source: Tutorials/FPAfit/FPAfit.htm @ 3718

Last change on this file since 3718 was 3718, checked in by toby, 3 years ago

restore lost Hold list; new tutorials; cleanup naming in constraint docs

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644
645<div class=WordSection1>
646
647<h1><span style='mso-bidi-font-family:"Times New Roman"'>Determining Profile
648Parameters from Fundamental Parameters<o:p></o:p></span></h1>
649
650<p class=MsoNormal><o:p>&nbsp;</o:p></p>
651
652<p class=MsoNormal><span style='font-size:14.0pt'>The goal of this exercise is
653to determine approximate instrument profile parameters by calculating peak
654profiles based on a fundamental parameters approach (FPA) description of a
655diffractometer. The peaks are then fit using the profile model terms within
656GSAS-II. Note that with fundamental parameters, it is possible to generate
657highly irregular peaks that GSAS-II will not be able to fit well. It is best to
658use instrument configurations that produce well-formed peaks, which can be modeled
659by a Voigt functions with the addition of asymmetry from angular divergence. <o:p></o:p></span></p>
660
661<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
662
663<p class=MsoNormal style='margin-bottom:12.0pt;line-height:15.0pt;mso-pagination:
664none;mso-layout-grid-align:none;text-autospace:none'><span style='font-size:
66514.0pt'>The FPA peak shapes are computed with the NIST FPA Python code (</span><b><span
666style='font-size:13.0pt;font-family:Times;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";
667mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:Times;color:blue'>http://dx.doi.org/10.6028/jres.120.014.c</span></b><span
668style='font-size:14.0pt'>), which should be cited using ÒH. Mendenhall, Marcus
669&amp; Mullen, Katharine &amp; P. Cline, James. (2015)<span class=GramE>. <i
670style='mso-bidi-font-style:normal'>An Implementation of the Fundamental
671Parameters Approach for Analysis of X-ray Powder Diffraction Line Profiles</i>.</span>
672<span class=GramE>Journal of Research of the National Institute of Standards
673and Technology.</span> <b style='mso-bidi-font-weight:normal'>120</b> 223-251. <a
674href="http://dx.doi.org/10.6028/jres.120.014"
675title="Link to Mendenhall et al paper">10.6028/jres.120.014</a>,Ó if this
676capability is used within GSAS-II. This code is used to generate a pattern with
677isolated peaks. The profile of these peaks is fit using profile parameters U,
678V, W, X, Y and SH/L. </span><span style='font-family:Times;mso-fareast-font-family:
679"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:
680Times;color:black'><o:p></o:p></span></p>
681
682<h2><span style='mso-bidi-font-weight:normal'>1.</span> Open the FPA module</h2>
683
684<p class=MsoNormal><o:p>&nbsp;</o:p></p>
685
686<p class=MsoNormal><span style='font-size:14.0pt'>To invoke this capability,
687the ÒImport/Powder Data/Fit instr. profile from fundamental <span class=SpellE>parms</span>ÉÓ
688menu command is used. This opens a dialog, as below <o:p></o:p></span></p>
689
690<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
691
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717
718<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
719
720<p class=MsoNormal><span style='font-size:14.0pt'>This describes how a pattern
721will be generated. The computation should be done over the angular range at
722least as large as the data range for analysis of samples. Since we will fit
723several profile terms, at least double that number of peaks should be computed.
