source: Tutorials/SAsize/Small Angle Size Distribution.htm @ 2349

Last change on this file since 2349 was 1739, checked in by vondreele, 9 years ago

update small angle size tutorial
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415  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 1"/>
416  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 1"/>
417  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 1"/>
418  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
419  <w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
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427  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 1"/>
428  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 1"/>
429  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 1"/>
430  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 1"/>
431  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
432  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 1"/>
433  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
434  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
435  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
436  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
437  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 2"/>
438  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 2"/>
439  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 2"/>
440  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 2"/>
441  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 2"/>
442  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 2"/>
443  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 2"/>
444  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 2"/>
445  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
446  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
447  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
448  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
449  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 3"/>
450  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 3"/>
451  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 3"/>
452  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 3"/>
453  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 3"/>
454  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 3"/>
455  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 3"/>
456  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 3"/>
457  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 3"/>
458  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 3"/>
459  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
460  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 3"/>
461  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
462  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 4"/>
463  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 4"/>
464  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 4"/>
465  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 4"/>
466  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
467  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 4"/>
468  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 4"/>
469  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 4"/>
470  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 4"/>
471  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 4"/>
472  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 4"/>
473  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
474  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 4"/>
475  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
476  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
477  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 5"/>
478  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 5"/>
479  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 5"/>
480  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 5"/>
481  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 5"/>
482  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
483  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 5"/>
484  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
485  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 5"/>
486  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 5"/>
487  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
488  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
489  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
490  <w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
491  <w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
492  <w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
493  <w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
494  <w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
495  <w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
496  <w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
497  <w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
498  <w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
499  <w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
500  <w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
501  <w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
502  <w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
503  <w:LsdException Locked="false" Priority="19" QFormat="true"
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505  <w:LsdException Locked="false" Priority="21" QFormat="true"
506   Name="Intense Emphasis"/>
507  <w:LsdException Locked="false" Priority="31" QFormat="true"
508   Name="Subtle Reference"/>
509  <w:LsdException Locked="false" Priority="32" QFormat="true"
510   Name="Intense Reference"/>
511  <w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
512  <w:LsdException Locked="false" Priority="37" SemiHidden="true"
513   UnhideWhenUsed="true" Name="Bibliography"/>
514  <w:LsdException Locked="false" Priority="39" SemiHidden="true"
515   UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
516  <w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
517  <w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
518  <w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
519  <w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
520  <w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
521  <w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
522  <w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
523  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
524  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
525  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
526  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark"/>
527  <w:LsdException Locked="false" Priority="51" Name="Grid Table 6 Colorful"/>
528  <w:LsdException Locked="false" Priority="52" Name="Grid Table 7 Colorful"/>
529  <w:LsdException Locked="false" Priority="46"
530   Name="Grid Table 1 Light Accent 1"/>
531  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 1"/>
532  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 1"/>
533  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 1"/>
534  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 1"/>
535  <w:LsdException Locked="false" Priority="51"
536   Name="Grid Table 6 Colorful Accent 1"/>
537  <w:LsdException Locked="false" Priority="52"
538   Name="Grid Table 7 Colorful Accent 1"/>
539  <w:LsdException Locked="false" Priority="46"
540   Name="Grid Table 1 Light Accent 2"/>
541  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 2"/>
542  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 2"/>
