source: Tutorials/SAfit/Fitting Small Angle Scattering Data.htm

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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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1218
1219<div class=WordSection1>
1220
1221<h1><strong>Fitting</strong><strong><span style='mso-bidi-font-weight:normal'>
1222Small Angle X-Ray Data – Alumina Powder</span><o:p></o:p></strong></h1>
1223
1224  <P><BL>
1225  <LI><B>A video version of this tutorial is available at
1226<A href="https://anl.box.com/v/FittingSmallAngleScatteringDat" target="_blank">
1227https://anl.box.com/v/FittingSmallAngleScatteringDat</A></B>
1228 <LI>Exercise files are found <A href="./data/" target="_blank">here</a>
1229</BL></P><P></P>
1230
1231<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'>In
1232this tutorial you will fit small angle scattering data for an alumina polishing
1233powder using data from a constant wavelength synchrotron X-ray USAXS
1234instrument. You will use both a lognormal distribution of spherical particles
1235model and a unified <span class=SpellE>Guinier-Porod</span> model. The data
1236were collected from <span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1237minor-latin;mso-bidi-font-weight:bold;mso-bidi-font-style:italic'>powders
1238spread onto sticky tape and covered with another layer of the same tape. The
1239data were corrected for background using data collected from two layers of
1240sticky tape. However, the sample thickness is not</span> accurately known <span
1241style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;
1242mso-bidi-font-weight:bold;mso-bidi-font-style:italic'>so the data are not
1243calibrated on an absolute scale.<o:p></o:p></span></p>
1244
1245<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1246
1247<h2>Step 1: read in the data file</h2>
1248
1249<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1250style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
1251style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>If
1252you have saved the GSAS-II project file from the <b style='mso-bidi-font-weight:
1253normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1254minor-latin;mso-hansi-theme-font:minor-latin'>Size Distribution</span></b>
1255tutorial, use <b style='mso-bidi-font-weight:normal'><span style='font-family:
1256"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1257minor-latin'>File/Open project…</span></b> menu item to retrieve the data;
1258plots of the size distribution and the data will appear. Then go to <!--[if supportFields]><b
1259style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1260mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'><span
1261style='mso-element:field-begin'></span><span
1262style='mso-spacerun:yes'> </span>REF _Ref386704789 \h<span
1263style='mso-spacerun:yes'>  </span>\* MERGEFORMAT <span style='mso-element:field-separator'></span></span></b><![endif]--><b
1264style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1265mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Step 2: Set
1266Limits<!--[if gte mso 9]><xml>
1267 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380036003700300034003700380039000000</w:data>
1268</xml><![endif]--></span></b><!--[if supportFields]><b style='mso-bidi-font-weight:
1269normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1270minor-latin;mso-hansi-theme-font:minor-latin'><span style='mso-element:field-end'></span></span></b><![endif]-->.
1271Otherwise, use the <b style='mso-bidi-font-weight:normal'><span
1272style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1273mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Import/Small
1274Angle Data/from q (A-1) step X-ray QIE data file</span></b> menu item to read
1275the data file into GSAS-II. This read option is set to read three column small
1276angle scattering data (SASD) as Q in Å<sup>-1</sup>, intensity and estimated
1277standard deviation in intensity; there may be a header with metadata
1278information in the front of this file.<span style='mso-spacerun:yes'> 
1279</span>Change the file directory to <span class=SpellE><b style='mso-bidi-font-weight:
1280normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1281minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>SAfit</span></b></span><b
1282style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1283mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1284minor-latin'>/data</span></b><span style='font-family:"Calibri",sans-serif;
1285mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1286minor-latin'> to find the file</span>; you will have to select the <b
1287style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1288mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file
1289(*.*)</span></b> filter to see it.</p>
1290
1291<p class=MsoListParagraphCxSpLast style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1292style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
1293style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
1294the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1295mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1296minor-latin'>alumina data.dat</span></b><span style='font-family:"Calibri",sans-serif;
1297mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1298minor-latin'> data</span> file in the first dialog and press <b
1299style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1300mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1301minor-latin'>Open</span></b>. There will be a Dialog box asking <span
1302class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1303"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1304minor-latin;mso-bidi-theme-font:minor-latin'>Is</span></b></span><b
1305style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1306mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1307minor-latin'> this the file you want?</span></b> Press <span class=GramE><b
