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

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add data link to tutorials

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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"/>
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424  <w:LsdException Locked="false" Priority="30" QFormat="true"
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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"
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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"
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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"
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562  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
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565  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 4"/>
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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"/>
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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"
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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"/>
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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"
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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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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><BL>
1225  <LI><B>A video version of this tutorial is available at
1226<A href="https://anl.box.com/v/SmallAngleSizeDistribution" target="_blank">
1227https://anl.box.com/v/SmallAngleSizeDistribution</A></B>
1228  <LI>Exercise files are found <A href="./data/" target="_blank">here</a>
1229</BL></P><P></P>
1230 
1231
1232<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'>In
1233this tutorial you will determine the size distribution of particles in an
1234alumina polishing powder using data from a constant wavelength synchrotron X-ray
1235USAXS instrument. You will use both Maximum Entropy (<span class=SpellE>MaxEnt</span>)
1236and Total Non-Negative Least Squares (TNNLS) methods assuming spherical
1237particles. The data were collected from <span style='mso-fareast-font-family:
1238Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold;
1239mso-bidi-font-style:italic'>powders spread onto sticky tape and covered with
1240another layer of the same tape. The data were corrected for background from
1241data collected from two layers of sticky tape. However, the sample thickness is
1242not</span> accurately known <span style='mso-fareast-font-family:Calibri;
1243mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold;mso-bidi-font-style:
1244italic'>so the data are not calibrated on an absolute scale.<o:p></o:p></span></p>
1245
1246<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1247
1248<h2>Step 1: read in the data file</h2>
1249
1250<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1251style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
1252style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
1253the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1254mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1255minor-latin'>Import/Small Angle Data/from q (A-1) step X-ray QIE data file</span></b>
1256menu item to read the data file into GSAS-II. This read option is set to read
1257three column small angle scattering data (SASD) as Q in Å<sup>-1</sup>,
1258intensity and estimated standard deviation in intensity; there may be a header
1259with metadata information in the front of this file.<span
1260style='mso-spacerun:yes'>  </span>Change the file directory to <span
1261class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1262"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1263minor-latin;mso-bidi-theme-font:minor-latin'>SAsize</span></b></span><b
1264style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1265mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1266minor-latin'>/data</span></b><span style='font-family:"Calibri",sans-serif;
1267mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1268minor-latin'> to find the file</span>; you will have to select the ‘<b
1269style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1270mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file
1271(*.*)</span></b>’ filter to see it.</p>
1272
1273<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1274style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
1275style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
1276the <b style='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'>alumina data.dat</span></b><span style='font-family:"Calibri",sans-serif;
1279mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1280minor-latin'> data</span> file in the first dialog and press <b
1281style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1282mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1283minor-latin'>Open</span></b>. There will be a Dialog box asking <b
1284style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1285mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1286minor-latin'>Is this the file you want?</span></b> Press <b style='mso-bidi-font-weight:
1287normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1288minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Yes</span></b>
1289button to proceed.</p>
1290
1291<p class=MsoNormal>At this point the <b style='mso-bidi-font-weight:normal'><span
1292style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1293mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>GSAS-II data
1294tree</span></b> window will have several entries and the plot window will show
1295the SASD pattern as a log-log plot of intensity vs. Q</p>
1296
1297<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
1298 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
1299 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1300 <v:stroke joinstyle="miter"/>
1301 <v:formulas>
1302  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
1303  <v:f eqn="sum @0 1 0"/>
1304  <v:f eqn="sum 0 0 @1"/>
1305  <v:f eqn="prod @2 1 2"/>
1306  <v:f eqn="prod @3 21600 pixelWidth"/>
1307  <v:f eqn="prod @3 21600 pixelHeight"/>
1308  <v:f eqn="sum @0 0 1"/>
1309  <v:f eqn="prod @6 1 2"/>
1310  <v:f eqn="prod @7 21600 pixelWidth"/>
1311  <v:f eqn="sum @8 21600 0"/>
1312  <v:f eqn="prod @7 21600 pixelHeight"/>
1313  <v:f eqn="sum @10 21600 0"/>
1314 </v:formulas>
1315 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1316 <o:lock v:ext="edit" aspectratio="t"/>
1317</v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_i1038" type="#_x0000_t75"
1318 style='width:525pt;height:450pt;visibility:visible;mso-wrap-style:square'>
1319 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image001.png"
1320  o:title=""/>
1321</v:shape><![endif]--><![if !vml]><img width=700 height=600
1322src="Small%20Angle%20Size%20Distribution_files/image001.png" v:shapes="Picture_x0020_1"><![endif]></span></p>
1323
1324<h2>Step 2: Set Limits</h2>
1325
1326<p class=MsoNormal>For this step we will reposition the limits to enclose only
1327that part of the SASD pattern suitable for size distribution analysis.