543  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 2"/>
544  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 2"/>
545  <w:LsdException Locked="false" Priority="51"
546   Name="Grid Table 6 Colorful Accent 2"/>
547  <w:LsdException Locked="false" Priority="52"
548   Name="Grid Table 7 Colorful Accent 2"/>
549  <w:LsdException Locked="false" Priority="46"
550   Name="Grid Table 1 Light Accent 3"/>
551  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 3"/>
552  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 3"/>
553  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 3"/>
554  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 3"/>
555  <w:LsdException Locked="false" Priority="51"
556   Name="Grid Table 6 Colorful Accent 3"/>
557  <w:LsdException Locked="false" Priority="52"
558   Name="Grid Table 7 Colorful Accent 3"/>
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561  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 4"/>
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567  <w:LsdException Locked="false" Priority="52"
568   Name="Grid Table 7 Colorful Accent 4"/>
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571  <w:LsdException Locked="false" Priority="47" Name="Grid Table 2 Accent 5"/>
572  <w:LsdException Locked="false" Priority="48" Name="Grid Table 3 Accent 5"/>
573  <w:LsdException Locked="false" Priority="49" Name="Grid Table 4 Accent 5"/>
574  <w:LsdException Locked="false" Priority="50" Name="Grid Table 5 Dark Accent 5"/>
575  <w:LsdException Locked="false" Priority="51"
576   Name="Grid Table 6 Colorful Accent 5"/>
577  <w:LsdException Locked="false" Priority="52"
578   Name="Grid Table 7 Colorful Accent 5"/>
579  <w:LsdException Locked="false" Priority="46"
580   Name="Grid Table 1 Light Accent 6"/>
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585  <w:LsdException Locked="false" Priority="51"
586   Name="Grid Table 6 Colorful Accent 6"/>
587  <w:LsdException Locked="false" Priority="52"
588   Name="Grid Table 7 Colorful Accent 6"/>
589  <w:LsdException Locked="false" Priority="46" Name="List Table 1 Light"/>
590  <w:LsdException Locked="false" Priority="47" Name="List Table 2"/>
591  <w:LsdException Locked="false" Priority="48" Name="List Table 3"/>
592  <w:LsdException Locked="false" Priority="49" Name="List Table 4"/>
593  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark"/>
594  <w:LsdException Locked="false" Priority="51" Name="List Table 6 Colorful"/>
595  <w:LsdException Locked="false" Priority="52" Name="List Table 7 Colorful"/>
596  <w:LsdException Locked="false" Priority="46"
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598  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 1"/>
599  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 1"/>
600  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 1"/>
601  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 1"/>
602  <w:LsdException Locked="false" Priority="51"
603   Name="List Table 6 Colorful Accent 1"/>
604  <w:LsdException Locked="false" Priority="52"
605   Name="List Table 7 Colorful Accent 1"/>
606  <w:LsdException Locked="false" Priority="46"
607   Name="List Table 1 Light Accent 2"/>
608  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 2"/>
609  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 2"/>
610  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 2"/>
611  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 2"/>
612  <w:LsdException Locked="false" Priority="51"
613   Name="List Table 6 Colorful Accent 2"/>
614  <w:LsdException Locked="false" Priority="52"
615   Name="List Table 7 Colorful Accent 2"/>
616  <w:LsdException Locked="false" Priority="46"
617   Name="List Table 1 Light Accent 3"/>
618  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 3"/>
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620  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 3"/>
621  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 3"/>
622  <w:LsdException Locked="false" Priority="51"
623   Name="List Table 6 Colorful Accent 3"/>
624  <w:LsdException Locked="false" Priority="52"
625   Name="List Table 7 Colorful Accent 3"/>
626  <w:LsdException Locked="false" Priority="46"
627   Name="List Table 1 Light Accent 4"/>
628  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 4"/>
629  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 4"/>
630  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 4"/>
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632  <w:LsdException Locked="false" Priority="51"
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634  <w:LsdException Locked="false" Priority="52"
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636  <w:LsdException Locked="false" Priority="46"
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638  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 5"/>
639  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 5"/>
640  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 5"/>
641  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 5"/>
642  <w:LsdException Locked="false" Priority="51"
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648  <w:LsdException Locked="false" Priority="47" Name="List Table 2 Accent 6"/>
649  <w:LsdException Locked="false" Priority="48" Name="List Table 3 Accent 6"/>
650  <w:LsdException Locked="false" Priority="49" Name="List Table 4 Accent 6"/>
651  <w:LsdException Locked="false" Priority="50" Name="List Table 5 Dark Accent 6"/>
652  <w:LsdException Locked="false" Priority="51"
653   Name="List Table 6 Colorful Accent 6"/>
654  <w:LsdException Locked="false" Priority="52"
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1199
1200<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1201
1202<div class=WordSection1>
1203
1204<h1><strong><span style='mso-bidi-font-weight:normal'>Small Angle X-Ray Data –
1205Size Distribution in Alumina Powder</span><o:p></o:p></strong></h1>
1206
1207<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'>In
1208this tutorial you will determine the size distribution of particles in an
1209alumina polishing powder using data from a constant wavelength synchrotron
1210X-ray USAXS instrument. You will use both Maximum Entropy (<span class=SpellE>MaxEnt</span>)
1211and Total Non-Negative Least Squares (TNNLS) methods assuming spherical
1212particles. The data were collected from <span style='mso-fareast-font-family:
1213Calibri;mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold;
1214mso-bidi-font-style:italic'>powders spread onto sticky tape and covered with
1215another layer of the same tape. The data were corrected for background from
1216data collected from two layers of sticky tape. However, the sample thickness is
1217not</span> accurately known <span style='mso-fareast-font-family:Calibri;
1218mso-fareast-theme-font:minor-latin;mso-bidi-font-weight:bold;mso-bidi-font-style:
1219italic'>so the data are not calibrated on an absolute scale.<o:p></o:p></span></p>
1220
1221<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1222
1223<h2>Step 1: read in the data file</h2>
1224
1225<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1226style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
1227style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
1228the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1229mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
1230Calibri;mso-bidi-theme-font:minor-latin'>Import/Small Angle Data/from q (A-1) step
1231X-ray QIE data file</span></b> menu item to read the data file into GSAS-II.
