source: Tutorials/SAsize/Small Angle Size Distribution.htm @ 4271

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finish web tutorials for now

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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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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><B>A video version of this tutorial is available at
1225<A href="https://anl.box.com/v/SmallAngleSizeDistribution" target="_blank">
1226https://anl.box.com/v/SmallAngleSizeDistribution</A></B></P>
1227 
1228
1229<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'>In
1230this tutorial you will determine the size distribution of particles in an
1231alumina polishing powder using data from a constant wavelength synchrotron X-ray
1232USAXS instrument. You will use both Maximum Entropy (<span class=SpellE>MaxEnt</span>)
1233and Total Non-Negative Least Squares (TNNLS) methods assuming spherical
1234particles. The data were collected from <span style='mso-fareast-font-family:
1235Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold;
1236mso-bidi-font-style:italic'>powders spread onto sticky tape and covered with
1237another layer of the same tape. The data were corrected for background from
1238data collected from two layers of sticky tape. However, the sample thickness is
1239not</span> accurately known <span style='mso-fareast-font-family:Calibri;
1240mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold;mso-bidi-font-style:
1241italic'>so the data are not calibrated on an absolute scale.<o:p></o:p></span></p>
1242
1243<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1244
1245<h2>Step 1: read in the data file</h2>
1246
1247<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1248style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
1249style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
1250the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1251mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1252minor-latin'>Import/Small Angle Data/from q (A-1) step X-ray QIE data file</span></b>
1253menu item to read the data file into GSAS-II. This read option is set to read
1254three column small angle scattering data (SASD) as Q in Å<sup>-1</sup>,
1255intensity and estimated standard deviation in intensity; there may be a header
1256with metadata information in the front of this file.<span
1257style='mso-spacerun:yes'>  </span>Change the file directory to <span
1258class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1259"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1260minor-latin;mso-bidi-theme-font:minor-latin'>SAsize</span></b></span><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;mso-bidi-theme-font:
1263minor-latin'>/data</span></b><span style='font-family:"Calibri",sans-serif;
1264mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1265minor-latin'> to find the file</span>; you will have to select the ‘<b
1266style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1267mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file
1268(*.*)</span></b>’ filter to see it.</p>
1269
1270<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1271style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
1272style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
1273the <b style='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'>alumina data.dat</span></b><span style='font-family:"Calibri",sans-serif;
1276mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1277minor-latin'> data</span> file in the first dialog and press <b
1278style='mso-bidi-font-weight:normal'><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'>Open</span></b>. There will be a Dialog box asking <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'>Is this the file you want?</span></b> Press <b style='mso-bidi-font-weight:
1284normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1285minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Yes</span></b>
1286button to proceed.</p>
1287
1288<p class=MsoNormal>At this point the <b style='mso-bidi-font-weight:normal'><span
1289style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1290mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>GSAS-II data
1291tree</span></b> window will have several entries and the plot window will show
1292the SASD pattern as a log-log plot of intensity vs. Q</p>
1293
1294<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
1295 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
1296 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1297 <v:stroke joinstyle="miter"/>
1298 <v:formulas>
1299  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
1300  <v:f eqn="sum @0 1 0"/>
1301  <v:f eqn="sum 0 0 @1"/>
1302  <v:f eqn="prod @2 1 2"/>
1303  <v:f eqn="prod @3 21600 pixelWidth"/>
1304  <v:f eqn="prod @3 21600 pixelHeight"/>
1305  <v:f eqn="sum @0 0 1"/>
1306  <v:f eqn="prod @6 1 2"/>
1307  <v:f eqn="prod @7 21600 pixelWidth"/>
1308  <v:f eqn="sum @8 21600 0"/>
1309  <v:f eqn="prod @7 21600 pixelHeight"/>
1310  <v:f eqn="sum @10 21600 0"/>
1311 </v:formulas>
1312 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1313 <o:lock v:ext="edit" aspectratio="t"/>
1314</v:shapetype><v:shape id="Picture_x0020_1" o:spid="_x0000_i1038" type="#_x0000_t75"
1315 style='width:525pt;height:450pt;visibility:visible;mso-wrap-style:square'>
1316 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image001.png"
1317  o:title=""/>
1318</v:shape><![endif]--><![if !vml]><img width=700 height=600
1319src="Small%20Angle%20Size%20Distribution_files/image001.png" v:shapes="Picture_x0020_1"><![endif]></span></p>
1320
1321<h2>Step 2: Set Limits</h2>
1322
1323<p class=MsoNormal>For this step we will reposition the limits to enclose only
1324that part of the SASD pattern suitable for size distribution analysis.
