source: trunk/FitBkgTut.htm @ 1903

Last change on this file since 1903 was 1903, checked in by vondreele, 7 years ago
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521<body lang=EN-US style='tab-interval:.5in'>
522
523<div class=WordSection1>
524
525<h1><span style='mso-fareast-font-family:"Times New Roman"'>Fitting the Starting
526Background using Fixed Points<o:p></o:p></span></h1>
527
528<h2><span style='mso-fareast-font-family:"Times New Roman"'>Introduction:<o:p></o:p></span></h2>
529
530<p class=MsoNormal>There are times when it can be difficult to establish a good
531initial model for the background in a Rietveld fit. The authors of GSAS-II feel
532that background models should always be refined in the final stages of
533refinement (on occasion when background levels interact highly with atomic
534displacement parameters, one may need to fix one or the other), but in the
535initial stages of the fit, it can be helpful to force the initial background
536fitting to follow a curve supplied by the user. This tutorial shows how to do
537this. </p>
538
539<p class=MsoNormal><o:p>&nbsp;</o:p></p>
540
541<p class=MsoNormal>For this example, we will fit data from 11-BM that has a fairly
542large broad background peak. </p>
543
544<h2>Step 1. Load the diffraction data</h2>
545
546<p class=MsoNormal>Import the data using Import/ÒPowder DataÓ/Òfrom GSAS powder
547data fileÓ. Change the directory to the location of this exercise (<b
548style='mso-bidi-font-weight:normal'>exercises/<span class=SpellE>FitBkg</span></b>
549&#8211; yours might be different). Switch the input file type to use zip
550archives (.zip). Select file OH_00.zip. </p>
551
552<p class=MsoNormal><o:p>&nbsp;</o:p></p>
553
554<p class=MsoNormal><span class=GramE>This will present a file browser where the
555data file</span>, <span class=GramE>OH_00.fxye can be selected</span>. </p>
556
557<p class=MsoNormal><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shapetype
558 id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
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579 <v:imagedata src="FitBkgTut_files/image001.png" o:title=""/>
580</v:shape><![endif]--><![if !vml]><img width=204 height=199
581src="FitBkgTut_files/image002.png" v:shapes="Picture_x0020_2"><![endif]></span></p>
582
583<p class=MsoNormal>A prompt is presented where the header of the file is shown.
584Press ÒYesÓ. The instrument parameter file will be read automatically from the
585.zip file for you. </p>
586
587<p class=MsoNormal><o:p>&nbsp;</o:p></p>
588
589<p class=MsoNormal>The initial plot of the data does not show much of a
590background, </p>
591
592<p class=MsoNormal><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
593 id="Picture_x0020_3" o:spid="_x0000_i1033" type="#_x0000_t75" style='width:220pt;
594 height:190pt;visibility:visible;mso-wrap-style:square'>
595 <v:imagedata src="FitBkgTut_files/image003.png" o:title=""/>
596</v:shape><![endif]--><![if !vml]><img width=222 height=192
597src="FitBkgTut_files/image004.png" v:shapes="Picture_x0020_3"><![endif]><o:p></o:p></span></p>
598
599<p class=MsoNormal><o:p>&nbsp;</o:p></p>
600
601<p class=MsoNormal>But if this plot is magnified, it becomes clear that there
602are three effects taking place.</p>
603
604<p class=MsoNormal><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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607 <v:imagedata src="FitBkgTut_files/image005.png" o:title=""/>
608</v:shape><![endif]--><![if !vml]><img width=378 height=325
609src="FitBkgTut_files/image006.png" v:shapes="Picture_x0020_4"><![endif]></span></p>
610
611<p class=MsoNormal>At low angles (below 3<b style='mso-bidi-font-weight:normal'><span
612style='mso-bidi-font-family:"Lucida Grande";color:black'>¡ </span></b>2<span
613style='mso-bidi-font-family:"Lucida Grande";color:black'>&#952;), there is a
614strong fall-off in background (this is due to air scattering); between </span>3<b
615style='mso-bidi-font-weight:normal'><span style='mso-bidi-font-family:"Lucida Grande";
616color:black'>¡</span></b><span style='mso-bidi-font-family:"Lucida Grande";
617color:black'> and </span>10<b style='mso-bidi-font-weight:normal'><span
618style='mso-bidi-font-family:"Lucida Grande";color:black'>¡ </span></b>2<span
619style='mso-bidi-font-family:"Lucida Grande";color:black'>&#952; there is a
620broad feature (from <span class=SpellE>kapton</span> used to hold the sample)
621and finally beyond 10<b style='mso-bidi-font-weight:normal'>¡</b> the background
622is relatively flat. There may be some minor ripple in this, but this is better
623explored late in the refinement by looking at the difference curve. <o:p></o:p></span></p>
624
625<h2>Step 2. Define fixed points</h2>
626
627<p class=MsoNormal><span style='mso-bidi-font-family:"Lucida Grande";
628color:black'>To fit this, we will initially define points where we think the
629background should be using the mouse (be sure that the plot zoom &amp; reposition
630buttons are not selected). Select the Background tree item (child of the PWDR OH_00É
631item) and from the menu select ÒFixed PointsÓ/Add (Add will then have a
632checkmark). Click the mouse at locations across the pattern to define where the
633background should go. Select at least two points for every term that you will
634want to fit. It is a good idea to have a point below the lower data limit and
635one above the upper data limit, as these will be used in extrapolation. <o:p></o:p></span></p>
636
637<p class=MsoNormal><span style='mso-bidi-font-family:"Lucida Grande";
638color:black'><o:p>&nbsp;</o:p></span></p>
639
640<p class=MsoNormal><span style='mso-bidi-font-family:"Lucida Grande";
641color:black'>Note that any unwanted points <span class=GramE>can</span> be deleted
642by selecting ÒFixed PointsÓ/Delete and then by clicking on the points.
