source: Tutorials/SAseqref/Sequential Refinement of Small Angle Scattering Data.htm @ 3553

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finish web tutorials for now

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414  <w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
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"
422   Name="List Paragraph"/>
423  <w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
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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1216
1217<body lang=EN-US link=blue vlink=purple style='tab-interval:.5in'>
1218
1219<div class=WordSection1>
1220
1221<h1><strong><span style='mso-bidi-font-weight:normal'>Sequential Refinement of
1222Small Angle Scattering Data</span><o:p></o:p></strong></h1>
1223
1224<P><B>A video version of this tutorial is available at
1225<A href="https://anl.box.com/v/SequentialRefinementofSmallAng" target="_blank">
1226https://anl.box.com/v/SequentialRefinementofSmallAng</A></B></P>
1227
1228 
1229<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'>In
1230this tutorial you will fit USAXS small angle scattering data for “<span
1231class=SpellE>Ludox</span>” colloidal silica (Aldrich, LUDOX TM-50?) prepared in
1232a range of dilutions to demonstrate the sequential refinement technique in
1233GSAS-II for SASD and demonstrate fitting with a hard sphere structure factor
1234for non-dilute systems.<span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1235minor-latin;mso-bidi-font-weight:bold;mso-bidi-font-style:italic'><o:p></o:p></span></p>
1236
1237<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1238
1239<h2>Step 1: read in the data files</h2>
1240
1241<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1242style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
1243style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
1244the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1245mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1246minor-latin'>Import/Small Angle Data/from q (A-1) step X-ray QIE data file</span></b>
1247menu item to read the data files into GSAS-II. This read option is set to read
1248three column small angle scattering data (SASD) as Q in Å<sup>-1</sup>,
1249intensity and estimated standard deviation in intensity; there may be a header
1250with metadata information in the front of this file.<span
1251style='mso-spacerun:yes'>  </span>It will read multiple files from a single
1252directory. Change the file directory to <span class=SpellE><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;mso-bidi-theme-font:minor-latin'>SAseqref</span></b></span><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-theme-font:
1257minor-latin'>/data</span></b><span style='font-family:"Calibri",sans-serif;
1258mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1259minor-latin'> to find the files.</span></p>
1260
1261<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1262style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
1263style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
1264the six<span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1265mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'> data</span>
1266files with ‘<span class=SpellE><b style='mso-bidi-font-weight:normal'><span
1267style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1268mso-hansi-theme-font:minor-latin'>Ludox</span></b></span>’ in their name in the
1269first dialog and press <b style='mso-bidi-font-weight:normal'><span
1270style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1271mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Open</span></b>.
1272All six will immediately be read into GSAS-II; you will have to select the <b
1273style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1274mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file
1275(*.*)</span></b> filter to see them.</p>
1276
1277<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
1278
1279<p class=MsoNormal>At this point the <b style='mso-bidi-font-weight:normal'><span
1280style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1281mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>GSAS-II data
1282tree</span></b> window will have several entries and the plot window will show
1283the SASD pattern for one as a log-log plot of intensity vs. Q; enter ‘<b
1284style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1285mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>m</span></b>’
1286on the plot. Now all are shown; one shows error bars (<b style='mso-bidi-font-weight:
1287normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1288minor-latin;mso-hansi-theme-font:minor-latin'>SASD S49_Ludox6_1pct.dat</span></b>)
1289as it is the selected tree entry and the others as lines.</p>
1290
1291<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
1292 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
1293 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1294 <v:stroke joinstyle="miter"/>
1295 <v:formulas>
1296  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
1297  <v:f eqn="sum @0 1 0"/>
1298  <v:f eqn="sum 0 0 @1"/>
1299  <v:f eqn="prod @2 1 2"/>
1300  <v:f eqn="prod @3 21600 pixelWidth"/>
1301  <v:f eqn="prod @3 21600 pixelHeight"/>
1302  <v:f eqn="sum @0 0 1"/>
1303  <v:f eqn="prod @6 1 2"/>
1304  <v:f eqn="prod @7 21600 pixelWidth"/>
1305  <v:f eqn="sum @8 21600 0"/>
1306  <v:f eqn="prod @7 21600 pixelHeight"/>
1307  <v:f eqn="sum @10 21600 0"/>
1308 </v:formulas>
1309 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1310 <o:lock v:ext="edit" aspectratio="t"/>
1311</v:shapetype><v:shape id="Picture_x0020_33" o:spid="_x0000_i1055" type="#_x0000_t75"
1312 style='width:468pt;height:401.25pt;visibility:visible;mso-wrap-style:square'>
1313 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image002.png"
1314  o:title=""/>
1315</v:shape><![endif]--><![if !vml]><img width=624 height=535
1316src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image005.png"
