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

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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><BL>
1225  <LI><B>A video version of this tutorial is available at
1226<A href="https://anl.box.com/v/SequentialRefinementofSmallAng" target="_blank">
1227https://anl.box.com/v/SequentialRefinementofSmallAng</A></B>
1228 <LI>Exercise files are found <A href="./data/" target="_blank">here</a>
1229</BL></P><P></P>
1230
1231 
1232<p class=MsoNormal style='mso-layout-grid-align:none;text-autospace:none'>In
1233this tutorial you will fit USAXS small angle scattering data for “<span
1234class=SpellE>Ludox</span>” colloidal silica (Aldrich, LUDOX TM-50?) prepared in
1235a range of dilutions to demonstrate the sequential refinement technique in
1236GSAS-II for SASD and demonstrate fitting with a hard sphere structure factor
1237for non-dilute systems.<span style='mso-fareast-font-family:Calibri;mso-fareast-theme-font:
1238minor-latin;mso-bidi-font-weight:bold;mso-bidi-font-style:italic'><o:p></o:p></span></p>
1239
1240<p class=MsoNormal>If you have not done so already, start GSAS-II.</p>
1241
1242<h2>Step 1: read in the data files</h2>
1243
1244<p class=MsoListParagraphCxSpFirst style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1245style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>1.<span
1246style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Use
1247the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1248mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1249minor-latin'>Import/Small Angle Data/from q (A-1) step X-ray QIE data file</span></b>
1250menu item to read the data files into GSAS-II. This read option is set to read
1251three column small angle scattering data (SASD) as Q in Å<sup>-1</sup>,
1252intensity and estimated standard deviation in intensity; there may be a header
1253with metadata information in the front of this file.<span
1254style='mso-spacerun:yes'>  </span>It will read multiple files from a single
1255directory. Change the file directory to <span class=SpellE><b style='mso-bidi-font-weight:
1256normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1257minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>SAseqref</span></b></span><b
1258style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1259mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1260minor-latin'>/data</span></b><span style='font-family:"Calibri",sans-serif;
1261mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:
1262minor-latin'> to find the files.</span></p>
1263
1264<p class=MsoListParagraphCxSpMiddle style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span
1265style='mso-fareast-font-family:"Times New Roman"'><span style='mso-list:Ignore'>2.<span
1266style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]>Select
1267the six<span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1268mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'> data</span>
1269files with ‘<span class=SpellE><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'>Ludox</span></b></span>’ in their name in the
1272first dialog and press <b style='mso-bidi-font-weight:normal'><span
1273style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1274mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>Open</span></b>.
1275All six will immediately be read into GSAS-II; you will have to select the <b
1276style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1277mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>any file
1278(*.*)</span></b> filter to see them.</p>
1279
1280<p class=MsoListParagraphCxSpLast><o:p>&nbsp;</o:p></p>
1281
1282<p class=MsoNormal>At this point the <b style='mso-bidi-font-weight:normal'><span
1283style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1284mso-hansi-theme-font:minor-latin;mso-bidi-theme-font:minor-latin'>GSAS-II data
1285tree</span></b> window will have several entries and the plot window will show
1286the SASD pattern for one as a log-log plot of intensity vs. Q; enter ‘<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'>m</span></b>’
1289on the plot. Now all are shown; one shows error bars (<b style='mso-bidi-font-weight:
1290normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1291minor-latin;mso-hansi-theme-font:minor-latin'>SASD S49_Ludox6_1pct.dat</span></b>)
1292as it is the selected tree entry and the others as lines.</p>
1293
1294<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
1295 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
1296 path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
1297 <v:stroke joinstyle="miter"/>
1298 <v:formulas>
1299  <v:f eqn="if lineDrawn pixelLineWidth 0"/>
1300  <v:f eqn="sum @0 1 0"/>
1301  <v:f eqn="sum 0 0 @1"/>
1302  <v:f eqn="prod @2 1 2"/>
1303  <v:f eqn="prod @3 21600 pixelWidth"/>
1304  <v:f eqn="prod @3 21600 pixelHeight"/>
1305  <v:f eqn="sum @0 0 1"/>
1306  <v:f eqn="prod @6 1 2"/>
1307  <v:f eqn="prod @7 21600 pixelWidth"/>
1308  <v:f eqn="sum @8 21600 0"/>
1309  <v:f eqn="prod @7 21600 pixelHeight"/>
1310  <v:f eqn="sum @10 21600 0"/>
1311 </v:formulas>
1312 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
1313 <o:lock v:ext="edit" aspectratio="t"/>
1314</v:shapetype><v:shape id="Picture_x0020_33" o:spid="_x0000_i1055" type="#_x0000_t75"
1315 style='width:468pt;height:401.25pt;visibility:visible;mso-wrap-style:square'>
1316 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image002.png"
1317  o:title=""/>
1318</v:shape><![endif]--><![if !vml]><img width=624 height=535
1319src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image005.png"
1320v:shapes="Picture_x0020_33"><![endif]></span></p>
1321
1322<h2><a name="_Ref386704789">Step 2: Set Limits</a></h2>
1323
1324<p class=MsoNormal>For this step we will reposition the limits to exclude the