1232This read option is set to read three column small angle scattering data (SASD)
1233as Q in Å<sup>-1</sup>, intensity and estimated standard deviation in
1234intensity; there may be a header with metadata information in the front of this
1235file.<span style='mso-spacerun:yes'>  </span>Change the file directory to <b
1236style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1237mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
1238Calibri;mso-bidi-theme-font:minor-latin'>exercises/<span class=SpellE>SAsize</span></span></b><span
1239style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1240mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
1241minor-latin'> to find the file</span>; you will have to select the ‘<b
1242style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1243mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file
1244(*.*)</span></b>’ filter to see it.</p>
1245
1246<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1247style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
1248style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
1249the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1250mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
1251Calibri;mso-bidi-theme-font:minor-latin'>alumina data.dat</span></b><span
1252style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1253mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
1254minor-latin'> data</span> file in the first dialog and press <b
1255style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1256mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
1257Calibri;mso-bidi-theme-font:minor-latin'>Open</span></b>. There will be a
1258Dialog box asking <span class=GramE><b style='mso-bidi-font-weight:normal'><span
1259style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1260mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
1261minor-latin'>Is</span></b></span><b style='mso-bidi-font-weight:normal'><span
1262style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1263mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
1264minor-latin'> this the file you want?</span></b> Press <span class=GramE><b
1265style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1266mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:
1267Calibri;mso-bidi-theme-font:minor-latin'>Yes</span></b></span> button to
1268proceed.</p>
1269
1270<p class=MsoNormal>At this point the <b style='mso-bidi-font-weight:normal'><span
1271style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1272mso-hansi-theme-font:minor-latin;mso-bidi-font-family:Calibri;mso-bidi-theme-font:
1273minor-latin'>GSAS-II data tree</span></b> window will have several entries and
1274the plot window will show the SASD pattern as a log-log plot of intensity vs. Q</p>
1275
1276<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
1277 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
1278 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1279 <v:stroke joinstyle="miter"/>
1280 <v:formulas>
1281  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
1282  <v:f eqn="sum @0 1 0"/>
1283  <v:f eqn="sum 0 0 @1"/>
1284  <v:f eqn="prod @2 1 2"/>
1285  <v:f eqn="prod @3 21600 pixelWidth"/>
1286  <v:f eqn="prod @3 21600 pixelHeight"/>
1287  <v:f eqn="sum @0 0 1"/>
1288  <v:f eqn="prod @6 1 2"/>
1289  <v:f eqn="prod @7 21600 pixelWidth"/>
1290  <v:f eqn="sum @8 21600 0"/>
1291  <v:f eqn="prod @7 21600 pixelHeight"/>
1292  <v:f eqn="sum @10 21600 0"/>
1293 </v:formulas>
1294 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1295 <o:lock v:ext="edit" aspectratio="t"/>
1296</v:shapetype><v:shape id="Picture_x0020_15" o:spid="_x0000_i1038" type="#_x0000_t75"
1297 style='width:525pt;height:450pt;visibility:visible;mso-wrap-style:square'>
1298 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image001.png"
1299  o:title=""/>
1300</v:shape><![endif]--><![if !vml]><img width=700 height=600
1301src="Small%20Angle%20Size%20Distribution_files/image001.png" v:shapes="Picture_x0020_15"><![endif]></span></p>
1302
1303<h2>Step 2: Set Limits</h2>
1304
1305<p class=MsoNormal>For this step we will reposition the limits to enclose only
1306that part of the SASD pattern suitable for size distribution analysis.
