source: Tutorials/SAsize/Small Angle Size Distribution.htm @ 3031

Last change on this file since 3031 was 3031, checked in by vondreele, 4 years ago

update to 2 frame version

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415  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 1"/>
416  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
417  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
418  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
419  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
420  <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
421  <w:LsdException Locked="false" Priority="34" QFormat="true"
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424  <w:LsdException Locked="false" Priority="30" QFormat="true"
425   Name="Intense Quote"/>
426  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 1"/>
427  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 1"/>
428  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
429  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
430  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
431  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
432  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
433  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
434  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
435  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
436  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
437  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
438  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
439  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
440  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
441  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
442  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
443  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
444  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
445  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
446  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
447  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
448  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
449  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
450  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
451  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
452  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
453  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
454  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
455  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
456  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
457  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
458  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
459  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
460  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
461  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
462  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
463  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
464  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
465  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
466  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
467  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
468  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
469  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
470  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
471  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
472  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
473  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
474  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
475  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
476  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
477  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
478  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
479  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
480  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
481  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
482  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
483  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
484  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
485  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
486  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
487  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
488  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
489  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
490  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
491  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
492  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
493  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
494  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
495  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
496  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
497  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
498  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
499  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
500  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
501  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
502  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
503  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
504  <w:LsdException Locked="false" Priority="19" QFormat="true"
505   Name="Subtle Emphasis"/>
506  <w:LsdException Locked="false" Priority="21" QFormat="true"
507   Name="Intense Emphasis"/>
508  <w:LsdException Locked="false" Priority="31" QFormat="true"
509   Name="Subtle Reference"/>
510  <w:LsdException Locked="false" Priority="32" QFormat="true"
511   Name="Intense Reference"/>
512  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
513  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
514   UnhideWhenUsed="true" Name="Bibliography"/>
515  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
516   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
517  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
518  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
519  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
520  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
521  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
522  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
523  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
524  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