724The default of 13 peaks, to space them 10 degrees apart, works well here and
725would not need to be increased if a larger data range were used. Lowering this
726number might be needed to keep peaks from overlapping, if very broad peaks and
727a small data range are used. The pattern step size should allow at least 10 points
728above the half-intensity point in each peak, which would need to be made
729smaller with narrow peaks. As will be shown, this is checked, so leaving this
730as the default value is fine. Computing each peak over a 2-degree range is
731likely way more than what is needed in this example, but also does not slow the
732computation noticeably.<span style="mso-spacerun:yes">&nbsp; </span>This might
733need to be changed with very broad or very narrow peaks. For this example, we
734will not change any parameters.<o:p></o:p></span></p>
735
736<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
737
738<h2><span style='mso-bidi-font-weight:normal'>2.</span> Input FPA parameters<o:p></o:p></h2>
739
740<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
741
742<p class=MsoNormal><span style='font-size:14.0pt'>The FP parameters can be
743input in one of two ways. They can be read from a file, which can be
744hand-edited to access the full range of capabilities in the NIST FPA Python
745code (discussed further in Ò7. Supplying NIST FPA input manuallyÓ below) or can
746be input from another dialog window. Press the ÒInput FP <span class=SpellE>vals</span>Ó
747button, which opens the window shown below:<o:p></o:p></span></p>
748
749<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
750
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758style='font-size:14.0pt'><o:p></o:p></span></p>
759
760<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
761
762<p class=MsoNormal><span style='font-size:14.0pt'>The top section of the dialog
763window specifies the details of the radiation source, where any number of
764components can be given. Two common default settings with Cu K</span><span
765style='font-family:"Lucida Grande";color:black'>&#945;</span><span
766style='font-size:14.0pt'> radiation modeled as a 2-line or 5-line spectrum.<span
767style="mso-spacerun:yes">&nbsp; </span>The input can also be switched from
768Point-detector mode (as is shown above) to position-sensitive-detector mode, by
769pressing the PSD button. Note that parameters are named similar to their use in
770the <span class=SpellE>Topas</span> program with the same units. <o:p></o:p></span></p>
771
772<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
773
774<h2><span style='mso-bidi-font-weight:normal'>3.</span> Plot the peak shape and
775convolution contributions (optional)<o:p></o:p></h2>
776
777<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
778
779<p class=MsoNormal><span style='font-size:14.0pt'>The ÒPlot peakÓ button at the
780bottom of the window can be used to visualize the resulting peak shape at any
781position in 2-theta, as well as all the contributions to <span class=GramE>the</span>
782peak shape, like this:<o:p></o:p></span></p>
783
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795 <v:imagedata src="FPAfit_files/image007.png" o:title=""/>
796</v:shape><![endif]--><![if !vml]><img border=0 width=254 height=208
797src="FPAfit_files/image008.png" v:shapes="Picture_x0020_4"><![endif]></span></p>
798
799<p class=MsoNormal><span style='font-size:14.0pt'>Note that distinguishing the
800components in the peak convolution functions plot can be difficult. Clicking on
801an entry in the legend changes the display of that component, as shown below
802where ÒemissionÓ in the legend was clicked:<o:p></o:p></span></p>
803
804<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
805mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5" o:spid="_x0000_i1032"
806 type="#_x0000_t75" style='width:324pt;height:226pt;visibility:visible;
807 mso-wrap-style:square'>
808 <v:imagedata src="FPAfit_files/image009.png" o:title=""/>
809</v:shape><![endif]--><![if !vml]><img border=0 width=326 height=228
810src="FPAfit_files/image010.png" v:shapes="Picture_x0020_5"><![endif]></span><span
811style='font-size:14.0pt'><o:p></o:p></span></p>
812
813<h2><span style='mso-bidi-font-weight:normal'><o:p>&nbsp;</o:p></span></h2>
814
815<h2><span style='mso-bidi-font-weight:normal'>4.</span> Accept the FPA values,
816correct the step size</h2>
817
818<p class=MsoNormal><span style='font-size:14.0pt'>For this example, we will not
819change any of the default FPA parameters. Press OK to accept the displayed values
820and to close the dialog window. The pattern step size is then checked,
821producing the following warning: <o:p></o:p></span></p>
822
823<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
824mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_6" o:spid="_x0000_i1031"
825 type="#_x0000_t75" style='width:4in;height:105pt;visibility:visible;
826 mso-wrap-style:square'>
827 <v:imagedata src="FPAfit_files/image011.png" o:title=""/>