1325low-Q (&lt;10<sup>-3</sup>) part of the patterns which do not seem to follow
1326the sequence evident in the 10<sup>-2</sup> – 10<sup>-1</sup> part. Select <b
1327style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1328mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Limits</span></b>
1329under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1330mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD
1331S35_Ludox1_40pct.dat</span></b> from the GSAS-II tree. Set the lower limit using
1332the cursor on the plot by picking a point somewhere in the flat region at
1333Q~3x10<sup>-3</sup> with the left mouse button. The limits window should look
1334something like</p>
1335
1336<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1337 id="Picture_x0020_34" o:spid="_x0000_i1054" type="#_x0000_t75" style='width:408pt;
1338 height:306.75pt;visibility:visible;mso-wrap-style:square'>
1339 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image007.png"
1340  o:title=""/>
1341</v:shape><![endif]--><![if !vml]><img width=544 height=409
1342src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image007.png"
1343v:shapes="Picture_x0020_34"><![endif]></span><span
1344style='mso-spacerun:yes'> </span></p>
1345
1346<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1347
1348<p class=MsoNormal>To copy these limits to the other data sets use the <b
1349style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1350mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Edit
1351Limits/Copy</span></b> command from the data window menu; a popup window will
1352give the selection of targets.<br>
1353<span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_35"
1354 o:spid="_x0000_i1053" type="#_x0000_t75" style='width:216.75pt;height:254.25pt;
1355 visibility:visible;mso-wrap-style:square'>
1356 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image008.png"
1357  o:title=""/>
1358</v:shape><![endif]--><![if !vml]><img width=289 height=339
1359src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image008.png"
1360v:shapes="Picture_x0020_35"><![endif]></span></p>
1361
1362<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1363
1364<p class=MsoNormal>Do <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'>Set All</span></b> (all boxes will be
1367checked) and then press <b style='mso-bidi-font-weight:normal'><span
1368style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1369mso-hansi-theme-font:minor-latin'>OK</span></b> to do the copy.</p>
1370
1371<h2>Step 3 Select the scattering substances for your sample</h2>
1372
1373<p class=MsoNormal><span style='mso-no-proof:yes'>Two substances need to be
1374defined for your sample to give the anticipated scattering contrast; in this
1375case one is silica and the other is water. Parameters for a number of
1376substances are defined in the file </span><b style='mso-bidi-font-weight:normal'><span
1377style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1378mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Substances.py</span></b><span
1379style='mso-no-proof:yes'>. You can add your own substances to this or better
1380put them in </span><b style='mso-bidi-font-weight:normal'><span
1381style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1382mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>UserSubstances.py</span></b><span
1383style='mso-no-proof:yes'>; this is read after Substances.py when you load
1384substances for your selection. </span>Select <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'>Substances</span></b> from the
1387GSAS-II tree. Then do <span class=GramE><b style='mso-bidi-font-weight:normal'><span
1388style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1389mso-hansi-theme-font:minor-latin'>Edit</span></b></span><b style='mso-bidi-font-weight:
1390normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1391minor-latin;mso-hansi-theme-font:minor-latin'> substance/Load substance</span></b>
1392from the menu; a popup window will appear with possible selections</p>
1393
1394<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1395 id="Picture_x0020_3" o:spid="_x0000_i1052" type="#_x0000_t75" style='width:259.5pt;
1396 height:252pt;visibility:visible;mso-wrap-style:square'>
1397 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image004.png"
1398  o:title=""/>
1399</v:shape><![endif]--><![if !vml]><img width=346 height=336
1400src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image004.png"
1401v:shapes="Picture_x0020_3"><![endif]><o:p></o:p></span></p>
1402
1403<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1404
1405<p class=MsoNormal>Notice that silica is not one of the choices; we will add it
1406in a moment (a-Quartz is but let’s ignore that). Select <b style='mso-bidi-font-weight:
1407normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1408minor-latin;mso-hansi-theme-font:minor-latin'>Water</span></b> and press <b
1409style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1410mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>;
1411the relevant data for water (and vacuum) are displayed next</p>
1412
1413<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1414 id="Picture_x0020_36" o:spid="_x0000_i1051" type="#_x0000_t75" style='width:408pt;
1415 height:306.75pt;visibility:visible;mso-wrap-style:square'>
1416 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image029.png"
1417  o:title=""/>
1418</v:shape><![endif]--><![if !vml]><img width=544 height=409
1419src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image029.png"
1420v:shapes="Picture_x0020_36"><![endif]></span><span
1421style='mso-spacerun:yes'> </span></p>
1422
1423<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1424
1425<p class=MsoNormal>If desired, you can load/add as many substances as you want
1426to this list; you can also delete any of them (except vacuum or unit scatter).