525  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
526  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
527  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
528  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
529  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
530  <w:LsdException Locked="false" Priority="46"
531   Name="Grid Table 1 Light Accent 1"/>
532  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
533  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
534  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
535  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
536  <w:LsdException Locked="false" Priority="51"
537   Name="Grid Table 6 Colorful Accent 1"/>
538  <w:LsdException Locked="false" Priority="52"
539   Name="Grid Table 7 Colorful Accent 1"/>
540  <w:LsdException Locked="false" Priority="46"
541   Name="Grid Table 1 Light Accent 2"/>
542  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
543  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
544  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
545  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
546  <w:LsdException Locked="false" Priority="51"
547   Name="Grid Table 6 Colorful Accent 2"/>
548  <w:LsdException Locked="false" Priority="52"
549   Name="Grid Table 7 Colorful Accent 2"/>
550  <w:LsdException Locked="false" Priority="46"
551   Name="Grid Table 1 Light Accent 3"/>
552  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
553  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
554  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
555  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
556  <w:LsdException Locked="false" Priority="51"
557   Name="Grid Table 6 Colorful Accent 3"/>
558  <w:LsdException Locked="false" Priority="52"
559   Name="Grid Table 7 Colorful Accent 3"/>
560  <w:LsdException Locked="false" Priority="46"
561   Name="Grid Table 1 Light Accent 4"/>
562  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
563  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 4"/>
564  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 4"/>
565  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
566  <w:LsdException Locked="false" Priority="51"
567   Name="Grid Table 6 Colorful Accent 4"/>
568  <w:LsdException Locked="false" Priority="52"
569   Name="Grid Table 7 Colorful Accent 4"/>
570  <w:LsdException Locked="false" Priority="46"
571   Name="Grid Table 1 Light Accent 5"/>
572  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
573  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
574  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
575  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
576  <w:LsdException Locked="false" Priority="51"
577   Name="Grid Table 6 Colorful Accent 5"/>
578  <w:LsdException Locked="false" Priority="52"
579   Name="Grid Table 7 Colorful Accent 5"/>
580  <w:LsdException Locked="false" Priority="46"
581   Name="Grid Table 1 Light Accent 6"/>
582  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 6"/>
583  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 6"/>
584  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 6"/>
585  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 6"/>
586  <w:LsdException Locked="false" Priority="51"
587   Name="Grid Table 6 Colorful Accent 6"/>
588  <w:LsdException Locked="false" Priority="52"
589   Name="Grid Table 7 Colorful Accent 6"/>
590  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
591  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
592  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
593  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
594  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
595  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
596  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
597  <w:LsdException Locked="false" Priority="46"
598   Name="List Table 1 Light Accent 1"/>
599  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
600  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
601  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
602  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
603  <w:LsdException Locked="false" Priority="51"
604   Name="List Table 6 Colorful Accent 1"/>
605  <w:LsdException Locked="false" Priority="52"
606   Name="List Table 7 Colorful Accent 1"/>
607  <w:LsdException Locked="false" Priority="46"
608   Name="List Table 1 Light Accent 2"/>
609  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
610  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
611  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
612  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
613  <w:LsdException Locked="false" Priority="51"
614   Name="List Table 6 Colorful Accent 2"/>
615  <w:LsdException Locked="false" Priority="52"
616   Name="List Table 7 Colorful Accent 2"/>
617  <w:LsdException Locked="false" Priority="46"
618   Name="List Table 1 Light Accent 3"/>
619  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
620  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 3"/>
621  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
622  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
623  <w:LsdException Locked="false" Priority="51"
624   Name="List Table 6 Colorful Accent 3"/>
625  <w:LsdException Locked="false" Priority="52"
626   Name="List Table 7 Colorful Accent 3"/>
627  <w:LsdException Locked="false" Priority="46"
628   Name="List Table 1 Light Accent 4"/>
629  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
630  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
631  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
632  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 4"/>
633  <w:LsdException Locked="false" Priority="51"
634   Name="List Table 6 Colorful Accent 4"/>
635  <w:LsdException Locked="false" Priority="52"
636   Name="List Table 7 Colorful Accent 4"/>
637  <w:LsdException Locked="false" Priority="46"
638   Name="List Table 1 Light Accent 5"/>
639  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
640  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
641  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
642  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
643  <w:LsdException Locked="false" Priority="51"
644   Name="List Table 6 Colorful Accent 5"/>
645  <w:LsdException Locked="false" Priority="52"
646   Name="List Table 7 Colorful Accent 5"/>
647  <w:LsdException Locked="false" Priority="46"