1317v:shapes="Picture_x0020_33"><![endif]></span></p>
1318
1319<h2><a name="_Ref386704789">Step 2: Set Limits</a></h2>
1320
1321<p class=MsoNormal>For this step we will reposition the limits to exclude the
1322low-Q (&lt;10<sup>-3</sup>) part of the patterns which do not seem to follow
1323the sequence evident in the 10<sup>-2</sup> – 10<sup>-1</sup> part. Select <b
1324style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1325mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Limits</span></b>
1326under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1327mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD
1328S35_Ludox1_40pct.dat</span></b> from the GSAS-II tree. Set the lower limit using
1329the cursor on the plot by picking a point somewhere in the flat region at
1330Q~3x10<sup>-3</sup> with the left mouse button. The limits window should look
1331something like</p>
1332
1333<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1334 id="Picture_x0020_34" o:spid="_x0000_i1054" type="#_x0000_t75" style='width:408pt;
1335 height:306.75pt;visibility:visible;mso-wrap-style:square'>
1336 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image007.png"
1337  o:title=""/>
1338</v:shape><![endif]--><![if !vml]><img width=544 height=409
1339src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image007.png"
1340v:shapes="Picture_x0020_34"><![endif]></span><span
1341style='mso-spacerun:yes'> </span></p>
1342
1343<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1344
1345<p class=MsoNormal>To copy these limits to the other data sets use the <b
1346style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1347mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
1348Limits/Copy</span></b> command from the data window menu; a popup window will
1349give the selection of targets.<br>
1350<span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35"
1351 o:spid="_x0000_i1053" type="#_x0000_t75" style='width:216.75pt;height:254.25pt;
1352 visibility:visible;mso-wrap-style:square'>
1353 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image008.png"
1354  o:title=""/>
1355</v:shape><![endif]--><![if !vml]><img width=289 height=339
1356src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image008.png"
1357v:shapes="Picture_x0020_35"><![endif]></span></p>
1358
1359<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1360
1361<p class=MsoNormal>Do <b style='mso-bidi-font-weight:normal'><span
1362style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1363mso-hansi-theme-font:minor-latin'>Set All</span></b> (all boxes will be
1364checked) and then press <b style='mso-bidi-font-weight:normal'><span
1365style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1366mso-hansi-theme-font:minor-latin'>OK</span></b> to do the copy.</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'>Two substances need to be
1371defined for your sample to give the anticipated scattering contrast; in this
1372case one is silica and the other is water. Parameters for a number of
1373substances are defined in the file </span><b style='mso-bidi-font-weight:normal'><span
1374style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1375mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1376style='mso-no-proof:yes'>. You can add your own substances to this or better
1377put them in </span><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;mso-no-proof:yes'>UserSubstances.py</span></b><span
1380style='mso-no-proof:yes'>; this is read after Substances.py when you load
1381substances for your selection. </span>Select <b style='mso-bidi-font-weight:
1382normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1383minor-latin;mso-hansi-theme-font:minor-latin'>Substances</span></b> from the
1384GSAS-II tree. Then do <span class=GramE><b style='mso-bidi-font-weight:normal'><span
1385style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1386mso-hansi-theme-font:minor-latin'>Edit</span></b></span><b style='mso-bidi-font-weight:
1387normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1388minor-latin;mso-hansi-theme-font:minor-latin'> substance/Load substance</span></b>
1389from the menu; a popup window will appear with possible selections</p>
1390
1391<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1392 id="Picture_x0020_3" o:spid="_x0000_i1052" type="#_x0000_t75" style='width:259.5pt;
1393 height:252pt;visibility:visible;mso-wrap-style:square'>
1394 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image004.png"
1395  o:title=""/>
1396</v:shape><![endif]--><![if !vml]><img width=346 height=336
1397src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image004.png"
1398v:shapes="Picture_x0020_3"><![endif]><o:p></o:p></span></p>
1399
1400<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1401
1402<p class=MsoNormal>Notice that silica is not one of the choices; we will add it
1403in a moment (a-Quartz is but let’s ignore that). Select <b style='mso-bidi-font-weight:
1404normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1405minor-latin;mso-hansi-theme-font:minor-latin'>Water</span></b> and press <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'>OK</span></b>;
1408the relevant data for water (and vacuum) are displayed next</p>
1409
1410<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1411 id="Picture_x0020_36" o:spid="_x0000_i1051" type="#_x0000_t75" style='width:408pt;
1412 height:306.75pt;visibility:visible;mso-wrap-style:square'>
1413 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image029.png"
1414  o:title=""/>
1415</v:shape><![endif]--><![if !vml]><img width=544 height=409
1416src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image029.png"
1417v:shapes="Picture_x0020_36"><![endif]></span><span
1418style='mso-spacerun:yes'> </span></p>
1419
1420<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1421
1422<p class=MsoNormal>If desired, you can load/add as many substances as you want
1423to this list; you can also delete any of them (except vacuum or unit scatter).