1427The composition, volume occupied by the atoms in the composition and the
1428density are given for each substance. These can each be edited; the other
1429values will change accordingly. Since we are going to say that silica wasn’t in
1430the list of known substances, do <b style='mso-bidi-font-weight:normal'><span
1431style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1432mso-hansi-theme-font:minor-latin'>Edit substance/Add substance</span></b> to
1433create it; you will be asked for a name – enter <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'>silica</span></b> and then a
1436periodic table of the elements will be shown. Select <b style='mso-bidi-font-weight:
1437normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1438minor-latin;mso-hansi-theme-font:minor-latin'>Si</span></b> and <b
1439style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1440mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>O</span></b></p>
1441
1442<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1443 id="Picture_x0020_6" o:spid="_x0000_i1050" type="#_x0000_t75" style='width:435pt;
1444 height:270pt;visibility:visible;mso-wrap-style:square'>
1445 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image006.png"
1446  o:title=""/>
1447</v:shape><![endif]--><![if !vml]><img width=580 height=360
1448src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image006.png"
1449v:shapes="Picture_x0020_6"><![endif]></span><span
1450style='mso-spacerun:yes'> </span></p>
1451
1452<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1453
1454<p class=MsoNormal>They appear in red. Press <b style='mso-bidi-font-weight:
1455normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1456minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b> and silica will be
1457added to your substance list</p>
1458
1459<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1460 id="_x0000_i1049" type="#_x0000_t75" style='width:408pt;height:306.75pt;
1461 visibility:visible;mso-wrap-style:square'>
1462 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image032.png"
1463  o:title=""/>
1464</v:shape><![endif]--><![if !vml]><img width=544 height=409
1465src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image032.png"
1466v:shapes="_x0000_i1049"><![endif]></span></p>
1467
1468<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1469
1470<p class=MsoNormal>Change the O-atom entry to <b style='mso-bidi-font-weight:
1471normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1472minor-latin;mso-hansi-theme-font:minor-latin'>2.0</span></b> and the density to
1473<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1474mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>2.65</span></b>,
1475on the section of data for silica;
1476the window will change each time giving new values and should finally show</p>
1477
1478<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1479 id="Picture_x0020_38" o:spid="_x0000_i1048" type="#_x0000_t75" style='width:408pt;
1480 height:306.75pt;visibility:visible;mso-wrap-style:square'>
1481 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image040.png"
1482  o:title=""/>
1483</v:shape><![endif]--><![if !vml]><img width=544 height=409
1484src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image040.png"
1485v:shapes="Picture_x0020_38"><![endif]></span><span
1486style='mso-spacerun:yes'> </span></p>
1487
1488<p class=MsoNormal>From this information the scattering density and that as
1489affected by resonant scattering for the listed wavelength is displayed (the
1490wavelength can be changed in the <b style='mso-bidi-font-weight:normal'><span
1491style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1492mso-hansi-theme-font:minor-latin'>Instrument Parameters</span></b> GSAS-II tree
1493item if needed). The real density value is used for contrast calculations.</p>
1494
1495<p class=MsoNormal>Just as for Limits, this information needs to be copied to
1496the other SASD entries in the GSAS-II tree. Do <b style='mso-bidi-font-weight:
1497normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1498minor-latin;mso-hansi-theme-font:minor-latin'>Edit substance/Copy substances</span></b>
1499from the data window menu and follow the same selection procedure as you used
1500for limits above.</p>
1501
1502<h2><a name="_Ref386699210">Step 4: Set Sample parameters</a> </h2>
1503
1504<p class=MsoNormal><span style='mso-no-proof:yes'>As these data sets were
1505collected from a sequence of samples where there was some variable changed in
1506their preparation, it would be useful to have this information available to
1507GSAS-II for subsequent analysis. Select Sample parameters from the data tree.