648   Name="List Table 1 Light Accent 6"/>
649  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
650  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
651  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
652  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
653  <w:LsdException Locked="false" Priority="51"
654   Name="List Table 6 Colorful Accent 6"/>
655  <w:LsdException Locked="false" Priority="52"
656   Name="List Table 7 Colorful Accent 6"/>
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1164-->
1165</style>
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1209<![endif]--><!--[if gte mso 9]><xml>
1210 <o:shapedefaults v:ext="edit" spidmax="1026"/>
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1215</head>
1216
1217<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1218
1219<div class=WordSection1>
1220
1221<h1><strong><span style='mso-bidi-font-weight:normal'>Small Angle X-Ray Data –
1222Size Distribution in Alumina Powder</span><o:p></o:p></strong></h1>
1223
1224<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'>In
1225this tutorial you will determine the size distribution of particles in an
1226alumina polishing powder using data from a constant wavelength synchrotron X-ray
1227USAXS instrument. You will use both Maximum Entropy (<span class=SpellE>MaxEnt</span>)
1228and Total Non-Negative Least Squares (TNNLS) methods assuming spherical
1229particles. The data were collected from <span style='mso-fareast-font-family:
1230Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold;
1231mso-bidi-font-style:italic'>powders spread onto sticky tape and covered with
1232another layer of the same tape. The data were corrected for background from
1233data collected from two layers of sticky tape. However, the sample thickness is
1234not</span> accurately known <span style='mso-fareast-font-family:Calibri;
1235mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold;mso-bidi-font-style:
1236italic'>so the data are not calibrated on an absolute scale.<o:p></o:p></span></p>
1237
1238<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1239
1240<h2>Step 1: read in the data file</h2>
1241
1242<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1243style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
1244style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
1245the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1246mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1247minor-latin'>Import/Small Angle Data/from q (A-1) step X-ray QIE data file</span></b>
1248menu item to read the data file into GSAS-II. This read option is set to read
1249three column small angle scattering data (SASD) as Q in Å<sup>-1</sup>,
1250intensity and estimated standard deviation in intensity; there may be a header
1251with metadata information in the front of this file.<span
1252style='mso-spacerun:yes'>  </span>Change the file directory to <span
1253class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1254"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1255minor-latin;mso-bidi-theme-font:minor-latin'>SAsize</span></b></span><b
1256style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1257mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1258minor-latin'>/data</span></b><span style='font-family:"Calibri",sans-serif;
1259mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1260minor-latin'> to find the file</span>; you will have to select the ‘<b
1261style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1262mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file
1263(*.*)</span></b>’ filter to see it.</p>
1264
1265<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1266style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
1267style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
1268the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1269mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1270minor-latin'>alumina data.dat</span></b><span style='font-family:"Calibri",sans-serif;
1271mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1272minor-latin'> data</span> file in the first dialog and press <b
1273style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1274mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1275minor-latin'>Open</span></b>. There will be a Dialog box asking <b
1276style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1277mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1278minor-latin'>Is this the file you want?</span></b> Press <b style='mso-bidi-font-weight:
1279normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1280minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Yes</span></b>
1281button to proceed.</p>
1282
1283<p class=MsoNormal>At this point the <b style='mso-bidi-font-weight:normal'><span
1284style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1285mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>GSAS-II data
1286tree</span></b> window will have several entries and the plot window will show
1287the SASD pattern as a log-log plot of intensity vs. Q</p>
1288
1289<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
1290 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
1291 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1292 <v:stroke joinstyle="miter"/>
1293 <v:formulas>
1294  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
1295  <v:f eqn="sum @0 1 0"/>
1296  <v:f eqn="sum 0 0 @1"/>
1297  <v:f eqn="prod @2 1 2"/>
1298  <v:f eqn="prod @3 21600 pixelWidth"/>
1299  <v:f eqn="prod @3 21600 pixelHeight"/>
1300  <v:f eqn="sum @0 0 1"/>
1301  <v:f eqn="prod @6 1 2"/>
1302  <v:f eqn="prod @7 21600 pixelWidth"/>
1303  <v:f eqn="sum @8 21600 0"/>
1304  <v:f eqn="prod @7 21600 pixelHeight"/>
1305  <v:f eqn="sum @10 21600 0"/>
1306 </v:formulas>
1307 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1308 <o:lock v:ext="edit" aspectratio="t"/>
1309</v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_i1038" type="#_x0000_t75"
1310 style='width:525pt;height:450pt;visibility:visible;mso-wrap-style:square'>
1311 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image001.png"
1312  o:title=""/>
1313</v:shape><![endif]--><![if !vml]><img width=700 height=600
1314src="Small%20Angle%20Size%20Distribution_files/image001.png" v:shapes="Picture_x0020_1"><![endif]></span></p>
1315
1316<h2>Step 2: Set Limits</h2>
1317
1318<p class=MsoNormal>For this step we will reposition the limits to enclose only
1319that part of the SASD pattern suitable for size distribution analysis.