1325Typically this covers 10<sup>-3</sup> &lt; Q &lt; 10<sup>-1</sup>; below this
1326range scattering is from very large objects not readily described by the size
1327distribution analysis and above the scattering is mostly background. Select <b
1328style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1329mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Limits</span></b>
1330under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1331mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1332data.dat</span></b> from the GSAS-II tree. Then set <b style='mso-bidi-font-weight:
1333normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1334minor-latin;mso-hansi-theme-font:minor-latin'>changed</span></b> to <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'>0.001</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'>Tmin</span></b></span> and <b
1340style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1341mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.1</span></b>
1342for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1343style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1344mso-hansi-theme-font:minor-latin'>Tmax</span></b></span>. You can also set the
1345limits using the cursor on the plot by either picking a point on the curve with
1346the left or right mouse button or by dragging the green and red vertical lines
1347to the desired positions. The limits window should look like</p>
1348
1349<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1350 id="Picture_x0020_15" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:415.5pt;
1351 height:267pt;visibility:visible;mso-wrap-style:square'>
1352 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image015.png"
1353  o:title=""/>
1354</v:shape><![endif]--><![if !vml]><img width=554 height=356
1355src="Small%20Angle%20Size%20Distribution_files/image016.png" v:shapes="Picture_x0020_15"><![endif]></span><span
1356style='mso-spacerun:yes'> </span></p>
1357
1358<h2>Step 3 Select the scattering substances for your sample</h2>
1359
1360<p class=MsoNormal><span style='mso-no-proof:yes'>Two scattering substances
1361need to be defined for your sample to give the anticipated scattering contrast;
1362in this case one is alumina and the other is “vacuum” (really air). Parameters
1363for a number of substances are defined in the file </span><b style='mso-bidi-font-weight:
1364normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1365minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1366style='mso-no-proof:yes'>. You can add your own substances to this or better
1367put them in </span><b style='mso-bidi-font-weight:normal'><span
1368style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1369mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>UserSubstances.py</span></b><span
1370style='mso-no-proof:yes'>; this is read after </span><b style='mso-bidi-font-weight:
1371normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1372minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1373style='mso-no-proof:yes'> when you load substances for your selection. </span>Select
1374<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1375mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Substances</span></b>
1376under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1377mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1378data.dat</span></b> from the GSAS-II tree. Then do <span class=GramE><b
1379style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1380mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit</span></b></span><b
1381style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1382mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>
1383substance/Load</span></b> <b style='mso-bidi-font-weight:normal'><span
1384style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1385mso-hansi-theme-font:minor-latin'>substance</span></b> from the menu; a popup
1386window will appear with possible selections</p>
1387
1388<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1389 id="_x0000_i1036" type="#_x0000_t75" style='width:259.5pt;height:252pt;
1390 visibility:visible;mso-wrap-style:square'>
1391 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image003.png"
1392  o:title=""/>
1393</v:shape><![endif]--><![if !vml]><img width=346 height=336
1394src="Small%20Angle%20Size%20Distribution_files/image003.png" v:shapes="_x0000_i1036"><![endif]><o:p></o:p></span></p>
1395
1396<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1397
1398<p class=MsoNormal>Select <b style='mso-bidi-font-weight:normal'><span
1399style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1400mso-hansi-theme-font:minor-latin'>Alumina</span></b> and press <b
1401style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1402mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>;
1403the relevant data for alumina (and vacuum) are displayed next</p>
1404
1405<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1406 id="Picture_x0020_17" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:431.25pt;
1407 height:275.25pt;visibility:visible;mso-wrap-style:square'>
1408 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image017.png"
1409  o:title=""/>
1410</v:shape><![endif]--><![if !vml]><img width=575 height=367
1411src="Small%20Angle%20Size%20Distribution_files/image017.png" v:shapes="Picture_x0020_17"><![endif]></span><span
1412style='mso-spacerun:yes'> </span></p>
1413
1414<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1415
1416<p class=MsoNormal>If desired you can load/add as many substances as you want