643Alternately, points can be repositioned by selecting ÒFixed PointsÓ/Move and
644then dragging the points to new locations. When done you should have a plot
645that looks like this:<o:p></o:p></span></p>
646
647<p class=MsoNormal><span style='mso-bidi-font-family:"Lucida Grande";
648color:black'><o:p>&nbsp;</o:p></span></p>
649
650<p class=MsoNormal><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><!--[if gte vml 1]><v:shape
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653 <v:imagedata src="FitBkgTut_files/image007.png" o:title=""/>
654</v:shape><![endif]--><![if !vml]><img width=434 height=374
655src="FitBkgTut_files/image008.png" v:shapes="Picture_x0020_5"><![endif]><o:p></o:p></span></p>
656
657<p class=MsoNormal><span style='mso-fareast-language:EN-US;mso-no-proof:yes'><o:p>&nbsp;</o:p></span></p>
658
659<h2>Step 3. Fit the background</h2>
660
661<p class=MsoNormal>At this point is becomes possible to fit different
662background models to the points to see how they do. <span
663style="mso-spacerun:yes">&nbsp;</span><span class=GramE>Change the function,
664the number of terms, refinement flag(s) and then press ÒFixed Points/ÒFit
665BackgroundÓ menu item.</span> Use of 12 <span class=SpellE>Chebyschev</span>
666terms gives an OK fit, as shown below, but does have some extraneous ÒblipsÓ: </p>
667
668<p class=MsoNormal><!--[if gte vml 1]><v:shape id="_x0000_i1035" type="#_x0000_t75"
669 style='width:256pt;height:99pt'>
670 <v:imagedata src="FitBkgTut_files/image009.png" o:title=""/>
671</v:shape><![endif]--><![if !vml]><img width=258 height=101
672src="FitBkgTut_files/image010.png" v:shapes="_x0000_i1035"><![endif]></p>
673
674<p class=MsoNormal><o:p>&nbsp;</o:p></p>
675
676<p class=MsoNormal><!--[if gte vml 1]><v:shape id="_x0000_i1037" type="#_x0000_t75"
677 style='width:6in;height:368pt'>
678 <v:imagedata src="FitBkgTut_files/image011.png" o:title=""/>
679</v:shape><![endif]--><![if !vml]><img width=434 height=370
680src="FitBkgTut_files/image012.png" v:shapes="_x0000_i1037"><![endif]></p>
681
682<p class=MsoNormal>Adding more terms does improve the fit. </p>
683
684<p class=MsoNormal><o:p>&nbsp;</o:p></p>
685
686<h2>Step 4. Add a background peak</h2>
687
688<p class=MsoNormal>A better choice is to reduce the number of terms and add a
689background peak to match the feature centered around 5.3 degrees. Initially set
690the intensity and peak width (but not the position) to be refined. </p>
691
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694 <v:imagedata src="FitBkgTut_files/image013.png" o:title=""/>
695</v:shape><![endif]--><![if !vml]><img width=276 height=115
696src="FitBkgTut_files/image014.png" v:shapes="_x0000_i1038"><![endif]></p>
697
698<p class=MsoNormal><o:p>&nbsp;</o:p></p>
699
700<p class=MsoNormal>The initial fit is not that <span class=GramE>good,</span> </p>
701
702<p class=MsoNormal><!--[if gte vml 1]><v:shape id="_x0000_i1040" type="#_x0000_t75"
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704 <v:imagedata src="FitBkgTut_files/image015.png" o:title=""/>
705</v:shape><![endif]--><![if !vml]><img width=434 height=373
706src="FitBkgTut_files/image016.png" v:shapes="_x0000_i1040"><![endif]></p>
707
708<p class=MsoNormal><o:p>&nbsp;</o:p></p>
709
710<p class=MsoNormal><span class=GramE>but</span> increasing the number of terms
711to 8 and refining the peak position as well does give a good fit:</p>
712