1328Typically this covers 10<sup>-3</sup> &lt; Q &lt; 10<sup>-1</sup>; below this
1329range scattering is from very large objects not readily described by the size
1330distribution analysis and above the scattering is mostly background. Select <b
1331style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1332mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Limits</span></b>
1333under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1334mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1335data.dat</span></b> from the GSAS-II tree. Then set <b style='mso-bidi-font-weight:
1336normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1337minor-latin;mso-hansi-theme-font:minor-latin'>changed</span></b> to <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'>0.001</span></b>
1340for <span class=SpellE><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'>Tmin</span></b></span> and <b
1343style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1344mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.1</span></b>
1345for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1346style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1347mso-hansi-theme-font:minor-latin'>Tmax</span></b></span>. You can also set the
1348limits using the cursor on the plot by either picking a point on the curve with
1349the left or right mouse button or by dragging the green and red vertical lines
1350to the desired positions. The limits window should look like</p>
1351
1352<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1353 id="Picture_x0020_15" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:415.5pt;
1354 height:267pt;visibility:visible;mso-wrap-style:square'>
1355 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image015.png"
1356  o:title=""/>
1357</v:shape><![endif]--><![if !vml]><img width=554 height=356
1358src="Small%20Angle%20Size%20Distribution_files/image016.png" v:shapes="Picture_x0020_15"><![endif]></span><span
1359style='mso-spacerun:yes'> </span></p>
1360
1361<h2>Step 3 Select the scattering substances for your sample</h2>
1362
1363<p class=MsoNormal><span style='mso-no-proof:yes'>Two scattering substances
1364need to be defined for your sample to give the anticipated scattering contrast;
1365in this case one is alumina and the other is “vacuum” (really air). Parameters
1366for a number of substances are defined in the file </span><b style='mso-bidi-font-weight:
1367normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1368minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1369style='mso-no-proof:yes'>. You can add your own substances to this or better
1370put them in </span><b style='mso-bidi-font-weight:normal'><span
1371style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1372mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>UserSubstances.py</span></b><span
1373style='mso-no-proof:yes'>; this is read after </span><b style='mso-bidi-font-weight:
1374normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1375minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1376style='mso-no-proof:yes'> when you load substances for your selection. </span>Select
1377<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1378mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Substances</span></b>
1379under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1380mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1381data.dat</span></b> from the GSAS-II tree. Then do <span class=GramE><b
1382style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1383mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit</span></b></span><b
1384style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1385mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>
1386substance/Load</span></b> <b style='mso-bidi-font-weight:normal'><span
1387style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1388mso-hansi-theme-font:minor-latin'>substance</span></b> from the menu; a popup
1389window will appear with possible selections</p>
1390
1391<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1392 id="_x0000_i1036" type="#_x0000_t75" style='width:259.5pt;height:252pt;
1393 visibility:visible;mso-wrap-style:square'>
1394 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image003.png"
1395  o:title=""/>
1396</v:shape><![endif]--><![if !vml]><img width=346 height=336
1397src="Small%20Angle%20Size%20Distribution_files/image003.png" v:shapes="_x0000_i1036"><![endif]><o:p></o:p></span></p>
1398
1399<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1400
1401<p class=MsoNormal>Select <b style='mso-bidi-font-weight:normal'><span
1402style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1403mso-hansi-theme-font:minor-latin'>Alumina</span></b> and press <b
1404style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1405mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>;
1406the relevant data for alumina (and vacuum) are displayed next</p>
1407
1408<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1409 id="Picture_x0020_17" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:431.25pt;
1410 height:275.25pt;visibility:visible;mso-wrap-style:square'>
1411 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image017.png"
1412  o:title=""/>
1413</v:shape><![endif]--><![if !vml]><img width=575 height=367
1414src="Small%20Angle%20Size%20Distribution_files/image017.png" v:shapes="Picture_x0020_17"><![endif]></span><span
1415style='mso-spacerun:yes'> </span></p>
1416
1417<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1418
1419<p class=MsoNormal>If desired you can load/add as many substances as you want