1417into this list; you can also delete any of them (except vacuum &amp; unit
1418scatter). The composition, volume occupied by the atoms in the composition and
1419the density are given for each substance. These can each be edited; the other
1420values will change accordingly. If your substance isn’t in the list, you can <b
1421style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1422mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
1423Substance/Add
1424substance</span></b> to create a new one (you will be asked for a name and the
1425set of elements in two successive popup windows). From this information the
1426scattering density and that as affected by resonant scattering for the listed
1427wavelength is displayed (the wavelength can be changed in the <b
1428style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1429mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Instrument
1430Parameters</span></b> GSAS-II tree item if needed). The real density value is
1431used for contrast calculations.</p>
1432
1433<h2>Step 4: Set Sample parameters </h2>
1434
1435<p class=MsoNormal>Two of the substances you have loaded into GSAS-II next need
1436to be selected for this size distribution analysis; Select <b style='mso-bidi-font-weight:
1437normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1438minor-latin;mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b>
1439under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1440mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1441data.dat</span></b> from the GSAS-II tree. Near the bottom of the window will
1442be two rows marked “<b style='mso-bidi-font-weight:normal'><span
1443style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1444mso-hansi-theme-font:minor-latin'>Material</span></b>”; select <b
1445style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1446mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Alumina</span></b>
1447from one of the pull downs (leave the other as <b style='mso-bidi-font-weight:
1448normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1449minor-latin;mso-hansi-theme-font:minor-latin'>vacuum</span></b>). The window
1450will show at the bottom the computed contrast between alumina and vacuum
1451without and with consideration of resonant scattering effects; the latter is
1452used in subsequent calculations.</p>
1453
1454<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1455 id="Picture_x0020_18" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:459pt;
1456 height:447pt;visibility:visible;mso-wrap-style:square'>
1457 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image018.png"
1458  o:title=""/>
1459</v:shape><![endif]--><![if !vml]><img width=612 height=596
1460src="Small%20Angle%20Size%20Distribution_files/image018.png" v:shapes="Picture_x0020_18"><![endif]></span></p>
1461
1462<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1463
1464<p class=MsoNormal>For experiments for which you know the transmission and the
1465sample thickness, you can manipulate the <b style='mso-bidi-font-weight:normal'><span
1466style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1467mso-hansi-theme-font:minor-latin'>volume fractions</span></b> to make the
1468calculated transmission match the observed one. Additionally, if you have
1469absolute scaling information, you can rescale the data by adjusting the <b
1470style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1471mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>histogram
1472scale factor</span></b>; multiple data sets can be scaled together via 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'>Command/Set
1475scale</span></b> menu item.</p>
1476
1477<h2>Step 5 Size distribution via Maximum Entropy</h2>
1478
1479<p class=MsoNormal>You are now ready to attempt a size distribution analysis
1480using the maximum entropy method. Select <b style='mso-bidi-font-weight:normal'><span
1481style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1482mso-hansi-theme-font:minor-latin'>Models</span></b> under <b style='mso-bidi-font-weight:
1483normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1484minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina data.dat</span></b>
1485from the GSAS-II tree; the window will display</p>
1486
1487<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1488 id="_x0000_i1033" type="#_x0000_t75" style='width:468pt;height:238.5pt;
1489 visibility:visible;mso-wrap-style:square'>
1490 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image019.png"
1491  o:title=""/>
1492</v:shape><![endif]--><![if !vml]><img width=624 height=318
1493src="Small%20Angle%20Size%20Distribution_files/image020.png" v:shapes="_x0000_i1033"><![endif]></span></p>
1494
1495<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1496
1497<p class=MsoNormal>Many selections are made by default for this analysis; however
1498it is important that an appropriate value is selected for the background. From
1499the high Q end of the data plot</p>
1500
1501<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1502 id="Picture_x0020_19" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt;
1503 height:450pt;visibility:visible;mso-wrap-style:square'>
1504 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image007.png"
1505  o:title=""/>
1506</v:shape><![endif]--><![if !vml]><img width=700 height=600
1507src="Small%20Angle%20Size%20Distribution_files/image007.png" v:shapes="Picture_x0020_19"><![endif]></span><span
1508style='mso-spacerun:yes'> </span></p>
1509
1510<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1511
1512<p class=MsoNormal>It is clear that the intensity levels off at an apparent