713<p class=MsoNormal><!--[if gte vml 1]><v:shape id="_x0000_i1043" type="#_x0000_t75"
714 style='width:431pt;height:371pt'>
715 <v:imagedata src="FitBkgTut_files/image017.png" o:title=""/>
716</v:shape><![endif]--><![if !vml]><img width=433 height=373
717src="FitBkgTut_files/image018.png" v:shapes="_x0000_i1043"><![endif]></p>
718
719<h2>Step 5. Try other models</h2>
720
721<p class=MsoNormal>One of the nice features of this approach is that we can try
722out different functions and see how well they do. </p>
723
724<p class=MsoNormal><o:p>&nbsp;</o:p></p>
725
726<p class=MsoNormal>The ÒQ^-2 power seriesÓ does a very nice job for the
727low-angle portion of the pattern with only 4 terms, but does not do very good
728job at higher angle, even if more terms are added: </p>
729
730<p class=MsoNormal><!--[if gte vml 1]><v:shape id="_x0000_i1047" type="#_x0000_t75"
731 style='width:292pt;height:114pt'>
732 <v:imagedata src="FitBkgTut_files/image019.png" o:title=""/>
733</v:shape><![endif]--><![if !vml]><img width=294 height=116
734src="FitBkgTut_files/image020.png" v:shapes="_x0000_i1047"><![endif]></p>
735
736<p class=MsoNormal><span style="mso-spacerun:yes">&nbsp;</span><!--[if gte vml 1]><v:shape
737 id="_x0000_i1046" type="#_x0000_t75" style='width:6in;height:398pt'>
738 <v:imagedata src="FitBkgTut_files/image021.png" o:title=""/>
739</v:shape><![endif]--><![if !vml]><img width=434 height=400
740src="FitBkgTut_files/image022.png" v:shapes="_x0000_i1046"><![endif]></p>
741
742<p class=MsoNormal><o:p>&nbsp;</o:p></p>
743
744<p class=MsoNormal>While the log-interpolate function does well with only 6
745background terms:</p>
746
747<p class=MsoNormal><!--[if gte vml 1]><v:shape id="_x0000_i1049" type="#_x0000_t75"
748 style='width:292pt;height:131pt'>
749 <v:imagedata src="FitBkgTut_files/image023.png" o:title=""/>
750</v:shape><![endif]--><![if !vml]><img width=294 height=133
751src="FitBkgTut_files/image024.png" v:shapes="_x0000_i1049"><![endif]></p>
752
753<p class=MsoNormal><!--[if gte vml 1]><v:shape id="_x0000_i1051" type="#_x0000_t75"
754 style='width:6in;height:396pt'>
755 <v:imagedata src="FitBkgTut_files/image025.png" o:title=""/>
756</v:shape><![endif]--><![if !vml]><img width=434 height=398
757src="FitBkgTut_files/image026.png" v:shapes="_x0000_i1051"><![endif]></p>
758
759<p class=MsoNormal><o:p>&nbsp;</o:p></p>
760
761<h2>Step 6. What to do next</h2>
762
763<p class=MsoNormal>The background points that have been defined are saved in
764the GSAS-II project (.<span class=SpellE>gpx</span>) file and will appear when
765the Background menu item is selected. They will not affect the refinement in
766any way. Nonetheless, you may wish to delete them so they do not appear on the
767background plot. To do this, use the <span
768style="mso-spacerun:yes">&nbsp;</span>ÒFixed Points/Clear menu item.</p>
769
770<p class=MsoNormal><o:p>&nbsp;</o:p></p>
771
772<p class=MsoNormal>With the one added background peak, and either the <span
773class=SpellE>Chebyschev</span> function with 8 terms or the log-interpolate
774function with 6 terms, one has a good background model to start the fitting.
775Turning off the refine flags in the early stages of the refinements will
776simplify the computations and ensure the model stays in a good place, but
777remember to turn the flags back on in the final stages of fitting. </p>
778
779</div>
780
781</body>
782
783</html>
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