1320Typically this covers 10<sup>-3</sup> &lt; Q &lt; 10<sup>-1</sup>; below this
1321range scattering is from very large objects not readily described by the size
1322distribution analysis and above the scattering is mostly background. Select <b
1323style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1324mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Limits</span></b>
1325under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1326mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1327data.dat</span></b> from the GSAS-II tree. Then set <b style='mso-bidi-font-weight:
1328normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1329minor-latin;mso-hansi-theme-font:minor-latin'>changed</span></b> to <b
1330style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1331mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.001</span></b>
1332for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1333style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1334mso-hansi-theme-font:minor-latin'>Tmin</span></b></span> and <b
1335style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1336mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.1</span></b>
1337for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1338style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1339mso-hansi-theme-font:minor-latin'>Tmax</span></b></span>. You can also set the
1340limits using the cursor on the plot by either picking a point on the curve with
1341the left or right mouse button or by dragging the green and red vertical lines
1342to the desired positions. The limits window should look like</p>
1343
1344<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1345 id="Picture_x0020_15" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:415.5pt;
1346 height:267pt;visibility:visible;mso-wrap-style:square'>
1347 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image015.png"
1348  o:title=""/>
1349</v:shape><![endif]--><![if !vml]><img width=554 height=356
1350src="Small%20Angle%20Size%20Distribution_files/image016.png" v:shapes="Picture_x0020_15"><![endif]></span><span
1351style='mso-spacerun:yes'> </span></p>
1352
1353<h2>Step 3 Select the scattering substances for your sample</h2>
1354
1355<p class=MsoNormal><span style='mso-no-proof:yes'>Two scsttering substances
1356need to be defined for your sample to give the anticipated scattering contrast;
1357in this case one is alumina and the other is “vacuum” (really air). Parameters
1358for a number of substances are defined in the file </span><b style='mso-bidi-font-weight:
1359normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1360minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1361style='mso-no-proof:yes'>. You can add your own substances to this or better
1362put them in </span><b style='mso-bidi-font-weight:normal'><span
1363style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1364mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>UserSubstances.py</span></b><span
1365style='mso-no-proof:yes'>; this is read after </span><b style='mso-bidi-font-weight:
1366normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1367minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1368style='mso-no-proof:yes'> when you load substances for your selection. </span>Select
1369<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1370mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Substances</span></b>
1371under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1372mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1373data.dat</span></b> from the GSAS-II tree. Then do <span class=GramE><b
1374style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1375mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit</span></b></span><b
1376style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1377mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>
1378substance/Load</span></b> <b style='mso-bidi-font-weight:normal'><span
1379style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1380mso-hansi-theme-font:minor-latin'>substance</span></b> from the menu; a popup
1381window will appear with possible selections</p>
1382
1383<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1384 id="_x0000_i1036" type="#_x0000_t75" style='width:259.5pt;height:252pt;
1385 visibility:visible;mso-wrap-style:square'>
1386 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image003.png"
1387  o:title=""/>
1388</v:shape><![endif]--><![if !vml]><img width=346 height=336
1389src="Small%20Angle%20Size%20Distribution_files/image003.png" v:shapes="_x0000_i1036"><![endif]><o:p></o:p></span></p>
1390
1391<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1392
1393<p class=MsoNormal>Select <b style='mso-bidi-font-weight:normal'><span
1394style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1395mso-hansi-theme-font:minor-latin'>Alumina</span></b> and press <b
1396style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1397mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>;
1398the relevant data for alumina (and vacuum) are displayed next</p>
1399
1400<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1401 id="Picture_x0020_17" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:431.25pt;
1402 height:275.25pt;visibility:visible;mso-wrap-style:square'>
1403 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image017.png"
1404  o:title=""/>
1405</v:shape><![endif]--><![if !vml]><img width=575 height=367
1406src="Small%20Angle%20Size%20Distribution_files/image017.png" v:shapes="Picture_x0020_17"><![endif]></span><span
1407style='mso-spacerun:yes'> </span></p>
1408
1409<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1410
1411<p class=MsoNormal>If desired you can load/add as many substances as you want
1412into this list; you can also delete any of them (except vacuum &amp; unit
1413scatter). The composition, volume occupied by the atoms in the composition and
1414the density are given for each substance. These can each be edited; the other
1415values will change accordingly. If your substance isn’t in the list, you can <b
1416style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1417mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add
1418substance</span></b> to create a new one (you will be asked for a name and the
1419set of elements in two successive popup windows). From this information the
1420scattering density and that as affected by resonant scattering for the listed
1421wavelength is displayed (the wavelength can be changed in the <b
1422style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1423mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Instrument
1424Parameters</span></b> GSAS-II tree item if needed). The real density value is
1425used for contrast calculations.</p>
1426