1308style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1309mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1310minor-latin'>Yes</span></b></span> button to proceed.</p>
1311
1312<p class=MsoNormal>At this point the <b style='mso-bidi-font-weight:normal'><span
1313style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1314mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>GSAS-II data
1315tree</span></b> window will have several entries and the plot window will show
1316the SASD pattern as a log-log plot of intensity vs. Q</p>
1317
1318<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
1319 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
1320 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1321 <v:stroke joinstyle="miter"/>
1322 <v:formulas>
1323  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
1324  <v:f eqn="sum @0 1 0"/>
1325  <v:f eqn="sum 0 0 @1"/>
1326  <v:f eqn="prod @2 1 2"/>
1327  <v:f eqn="prod @3 21600 pixelWidth"/>
1328  <v:f eqn="prod @3 21600 pixelHeight"/>
1329  <v:f eqn="sum @0 0 1"/>
1330  <v:f eqn="prod @6 1 2"/>
1331  <v:f eqn="prod @7 21600 pixelWidth"/>
1332  <v:f eqn="sum @8 21600 0"/>
1333  <v:f eqn="prod @7 21600 pixelHeight"/>
1334  <v:f eqn="sum @10 21600 0"/>
1335 </v:formulas>
1336 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1337 <o:lock v:ext="edit" aspectratio="t"/>
1338</v:shapetype><v:shape id="Picture_x0020_24" o:spid="_x0000_i1047" type="#_x0000_t75"
1339 style='width:468pt;height:401.25pt;visibility:visible;mso-wrap-style:square'>
1340 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image002.png"
1341  o:title=""/>
1342</v:shape><![endif]--><![if !vml]><img width=624 height=535
1343src="Fitting%20Small%20Angle%20Scattering%20Data_files/image001.png" v:shapes="Picture_x0020_24"><![endif]></span></p>
1344
1345<h2><a name="_Ref386704789">Step 2: Set Limits</a></h2>
1346
1347<p class=MsoNormal>For this step we will reposition the limits to exclude only
1348the last point in the pattern as it does appear to be somewhat suspect (see
1349plot). Select <b style='mso-bidi-font-weight:normal'><span style='font-family:
1350"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1351minor-latin'>Limits</span></b> under <b style='mso-bidi-font-weight:normal'><span
1352style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1353mso-hansi-theme-font:minor-latin'>SASD alumina data.dat</span></b> from the
1354GSAS-II tree. Set the upper limit using the cursor on the plot by picking the
1355next-to-last point on the curve with the left or right mouse button. If needed
1356reposition the lower limit to be the 1<sup>st</sup> data point. The limits window
1357should look like</p>
1358
1359<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1360 id="Picture_x0020_25" o:spid="_x0000_i1046" type="#_x0000_t75" style='width:382.5pt;
1361 height:276pt;visibility:visible;mso-wrap-style:square'>
1362 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image005.png"
1363  o:title=""/>
1364</v:shape><![endif]--><![if !vml]><img width=510 height=368
1365src="Fitting%20Small%20Angle%20Scattering%20Data_files/image005.png" v:shapes="Picture_x0020_25"><![endif]></span><span
1366style='mso-spacerun:yes'> </span></p>
1367
1368<h2>Step 3 Select the scattering substances for your sample</h2>
1369
1370<p class=MsoNormal><span style='mso-no-proof:yes'>If you have already done this
1371step in the </span><b style='mso-bidi-font-weight:normal'><span
1372style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1373mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Size Distribution</span></b><span
1374style='mso-no-proof:yes'> tutorial, skip to </span><!--[if supportFields]><b
1375style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1376mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:
1377yes'><span style='mso-element:field-begin'></span><span
1378style='mso-spacerun:yes'> </span>REF _Ref386699439 \h<span
1379style='mso-spacerun:yes'>  </span>\* MERGEFORMAT <span style='mso-element:field-separator'></span></span></b><![endif]--><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'>Step 4 Creation
1382and Refinement of Log Normal Particle Model<span style='mso-no-proof:yes'><!--[if gte mso 9]><xml>
1383 <w:data>08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380036003600390039003400330039000000</w:data>
1384</xml><![endif]--></span></span></b><!--[if supportFields]><b style='mso-bidi-font-weight:
1385normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1386minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'><span
1387style='mso-element:field-end'></span></span></b><![endif]--><span
1388style='mso-no-proof:yes'>. Two substances need to be defined for your sample to
1389give the anticipated scattering contrast; in this case one is alumina and the
1390other is “vacuum” (really air). Parameters for a number of substances are
1391defined in the file </span><b style='mso-bidi-font-weight:normal'><span
1392style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1393mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1394style='mso-no-proof:yes'>. You can add your own substances to this or better
1395put them in </span><b style='mso-bidi-font-weight:normal'><span
1396style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1397mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>UserSubstances.py</span></b><span
1398style='mso-no-proof:yes'>; this is read after Substances.py when you load
1399substances for your selection. </span>Select <b style='mso-bidi-font-weight:
1400normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1401minor-latin;mso-hansi-theme-font:minor-latin'>Substances</span></b> under <b
1402style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1403mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1404data.dat</span></b> from the GSAS-II tree. Then do <span class=GramE><b
1405style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1406mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit</span></b></span><b