1420into this list; you can also delete any of them (except vacuum &amp; unit
1421scatter). The composition, volume occupied by the atoms in the composition and
1422the density are given for each substance. These can each be edited; the other
1423values will change accordingly. If your substance isn’t in the list, you can <b
1424style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1425mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
1426Substance/Add
1427substance</span></b> to create a new one (you will be asked for a name and the
1428set of elements in two successive popup windows). From this information the
1429scattering density and that as affected by resonant scattering for the listed
1430wavelength is displayed (the wavelength can be changed in the <b
1431style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1432mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Instrument
1433Parameters</span></b> GSAS-II tree item if needed). The real density value is
1434used for contrast calculations.</p>
1435
1436<h2>Step 4: Set Sample parameters </h2>
1437
1438<p class=MsoNormal>Two of the substances you have loaded into GSAS-II next need
1439to be selected for this size distribution analysis; Select <b style='mso-bidi-font-weight:
1440normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1441minor-latin;mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b>
1442under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1443mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1444data.dat</span></b> from the GSAS-II tree. Near the bottom of the window will
1445be two rows marked “<b style='mso-bidi-font-weight:normal'><span
1446style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1447mso-hansi-theme-font:minor-latin'>Material</span></b>”; select <b
1448style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1449mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Alumina</span></b>
1450from one of the pull downs (leave the other as <b style='mso-bidi-font-weight:
1451normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1452minor-latin;mso-hansi-theme-font:minor-latin'>vacuum</span></b>). The window
1453will show at the bottom the computed contrast between alumina and vacuum
1454without and with consideration of resonant scattering effects; the latter is
1455used in subsequent calculations.</p>
1456
1457<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1458 id="Picture_x0020_18" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:459pt;
1459 height:447pt;visibility:visible;mso-wrap-style:square'>
1460 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image018.png"
1461  o:title=""/>
1462</v:shape><![endif]--><![if !vml]><img width=612 height=596
1463src="Small%20Angle%20Size%20Distribution_files/image018.png" v:shapes="Picture_x0020_18"><![endif]></span></p>
1464
1465<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1466
1467<p class=MsoNormal>For experiments for which you know the transmission and the
1468sample thickness, you can manipulate the <b style='mso-bidi-font-weight:normal'><span
1469style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1470mso-hansi-theme-font:minor-latin'>volume fractions</span></b> to make the
1471calculated transmission match the observed one. Additionally, if you have
1472absolute scaling information, you can rescale the data by adjusting the <b
1473style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1474mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>histogram
1475scale factor</span></b>; multiple data sets can be scaled together via the <b
1476style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1477mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Command/Set
1478scale</span></b> menu item.</p>
1479
1480<h2>Step 5 Size distribution via Maximum Entropy</h2>
1481
1482<p class=MsoNormal>You are now ready to attempt a size distribution analysis
1483using the maximum entropy method. Select <b style='mso-bidi-font-weight:normal'><span
1484style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1485mso-hansi-theme-font:minor-latin'>Models</span></b> under <b style='mso-bidi-font-weight:
1486normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1487minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina data.dat</span></b>
1488from the GSAS-II tree; the window will display</p>
1489
1490<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1491 id="_x0000_i1033" type="#_x0000_t75" style='width:468pt;height:238.5pt;
1492 visibility:visible;mso-wrap-style:square'>
1493 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image019.png"
1494  o:title=""/>
1495</v:shape><![endif]--><![if !vml]><img width=624 height=318
1496src="Small%20Angle%20Size%20Distribution_files/image020.png" v:shapes="_x0000_i1033"><![endif]></span></p>
1497
1498<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1499
1500<p class=MsoNormal>Many selections are made by default for this analysis; however
1501it is important that an appropriate value is selected for the background. From
1502the high Q end of the data plot</p>
1503
1504<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1505 id="Picture_x0020_19" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt;
1506 height:450pt;visibility:visible;mso-wrap-style:square'>
1507 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image007.png"
1508  o:title=""/>
1509</v:shape><![endif]--><![if !vml]><img width=700 height=600
1510src="Small%20Angle%20Size%20Distribution_files/image007.png" v:shapes="Picture_x0020_19"><![endif]></span><span
1511style='mso-spacerun:yes'> </span></p>
1512
1513<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1514