1307Typically this covers 10<sup>-3</sup> &lt; Q &lt; 10<sup>-1</sup>; below this
1308range scattering is from very large objects not readily described by the size
1309distribution analysis and above the scattering is mostly background. Select <b
1310style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1311mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Limits</span></b>
1312under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1313mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1314data.dat</span></b> from the GSAS-II tree. Then set <b style='mso-bidi-font-weight:
1315normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1316minor-latin;mso-hansi-theme-font:minor-latin'>changed</span></b> to <b
1317style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1318mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.001</span></b>
1319for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1320style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1321mso-hansi-theme-font:minor-latin'>Tmin</span></b></span> and <b
1322style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1323mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.1</span></b>
1324for <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1325style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1326mso-hansi-theme-font:minor-latin'>Tmax</span></b></span>. You can also set the
1327limits using the cursor on the plot by either picking a point on the curve with
1328the left or right mouse button or by dragging the green and red vertical lines
1329to the desired positions. The limits window should look like</p>
1330
1331<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1332 id="_x0000_i1037" type="#_x0000_t75" style='width:225pt;height:195pt;
1333 visibility:visible;mso-wrap-style:square'>
1334 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image002.png"
1335  o:title=""/>
1336</v:shape><![endif]--><![if !vml]><img width=300 height=260
1337src="Small%20Angle%20Size%20Distribution_files/image002.png" v:shapes="_x0000_i1037"><![endif]></span><span
1338style='mso-spacerun:yes'> </span></p>
1339
1340<h2>Step 3 Select the scattering substances for your sample</h2>
1341
1342<p class=MsoNormal><span style='mso-no-proof:yes'>Two scsttering substances need
1343to be defined for your sample to give the anticipated scattering contrast; in
1344this case one is alumina and the other is “vacuum” (really air). Parameters for
1345a number of substances are defined in the file </span><b style='mso-bidi-font-weight:
1346normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1347minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1348style='mso-no-proof:yes'>. You can add your own substances to this or better
1349put them in </span><b style='mso-bidi-font-weight:normal'><span
1350style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1351mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>UserSubstances.py</span></b><span
1352style='mso-no-proof:yes'>; this is read after </span><b style='mso-bidi-font-weight:
1353normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1354minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1355style='mso-no-proof:yes'> when you load substances for your selection. </span>Select
1356<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1357mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Substances</span></b>
1358under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1359mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1360data.dat</span></b> from the GSAS-II tree. Then do <b style='mso-bidi-font-weight:
1361normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1362minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Load</span></b> <b
1363style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1364mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>substance</span></b>
1365from the menu; a popup window will appear with possible selections</p>
1366
1367<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1368 id="Picture_x0020_23" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:259.5pt;
1369 height:252pt;visibility:visible;mso-wrap-style:square'>
1370 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image003.png"
1371  o:title=""/>
1372</v:shape><![endif]--><![if !vml]><img width=346 height=336
1373src="Small%20Angle%20Size%20Distribution_files/image003.png" v:shapes="Picture_x0020_23"><![endif]><o:p></o:p></span></p>
1374
1375<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1376
1377<p class=MsoNormal>Select <b style='mso-bidi-font-weight:normal'><span
1378style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1379mso-hansi-theme-font:minor-latin'>Alumina</span></b> and press <b
1380style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1381mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>;
1382the relevant data for alumina (and vacuum) are displayed next</p>
1383
1384<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1385 id="Picture_x0020_16" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:259.5pt;
1386 height:195pt;visibility:visible;mso-wrap-style:square'>
1387 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image004.png"
1388  o:title=""/>
1389</v:shape><![endif]--><![if !vml]><img width=346 height=260
1390src="Small%20Angle%20Size%20Distribution_files/image004.png" v:shapes="Picture_x0020_16"><![endif]></span><span
1391style='mso-spacerun:yes'> </span></p>
1392
1393<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1394
1395<p class=MsoNormal>If desired you can load/add as many substances as you desire
1396into this list; you can also delete any of them (except vacuum). The
1397composition, volume occupied by the atoms in the composition and the density
1398are given for each substance. These can each be edited; the other values will
1399change accordingly. If your substance isn’t in the list, you can <b
1400style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1401mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit/Add
1402substance</span></b> to create a new one (you will be asked for a name and the
1403set of elements in two successive popup windows). From this information the
1404scattering density and that as affected by resonant scattering for the listed
1405wavelength is displayed (the wavelength can be changed in the <b
1406style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1407mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Instrument
1408Parameters</span></b> GSAS-II tree item if needed). The resonant scattering
1409value is used for contrast calculations.</p>
1410
1411<h2>Step 4: Set Sample parameters </h2>
1412