1407style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1408mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>
1409substance/Load</span></b> <b style='mso-bidi-font-weight:normal'><span
1410style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1411mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>substance</span></b>
1412from the menu; a popup window will appear with possible selections</p>
1413
1414<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1415 id="Picture_x0020_3" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:259.5pt;
1416 height:252pt;visibility:visible;mso-wrap-style:square'>
1417 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image003.png"
1418  o:title=""/>
1419</v:shape><![endif]--><![if !vml]><img width=346 height=336
1420src="Fitting%20Small%20Angle%20Scattering%20Data_files/image003.png" v:shapes="Picture_x0020_3"><![endif]><o:p></o:p></span></p>
1421
1422<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1423
1424<p class=MsoNormal>Select <b style='mso-bidi-font-weight:normal'><span
1425style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1426mso-hansi-theme-font:minor-latin'>Alumina</span></b> and press <b
1427style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1428mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>;
1429the relevant data for alumina (and vacuum&amp; unit scatter) are displayed next</p>
1430
1431<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1432 id="Picture_x0020_26" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:417pt;
1433 height:269.25pt;visibility:visible;mso-wrap-style:square'>
1434 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image017.png"
1435  o:title=""/>
1436</v:shape><![endif]--><![if !vml]><img width=556 height=359
1437src="Fitting%20Small%20Angle%20Scattering%20Data_files/image017.png" v:shapes="Picture_x0020_26"><![endif]></span><span
1438style='mso-spacerun:yes'> </span></p>
1439
1440<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1441
1442<p class=MsoNormal>If desired you can load/add as many substances as you desire
1443into this list; you can also delete any of them (except vacuum &amp; unit
1444scatter). The composition, volume occupied by the atoms in the composition and
1445the density are given for each substance. These can each be edited; the other
1446values will change accordingly. If your substance isn’t in the list, you can <span
1447class=GramE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1448"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1449minor-latin'>Edit</span></b></span><b style='mso-bidi-font-weight:normal'><span
1450style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1451mso-hansi-theme-font:minor-latin'> substance/Add substance</span></b> to create
1452a new one (you will be asked for a name and the set of elements in two successive
1453popup windows). From this information the scattering density and that as
1454affected by resonant scattering for the listed wavelength is displayed (the
1455wavelength can be changed in the <b style='mso-bidi-font-weight:normal'><span
1456style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1457mso-hansi-theme-font:minor-latin'>Instrument Parameters</span></b> GSAS-II tree
1458item if needed). The resonant scattering value is used for contrast
1459calculations.</p>
1460
1461<h2><a name="_Ref386699439"></a><a name="_Ref386699331"><span style='mso-bookmark:
1462_Ref386699439'>Step 4 </span></a><span style='mso-bookmark:_Ref386699439'>Creation
1463and Refinement of Log Normal Particle Model</span></h2>
1464
1465<p class=MsoNormal>You are now ready to attempt fitting the data with a log
1466normal distribution of spherical particles. Thus you’ll need to select <b
1467style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1468mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models</span></b>
1469under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1470mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD alumina
1471data.dat</span></b> from the GSAS-II tree; the data window will display the <b
1472style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1473mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Size dist.</span></b>
1474display;<span style='mso-no-proof:yes'> </span>change this to <b
1475style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1476mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Particle fit</span></b>
1477using the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1478mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Modeling by</span></b>
1479pull down. NB: GSAS-II will remember your selection the next time you enter
1480this <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1481mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models</span></b>
1482data tree item.</p>
1483
1484<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1485 id="Picture_x0020_27" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:468pt;
1486 height:227.25pt;visibility:visible;mso-wrap-style:square'>
1487 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image029.png"
1488  o:title=""/>
1489</v:shape><![endif]--><![if !vml]><img width=624 height=303
1490src="Fitting%20Small%20Angle%20Scattering%20Data_files/image006.png" v:shapes="Picture_x0020_27"><![endif]></span></p>
1491
1492<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1493
1494<p class=MsoNormal>If you had done the <b style='mso-bidi-font-weight:normal'><span
1495style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1496mso-hansi-theme-font:minor-latin'>Size Distribution</span></b> tutorial, you
1497would know that there were two populations of particles in the sample. One had
1498a mean diameter of ~1300A and the other had a mean diameter of ~150A. You will
1499also need something to describe the very lowest Q portion of the data. Do <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'>Models/Add</span></b>
1502from the menu; the data window will change and the plots will be refreshed.