1508It shows (for </span><b style='mso-bidi-font-weight:normal'><span
1509style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1510mso-hansi-theme-font:minor-latin'>SASD S49_Ludox6_1pct.dat)<o:p></o:p></span></b></p>
1511
1512<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1513 id="Picture_x0020_39" o:spid="_x0000_i1047" type="#_x0000_t75" style='width:438pt;
1514 height:435.75pt;visibility:visible;mso-wrap-style:square'>
1515 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image041.png"
1516  o:title=""/>
1517</v:shape><![endif]--><![if !vml]><img width=584 height=581
1518src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image042.png"
1519v:shapes="Picture_x0020_39"><![endif]><o:p></o:p></span></p>
1520
1521<p class=MsoNormal><span style='mso-no-proof:yes'><o:p>&nbsp;</o:p></span></p>
1522
1523<p class=MsoNormal><span style='mso-no-proof:yes'>NB: we will not be needing to
1524select the </span><b style='mso-bidi-font-weight:normal'><span
1525style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1526mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Material</span></b><span
1527style='mso-no-proof:yes'> for this analysis; material selection is only
1528required for </span><b style='mso-bidi-font-weight:normal'><span
1529style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1530mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>Size distribution</span></b><span
1531style='mso-no-proof:yes'> analysis. Notice that the last three column names can
1532be changed; pick the first one and change it to </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'>fraction</span></b><span
1535style='mso-no-proof:yes'>. Then enter </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'>0.01</span></b><span
1538style='mso-no-proof:yes'> which corresponds to the ‘</span><b style='mso-bidi-font-weight:
1539normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1540minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:yes'>1pct</span></b><span
1541style='mso-no-proof:yes'>’ in the file name. The data window should look like<o:p></o:p></span></p>
1542
1543<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1544 id="Picture_x0020_40" o:spid="_x0000_i1046" type="#_x0000_t75" style='width:447.75pt;
1545 height:445.5pt;visibility:visible;mso-wrap-style:square'>
1546 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image043.png"
1547  o:title=""/>
1548</v:shape><![endif]--><![if !vml]><img width=597 height=594
1549src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image043.png"
1550v:shapes="Picture_x0020_40"><![endif]><o:p></o:p></span></p>
1551
1552<p class=MsoNormal><span style='mso-no-proof:yes'><o:p>&nbsp;</o:p></span></p>
1553
1554<p class=MsoNormal><span style='mso-no-proof:yes'>Now do the same for the </span><b
1555style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1556mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin;mso-no-proof:
1557yes'>Sample Parameters</span></b><span style='mso-no-proof:yes'> for the other
1558data sets putting in the correct fraction from the respective file names. If
1559you first </span><b style='mso-bidi-font-weight:normal'><span style='font-family:
1560"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1561minor-latin;mso-no-proof:yes'>Copy</span></b><span style='mso-no-proof:yes'>
1562this one to the others, that will save you the step of changing the names. You
1563will end up on the </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;mso-no-proof:yes'>Sample parameters</span></b><span
1566style='mso-no-proof:yes'> page for </span><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'>SASD S35_Ludox1_40pct.dat </span></b>GSAS-II
1569data tree.</p>
1570
1571<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1572 id="Picture_x0020_41" o:spid="_x0000_i1045" type="#_x0000_t75" style='width:444pt;
1573 height:441.75pt;visibility:visible;mso-wrap-style:square'>
1574 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image044.png"
1575  o:title=""/>
1576</v:shape><![endif]--><![if !vml]><img width=592 height=589
1577src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image044.png"
1578v:shapes="Picture_x0020_41"><![endif]></span><span
1579style='mso-spacerun:yes'> </span><span style='mso-no-proof:yes'><o:p></o:p></span></p>
1580
1581<h2>Step 5: Set Model parameters </h2>
1582
1583<p class=MsoNormal>Looking at the data plot (key ‘<b style='mso-bidi-font-weight:
1584normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1585minor-latin;mso-hansi-theme-font:minor-latin'>m</span></b>’ to select a single
1586data set) for <b style='mso-bidi-font-weight:normal'><span style='font-family:
1587"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1588minor-latin'>SASD S35_Ludox1_40pct.dat</span></b>, one sees just one feature
1589with oscillations at higher Q. This is the signal for a non-dilute <span
1590class=SpellE>scatterer</span>. </p>
1591
1592<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1593 id="Picture_x0020_42" o:spid="_x0000_i1044" type="#_x0000_t75" style='width:453pt;
1594 height:388.5pt;visibility:visible;mso-wrap-style:square'>
1595 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image045.png"
1596  o:title=""/>
1597</v:shape><![endif]--><![if !vml]><img width=604 height=518
1598src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image046.png"
1599v:shapes="Picture_x0020_42"><![endif]></span></p>
1600
1601<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1602
1603<p class=MsoNormal>Select <b style='mso-bidi-font-weight:normal'><span
1604style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1605mso-hansi-theme-font:minor-latin'>Models</span></b> from the GSASII data tree
1606under <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1607mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SASD
1608S35_Ludox1_40pct.dat</span></b>, switch <b style='mso-bidi-font-weight:normal'><span
1609style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1610mso-hansi-theme-font:minor-latin'>Size dist.</span></b> to <b style='mso-bidi-font-weight:
1611normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1612minor-latin;mso-hansi-theme-font:minor-latin'>Particle fit</span></b>, and add
1613a reasonable value (<b style='mso-bidi-font-weight:normal'><span
1614style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1615mso-hansi-theme-font:minor-latin'>0.25</span></b>) for the <b style='mso-bidi-font-weight:
1616normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1617minor-latin;mso-hansi-theme-font:minor-latin'>Background</span></b>; a
1618horizontal red line will appear. Next do <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'>Models/Add</span></b>; the window will
1621display a default component; change the <b style='mso-bidi-font-weight:normal'><span
1622style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1623mso-hansi-theme-font:minor-latin'>Material</span></b> to <b style='mso-bidi-font-weight:
1624normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1625minor-latin;mso-hansi-theme-font:minor-latin'>silica</span></b>. Also change
1626the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1627mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Matrix</span></b>
1628to <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1629mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Water</span></b>;
1630the calculated contrast should be 175.60 10<sup>20</sup>cm<sup>-4</sup>. The
1631plot will show a green curve corresponding to the default values.</p>
1632
1633<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1634 id="Picture_x0020_43" o:spid="_x0000_i1043" type="#_x0000_t75" style='width:450.75pt;
1635 height:386.25pt;visibility:visible;mso-wrap-style:square'>
1636 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image047.png"
1637  o:title=""/>
1638</v:shape><![endif]--><![if !vml]><img width=601 height=515
1639src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image048.png"
1640v:shapes="Picture_x0020_43"><![endif]></span></p>
1641
1642<p class=MsoNormal><span style='mso-no-proof:yes'><o:p>&nbsp;</o:p></span></p>
1643
1644<p class=MsoNormal>The default <span class=SpellE><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'>Dist</span></b></span><b
1647style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1648mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Mean</span></b>
1649of <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1650mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>1e+03</span></b>
1651is too large, try something smaller and increase the <span class=SpellE><b
1652style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1653mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1654style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1655mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Volume</span></b>
1656(the sliders work well for this). Since this is a non-dilute system, change the
1657<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1658mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Structure
1659factor</span></b> to <b style='mso-bidi-font-weight:normal'><span
1660style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1661mso-hansi-theme-font:minor-latin'>Hard sphere</span></b> and set the <b
1662style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1663mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SF <span
1664class=SpellE>VolFr</span></span></b> to <b style='mso-bidi-font-weight:normal'><span
1665style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1666mso-hansi-theme-font:minor-latin'>0.4</span></b>. Your data window should look
1667something like</p>
1668
1669<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1670 id="Picture_x0020_44" o:spid="_x0000_i1042" type="#_x0000_t75" style='width:468pt;
1671 height:276pt;visibility:visible;mso-wrap-style:square'>
1672 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image049.png"
1673  o:title=""/>
1674</v:shape><![endif]--><![if !vml]><img width=624 height=368
1675src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image050.png"
1676v:shapes="Picture_x0020_44"><![endif]></span></p>
1677
1678<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1679
1680<p class=MsoNormal>And the plot will be</p>
1681
1682<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1683 id="Picture_x0020_45" o:spid="_x0000_i1041" type="#_x0000_t75" style='width:438.75pt;
1684 height:376.5pt;visibility:visible;mso-wrap-style:square'>
1685 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image051.png"
1686  o:title=""/>
1687</v:shape><![endif]--><![if !vml]><img width=585 height=502
1688src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image052.png"
1689v:shapes="Picture_x0020_45"><![endif]></span><br clear=all style='mso-special-character:
1690line-break'>
1691</p>
1692
1693<p class=MsoNormal>The calculated curve shows oscillations but they are not in
1694the right place and are too broad. Try the <span class=SpellE><b
1695style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1696mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1697style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1698mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> <span
1699class=SpellE>StdDev</span></span></b> slider and make it smaller; somewhere
1700about <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1701mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0.132</span></b>
1702gives a curve with the right shape but too high. Reduce the <span class=SpellE><b
1703style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1704mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Dist</span></b></span><b
1705style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1706mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'> Volume</span></b>
1707to improve the match. Shift the <b style='mso-bidi-font-weight:normal'><span
1708style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1709mso-hansi-theme-font:minor-latin'>SF <span class=SpellE>Dist</span></span></b>
1710and <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1711mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>SF <span
1712class=SpellE>VolFr</span></span></b> as well to get the curves to match.