1513background level of ~<b style='mso-bidi-font-weight:normal'><span
1514style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1515mso-hansi-theme-font:minor-latin'>0.12</span></b>; enter that into the
1516appropriate place in the data window next to <B>Background</B>. The plot will be redrawn showing a
1517horizontal red line for the background. All the other parameters seem
1518reasonable for a 1<sup>st</sup> attempt at a <span class=SpellE>MaxEnt</span>
1519solution. Do <b style='mso-bidi-font-weight:normal'><span style='font-family:
1520"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1521minor-latin'>Models/Fit</span></b>; the console window will show that the
1522calculation did not converge and the <b style='mso-bidi-font-weight:normal'><span
1523style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1524mso-hansi-theme-font:minor-latin'>Size Distribution</span></b> plot has a
1525“choppy” appearance.</p>
1526
1527<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1528 id="Picture_x0020_20" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
1529 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1530 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image021.png"
1531  o:title=""/>
1532</v:shape><![endif]--><![if !vml]><img width=624 height=535
1533src="Small%20Angle%20Size%20Distribution_files/image022.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
1534
1535<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1536
1537<p class=MsoNormal>This is not a satisfactory result, but the suggestion given
1538in the console window is worth trying. Change the <b style='mso-bidi-font-weight:
1539normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1540minor-latin;mso-hansi-theme-font:minor-latin'>Error multiplier</span></b> to <b
1541style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1542mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>5</span></b>
1543(notice the increased error bars on the data plot) and repeat <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'>Model/Fit</span></b>.
1546Convergence is now achieved in &lt;10 cycles (see console window for details)
1547and a much smoother size distribution results</p>
1548
1549<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1550 id="Picture_x0020_21" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;
1551 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1552 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image023.png"
1553  o:title=""/>
1554</v:shape><![endif]--><![if !vml]><img width=624 height=535
1555src="Small%20Angle%20Size%20Distribution_files/image024.png" v:shapes="Picture_x0020_21"><![endif]></span></p>
1556
1557<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1558
1559<p class=MsoNormal>This is a good result: clearly the alumina polishing powder
1560has a bimodal distribution with diameters centered about ~1600Å and ~160Å (not
1561500Å and 1µm as advertised by the manufacturer!).</p>
1562
1563<p class=MsoNormal>You may wish to explore the effect of some of the other
1564parameters in the data window. Most are obvious but <b style='mso-bidi-font-weight:
1565normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1566minor-latin;mso-hansi-theme-font:minor-latin'>Log floor factor</span></b> needs
1567a bit of explanation. This is the log of the minimum size distribution (scaled
1568by the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1569mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>histogram
1570scale factor</span></b> and the <b style='mso-bidi-font-weight:normal'><span
1571style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1572mso-hansi-theme-font:minor-latin'>contrast</span></b>). This size distribution
1573minimum needs to be set within 1-2 orders of magnitude of the optimal value and
1574can differ from the default of 10<sup>-3; </sup>it is worth changing if
1575convergence is poor despite trying different error multipliers. Try changing it
1576to see what effect it has on the result. With the original settings the data
1577fit looks like</p>
1578
1579<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1580 id="Picture_x0020_22" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:426.75pt;
1581 height:366pt;visibility:visible;mso-wrap-style:square'>
1582 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image025.png"
1583  o:title=""/>
1584</v:shape><![endif]--><![if !vml]><img width=569 height=488
1585src="Small%20Angle%20Size%20Distribution_files/image026.png" v:shapes="Picture_x0020_22"><![endif]></span></p>
1586
1587<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1588
1589<p class=MsoNormal>The green curve is the result calculated from the size
1590distribution. Notice that it is not perfect, there is appreciable misfit around
1591Q=0.003Å<sup>-1</sup>. This may be due to the assumption that the particles are
1592spheres; they could be some other shape (I could get a better fit by setting
1593the Spheroid aspect ratio to 2.0), however this tool is not really the
1594appropriate one to make this determination.</p>
1595
1596<h2>Step 6 Size Distribution <i style='mso-bidi-font-style:normal'>via</i>
1597Total Non-Negative Least Squares (TNNLS)</h2>
1598
1599<p class=MsoNormal>An alternative method for determining size distributions is
1600the TNNLS or Interior-Point Gradient (IPG) method. As the name implies this is
1601a gradient refinement method for the special case of all positive data and
1602parameter values. To try it on this alumina data, select <b style='mso-bidi-font-weight:
1603normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1604minor-latin;mso-hansi-theme-font:minor-latin'>IPG</span></b> from the <b
1605style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1606mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Fitting
1607method</span></b> pull down. The data window will change to give</p>
1608
1609<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1610 id="Picture_x0020_23" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:468pt;
1611 height:238.5pt;visibility:visible;mso-wrap-style:square'>
1612 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image027.png"
1613  o:title=""/>
1614</v:shape><![endif]--><![if !vml]><img width=624 height=318
1615src="Small%20Angle%20Size%20Distribution_files/image028.png" v:shapes="Picture_x0020_23"><![endif]></span></p>
1616
1617<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1618
1619<p class=MsoNormal>Reset the Error multiplier back to <b style='mso-bidi-font-weight:
1620normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1621minor-latin;mso-hansi-theme-font:minor-latin'>1.0</span></b> and then do <b
1622style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1623mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models/Fit</span></b>
1624to run the IPG fitting. The IPG algorithm did not converge in 100 cycles and
1625resulting size distribution is a little choppy but has roughly the same bimodal
1626distribution found by <span class=SpellE>MaxEnt</span>.</p>
1627
1628<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1629 id="Picture_x0020_24" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;
1630 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1631 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image029.png"
1632  o:title=""/>
1633</v:shape><![endif]--><![if !vml]><img width=624 height=535
1634src="Small%20Angle%20Size%20Distribution_files/image030.png" v:shapes="Picture_x0020_24"><![endif]></span></p>
1635
1636<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1637
1638<p class=MsoNormal>This can be considerably improved by setting the <b
1639style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1640mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Error
1641multiplier</span></b> to <b style='mso-bidi-font-weight:normal'><span
1642style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1643mso-hansi-theme-font:minor-latin'>2.0</span></b>; the IPG fit con<span
1644style='mso-no-proof:yes'>verges in &lt;20 cycles and gives a smoother size
1645distribution.<o:p></o:p></span></p>
1646
1647<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1648 id="Picture_x0020_25" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:468pt;
1649 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1650 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image031.png"
1651  o:title=""/>
1652</v:shape><![endif]--><![if !vml]><img width=624 height=535
1653src="Small%20Angle%20Size%20Distribution_files/image032.png" v:shapes="Picture_x0020_25"><![endif]></span></p>
1654
1655<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1656
1657<p class=MsoNormal>The bimodal distribution is again quite clear with ~1400Å
1658and ~150Å diameter particles. This method appears to give a better fit to the
1659data than the <span class=SpellE>MaxEnt</span> method particularly in the
1660Q~0.003Å<sup>-1</sup> region’</p>
1661
1662<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1663 id="Picture_x0020_26" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:450pt;
1664 height:385.5pt;visibility:visible;mso-wrap-style:square'>
1665 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image033.png"
1666  o:title=""/>
1667</v:shape><![endif]--><![if !vml]><img width=600 height=514
1668src="Small%20Angle%20Size%20Distribution_files/image034.png" v:shapes="Picture_x0020_26"><![endif]></span></p>
1669
1670<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1671
1672<p class=MsoNormal>You may wish to explore the other parameters for the IPG
1673fitting. If <b style='mso-bidi-font-weight:normal'><span style='font-family:
1674"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1675minor-latin'>Q power weight</span></b> is set to <b style='mso-bidi-font-weight:
1676normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1677minor-latin;mso-hansi-theme-font:minor-latin'>0-4</span></b>, that changes the
1678data weighting to <span class=SpellE>Q<sup>p</sup></span>. This can change the convergence
1679of the IPG method and yield improved results if one is unsuccessful with the
1680default settings. I got a nice fit with a <b style='mso-bidi-font-weight:normal'><span
1681style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1682mso-hansi-theme-font:minor-latin'>Q power weight</span></b> of <b
1683style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1684mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>3</span></b>
1685and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1686mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Error
1687multiplier</span></b> of <b style='mso-bidi-font-weight:normal'><span
1688style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1689mso-hansi-theme-font:minor-latin'>2.0</span></b>.</p>
1690
1691<p class=MsoNormal>You should save this GSAS-II project as it will be used in the
1692tutorial for fitting small angle scattering data; I used <span class=SpellE><b
1693style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1694mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>alumina.gpx</span></b></span>.</p>
1695
1696</div>
1697
1698</body>
1699
1700</html>
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