1503Your first step is to change the <b style='mso-bidi-font-weight:normal'><span
1504style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1505mso-hansi-theme-font:minor-latin'>Material</span></b> to <b style='mso-bidi-font-weight:
1506normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1507minor-latin;mso-hansi-theme-font:minor-latin'>Alumina</span></b> and make sure
1508the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1509mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>
1510is something reasonable (<b style='mso-bidi-font-weight:normal'><span
1511style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1512mso-hansi-theme-font:minor-latin'>0.12</span></b>) based on the data at highest
1513Q; again the data window and plots will be refreshed. Click on one of the
1514slider buttons to force a calculation.</p>
1515
1516<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1517 id="Picture_x0020_28" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:468pt;
1518 height:258pt;visibility:visible;mso-wrap-style:square'>
1519 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image031.png"
1520  o:title=""/>
1521</v:shape><![endif]--><![if !vml]><img width=624 height=344
1522src="Fitting%20Small%20Angle%20Scattering%20Data_files/image007.png" v:shapes="Picture_x0020_28"><![endif]></span></p>
1523
1524<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1525
1526<p class=MsoNormal>The data plot shows a horizontal red line for the background
1527and a green one calculated from your selected model. </p>
1528
1529<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1530 id="Picture_x0020_29" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:412.5pt;
1531 height:354pt;visibility:visible;mso-wrap-style:square'>
1532 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image033.png"
1533  o:title=""/>
1534</v:shape><![endif]--><![if !vml]><img width=550 height=472
1535src="Fitting%20Small%20Angle%20Scattering%20Data_files/image008.png" v:shapes="Picture_x0020_29"><![endif]></span></p>
1536
1537<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1538
1539<p class=MsoNormal>You can manually adjust the calculated curve by using the
1540sliders: increase <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1541style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1542mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:
1543normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1544minor-latin;mso-hansi-theme-font:minor-latin'> Volume</span></b> and decrease <span
1545class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1546"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1547minor-latin'>Dist</span></b></span><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'> Mean</span></b> to improve the fit. NB: The <span
1550class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1551"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1552minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1553style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1554mso-hansi-theme-font:minor-latin'> Mean</span></b> is a radius so its value is
1555roughly œ the <b style='mso-bidi-font-weight:normal'><span style='font-family:
1556"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1557minor-latin'>Size Distribution</span></b> result. The sliders cover 2 orders of
1558magnitude; their range is reset if a value is entered in the value field. After
1559changing <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1560style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1561mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:
1562normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1563minor-latin;mso-hansi-theme-font:minor-latin'> Mean</span></b> to <b
1564style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1565mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>700</span></b>
1566and <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1567style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1568mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:
1569normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1570minor-latin;mso-hansi-theme-font:minor-latin'> Volume</span></b> to <b
1571style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1572mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.0953</span></b>
1573my plot is</p>
1574
1575<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1576 id="Picture_x0020_30" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:441.75pt;
1577 height:378.75pt;visibility:visible;mso-wrap-style:square'>
1578 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image035.png"
1579  o:title=""/>
1580</v:shape><![endif]--><![if !vml]><img width=589 height=505
1581src="Fitting%20Small%20Angle%20Scattering%20Data_files/image009.png" v:shapes="Picture_x0020_30"><![endif]></span></p>
1582
1583<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1584
1585<p class=MsoNormal>There is an obvious discrepancy at low Q and a much less
1586obvious one at Q~0.03-4Å<sup>-1</sup>; the latter is responsible for the ~150Å
1587peak in the <b style='mso-bidi-font-weight:normal'><span style='font-family:
1588"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1589minor-latin'>Size Distribution</span></b> result. Do another <b
1590style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1591mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models/Add</span></b>
1592to include it. The data window now shows two components</p>
1593
1594<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1595 id="Picture_x0020_31" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:468pt;
1596 height:398.25pt;visibility:visible;mso-wrap-style:square'>
1597 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image037.png"
1598  o:title=""/>
1599</v:shape><![endif]--><![if !vml]><img width=624 height=531
1600src="Fitting%20Small%20Angle%20Scattering%20Data_files/image010.png" v:shapes="Picture_x0020_31"><![endif]></span></p>
1601