1424The composition, volume occupied by the atoms in the composition and the
1425density are given for each substance. These can each be edited; the other
1426values will change accordingly. Since we are going to say that silica wasn’t in
1427the list of known substances, do <b style='mso-bidi-font-weight:normal'><span
1428style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1429mso-hansi-theme-font:minor-latin'>Edit substance/Add substance</span></b> to
1430create it; you will be asked for a name – enter <b style='mso-bidi-font-weight:
1431normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1432minor-latin;mso-hansi-theme-font:minor-latin'>silica</span></b> and then a
1433periodic table of the elements will be shown. Select <b style='mso-bidi-font-weight:
1434normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1435minor-latin;mso-hansi-theme-font:minor-latin'>Si</span></b> and <b
1436style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1437mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>O</span></b></p>
1438
1439<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1440 id="Picture_x0020_6" o:spid="_x0000_i1050" type="#_x0000_t75" style='width:435pt;
1441 height:270pt;visibility:visible;mso-wrap-style:square'>
1442 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image006.png"
1443  o:title=""/>
1444</v:shape><![endif]--><![if !vml]><img width=580 height=360
1445src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image006.png"
1446v:shapes="Picture_x0020_6"><![endif]></span><span
1447style='mso-spacerun:yes'> </span></p>
1448
1449<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1450
1451<p class=MsoNormal>They appear in red. Press <b style='mso-bidi-font-weight:
1452normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1453minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> and silica will be
1454added to your substance list</p>
1455
1456<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1457 id="_x0000_i1049" type="#_x0000_t75" style='width:408pt;height:306.75pt;
1458 visibility:visible;mso-wrap-style:square'>
1459 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image032.png"
1460  o:title=""/>
1461</v:shape><![endif]--><![if !vml]><img width=544 height=409
1462src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image032.png"
1463v:shapes="_x0000_i1049"><![endif]></span></p>
1464
1465<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1466
1467<p class=MsoNormal>Change the O-atom entry to <b style='mso-bidi-font-weight:
1468normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1469minor-latin;mso-hansi-theme-font:minor-latin'>2.0</span></b> and the density to
1470<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1471mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.65</span></b>,
1472on the section of data for silica;
1473the window will change each time giving new values and should finally show</p>
1474
1475<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1476 id="Picture_x0020_38" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:408pt;
1477 height:306.75pt;visibility:visible;mso-wrap-style:square'>
1478 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image040.png"
1479  o:title=""/>
1480</v:shape><![endif]--><![if !vml]><img width=544 height=409
1481src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image040.png"
1482v:shapes="Picture_x0020_38"><![endif]></span><span
1483style='mso-spacerun:yes'> </span></p>
1484
1485<p class=MsoNormal>From this information the scattering density and that as
1486affected by resonant scattering for the listed wavelength is displayed (the
1487wavelength can be changed in the <b style='mso-bidi-font-weight:normal'><span
1488style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1489mso-hansi-theme-font:minor-latin'>Instrument Parameters</span></b> GSAS-II tree
1490item if needed). The real density value is used for contrast calculations.</p>
1491
1492<p class=MsoNormal>Just as for Limits, this information needs to be copied to
1493the other SASD entries in the GSAS-II tree. Do <b style='mso-bidi-font-weight:
1494normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1495minor-latin;mso-hansi-theme-font:minor-latin'>Edit substance/Copy substances</span></b>
1496from the data window menu and follow the same selection procedure as you used
1497for limits above.</p>
1498
1499<h2><a name="_Ref386699210">Step 4: Set Sample parameters</a> </h2>
1500
1501<p class=MsoNormal><span style='mso-no-proof:yes'>As these data sets were
1502collected from a sequence of samples where there was some variable changed in
1503their preparation, it would be useful to have this information available to
1504GSAS-II for subsequent analysis. Select Sample parameters from the data tree.