1713Carefully manipulate each of the sliders to see what effect they have on the
1714calculated curve. With some adjustments I got</p>
1715
1716<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1717 id="Picture_x0020_46" o:spid="_x0000_i1040" type="#_x0000_t75" style='width:468pt;
1718 height:276pt;visibility:visible;mso-wrap-style:square'>
1719 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image053.png"
1720  o:title=""/>
1721</v:shape><![endif]--><![if !vml]><img width=624 height=368
1722src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image054.png"
1723v:shapes="Picture_x0020_46"><![endif]></span></p>
1724
1725<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1726
1727<p class=MsoNormal>to give a pretty nice initial fit.</p>
1728
1729<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1730 id="Picture_x0020_47" o:spid="_x0000_i1039" type="#_x0000_t75" style='width:468pt;
1731 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1732 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image055.png"
1733  o:title=""/>
1734</v:shape><![endif]--><![if !vml]><img width=624 height=535
1735src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image056.png"
1736v:shapes="Picture_x0020_47"><![endif]></span></p>
1737
1738<h2>Step 6: Initial refinement</h2>
1739
1740<p class=MsoNormal>We can be brave and set all six <b style='mso-bidi-font-weight:
1741normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1742minor-latin;mso-hansi-theme-font:minor-latin'>Refine?</span></b> boxes (NB: the
1743one for <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1744mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Matrix
1745Volume fraction</span></b> currently does not operate – ignore it). Then do <b
1746style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1747mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Models/Fit</span></b>;
1748the least squares very quickly minimizes to give</p>
1749
1750<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1751 id="Picture_x0020_48" o:spid="_x0000_i1038" type="#_x0000_t75" style='width:468pt;
1752 height:276pt;visibility:visible;mso-wrap-style:square'>
1753 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image057.png"
1754  o:title=""/>
1755</v:shape><![endif]--><![if !vml]><img width=624 height=368
1756src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image058.png"
1757v:shapes="Picture_x0020_48"><![endif]></span></p>
1758
1759<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1760
1761<p class=MsoNormal>The console window lists the results</p>
1762
1763<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1764 id="Picture_x0020_49" o:spid="_x0000_i1037" type="#_x0000_t75" style='width:468pt;
1765 height:149.25pt;visibility:visible;mso-wrap-style:square'>
1766 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image059.png"
1767  o:title=""/>
1768</v:shape><![endif]--><![if !vml]><img width=624 height=199
1769src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image060.png"
1770v:shapes="Picture_x0020_49"><![endif]></span></p>
1771
1772<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1773
1774<p class=MsoNormal>And the plot shows the fit graphically</p>
1775
1776<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1777 id="Picture_x0020_50" o:spid="_x0000_i1036" type="#_x0000_t75" style='width:468pt;
1778 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1779 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image061.png"
1780  o:title=""/>
1781</v:shape><![endif]--><![if !vml]><img width=624 height=535
1782src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image062.png"
1783v:shapes="Picture_x0020_50"><![endif]></span></p>
1784
1785<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1786
1787<p class=MsoNormal>The fit is OK except for a region Q~0.03Å<sup>-1</sup>; this
1788is probably due to a failure of the simple hard sphere model in this
1789concentrated system.</p>
1790
1791<h2>Step 7: Sequential refinement</h2>
1792
1793<p class=MsoNormal>We are now ready to try a sequential refinement starting
1794with this fit for the 1<sup>st</sup> data set. Do <b style='mso-bidi-font-weight:
1795normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1796minor-latin;mso-hansi-theme-font:minor-latin'>Models/Sequential fit</span></b>;
1797a dialog box will appear for selection of the data sets.</p>
1798
1799<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1800 id="Picture_x0020_51" o:spid="_x0000_i1035" type="#_x0000_t75" style='width:223.5pt;
1801 height:289.5pt;visibility:visible;mso-wrap-style:square'>
1802 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image063.png"
1803  o:title=""/>
1804</v:shape><![endif]--><![if !vml]><img width=298 height=386
1805src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image063.png"
1806v:shapes="Picture_x0020_51"><![endif]></span></p>
1807
1808<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1809
1810<p class=MsoNormal>Press <b style='mso-bidi-font-weight:normal'><span
1811style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1812mso-hansi-theme-font:minor-latin'>Set <span class=GramE>All</span></span></b>,
1813all boxes will be checked showing selection of the data sets. This also allows
1814you to instruct the sequential refinement to start at the last data set and
1815proceed backwards through them (<b style='mso-bidi-font-weight:normal'><span
1816style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1817mso-hansi-theme-font:minor-latin'>Reverse order</span></b>). It also allows you
1818to instruct the sequential refinement to use the current parameters as starting
1819values for the next data set. This works in either direction and facilitates
1820the initial sequential refinements. NB: some sequential refinements do not work
1821well in both directions; in this particular case starting with a fitted 1%
1822pattern and going in reverse through the data fails on the 5% data set.
1823Apparently the change in parameters is too great for the least squares to
1824handle; going in the forward direction works just fine (as you will see next).