1602<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1603
1604<p class=MsoNormal>Note the <b style='mso-bidi-font-weight:normal'><span
1605style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1606mso-hansi-theme-font:minor-latin'>Material</span></b> for the new one is preset
1607to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1608mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Alumina</span></b>
1609to save you the easily forgotten step of setting it. Change <span class=SpellE><b
1610style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1611mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1612style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1613mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Mean</span></b>
1614to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1615mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>75</span></b>
1616(i.e. œ of 150) and reduce <span class=SpellE><b style='mso-bidi-font-weight:
1617normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1618minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1619style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1620mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Volume</span></b>
1621to make the green curve better match the data (you can inset ‘<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'>0</span></b>’s
1624in the value &amp; play with the slider – something like <b style='mso-bidi-font-weight:
1625normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1626minor-latin;mso-hansi-theme-font:minor-latin'>0.0003</span></b> looks good). My
1627fit looked like</p>
1628
1629<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1630 id="Picture_x0020_32" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:435pt;
1631 height:372.75pt;visibility:visible;mso-wrap-style:square'>
1632 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image039.png"
1633  o:title=""/>
1634</v:shape><![endif]--><![if !vml]><img width=580 height=497
1635src="Fitting%20Small%20Angle%20Scattering%20Data_files/image011.png" v:shapes="Picture_x0020_32"><![endif]></span></p>
1636
1637<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1638
1639<p class=MsoNormal>Finally we need to deal with the low Q region – this is
1640probably due to some agglomeration of the 1300Å articles which is best
1641described by a pure <span class=SpellE>Porod</span> power law scattering model.
1642Do another <b style='mso-bidi-font-weight:normal'><span style='font-family:
1643"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1644minor-latin'>Models/Add</span></b> and change the <b style='mso-bidi-font-weight:
1645normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1646minor-latin;mso-hansi-theme-font:minor-latin'>Distribution </span></b>selection
1647to <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1648style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1649mso-hansi-theme-font:minor-latin'>Porod</span></b></span>. The third component
1650is then (I’ve shrunk the window &amp; moved the scroll bar).</p>
1651
1652<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1653 id="Picture_x0020_33" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:468pt;
1654 height:313.5pt;visibility:visible;mso-wrap-style:square'>
1655 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image041.png"
1656  o:title=""/>
1657</v:shape><![endif]--><![if !vml]><img width=624 height=418
1658src="Fitting%20Small%20Angle%20Scattering%20Data_files/image012.png" v:shapes="Picture_x0020_33"><![endif]></span></p>
1659
1660<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1661
1662<p class=MsoNormal>The green curve on the plot looks very poor</p>
1663
1664<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1665 id="Picture_x0020_34" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:444pt;
1666 height:380.25pt;visibility:visible;mso-wrap-style:square'>
1667 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image043.png"
1668  o:title=""/>
1669</v:shape><![endif]--><![if !vml]><img width=592 height=507
1670src="Fitting%20Small%20Angle%20Scattering%20Data_files/image013.png" v:shapes="Picture_x0020_34"><![endif]></span></p>
1671
1672<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1673
1674<p class=MsoNormal>Not to worry, all the problem is in the <span class=SpellE>Porod</span>
1675component variables. Remembering that this is likely to be an agglomeration of
16761300Å particles; set the <span class=SpellE><b style='mso-bidi-font-weight:
1677normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1678minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1679style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1680mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Cutoff</span></b>
1681to that value. That immediately restores the higher Q portion of the fit.</p>
1682
1683<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1684 id="Picture_x0020_35" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:468pt;
1685 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1686 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image045.png"
1687  o:title=""/>
1688</v:shape><![endif]--><![if !vml]><img width=624 height=535
1689src="Fitting%20Small%20Angle%20Scattering%20Data_files/image014.png" v:shapes="Picture_x0020_35"><![endif]></span></p>
1690
1691<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1692
1693<p class=MsoNormal>Next use the <span class=SpellE><b style='mso-bidi-font-weight:
1694normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1695minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1696style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1697mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> P</span></b>
1698(power law exponent) slider to adjust the fit. In this case setting <span
1699class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1700"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1701minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1702style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1703mso-hansi-theme-font:minor-latin'> P</span></b> to ~<b style='mso-bidi-font-weight:
1704normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1705minor-latin;mso-hansi-theme-font:minor-latin'>3.25</span></b> gives a pretty
1706good fit without needing to adjust the <span class=SpellE><b style='mso-bidi-font-weight:
1707normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1708minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1709style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1710mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> B</span></b>
1711<span class=SpellE>prefactor</span>.</p>
1712
1713<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1714 id="Picture_x0020_36" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:468pt;
1715 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1716 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image047.png"
1717  o:title=""/>
1718</v:shape><![endif]--><![if !vml]><img width=624 height=535
1719src="Fitting%20Small%20Angle%20Scattering%20Data_files/image015.png" v:shapes="Picture_x0020_36"><![endif]></span></p>
1720
1721<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1722
1723<p class=MsoNormal>Finally, you can refine these coefficients to find the best
1724fit to the data. As a beginner, I’d start by refining just the two <span
1725class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1726"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1727minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1728style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1729mso-hansi-theme-font:minor-latin'> Volume</span></b> and the <span
1730class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1731"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1732minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1733style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1734mso-hansi-theme-font:minor-latin'> B</span></b> along with the <b
1735style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1736mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>
1737parameter (one might be able to refine “everything” at once, but then again it
1738might not work). Check the <b style='mso-bidi-font-weight:normal'><span
1739style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1740mso-hansi-theme-font:minor-latin'>Refine?</span></b> <span class=GramE>boxes</span>
1741for these parameters. Do <b style='mso-bidi-font-weight:normal'><span
1742style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1743mso-hansi-theme-font:minor-latin'>Models/Fit </span></b>to do the least squares
1744refinement; convergence will occur very quickly. NB: if the refinement messes
1745up, you can recover the previous result; do <b style='mso-bidi-font-weight:
1746normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1747minor-latin;mso-hansi-theme-font:minor-latin'>Models/Undo</span></b> to
1748recover. Then add the two <span class=SpellE><b style='mso-bidi-font-weight:
1749normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1750minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1751style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1752mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Mean</span></b>
1753and <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1754style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1755mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:
1756normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1757minor-latin;mso-hansi-theme-font:minor-latin'> P</span></b> parameters to the
1758refinement, again convergence is easily obtained. Finally, add the two <span
1759class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1760"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1761minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1762style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1763mso-hansi-theme-font:minor-latin'> <span class=SpellE>StdDev</span></span></b>
1764and <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1765style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1766mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:
1767normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1768minor-latin;mso-hansi-theme-font:minor-latin'> Cutoff</span></b> parameters (a
1769total of ten) to the list. The result is a really nice fit to the data with
1770reasonable values; the console window shows the full results of the refinement</p>
1771
1772<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1773 id="Picture_x0020_37" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt;
1774 height:196.5pt;visibility:visible;mso-wrap-style:square'>
1775 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image049.png"
1776  o:title=""/>
1777</v:shape><![endif]--><![if !vml]><img width=624 height=262
1778src="Fitting%20Small%20Angle%20Scattering%20Data_files/image016.png" v:shapes="Picture_x0020_37"><![endif]></span></p>
1779
1780<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1781
1782<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1783 id="Picture_x0020_38" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:429pt;
1784 height:367.5pt;visibility:visible;mso-wrap-style:square'>
1785 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image051.png"
1786  o:title=""/>
1787</v:shape><![endif]--><![if !vml]><img width=572 height=490
1788src="Fitting%20Small%20Angle%20Scattering%20Data_files/image024.png" v:shapes="Picture_x0020_38"><![endif]></span></p>
1789
1790<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1791
1792<p class=MsoNormal>If you had done a <b style='mso-bidi-font-weight:normal'><span
1793style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1794mso-hansi-theme-font:minor-latin'>Size Distribution</span></b> analysis, these
1795results are plotted as component curves on that plot as well</p>
1796
1797<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1798 id="Picture_x0020_39" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:468pt;