1515<p class=MsoNormal>It is clear that the intensity levels off at an apparent
1516background level of ~<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'>0.12</span></b>; enter that into the
1519appropriate place in the data window next to <B>Background</B>. The plot will be redrawn showing a
1520horizontal red line for the background. All the other parameters seem
1521reasonable for a 1<sup>st</sup> attempt at a <span class=SpellE>MaxEnt</span>
1522solution. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:
1523"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1524minor-latin'>Models/Fit</span></b>; the console window will show that the
1525calculation did not converge and the <b style='mso-bidi-font-weight:normal'><span
1526style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1527mso-hansi-theme-font:minor-latin'>Size Distribution</span></b> plot has a
1528“choppy” appearance.</p>
1529
1530<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1531 id="Picture_x0020_20" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
1532 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1533 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image021.png"
1534  o:title=""/>
1535</v:shape><![endif]--><![if !vml]><img width=624 height=535
1536src="Small%20Angle%20Size%20Distribution_files/image022.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
1537
1538<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1539
1540<p class=MsoNormal>This is not a satisfactory result, but the suggestion given
1541in the console window is worth trying. Change the <b style='mso-bidi-font-weight:
1542normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1543minor-latin;mso-hansi-theme-font:minor-latin'>Error multiplier</span></b> to <b
1544style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1545mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>5</span></b>
1546(notice the increased error bars on the data plot) and repeat <b
1547style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1548mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Model/Fit</span></b>.
1549Convergence is now achieved in &lt;10 cycles (see console window for details)
1550and a much smoother size distribution results</p>
1551
1552<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1553 id="Picture_x0020_21" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;
1554 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1555 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image023.png"
1556  o:title=""/>
1557</v:shape><![endif]--><![if !vml]><img width=624 height=535
1558src="Small%20Angle%20Size%20Distribution_files/image024.png" v:shapes="Picture_x0020_21"><![endif]></span></p>
1559
1560<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1561
1562<p class=MsoNormal>This is a good result: clearly the alumina polishing powder
1563has a bimodal distribution with diameters centered about ~1600Å and ~160Å (not
1564500Å and 1µm as advertised by the manufacturer!).</p>
1565
1566<p class=MsoNormal>You may wish to explore the effect of some of the other
1567parameters in the data window. Most are obvious but <b style='mso-bidi-font-weight:
1568normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1569minor-latin;mso-hansi-theme-font:minor-latin'>Log floor factor</span></b> needs
1570a bit of explanation. This is the log of the minimum size distribution (scaled
1571by the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1572mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>histogram
1573scale factor</span></b> and the <b style='mso-bidi-font-weight:normal'><span
1574style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1575mso-hansi-theme-font:minor-latin'>contrast</span></b>). This size distribution
1576minimum needs to be set within 1-2 orders of magnitude of the optimal value and
1577can differ from the default of 10<sup>-3; </sup>it is worth changing if
1578convergence is poor despite trying different error multipliers. Try changing it
1579to see what effect it has on the result. With the original settings the data
1580fit looks like</p>
1581
1582<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1583 id="Picture_x0020_22" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:426.75pt;
1584 height:366pt;visibility:visible;mso-wrap-style:square'>
1585 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image025.png"
1586  o:title=""/>
1587</v:shape><![endif]--><![if !vml]><img width=569 height=488
1588src="Small%20Angle%20Size%20Distribution_files/image026.png" v:shapes="Picture_x0020_22"><![endif]></span></p>
1589
1590<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1591
1592<p class=MsoNormal>The green curve is the result calculated from the size
1593distribution. Notice that it is not perfect, there is appreciable misfit around
1594Q=0.003Å<sup>-1</sup>. This may be due to the assumption that the particles are
1595spheres; they could be some other shape (I could get a better fit by setting
1596the Spheroid aspect ratio to 2.0), however this tool is not really the
1597appropriate one to make this determination.</p>
1598
1599<h2>Step 6 Size Distribution <i style='mso-bidi-font-style:normal'>via</i>
1600Total Non-Negative Least Squares (TNNLS)</h2>
1601
1602<p class=MsoNormal>An alternative method for determining size distributions is
1603the TNNLS or Interior-Point Gradient (IPG) method. As the name implies this is
1604a gradient refinement method for the special case of all positive data and
1605parameter values. To try it on this alumina data, select <b style='mso-bidi-font-weight:
1606normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1607minor-latin;mso-hansi-theme-font:minor-latin'>IPG</span></b> from the <b
1608style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1609mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Fitting
1610method</span></b> pull down. The data window will change to give</p>
1611
1612<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1613 id="Picture_x0020_23" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:468pt;
1614 height:238.5pt;visibility:visible;mso-wrap-style:square'>
1615 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image027.png"
1616  o:title=""/>
1617</v:shape><![endif]--><![if !vml]><img width=624 height=318
1618src="Small%20Angle%20Size%20Distribution_files/image028.png" v:shapes="Picture_x0020_23"><![endif]></span></p>
1619
1620<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1621
1622<p class=MsoNormal>Reset the Error multiplier back to <b style='mso-bidi-font-weight:
1623normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1624minor-latin;mso-hansi-theme-font:minor-latin'>1.0</span></b> and then do <b
1625style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1626mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models/Fit</span></b>
1627to run the IPG fitting. The IPG algorithm did not converge in 100 cycles and
1628resulting size distribution is a little choppy but has roughly the same bimodal
1629distribution found by <span class=SpellE>MaxEnt</span>.</p>
1630
1631<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1632 id="Picture_x0020_24" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;
1633 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1634 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image029.png"
1635  o:title=""/>
1636</v:shape><![endif]--><![if !vml]><img width=624 height=535
1637src="Small%20Angle%20Size%20Distribution_files/image030.png" v:shapes="Picture_x0020_24"><![endif]></span></p>
1638
1639<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1640
1641<p class=MsoNormal>This can be considerably improved by setting the <b
1642style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1643mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Error
1644multiplier</span></b> to <b style='mso-bidi-font-weight:normal'><span
1645style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1646mso-hansi-theme-font:minor-latin'>2.0</span></b>; the IPG fit con<span
1647style='mso-no-proof:yes'>verges in &lt;20 cycles and gives a smoother size
1648distribution.<o:p></o:p></span></p>
1649
1650<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1651 id="Picture_x0020_25" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:468pt;
1652 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1653 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image031.png"
1654  o:title=""/>
1655</v:shape><![endif]--><![if !vml]><img width=624 height=535
1656src="Small%20Angle%20Size%20Distribution_files/image032.png" v:shapes="Picture_x0020_25"><![endif]></span></p>
1657
1658<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1659
1660<p class=MsoNormal>The bimodal distribution is again quite clear with ~1400Å
1661and ~150Å diameter particles. This method appears to give a better fit to the
1662data than the <span class=SpellE>MaxEnt</span> method particularly in the
1663Q~0.003Å<sup>-1</sup> region’</p>
1664
1665<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1666 id="Picture_x0020_26" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:450pt;
1667 height:385.5pt;visibility:visible;mso-wrap-style:square'>
1668 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image033.png"
1669  o:title=""/>
1670</v:shape><![endif]--><![if !vml]><img width=600 height=514
1671src="Small%20Angle%20Size%20Distribution_files/image034.png" v:shapes="Picture_x0020_26"><![endif]></span></p>
1672
1673<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1674
1675<p class=MsoNormal>You may wish to explore the other parameters for the IPG
1676fitting. If <b style='mso-bidi-font-weight:normal'><span style='font-family:
1677"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1678minor-latin'>Q power weight</span></b> is set to <b style='mso-bidi-font-weight:
1679normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1680minor-latin;mso-hansi-theme-font:minor-latin'>0-4</span></b>, that changes the
1681data weighting to <span class=SpellE>Q<sup>p</sup></span>. This can change the convergence
1682of the IPG method and yield improved results if one is unsuccessful with the
1683default settings. I got a nice fit with a <b style='mso-bidi-font-weight:normal'><span
1684style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1685mso-hansi-theme-font:minor-latin'>Q power weight</span></b> of <b
1686style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1687mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>3</span></b>
1688and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1689mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Error
1690multiplier</span></b> of <b style='mso-bidi-font-weight:normal'><span
1691style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1692mso-hansi-theme-font:minor-latin'>2.0</span></b>.</p>
1693
1694<p class=MsoNormal>You should save this GSAS-II project as it will be used in the
1695tutorial for fitting small angle scattering data; I used <span class=SpellE><b
1696style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1697mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>alumina.gpx</span></b></span>.</p>
1698
1699</div>
1700
1701</body>
1702
1703</html>
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