1427<h2>Step 4: Set Sample parameters </h2>
1428
1429<p class=MsoNormal>Two of the substances you have loaded into GSAS-II next need
1430to be selected for this size distribution analysis; Select <b style='mso-bidi-font-weight:
1431normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1432minor-latin;mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b>
1433under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1434mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1435data.dat</span></b> from the GSAS-II tree. Near the bottom of the window will
1436be two rows marked “<b style='mso-bidi-font-weight:normal'><span
1437style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1438mso-hansi-theme-font:minor-latin'>Material</span></b>”; select <b
1439style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1440mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Alumina</span></b>
1441from one of the pull downs (leave the other as <b style='mso-bidi-font-weight:
1442normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1443minor-latin;mso-hansi-theme-font:minor-latin'>vacuum</span></b>). The window
1444will show at the bottom the computed contrast between alumina and vacuum
1445without and with consideration of resonant scattering effects; the latter is
1446used in subsequent calculations.</p>
1447
1448<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1449 id="Picture_x0020_18" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:459pt;
1450 height:447pt;visibility:visible;mso-wrap-style:square'>
1451 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image018.png"
1452  o:title=""/>
1453</v:shape><![endif]--><![if !vml]><img width=612 height=596
1454src="Small%20Angle%20Size%20Distribution_files/image018.png" v:shapes="Picture_x0020_18"><![endif]></span></p>
1455
1456<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1457
1458<p class=MsoNormal>For experiments for which you know the transmission and the
1459sample thickness, you can manipulate the <b style='mso-bidi-font-weight:normal'><span
1460style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1461mso-hansi-theme-font:minor-latin'>volume fractions</span></b> to make the
1462calculated transmission match the observed one. Additionally, if you have
1463absolute scaling information, you can rescale the data by adjusting the <b
1464style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1465mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>histogram
1466scale factor</span></b>; multiple data sets can be scaled together via the <b
1467style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1468mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Command/Set
1469scale</span></b> menu item.</p>
1470
1471<h2>Step 5 Size distribution via Maximum Entropy</h2>
1472
1473<p class=MsoNormal>You are now ready to attempt a size distribution analysis
1474using the maximum entropy method. Select <b style='mso-bidi-font-weight:normal'><span
1475style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1476mso-hansi-theme-font:minor-latin'>Models</span></b> under <b style='mso-bidi-font-weight:
1477normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1478minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina data.dat</span></b>
1479from the GSAS-II tree; the window will display</p>
1480
1481<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1482 id="_x0000_i1033" type="#_x0000_t75" style='width:468pt;height:238.5pt;
1483 visibility:visible;mso-wrap-style:square'>
1484 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image019.png"
1485  o:title=""/>
1486</v:shape><![endif]--><![if !vml]><img width=624 height=318
1487src="Small%20Angle%20Size%20Distribution_files/image020.png" v:shapes="_x0000_i1033"><![endif]></span></p>
1488
1489<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1490
1491<p class=MsoNormal>Many selections are made by default for this analysis; however
1492it is important that an appropriate value is selected for the background. From
1493the high Q end of the data plot</p>
1494
1495<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1496 id="Picture_x0020_19" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt;
1497 height:450pt;visibility:visible;mso-wrap-style:square'>
1498 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image007.png"
1499  o:title=""/>
1500</v:shape><![endif]--><![if !vml]><img width=700 height=600
1501src="Small%20Angle%20Size%20Distribution_files/image007.png" v:shapes="Picture_x0020_19"><![endif]></span><span
1502style='mso-spacerun:yes'> </span></p>
1503
1504<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1505
1506<p class=MsoNormal>It is clear that the intensity levels off at an apparent
1507background level of ~<b style='mso-bidi-font-weight:normal'><span
1508style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1509mso-hansi-theme-font:minor-latin'>0.12</span></b>; enter that into the
1510appropriate place in the data window. The plot will be redrawn showing a
1511horizontal red line for the background. All the other parameters seem
1512reasonable for a 1<sup>st</sup> attempt at a <span class=SpellE>MaxEnt</span>
1513solution. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:
1514"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1515minor-latin'>Models/Fit</span></b>; the console window will show that the
1516calculation did not converge and the <b style='mso-bidi-font-weight:normal'><span
1517style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1518mso-hansi-theme-font:minor-latin'>Size Distribution</span></b> plot has a
1519“choppy” appearance.</p>
1520
1521<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1522 id="Picture_x0020_20" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
1523 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1524 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image021.png"
1525  o:title=""/>
1526</v:shape><![endif]--><![if !vml]><img width=624 height=535
1527src="Small%20Angle%20Size%20Distribution_files/image022.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
1528
1529<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1530
1531<p class=MsoNormal>This is not a satisfactory result, but the suggestion given
1532in the console window is worth trying. Change the <b style='mso-bidi-font-weight:
1533normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1534minor-latin;mso-hansi-theme-font:minor-latin'>Error multiplier</span></b> to <b
1535style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1536mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>5</span></b>
1537(notice the increased error bars on the data plot) and repeat <b
1538style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1539mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Model/Fit</span></b>.