1413<p class=MsoNormal>Two of the substances you have loaded into GSAS-II next need
1414to be selected for this size distribution analysis; Select <b style='mso-bidi-font-weight:
1415normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1416minor-latin;mso-hansi-theme-font:minor-latin'>Sample Parameters</span></b>
1417under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1418mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1419data.dat</span></b> from the GSAS-II tree. Near the bottom of the window will
1420be two rows marked “<b style='mso-bidi-font-weight:normal'><span
1421style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1422mso-hansi-theme-font:minor-latin'>Material</span></b>”; select <b
1423style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1424mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Alumina</span></b>
1425from one of the pull downs (leave the other as <b style='mso-bidi-font-weight:
1426normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1427minor-latin;mso-hansi-theme-font:minor-latin'>vacuum</span></b>). The window
1428will show at the bottom the computed contrast between alumina and vacuum
1429without and with consideration of resonant scattering effects; the latter is
1430used in subsequent calculations.</p>
1431
1432<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1433 id="Picture_x0020_17" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:305.25pt;
1434 height:408pt;visibility:visible;mso-wrap-style:square'>
1435 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image005.png"
1436  o:title=""/>
1437</v:shape><![endif]--><![if !vml]><img width=407 height=544
1438src="Small%20Angle%20Size%20Distribution_files/image005.png" v:shapes="Picture_x0020_17"><![endif]></span></p>
1439
1440<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1441
1442<p class=MsoNormal>For experiments for which you know the transmission and the
1443sample thickness, you can manipulate the <b style='mso-bidi-font-weight:normal'><span
1444style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1445mso-hansi-theme-font:minor-latin'>volume fractions</span></b> to make the
1446calculated transmission match the observed one. Additionally, if you have
1447absolute scaling information, you can rescale the data by adjusting the <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'>histogram
1450scale factor</span></b>; multiple data sets can be scaled together via the <b
1451style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1452mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Command/Set
1453scale</span></b> menu item.</p>
1454
1455<h2>Step 5 Size distribution via Maximum Entropy</h2>
1456
1457<p class=MsoNormal>You are now ready to attempt a size distribution analysis
1458using the maximum entropy method. Select <b style='mso-bidi-font-weight:normal'><span
1459style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1460mso-hansi-theme-font:minor-latin'>Models</span></b> under <b style='mso-bidi-font-weight:
1461normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1462minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina data.dat</span></b>
1463from the GSAS-II tree; the window will display</p>
1464
1465<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1466 id="Picture_x0020_18" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:361.5pt;
1467 height:191.25pt;visibility:visible;mso-wrap-style:square'>
1468 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image006.png"
1469  o:title=""/>
1470</v:shape><![endif]--><![if !vml]><img width=482 height=255
1471src="Small%20Angle%20Size%20Distribution_files/image006.png" v:shapes="Picture_x0020_18"><![endif]></span></p>
1472
1473<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1474
1475<p class=MsoNormal>Many selections are made by default for this analysis;
1476however it is important that an appropriate value is selected for the
1477background. From the high Q end of the data plot</p>
1478
1479<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1480 id="Picture_x0020_19" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:525pt;
1481 height:450pt;visibility:visible;mso-wrap-style:square'>
1482 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image007.png"
1483  o:title=""/>
1484</v:shape><![endif]--><![if !vml]><img width=700 height=600
1485src="Small%20Angle%20Size%20Distribution_files/image007.png" v:shapes="Picture_x0020_19"><![endif]></span><span
1486style='mso-spacerun:yes'> </span></p>
1487
1488<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1489
1490<p class=MsoNormal>It is clear that the intensity levels off at an apparent
1491background level of ~<b style='mso-bidi-font-weight:normal'><span
1492style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1493mso-hansi-theme-font:minor-latin'>0.12</span></b>; enter that into the
1494appropriate place in the data window. The plot will be redrawn showing a horizontal
1495red line for the background. All the other parameters seem reasonable for a 1<sup>st</sup>
1496attempt at a <span class=SpellE>MaxEnt</span> solution. Do <b style='mso-bidi-font-weight:
1497normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1498minor-latin;mso-hansi-theme-font:minor-latin'>Models/Fit</span></b>; the
1499console window will show that the calculation did not converge and the <b
1500style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1501mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Size
1502Distribution</span></b> plot has a “choppy” appearance.</p>
1503
1504<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1505 id="Picture_x0020_28" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:525pt;
1506 height:450pt;visibility:visible;mso-wrap-style:square'>
1507 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image008.png"
1508  o:title=""/>
1509</v:shape><![endif]--><![if !vml]><img width=700 height=600
1510src="Small%20Angle%20Size%20Distribution_files/image008.png" v:shapes="Picture_x0020_28"><![endif]></span></p>
1511
1512<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1513
1514<p class=MsoNormal>This is not a satisfactory result, but the suggestion given
1515in the console window is worth trying. Change the <b style='mso-bidi-font-weight:
1516normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1517minor-latin;mso-hansi-theme-font:minor-latin'>Error multiplier</span></b> to <b
1518style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1519mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>5</span></b>
1520(notice the increased error bars on the data plot) and repeat <b
1521style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1522mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Model/Fit</span></b>.