1825Select <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1826mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Copy to next</span></b>
1827and press <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1828mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>OK</span></b>;
1829the sequential refinement will proceed very rapidly displaying results for each
1830data set on the console and finally ending by displaying the <b
1831style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1832mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Sequential refinement
1833results.<o:p></o:p></span></b></p>
1834
1835<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1836 id="Picture_x0020_53" o:spid="_x0000_i1034" type="#_x0000_t75" style='width:459pt;
1837 height:234pt;visibility:visible;mso-wrap-style:square'>
1838 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image064.png"
1839  o:title=""/>
1840</v:shape><![endif]--><![if !vml]><img width=612 height=312
1841src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image065.png"
1842v:shapes="Picture_x0020_53"><![endif]></span></p>
1843
1844<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1845
1846<p class=MsoNormal>Note the comment in the plot status bar: double click on the
1847<b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1848mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0<span
1849class=GramE>;Volume</span></span></b> and a new plot will appear.</p>
1850
1851<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1852 id="Picture_x0020_54" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:468pt;
1853 height:401.25pt;visibility:visible;mso-wrap-style:square'>
1854 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image066.png"
1855  o:title=""/>
1856</v:shape><![endif]--><![if !vml]><img width=624 height=535
1857src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image067.png"
1858v:shapes="Picture_x0020_54"><![endif]></span></p>
1859
1860<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1861
1862<p class=MsoNormal>Each point has an error bar extracted from the least squares
1863– it represents a 1 &#963; variation in the value. Now press the <b
1864style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1865mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>s</span></b>
1866key (or select <b style='mso-bidi-font-weight:normal'><span style='font-family:
1867"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1868minor-latin'>s</span></b> from the <b style='mso-bidi-font-weight:normal'><span
1869style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1870mso-hansi-theme-font:minor-latin'>K</span></b> box); a dialog box will appear with
1871a selection of parameters to plot along the x-axis. Select <b style='mso-bidi-font-weight:
1872normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1873minor-latin;mso-hansi-theme-font:minor-latin'>fraction</span></b> and the plot
1874will be redrawn (it may require selection of another column &amp; then <b
1875style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1876mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0<span
1877class=GramE>;Volume</span></span></b> to make it appear).</p>
1878
1879<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1880 id="Picture_x0020_55" o:spid="_x0000_i1032" type="#_x0000_t75" style='width:445.5pt;
1881 height:381.75pt;visibility:visible;mso-wrap-style:square'>
1882 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image068.png"
1883  o:title=""/>
1884</v:shape><![endif]--><![if !vml]><img width=594 height=509
1885src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image069.png"
1886v:shapes="Picture_x0020_55"><![endif]></span></p>
1887
1888<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1889
1890<p class=MsoNormal>It is gratifying how this relation between Volume and the composition
1891is linear. You can now determine the slope &amp; intercept (or fit to some
1892other function!) directly with GSAS-II; do <b style='mso-bidi-font-weight:normal'><span
1893style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1894mso-hansi-theme-font:minor-latin'>Parametric Fit/Add equation</span></b> and
1895the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1896mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Expression
1897Editor</span></b> dialog box will appear.</p>
1898
1899<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1900 id="Picture_x0020_56" o:spid="_x0000_i1031" type="#_x0000_t75" style='width:465pt;
1901 height:255pt;visibility:visible;mso-wrap-style:square'>
1902 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image070.png"
1903  o:title=""/>
1904</v:shape><![endif]--><![if !vml]><img width=620 height=340
1905src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image070.png"
1906v:shapes="Picture_x0020_56"><![endif]></span></p>
1907
1908<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1909
1910<p class=MsoNormal>The pull down in the upper left corner has two choices;
1911select <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1912mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Global</span></b>
1913and a new dialog box will appear giving you choices from the <b
1914style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1915mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Sequential
1916results</span></b> table. Select <b style='mso-bidi-font-weight:normal'><span
1917style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1918mso-hansi-theme-font:minor-latin'>0<span class=GramE>;Volume</span></span></b>
1919and the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1920mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Expression
1921Editor</span></b> will reappear.</p>
1922
1923<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1924 id="Picture_x0020_57" o:spid="_x0000_i1030" type="#_x0000_t75" style='width:465pt;
1925 height:255pt;visibility:visible;mso-wrap-style:square'>
1926 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image071.png"
1927  o:title=""/>
1928</v:shape><![endif]--><![if !vml]><img width=620 height=340
1929src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image071.png"
1930v:shapes="Picture_x0020_57"><![endif]></span></p>
1931
1932<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1933
1934<p class=MsoNormal>Next enter the function you wish to use in fitting <b
1935style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1936mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>0<span