1505It shows (for </span><b style='mso-bidi-font-weight:normal'><span
1506style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1507mso-hansi-theme-font:minor-latin'>SASD S49_Ludox6_1pct.dat)<o:p></o:p></span></b></p>
1508
1509<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1510 id="Picture_x0020_39" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:438pt;
1511 height:435.75pt;visibility:visible;mso-wrap-style:square'>
1512 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image041.png"
1513  o:title=""/>
1514</v:shape><![endif]--><![if !vml]><img width=584 height=581
1515src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image042.png"
1516v:shapes="Picture_x0020_39"><![endif]><o:p></o:p></span></p>
1517
1518<p class=MsoNormal><span style='mso-no-proof:yes'><o:p>&nbsp;</o:p></span></p>
1519
1520<p class=MsoNormal><span style='mso-no-proof:yes'>NB: we will not be needing to
1521select the </span><b style='mso-bidi-font-weight:normal'><span
1522style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1523mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Material</span></b><span
1524style='mso-no-proof:yes'> for this analysis; material selection is only
1525required for </span><b style='mso-bidi-font-weight:normal'><span
1526style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1527mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Size distribution</span></b><span
1528style='mso-no-proof:yes'> analysis. Notice that the last three column names can
1529be changed; pick the first one and change it to </span><b style='mso-bidi-font-weight:
1530normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1531minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>fraction</span></b><span
1532style='mso-no-proof:yes'>. Then enter </span><b style='mso-bidi-font-weight:
1533normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1534minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>0.01</span></b><span
1535style='mso-no-proof:yes'> which corresponds to the ‘</span><b style='mso-bidi-font-weight:
1536normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1537minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>1pct</span></b><span
1538style='mso-no-proof:yes'>’ in the file name. The data window should look like<o:p></o:p></span></p>
1539
1540<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1541 id="Picture_x0020_40" o:spid="_x0000_i1046" type="#_x0000_t75" style='width:447.75pt;
1542 height:445.5pt;visibility:visible;mso-wrap-style:square'>
1543 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image043.png"
1544  o:title=""/>
1545</v:shape><![endif]--><![if !vml]><img width=597 height=594
1546src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image043.png"
1547v:shapes="Picture_x0020_40"><![endif]><o:p></o:p></span></p>
1548
1549<p class=MsoNormal><span style='mso-no-proof:yes'><o:p>&nbsp;</o:p></span></p>
1550
1551<p class=MsoNormal><span style='mso-no-proof:yes'>Now do the same for the </span><b
1552style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1553mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:
1554yes'>Sample Parameters</span></b><span style='mso-no-proof:yes'> for the other
1555data sets putting in the correct fraction from the respective file names. If
1556you first </span><b style='mso-bidi-font-weight:normal'><span style='font-family:
1557"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1558minor-latin;mso-no-proof:yes'>Copy</span></b><span style='mso-no-proof:yes'>
1559this one to the others, that will save you the step of changing the names. You
1560will end up on the </span><b style='mso-bidi-font-weight:normal'><span
1561style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1562mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Sample parameters</span></b><span
1563style='mso-no-proof:yes'> page for </span><b style='mso-bidi-font-weight:normal'><span
1564style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1565mso-hansi-theme-font:minor-latin'>SASD S35_Ludox1_40pct.dat </span></b>GSAS-II
1566data tree.</p>
1567
1568<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1569 id="Picture_x0020_41" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:444pt;
1570 height:441.75pt;visibility:visible;mso-wrap-style:square'>
1571 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image044.png"
1572  o:title=""/>
1573</v:shape><![endif]--><![if !vml]><img width=592 height=589
1574src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image044.png"
1575v:shapes="Picture_x0020_41"><![endif]></span><span
1576style='mso-spacerun:yes'> </span><span style='mso-no-proof:yes'><o:p></o:p></span></p>
1577
1578<h2>Step 5: Set Model parameters </h2>
1579
1580<p class=MsoNormal>Looking at the data plot (key ‘<b style='mso-bidi-font-weight:
1581normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1582minor-latin;mso-hansi-theme-font:minor-latin'>m</span></b>’ to select a single
1583data set) for <b style='mso-bidi-font-weight:normal'><span style='font-family:
1584"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1585minor-latin'>SASD S35_Ludox1_40pct.dat</span></b>, one sees just one feature
1586with oscillations at higher Q. This is the signal for a non-dilute <span
1587class=SpellE>scatterer</span>. </p>
1588
1589<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1590 id="Picture_x0020_42" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:453pt;
1591 height:388.5pt;visibility:visible;mso-wrap-style:square'>
1592 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image045.png"
1593  o:title=""/>
1594</v:shape><![endif]--><![if !vml]><img width=604 height=518
1595src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image046.png"
1596v:shapes="Picture_x0020_42"><![endif]></span></p>
1597
1598<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1599
1600<p class=MsoNormal>Select <b style='mso-bidi-font-weight:normal'><span
1601style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1602mso-hansi-theme-font:minor-latin'>Models</span></b> from the GSASII data tree
1603under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1604mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD
1605S35_Ludox1_40pct.dat</span></b>, switch <b style='mso-bidi-font-weight:normal'><span