1523Convergence is now achieved in &lt;10 cycles (see console window for details)
1524and a much smoother size distribution results</p>
1525
1526<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1527 id="Picture_x0020_29" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:525pt;
1528 height:450pt;visibility:visible;mso-wrap-style:square'>
1529 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image009.png"
1530  o:title=""/>
1531</v:shape><![endif]--><![if !vml]><img width=700 height=600
1532src="Small%20Angle%20Size%20Distribution_files/image009.png" v:shapes="Picture_x0020_29"><![endif]></span></p>
1533
1534<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1535
1536<p class=MsoNormal>This is a good result: clearly the alumina polishing powder
1537has a bimodal distribution with diameters centered about ~1600Å and ~160Å (not
1538500Å and 1µm as advertised by the manufacturer!).</p>
1539
1540<p class=MsoNormal>You may wish to explore the effect of some of the other
1541parameters in the data window. Most are obvious but <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'>Log floor factor</span></b> needs
1544a bit of explanation. This is the log of the minimum size distribution (scaled
1545by the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1546mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>histogram
1547scale factor</span></b> and the <b style='mso-bidi-font-weight:normal'><span
1548style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1549mso-hansi-theme-font:minor-latin'>contrast</span></b>). This size distribution
1550minimum needs to be set within 1-2 orders of magnitude of the optimal value and
1551can differ from the default of 10<sup>-3; </sup>it is worth changing if
1552convergence is poor despite trying different error multipliers. Try changing it
1553to see what effect it has on the result. With the original settings the data
1554fit looks like</p>
1555
1556<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1557 id="Picture_x0020_20" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:525pt;
1558 height:450pt;visibility:visible;mso-wrap-style:square'>
1559 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image010.png"
1560  o:title=""/>
1561</v:shape><![endif]--><![if !vml]><img width=700 height=600
1562src="Small%20Angle%20Size%20Distribution_files/image010.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
1563
1564<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1565
1566<p class=MsoNormal>The green curve is the result calculated from the size
1567distribution. Notice that it is not perfect, there is appreciable misfit around
1568Q=0.003Å<sup>-1</sup>. This may be due to the assumption that the particles are
1569spheres; they could be some other shape (I could get a better fit by setting
1570the Spheroid aspect ratio to 2.0), however this tool is not really the
1571appropriate one to make this determination.</p>
1572
1573<h2>Step 6 Size Distribution <i style='mso-bidi-font-style:normal'>via</i>
1574Total Non-Negative Least Squares (TNNLS)</h2>
1575
1576<p class=MsoNormal>An alternative method for determining size distributions is
1577the TNNLS or Interior-Point Gradient (IPG) method. As the name implies this is
1578a gradient refinement method for the special case of all positive data and
1579parameter values. To try it on this alumina data, select <b style='mso-bidi-font-weight:
1580normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1581minor-latin;mso-hansi-theme-font:minor-latin'>IPG</span></b> from the <b
1582style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1583mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Fitting
1584method</span></b> pull down. The data window will change to give</p>
1585
1586<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1587 id="Picture_x0020_21" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:375.75pt;
1588 height:191.25pt;visibility:visible;mso-wrap-style:square'>
1589 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image011.png"
1590  o:title=""/>
1591</v:shape><![endif]--><![if !vml]><img width=501 height=255
1592src="Small%20Angle%20Size%20Distribution_files/image011.png" v:shapes="Picture_x0020_21"><![endif]></span></p>
1593
1594<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1595
1596<p class=MsoNormal>Reset the Error multiplier back to <b style='mso-bidi-font-weight:
1597normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1598minor-latin;mso-hansi-theme-font:minor-latin'>1.0</span></b> and then do <b