1937class=GramE>:Volume</span></span></b>; enter <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'>m*<span class=SpellE>x+b</span></span></b>
1940(equation for a straight line). After a pause, the <b style='mso-bidi-font-weight:
1941normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1942minor-latin;mso-hansi-theme-font:minor-latin'>Expression Editor</span></b> will
1943be redrawn allowing you to assign <b style='mso-bidi-font-weight:normal'><span
1944style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1945mso-hansi-theme-font:minor-latin'>b</span></b>, <b style='mso-bidi-font-weight:
1946normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1947minor-latin;mso-hansi-theme-font:minor-latin'>m</span></b> &amp; <b
1948style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1949mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>x</span></b>.</p>
1950
1951<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1952 id="Picture_x0020_58" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:465pt;
1953 height:255pt;visibility:visible;mso-wrap-style:square'>
1954 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image072.png"
1955  o:title=""/>
1956</v:shape><![endif]--><![if !vml]><img width=620 height=340
1957src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image072.png"
1958v:shapes="Picture_x0020_58"><![endif]></span></p>
1959
1960<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1961
1962<p class=MsoNormal>For <b style='mso-bidi-font-weight:normal'><span
1963style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1964mso-hansi-theme-font:minor-latin'>b</span></b> &amp; <b style='mso-bidi-font-weight:
1965normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1966minor-latin;mso-hansi-theme-font:minor-latin'>m</span></b> select <b
1967style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1968mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Free</span></b>;
1969these will be the parameters for your fit. For <b style='mso-bidi-font-weight:
1970normal'><span style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:
1971minor-latin;mso-hansi-theme-font:minor-latin'>x</span></b> select <b
1972style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
1973mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Global</span></b>;
1974a new dialog box will appear giving you several choices.</p>
1975
1976<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1977 id="Picture_x0020_37" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:468pt;
1978 height:187.5pt;visibility:visible;mso-wrap-style:square'>
1979 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image037.png"
1980  o:title=""/>
1981</v:shape><![endif]--><![if !vml]><img width=624 height=250
1982src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image037.png"
1983v:shapes="Picture_x0020_37"><![endif]></span></p>
1984
1985<p class=MsoNormal><o:p>&nbsp;</o:p></p>
1986
1987<p class=MsoNormal>Select the last line (<b style='mso-bidi-font-weight:normal'><span
1988style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1989mso-hansi-theme-font:minor-latin'>fraction…</span></b>); it will appear in
1990blue. Then press <b style='mso-bidi-font-weight:normal'><span style='font-family:
1991"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:
1992minor-latin'>OK</span></b>; the <b style='mso-bidi-font-weight:normal'><span
1993style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
1994mso-hansi-theme-font:minor-latin'>Expression Editor</span></b> will reappear
1995with more information.</p>
1996
1997<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
1998 id="Picture_x0020_59" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:465pt;
1999 height:255pt;visibility:visible;mso-wrap-style:square'>
2000 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image073.png"
2001  o:title=""/>
2002</v:shape><![endif]--><![if !vml]><img width=620 height=340
2003src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image073.png"
2004v:shapes="Picture_x0020_59"><![endif]></span></p>
2005
2006<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2007
2008<p class=MsoNormal>Next press <b style='mso-bidi-font-weight:normal'><span
2009style='font-family:"Calibri",sans-serif;mso-ascii-theme-font:minor-latin;
2010mso-hansi-theme-font:minor-latin'>OK</span></b>; the equation will be fitted to
2011the data and the results displayed on the console</p>
2012
2013<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2014 id="Picture_x0020_60" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:354pt;
2015 height:116.25pt;visibility:visible;mso-wrap-style:square'>
2016 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image074.png"
2017  o:title=""/>
2018</v:shape><![endif]--><![if !vml]><img width=472 height=155
2019src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image074.png"
2020v:shapes="Picture_x0020_60"><![endif]></span></p>
2021
2022<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2023
2024<p class=MsoNormal>And the plot shows the curve (in red) calculated from the
2025best fit, weighted by the <span class=SpellE>esds</span> on the data points, to
2026the model equation for a straight line.</p>
2027
2028<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
2029 id="Picture_x0020_61" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:468pt;
2030 height:401.25pt;visibility:visible;mso-wrap-style:square'>
2031 <v:imagedata src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image075.png"
2032  o:title=""/>
2033</v:shape><![endif]--><![if !vml]><img width=624 height=535
2034src="Sequential%20Refinement%20of%20Small%20Angle%20Scattering%20Data_files/image076.png"
2035v:shapes="Picture_x0020_61"><![endif]></span></p>
2036
2037<p class=MsoNormal><o:p>&nbsp;</o:p></p>
2038
2039<p class=MsoNormal>For this particular experiment there was an expectation that
2040the <b style='mso-bidi-font-weight:normal'><span style='font-family:"Calibri",sans-serif;
2041mso-ascii-theme-font:minor-latin;mso-hansi-theme-font:minor-latin'>Volume</span></b>s
2042obtained from the SASD model fits would match the makeup concentrations for
2043these samples so that the slope for this plot would be unity. One possible
2044explanation for the discrepancy is that the silica particles are partially
2045hydrated thus reducing the contrast from 175.6x10<sup>20</sup> cm<sup>-4</sup>
2046to something like 98x10<sup>20</sup>cm<sup>-4</sup>. This concludes the small
2047angle sequential fit tutorial; you may save the project.</p>
2048
2049</div>
2050
2051</body>
2052
2053</html>
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