1606style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1607mso-hansi-theme-font:minor-latin'>Size dist.</span></b> to <b style='mso-bidi-font-weight:
1608normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1609minor-latin;mso-hansi-theme-font:minor-latin'>Particle fit</span></b>, and add
1610a reasonable value (<b style='mso-bidi-font-weight:normal'><span
1611style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1612mso-hansi-theme-font:minor-latin'>0.25</span></b>) for the <b style='mso-bidi-font-weight:
1613normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1614minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>; a
1615horizontal red line will appear. Next do <b style='mso-bidi-font-weight:normal'><span
1616style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1617mso-hansi-theme-font:minor-latin'>Models/Add</span></b>; the window will
1618display a default component; change the <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'>Material</span></b> to <b style='mso-bidi-font-weight:
1621normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1622minor-latin;mso-hansi-theme-font:minor-latin'>silica</span></b>. Also change
1623the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1624mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Matrix</span></b>
1625to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1626mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Water</span></b>;
1627the calculated contrast should be 175.60 10<sup>20</sup>cm<sup>-4</sup>. The
1628plot will show a green curve corresponding to the default values.</p>
1629
1630<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1631 id="Picture_x0020_43" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:450.75pt;
1632 height:386.25pt;visibility:visible;mso-wrap-style:square'>
1633 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image047.png"
1634  o:title=""/>
1635</v:shape><![endif]--><![if !vml]><img width=601 height=515
1636src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image048.png"
1637v:shapes="Picture_x0020_43"><![endif]></span></p>
1638
1639<p class=MsoNormal><span style='mso-no-proof:yes'><o:p>&nbsp;</o:p></span></p>
1640
1641<p class=MsoNormal>The default <span class=SpellE><b style='mso-bidi-font-weight:
1642normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1643minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1644style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1645mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Mean</span></b>
1646of <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1647mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>1e+03</span></b>
1648is too large, try something smaller and increase the <span class=SpellE><b
1649style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1650mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1651style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1652mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Volume</span></b>
1653(the sliders work well for this). Since this is a non-dilute system, change the
1654<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1655mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Structure
1656factor</span></b> to <b style='mso-bidi-font-weight:normal'><span
1657style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1658mso-hansi-theme-font:minor-latin'>Hard sphere</span></b> and set the <b
1659style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1660mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SF <span
1661class=SpellE>VolFr</span></span></b> to <b style='mso-bidi-font-weight:normal'><span
1662style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1663mso-hansi-theme-font:minor-latin'>0.4</span></b>. Your data window should look
1664something like</p>
1665
1666<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1667 id="Picture_x0020_44" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:468pt;
1668 height:276pt;visibility:visible;mso-wrap-style:square'>
1669 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image049.png"
1670  o:title=""/>
1671</v:shape><![endif]--><![if !vml]><img width=624 height=368
1672src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image050.png"
1673v:shapes="Picture_x0020_44"><![endif]></span></p>
1674
1675<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1676
1677<p class=MsoNormal>And the plot will be</p>
1678
1679<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1680 id="Picture_x0020_45" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:438.75pt;
1681 height:376.5pt;visibility:visible;mso-wrap-style:square'>
1682 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image051.png"
1683  o:title=""/>
1684</v:shape><![endif]--><![if !vml]><img width=585 height=502
1685src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image052.png"
1686v:shapes="Picture_x0020_45"><![endif]></span><br clear=all style='mso-special-character:
1687line-break'>
1688</p>
1689
1690<p class=MsoNormal>The calculated curve shows oscillations but they are not in
1691the right place and are too broad. Try the <span class=SpellE><b
1692style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1693mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1694style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1695mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> <span
1696class=SpellE>StdDev</span></span></b> slider and make it smaller; somewhere
1697about <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1698mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.132</span></b>
1699gives a curve with the right shape but too high. Reduce the <span class=SpellE><b
1700style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1701mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1702style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1703mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Volume</span></b>
1704to improve the match. Shift the <b style='mso-bidi-font-weight:normal'><span
1705style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1706mso-hansi-theme-font:minor-latin'>SF <span class=SpellE>Dist</span></span></b>
1707and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1708mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SF <span
1709class=SpellE>VolFr</span></span></b> as well to get the curves to match.