1799 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1800 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image053.png"
1801  o:title=""/>
1802</v:shape><![endif]--><![if !vml]><img width=624 height=535
1803src="Fitting%20Small%20Angle%20Scattering%20Data_files/image025.png" v:shapes="Picture_x0020_39"><![endif]></span></p>
1804
1805<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1806
1807<p class=MsoNormal>This is the sort of agreement one should expect between the best
1808log normal fit and the size distribution. To save these results you must do <b
1809style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1810mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Save
1811project </span></b>in the main <b style='mso-bidi-font-weight:normal'><span
1812style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1813mso-hansi-theme-font:minor-latin'>GSAS-II data tree</span></b> menu.</p>
1814
1815<h2>Step 6 Creation of a Unified <span class=SpellE>Guinier-Porod</span> Model</h2>
1816
1817<p class=MsoNormal>For the Unified model there is assumed to be particles with some
1818radius of gyration (<span class=SpellE>Guinier</span> model) with a power law
1819distribution tail (<span class=SpellE>Porod</span> model). This can be set for
1820your model by changing the <b style='mso-bidi-font-weight:normal'><span
1821style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1822mso-hansi-theme-font:minor-latin'>Distribution</span></b> for the first two
1823components to <b style='mso-bidi-font-weight:normal'><span style='font-family:
1824"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1825minor-latin'>Unified</span></b>. NB: the log normal coefficients are not lost
1826by this step; they can be recovered by simply changing the <b style='mso-bidi-font-weight:
1827normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1828minor-latin;mso-hansi-theme-font:minor-latin'>Distribution</span></b> back to <span
1829class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1830"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1831minor-latin'>LogNormal</span></b></span>. The data window values give the
1832defaults for these components</p>
1833
1834<p class=MsoNormal><span style='mso-no-proof:yes'><span
1835style='mso-spacerun:yes'> </span><!--[if gte vml 1]><v:shape id="Picture_x0020_40"
1836 o:spid="_x0000_i1030" type="#_x0000_t75" style='width:468pt;height:459.75pt;
1837 visibility:visible;mso-wrap-style:square'>
1838 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image026.png"
1839  o:title=""/>
1840</v:shape><![endif]--><![if !vml]><img width=624 height=613
1841src="Fitting%20Small%20Angle%20Scattering%20Data_files/image027.png" v:shapes="Picture_x0020_40"><![endif]></span></p>
1842
1843<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1844
1845<p class=MsoNormal>And the plot shows a poor fit</p>
1846
1847<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1848 id="Picture_x0020_41" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:468pt;
1849 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1850 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image028.png"
1851  o:title=""/>
1852</v:shape><![endif]--><![if !vml]><img width=624 height=535
1853src="Fitting%20Small%20Angle%20Scattering%20Data_files/image055.png" v:shapes="Picture_x0020_41"><![endif]></span></p>
1854
1855<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1856
1857<p class=MsoNormal>First, change the <span class=SpellE><b style='mso-bidi-font-weight:
1858normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1859minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1860style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1861mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> <span
1862class=SpellE>Rg</span></span></b> values to be about œ the <b style='mso-bidi-font-weight:
1863normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1864minor-latin;mso-hansi-theme-font:minor-latin'>Size Distribution</span></b>
1865results (e.g. <b style='mso-bidi-font-weight:normal'><span style='font-family:
1866"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1867minor-latin'>700</span></b> &amp; <b style='mso-bidi-font-weight:normal'><span
1868style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1869mso-hansi-theme-font:minor-latin'>75</span></b>), then set the <span
1870class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1871"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1872minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1873style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1874mso-hansi-theme-font:minor-latin'> Cutoff</span></b> value for the <span
1875class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1876"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1877minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1878style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1879mso-hansi-theme-font:minor-latin'> <span class=SpellE>Rg</span></span></b>=700
1880one to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1881mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>100</span></b>.
1882Next, change the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1883style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1884mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:
1885normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1886minor-latin;mso-hansi-theme-font:minor-latin'> G</span></b> for the <span
1887class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1888"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1889minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1890style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1891mso-hansi-theme-font:minor-latin'> <span class=SpellE>Rg</span>=700</span></b>
1892one to be about the Intensity value for the lower Q bump in the data (~<b
1893style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1894mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>1.0e6</span></b>).
