338style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1339mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Q power
1340weight</span></b> of <b style='mso-bidi-font-weight:normal'><span
1341style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;
1342mso-hansi-theme-font:minor-latin'>3</span></b> and <b style='mso-bidi-font-weight:
1343normal'><span style='font-family:"Calibri","sans-serif";mso-ascii-theme-font:
1344minor-latin;mso-hansi-theme-font:minor-latin'>Error multiplier</span></b> of <b
1345style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri","sans-serif";
1346mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.0</span></b>.</p>
1347
1348<p class=MsoNormal>You should save this GSAS-II project as it will be used in
1349the tutorial for fitting small angle scattering data; I used <span
1350class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1351"Calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1352minor-latin'>alumina.gpx</span></b></span>.</p>
1353
1354</div>
1355
1356</body>
1357
1358</html>
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