1710Carefully manipulate each of the sliders to see what effect they have on the
1711calculated curve. With some adjustments I got</p>
1712
1713<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1714 id="Picture_x0020_46" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:468pt;
1715 height:276pt;visibility:visible;mso-wrap-style:square'>
1716 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image053.png"
1717  o:title=""/>
1718</v:shape><![endif]--><![if !vml]><img width=624 height=368
1719src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image054.png"
1720v:shapes="Picture_x0020_46"><![endif]></span></p>
1721
1722<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1723
1724<p class=MsoNormal>to give a pretty nice initial fit.</p>
1725
1726<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1727 id="Picture_x0020_47" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:468pt;
1728 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1729 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image055.png"
1730  o:title=""/>
1731</v:shape><![endif]--><![if !vml]><img width=624 height=535
1732src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image056.png"
1733v:shapes="Picture_x0020_47"><![endif]></span></p>
1734
1735<h2>Step 6: Initial refinement</h2>
1736
1737<p class=MsoNormal>We can be brave and set all six <b style='mso-bidi-font-weight:
1738normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1739minor-latin;mso-hansi-theme-font:minor-latin'>Refine?</span></b> boxes (NB: the
1740one for <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1741mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Matrix
1742Volume fraction</span></b> currently does not operate – ignore it). Then do <b
1743style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1744mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models/Fit</span></b>;
1745the least squares very quickly minimizes to give</p>
1746
1747<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1748 id="Picture_x0020_48" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:468pt;
1749 height:276pt;visibility:visible;mso-wrap-style:square'>
1750 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image057.png"
1751  o:title=""/>
1752</v:shape><![endif]--><![if !vml]><img width=624 height=368
1753src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image058.png"
1754v:shapes="Picture_x0020_48"><![endif]></span></p>
1755
1756<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1757
1758<p class=MsoNormal>The console window lists the results</p>
1759
1760<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1761 id="Picture_x0020_49" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:468pt;
1762 height:149.25pt;visibility:visible;mso-wrap-style:square'>
1763 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image059.png"
1764  o:title=""/>
1765</v:shape><![endif]--><![if !vml]><img width=624 height=199
1766src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image060.png"
1767v:shapes="Picture_x0020_49"><![endif]></span></p>
1768
1769<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1770
1771<p class=MsoNormal>And the plot shows the fit graphically</p>
1772
1773<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1774 id="Picture_x0020_50" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt;
1775 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1776 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image061.png"
1777  o:title=""/>
1778</v:shape><![endif]--><![if !vml]><img width=624 height=535
1779src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image062.png"
1780v:shapes="Picture_x0020_50"><![endif]></span></p>
1781
1782<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1783
1784<p class=MsoNormal>The fit is OK except for a region Q~0.03Å<sup>-1</sup>; this
1785is probably due to a failure of the simple hard sphere model in this
1786concentrated system.</p>
1787
1788<h2>Step 7: Sequential refinement</h2>
1789
1790<p class=MsoNormal>We are now ready to try a sequential refinement starting
1791with this fit for the 1<sup>st</sup> data set. Do <b style='mso-bidi-font-weight:
1792normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1793minor-latin;mso-hansi-theme-font:minor-latin'>Models/Sequential fit</span></b>;
1794a dialog box will appear for selection of the data sets.</p>
1795
1796<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1797 id="Picture_x0020_51" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:223.5pt;
1798 height:289.5pt;visibility:visible;mso-wrap-style:square'>
1799 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image063.png"
1800  o:title=""/>
1801</v:shape><![endif]--><![if !vml]><img width=298 height=386
1802src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image063.png"
1803v:shapes="Picture_x0020_51"><![endif]></span></p>
1804
1805<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1806
1807<p class=MsoNormal>Press <b style='mso-bidi-font-weight:normal'><span
1808style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1809mso-hansi-theme-font:minor-latin'>Set <span class=GramE>All</span></span></b>,
1810all boxes will be checked showing selection of the data sets. This also allows
1811you to instruct the sequential refinement to start at the last data set and
1812proceed backwards through them (<b style='mso-bidi-font-weight:normal'><span
1813style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1814mso-hansi-theme-font:minor-latin'>Reverse order</span></b>). It also allows you
1815to instruct the sequential refinement to use the current parameters as starting
1816values for the next data set. This works in either direction and facilitates
1817the initial sequential refinements. NB: some sequential refinements do not work
1818well in both directions; in this particular case starting with a fitted 1%
1819pattern and going in reverse through the data fails on the 5% data set.