1540Convergence is now achieved in &lt;10 cycles (see console window for details)
1541and a much smoother size distribution results</p>
1542
1543<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1544 id="Picture_x0020_21" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;
1545 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1546 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image023.png"
1547  o:title=""/>
1548</v:shape><![endif]--><![if !vml]><img width=624 height=535
1549src="Small%20Angle%20Size%20Distribution_files/image024.png" v:shapes="Picture_x0020_21"><![endif]></span></p>
1550
1551<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1552
1553<p class=MsoNormal>This is a good result: clearly the alumina polishing powder
1554has a bimodal distribution with diameters centered about ~1600Å and ~160Å (not
1555500Å and 1µm as advertised by the manufacturer!).</p>
1556
1557<p class=MsoNormal>You may wish to explore the effect of some of the other
1558parameters in the data window. Most are obvious but <b style='mso-bidi-font-weight:
1559normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1560minor-latin;mso-hansi-theme-font:minor-latin'>Log floor factor</span></b> needs
1561a bit of explanation. This is the log of the minimum size distribution (scaled
1562by the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1563mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>histogram
1564scale factor</span></b> and the <b style='mso-bidi-font-weight:normal'><span
1565style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1566mso-hansi-theme-font:minor-latin'>contrast</span></b>). This size distribution
1567minimum needs to be set within 1-2 orders of magnitude of the optimal value and
1568can differ from the default of 10<sup>-3; </sup>it is worth changing if
1569convergence is poor despite trying different error multipliers. Try changing it
1570to see what effect it has on the result. With the original settings the data
1571fit looks like</p>
1572
1573<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1574 id="Picture_x0020_22" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:426.75pt;
1575 height:366pt;visibility:visible;mso-wrap-style:square'>
1576 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image025.png"
1577  o:title=""/>
1578</v:shape><![endif]--><![if !vml]><img width=569 height=488
1579src="Small%20Angle%20Size%20Distribution_files/image026.png" v:shapes="Picture_x0020_22"><![endif]></span></p>
1580
1581<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1582
1583<p class=MsoNormal>The green curve is the result calculated from the size
1584distribution. Notice that it is not perfect, there is appreciable misfit around
1585Q=0.003Å<sup>-1</sup>. This may be due to the assumption that the particles are
1586spheres; they could be some other shape (I could get a better fit by setting
1587the Spheroid aspect ratio to 2.0), however this tool is not really the
1588appropriate one to make this determination.</p>
1589
1590<h2>Step 6 Size Distribution <i style='mso-bidi-font-style:normal'>via</i>
1591Total Non-Negative Least Squares (TNNLS)</h2>
1592
1593<p class=MsoNormal>An alternative method for determining size distributions is
1594the TNNLS or Interior-Point Gradient (IPG) method. As the name implies this is
1595a gradient refinement method for the special case of all positive data and
1596parameter values. To try it on this alumina data, select <b style='mso-bidi-font-weight:
1597normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1598minor-latin;mso-hansi-theme-font:minor-latin'>IPG</span></b> from the <b
1599style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1600mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Fitting
1601method</span></b> pull down. The data window will change to give</p>
1602
1603<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1604 id="Picture_x0020_23" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:468pt;
1605 height:238.5pt;visibility:visible;mso-wrap-style:square'>
1606 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image027.png"
1607  o:title=""/>
1608</v:shape><![endif]--><![if !vml]><img width=624 height=318
1609src="Small%20Angle%20Size%20Distribution_files/image028.png" v:shapes="Picture_x0020_23"><![endif]></span></p>
1610
1611<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1612
1613<p class=MsoNormal>Reset the Error multiplier back to <b style='mso-bidi-font-weight:
1614normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1615minor-latin;mso-hansi-theme-font:minor-latin'>1.0</span></b> and then do <b