1599style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1600mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models/Fit</span></b>
1601to run the IPG fitting. The IPG algorithm did not converge in 100 cycles and
1602resulting size distribution is a little choppy but has roughly the same bimodal
1603distribution found by <span class=SpellE>MaxEnt</span>.</p>
1604
1605<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1606 id="Picture_x0020_289" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:621.75pt;
1607 height:450pt;visibility:visible;mso-wrap-style:square'>
1608 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image012.png"
1609  o:title=""/>
1610</v:shape><![endif]--><![if !vml]><img width=829 height=600
1611src="Small%20Angle%20Size%20Distribution_files/image012.png" v:shapes="Picture_x0020_289"><![endif]></span></p>
1612
1613<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1614
1615<p class=MsoNormal>This can be considerably improved by setting the <b
1616style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1617mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Error
1618multiplier</span></b> to <b style='mso-bidi-font-weight:normal'><span
1619style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1620mso-hansi-theme-font:minor-latin'>2.0</span></b>; the IPG fit con<span
1621style='mso-no-proof:yes'>verges in &lt;20 cycles and gives a smoother size
1622distribution.<o:p></o:p></span></p>
1623
1624<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1625 id="Picture_x0020_291" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:621.75pt;
1626 height:450pt;visibility:visible;mso-wrap-style:square'>
1627 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image013.png"
1628  o:title=""/>
1629</v:shape><![endif]--><![if !vml]><img width=829 height=600
1630src="Small%20Angle%20Size%20Distribution_files/image013.png" v:shapes="Picture_x0020_291"><![endif]></span></p>
1631
1632<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1633
1634<p class=MsoNormal>The bimodal distribution is again quite clear with ~1400Å
1635and ~150Å diameter particles. This method appears to give a better fit to the
1636data than the <span class=SpellE>MaxEnt</span> method particularly in the
1637Q~0.003Å<sup>-1</sup> region’</p>
1638
1639<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1640 id="Picture_x0020_22" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:525pt;
1641 height:450pt;visibility:visible;mso-wrap-style:square'>
1642 <v:imagedata src="Small%20Angle%20Size%20Distribution_files/image014.png"
1643  o:title=""/>
1644</v:shape><![endif]--><![if !vml]><img width=700 height=600
1645src="Small%20Angle%20Size%20Distribution_files/image014.png" v:shapes="Picture_x0020_22"><![endif]></span></p>
1646
1647<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1648
1649<p class=MsoNormal>You may wish to explore the other parameters for the IPG
1650fitting. If <b style='mso-bidi-font-weight:normal'><span style='font-family:
1651"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1652minor-latin'>Q power weight</span></b> is set to <b style='mso-bidi-font-weight:
1653normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1654minor-latin;mso-hansi-theme-font:minor-latin'>0-4</span></b>, that changes the
1655data weighting to <span class=SpellE><span class=GramE>Q<sup>p</sup></span></span>.
1656This can change the convergence of the IPG method and yield improved results if
1657one is unsuccessful with the default settings. I got a nice fit with a <b
1658style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1659mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Q power
1660weight</span></b> of <b style='mso-bidi-font-weight:normal'><span
1661style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1662mso-hansi-theme-font:minor-latin'>3</span></b> and <b style='mso-bidi-font-weight:
1663normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1664minor-latin;mso-hansi-theme-font:minor-latin'>Error multiplier</span></b> of <b
1665style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1666mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.0</span></b>.</p>
1667
1668<p class=MsoNormal>You should save this GSAS-II project as it will be used in the
1669tutorial for fitting small angle scattering data; I used <span class=SpellE><b
1670style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1671mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>alumina.gpx</span></b></span>.</p>
1672
1673</div>
1674
1675</body>
1676
1677</html>
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