1895Finally, reduce the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1896style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1897mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:
1898normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1899minor-latin;mso-hansi-theme-font:minor-latin'> G</span></b> value for the <span
1900class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1901"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1902minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1903style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1904mso-hansi-theme-font:minor-latin'> <span class=SpellE>Rg</span>=75</span></b>
1905component to get the best fit to the data (~<b style='mso-bidi-font-weight:
1906normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1907minor-latin;mso-hansi-theme-font:minor-latin'>210</span></b>). The data window
1908looks like</p>
1909
1910<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1911 id="Picture_x0020_42" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:446.25pt;
1912 height:438.75pt;visibility:visible;mso-wrap-style:square'>
1913 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image056.png"
1914  o:title=""/>
1915</v:shape><![endif]--><![if !vml]><img width=595 height=585
1916src="Fitting%20Small%20Angle%20Scattering%20Data_files/image057.png" v:shapes="Picture_x0020_42"><![endif]></span></p>
1917
1918<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1919
1920<p class=MsoNormal>And the plot looks like</p>
1921
1922<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1923 id="Picture_x0020_43" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:468pt;
1924 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1925 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image058.png"
1926  o:title=""/>
1927</v:shape><![endif]--><![if !vml]><img width=624 height=535
1928src="Fitting%20Small%20Angle%20Scattering%20Data_files/image059.png" v:shapes="Picture_x0020_43"><![endif]></span></p>
1929
1930<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1931
1932<p class=MsoNormal>This is probably close enough to do a refinement. Select <b
1933style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1934mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Refine?</span></b>
1935For <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1936style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1937mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:
1938normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1939minor-latin;mso-hansi-theme-font:minor-latin'> G</span></b>, <span
1940class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1941"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1942minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1943style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1944mso-hansi-theme-font:minor-latin'> <span class=SpellE>Rg</span></span></b> and <span
1945class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1946"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1947minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1948style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1949mso-hansi-theme-font:minor-latin'> B</span></b> for both components (the <span
1950class=SpellE><b style='mso-bidi-font-weight:normal'><span style='font-family:
1951"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1952minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:normal'><span
1953style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1954mso-hansi-theme-font:minor-latin'> B</span></b>, <span class=SpellE><b
1955style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1956mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1957style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1958mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> P</span></b>
1959and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1960mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Background
1961Refine?</span></b> boxes should also be checked). Then do <b style='mso-bidi-font-weight:
1962normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1963minor-latin;mso-hansi-theme-font:minor-latin'>Models/Fit</span></b>; it should
1964rapidly converge to give in the console window</p>
1965
1966<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1967 id="Picture_x0020_44" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:449.25pt;
1968 height:198pt;visibility:visible;mso-wrap-style:square'>
1969 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image060.png"
1970  o:title=""/>
1971</v:shape><![endif]--><![if !vml]><img width=599 height=264
1972src="Fitting%20Small%20Angle%20Scattering%20Data_files/image061.png" v:shapes="Picture_x0020_44"><![endif]></span></p>
1973
1974<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1975
1976<p class=MsoNormal>And the closeness of the fit to the data in the plot is</p>
1977
1978<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1979 id="Picture_x0020_45" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:439.5pt;
1980 height:376.5pt;visibility:visible;mso-wrap-style:square'>
1981 <v:imagedata src="Fitting%20Small%20Angle%20Scattering%20Data_files/image062.png"
1982  o:title=""/>
1983</v:shape><![endif]--><![if !vml]><img width=586 height=502
1984src="Fitting%20Small%20Angle%20Scattering%20Data_files/image063.png" v:shapes="Picture_x0020_45"><![endif]></span></p>
1985
1986<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1987
1988<p class=MsoNormal>This fit is almost as close as the log normal one done
1989earlier. However, the <span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1990style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1991mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b style='mso-bidi-font-weight:
1992normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1993minor-latin;mso-hansi-theme-font:minor-latin'> <span class=SpellE>Rg</span></span></b>
1994values are a bit less than the corresponding <span class=SpellE><b
1995style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1996mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1997style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1998mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Mean</span></b>
1999values obtained earlier. Also note that this model makes no reference to the
2000substance contrast used earlier (the <b style='mso-bidi-font-weight:normal'><span
2001style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2002mso-hansi-theme-font:minor-latin'>Size Distribution</span></b> plot will not
2003have curves calculated from this model). To save these results you must do <b
2004style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2005mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>File/Save
2006project </span></b>in the main <b style='mso-bidi-font-weight:normal'><span
2007style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2008mso-hansi-theme-font:minor-latin'>GSAS-II data tree</span></b> window.</p>
2009
2010<p class=MsoNormal>This concludes the SASD modeling tutorial.</p>
2011
2012<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2013
2014<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2015
2016</div>
2017
2018</body>
2019
2020</html>
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