1820Apparently the change in parameters is too great for the least squares to
1821handle; going in the forward direction works just fine (as you will see next).
1822Select <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1823mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Copy to next</span></b>
1824and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1825mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>;
1826the sequential refinement will proceed very rapidly displaying results for each
1827data set on the console and finally ending by displaying the <b
1828style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1829mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Sequential refinement
1830results.<o:p></o:p></span></b></p>
1831
1832<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1833 id="Picture_x0020_53" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:459pt;
1834 height:234pt;visibility:visible;mso-wrap-style:square'>
1835 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image064.png"
1836  o:title=""/>
1837</v:shape><![endif]--><![if !vml]><img width=612 height=312
1838src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image065.png"
1839v:shapes="Picture_x0020_53"><![endif]></span></p>
1840
1841<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1842
1843<p class=MsoNormal>Note the comment in the plot status bar: double click on the
1844<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1845mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0<span
1846class=GramE>;Volume</span></span></b> and a new plot will appear.</p>
1847
1848<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1849 id="Picture_x0020_54" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt;
1850 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1851 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image066.png"
1852  o:title=""/>
1853</v:shape><![endif]--><![if !vml]><img width=624 height=535
1854src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image067.png"
1855v:shapes="Picture_x0020_54"><![endif]></span></p>
1856
1857<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1858
1859<p class=MsoNormal>Each point has an error bar extracted from the least squares
1860– it represents a 1 &#963; variation in the value. Now press the <b
1861style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1862mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>s</span></b>
1863key (or select <b style='mso-bidi-font-weight:normal'><span style='font-family:
1864"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1865minor-latin'>s</span></b> from the <b style='mso-bidi-font-weight:normal'><span
1866style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1867mso-hansi-theme-font:minor-latin'>K</span></b> box); a dialog box will appear with
1868a selection of parameters to plot along the x-axis. Select <b style='mso-bidi-font-weight:
1869normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1870minor-latin;mso-hansi-theme-font:minor-latin'>fraction</span></b> and the plot
1871will be redrawn (it may require selection of another column &amp; then <b
1872style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1873mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0<span
1874class=GramE>;Volume</span></span></b> to make it appear).</p>
1875
1876<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1877 id="Picture_x0020_55" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:445.5pt;
1878 height:381.75pt;visibility:visible;mso-wrap-style:square'>
1879 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image068.png"
1880  o:title=""/>
1881</v:shape><![endif]--><![if !vml]><img width=594 height=509
1882src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image069.png"
1883v:shapes="Picture_x0020_55"><![endif]></span></p>
1884
1885<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1886
1887<p class=MsoNormal>It is gratifying how this relation between Volume and the composition
1888is linear. You can now determine the slope &amp; intercept (or fit to some
1889other function!) directly with GSAS-II; do <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'>Parametric Fit/Add equation</span></b> and
1892the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1893mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Expression
1894Editor</span></b> dialog box will appear.</p>
1895
1896<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1897 id="Picture_x0020_56" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:465pt;
1898 height:255pt;visibility:visible;mso-wrap-style:square'>
1899 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image070.png"
1900  o:title=""/>
1901</v:shape><![endif]--><![if !vml]><img width=620 height=340
1902src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image070.png"
1903v:shapes="Picture_x0020_56"><![endif]></span></p>
1904
1905<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1906
1907<p class=MsoNormal>The pull down in the upper left corner has two choices;
1908select <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1909mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Global</span></b>
1910and a new dialog box will appear giving you choices from the <b
1911style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1912mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Sequential
1913results</span></b> table. Select <b style='mso-bidi-font-weight:normal'><span
1914style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1915mso-hansi-theme-font:minor-latin'>0<span class=GramE>;Volume</span></span></b>
1916and the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1917mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Expression
1918Editor</span></b> will reappear.</p>
1919
1920<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1921 id="Picture_x0020_57" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:465pt;
1922 height:255pt;visibility:visible;mso-wrap-style:square'>
1923 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image071.png"
1924  o:title=""/>
1925</v:shape><![endif]--><![if !vml]><img width=620 height=340
1926src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image071.png"
1927v:shapes="Picture_x0020_57"><![endif]></span></p>
1928
1929<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1930
1931<p class=MsoNormal>Next enter the function you wish to use in fitting <b