1616style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1617mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models/Fit</span></b>
1618to run the IPG fitting. The IPG algorithm did not converge in 100 cycles and
1619resulting size distribution is a little choppy but has roughly the same bimodal
1620distribution found by <span class=SpellE>MaxEnt</span>.</p>
1621
1622<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1623 id="Picture_x0020_24" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;
1624 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1625 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image029.png"
1626  o:title=""/>
1627</v:shape><![endif]--><![if !vml]><img width=624 height=535
1628src="Small%20Angle%20Size%20Distribution_files/image030.png" v:shapes="Picture_x0020_24"><![endif]></span></p>
1629
1630<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1631
1632<p class=MsoNormal>This can be considerably improved by setting the <b
1633style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1634mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Error
1635multiplier</span></b> to <b style='mso-bidi-font-weight:normal'><span
1636style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1637mso-hansi-theme-font:minor-latin'>2.0</span></b>; the IPG fit con<span
1638style='mso-no-proof:yes'>verges in &lt;20 cycles and gives a smoother size
1639distribution.<o:p></o:p></span></p>
1640
1641<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1642 id="Picture_x0020_25" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:468pt;
1643 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1644 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image031.png"
1645  o:title=""/>
1646</v:shape><![endif]--><![if !vml]><img width=624 height=535
1647src="Small%20Angle%20Size%20Distribution_files/image032.png" v:shapes="Picture_x0020_25"><![endif]></span></p>
1648
1649<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1650
1651<p class=MsoNormal>The bimodal distribution is again quite clear with ~1400Å
1652and ~150Å diameter particles. This method appears to give a better fit to the
1653data than the <span class=SpellE>MaxEnt</span> method particularly in the
1654Q~0.003Å<sup>-1</sup> region’</p>
1655
1656<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1657 id="Picture_x0020_26" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:450pt;
1658 height:385.5pt;visibility:visible;mso-wrap-style:square'>
1659 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image033.png"
1660  o:title=""/>
1661</v:shape><![endif]--><![if !vml]><img width=600 height=514
1662src="Small%20Angle%20Size%20Distribution_files/image034.png" v:shapes="Picture_x0020_26"><![endif]></span></p>
1663
1664<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1665
1666<p class=MsoNormal>You may wish to explore the other parameters for the IPG
1667fitting. If <b style='mso-bidi-font-weight:normal'><span style='font-family:
1668"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1669minor-latin'>Q power weight</span></b> is set to <b style='mso-bidi-font-weight:
1670normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1671minor-latin;mso-hansi-theme-font:minor-latin'>0-4</span></b>, that changes the
1672data weighting to <span class=SpellE>Q<sup>p</sup></span>. This can change the convergence
1673of the IPG method and yield improved results if one is unsuccessful with the
1674default settings. I got a nice fit with a <b style='mso-bidi-font-weight:normal'><span
1675style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1676mso-hansi-theme-font:minor-latin'>Q power weight</span></b> of <b
1677style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1678mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>3</span></b>
1679and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1680mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Error
1681multiplier</span></b> of <b style='mso-bidi-font-weight:normal'><span
1682style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1683mso-hansi-theme-font:minor-latin'>2.0</span></b>.</p>
1684
1685<p class=MsoNormal>You should save this GSAS-II project as it will be used in the
1686tutorial for fitting small angle scattering data; I used <span class=SpellE><b
1687style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1688mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>alumina.gpx</span></b></span>.</p>
1689
1690</div>
1691
1692</body>
1693
1694</html>
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