1932style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1933mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0<span
1934class=GramE>:Volume</span></span></b>; enter <b style='mso-bidi-font-weight:
1935normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1936minor-latin;mso-hansi-theme-font:minor-latin'>m*<span class=SpellE>x+b</span></span></b>
1937(equation for a straight line). After a pause, the <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'>Expression Editor</span></b> will
1940be redrawn allowing you to assign <b style='mso-bidi-font-weight:normal'><span
1941style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1942mso-hansi-theme-font:minor-latin'>b</span></b>, <b style='mso-bidi-font-weight:
1943normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1944minor-latin;mso-hansi-theme-font:minor-latin'>m</span></b> &amp; <b
1945style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1946mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>x</span></b>.</p>
1947
1948<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1949 id="Picture_x0020_58" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:465pt;
1950 height:255pt;visibility:visible;mso-wrap-style:square'>
1951 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image072.png"
1952  o:title=""/>
1953</v:shape><![endif]--><![if !vml]><img width=620 height=340
1954src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image072.png"
1955v:shapes="Picture_x0020_58"><![endif]></span></p>
1956
1957<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1958
1959<p class=MsoNormal>For <b style='mso-bidi-font-weight:normal'><span
1960style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1961mso-hansi-theme-font:minor-latin'>b</span></b> &amp; <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'>m</span></b> select <b
1964style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1965mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Free</span></b>;
1966these will be the parameters for your fit. For <b style='mso-bidi-font-weight:
1967normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1968minor-latin;mso-hansi-theme-font:minor-latin'>x</span></b> select <b
1969style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1970mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Global</span></b>;
1971a new dialog box will appear giving you several choices.</p>
1972
1973<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1974 id="Picture_x0020_37" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:468pt;
1975 height:187.5pt;visibility:visible;mso-wrap-style:square'>
1976 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image037.png"
1977  o:title=""/>
1978</v:shape><![endif]--><![if !vml]><img width=624 height=250
1979src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image037.png"
1980v:shapes="Picture_x0020_37"><![endif]></span></p>
1981
1982<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1983
1984<p class=MsoNormal>Select the last line (<b style='mso-bidi-font-weight:normal'><span
1985style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1986mso-hansi-theme-font:minor-latin'>fraction…</span></b>); it will appear in
1987blue. Then press <b style='mso-bidi-font-weight:normal'><span style='font-family:
1988"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1989minor-latin'>OK</span></b>; the <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'>Expression Editor</span></b> will reappear
1992with more information.</p>
1993
1994<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1995 id="Picture_x0020_59" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:465pt;
1996 height:255pt;visibility:visible;mso-wrap-style:square'>
1997 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image073.png"
1998  o:title=""/>
1999</v:shape><![endif]--><![if !vml]><img width=620 height=340
2000src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image073.png"
2001v:shapes="Picture_x0020_59"><![endif]></span></p>
2002
2003<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2004
2005<p class=MsoNormal>Next press <b style='mso-bidi-font-weight:normal'><span
2006style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2007mso-hansi-theme-font:minor-latin'>OK</span></b>; the equation will be fitted to
2008the data and the results displayed on the console</p>
2009
2010<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2011 id="Picture_x0020_60" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:354pt;
2012 height:116.25pt;visibility:visible;mso-wrap-style:square'>
2013 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image074.png"
2014  o:title=""/>
2015</v:shape><![endif]--><![if !vml]><img width=472 height=155
2016src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image074.png"
2017v:shapes="Picture_x0020_60"><![endif]></span></p>
2018
2019<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2020
2021<p class=MsoNormal>And the plot shows the curve (in red) calculated from the
2022best fit, weighted by the <span class=SpellE>esds</span> on the data points, to
2023the model equation for a straight line.</p>
2024
2025<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2026 id="Picture_x0020_61" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt;
2027 height:401.25pt;visibility:visible;mso-wrap-style:square'>
2028 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image075.png"
2029  o:title=""/>
2030</v:shape><![endif]--><![if !vml]><img width=624 height=535
2031src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image076.png"
2032v:shapes="Picture_x0020_61"><![endif]></span></p>
2033
2034<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2035
2036<p class=MsoNormal>For this particular experiment there was an expectation that
2037the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2038mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Volume</span></b>s
2039obtained from the SASD model fits would match the makeup concentrations for
2040these samples so that the slope for this plot would be unity. One possible
2041explanation for the discrepancy is that the silica particles are partially
2042hydrated thus reducing the contrast from 175.6x10<sup>20</sup> cm<sup>-4</sup>
2043to something like 98x10<sup>20</sup>cm<sup>-4</sup>. This concludes the small
2044angle sequential fit tutorial; you may save the project.</p>
2045
2046</div>
2047
2048</body>
2049
2050</html>
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