828</v:shape><![endif]--><![if !vml]><img border=0 width=290 height=107
829src="FPAfit_files/image012.png" v:shapes="Picture_x0020_6"><![endif]></span><span
830style='font-size:14.0pt'><o:p></o:p></span></p>
831
832<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
833
834<p class=MsoNormal><span style='font-size:14.0pt'>Note that the Pattern step
835size is changed, as below. <span style="mso-spacerun:yes">&nbsp;</span><o:p></o:p></span></p>
836
837<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
838mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_7" o:spid="_x0000_i1030"
839 type="#_x0000_t75" style='width:324pt;height:275pt;visibility:visible;
840 mso-wrap-style:square'>
841 <v:imagedata src="FPAfit_files/image013.png" o:title=""/>
842</v:shape><![endif]--><![if !vml]><img border=0 width=326 height=277
843src="FPAfit_files/image014.png" v:shapes="Picture_x0020_7"><![endif]></span><span
844style='font-size:14.0pt'><o:p></o:p></span></p>
845
846<p class=MsoNormal><span style='font-size:14.0pt'>Also note that after values
847have been entered, the ÒSave FPA <span class=SpellE>dict</span>Ó button is now
848available. <o:p></o:p></span></p>
849
850<h2><span style='mso-bidi-font-weight:normal'>5.</span> Perform the computation<o:p></o:p></h2>
851
852<p class=MsoNormal><span style='font-size:14.0pt'>Press OK to start the
853computation. A Òplease waitÓ message is displayed<o:p></o:p></span></p>
854
855<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
856mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8" o:spid="_x0000_i1029"
857 type="#_x0000_t75" style='width:262pt;height:161pt;visibility:visible;
858 mso-wrap-style:square'>
859 <v:imagedata src="FPAfit_files/image015.png" o:title=""/>
860</v:shape><![endif]--><![if !vml]><img border=0 width=264 height=163
861src="FPAfit_files/image016.png" v:shapes="Picture_x0020_8"><![endif]></span><span
862style='font-size:14.0pt'><o:p></o:p></span></p>
863
864<p class=MsoNormal><span class=GramE><span style='font-size:14.0pt'>as</span></span><span
865style='font-size:14.0pt'> the fitting may take a few minutes (output can be
866seen in the console window as the fit progresses). When the fit is complete,
867you will be provided with a window to save the instrument parameters to <span
868class=GramE>an .<span class=SpellE>instparm</span></span> file. After the
869parameters have been saved, the fit will be plotted (here I have switched to
870the main PWDR tree entry and dragged the difference curve down so that it can
871be seen better.) <o:p></o:p></span></p>
872
873<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
874mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9" o:spid="_x0000_i1028"
875 type="#_x0000_t75" style='width:364pt;height:262pt;visibility:visible;
876 mso-wrap-style:square'>
877 <v:imagedata src="FPAfit_files/image017.png" o:title=""/>
878</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=264
879src="FPAfit_files/image018.png" v:shapes="Picture_x0020_9"><![endif]></span><span
880style='font-size:14.0pt'><o:p></o:p></span></p>
881
882<p class=MsoNormal><span style='font-size:14.0pt'>Clicking on the Instrument Parameters
883tree entry causes the powder profile terms to be plotted: <o:p></o:p></span></p>
884
885<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
886mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10" o:spid="_x0000_i1027"
887 type="#_x0000_t75" style='width:324pt;height:236pt;visibility:visible;
888 mso-wrap-style:square'>
889 <v:imagedata src="FPAfit_files/image019.png" o:title=""/>
890</v:shape><![endif]--><![if !vml]><img border=0 width=326 height=238
891src="FPAfit_files/image020.png" v:shapes="Picture_x0020_10"><![endif]></span><span
892style='font-size:14.0pt'><span style="mso-spacerun:yes">&nbsp;</span><o:p></o:p></span></p>
893
894<h2><span style='mso-bidi-font-weight:normal'><o:p>&nbsp;</o:p></span></h2>
895
896<h2><span style='mso-bidi-font-weight:normal'>6.</span> Improve the profile
897parameters. </h2>
898
899<p class=MsoNormal><span style='font-size:14.0pt'>Note that due to correlation
900between the peak asymmetry parameter (SH/L) and the <span class=SpellE>Lorentzian</span>
901broadening terms, the Gamma (Lorentz width) terms refine to negative values for
902the first few low angle peaks. This can be addressed by setting X to 0.0 and
903refining U, V, W, Y and SH/L but not X in the ÒInstrument ParametersÓ tree item.
904Then return to the ÒPeak ListÓ tree item to use the Peak Fitting/<span
905class=SpellE>Peakfit</span> menu command. Finally, return to ÒInstrument
906ParametersÓ and use Operations/Save Profile to write the improved values to <span
907class=GramE>an .<span class=SpellE>instparm</span></span> file.<o:p></o:p></span></p>
908
909<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
910
911<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
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914 mso-wrap-style:square'>
915 <v:imagedata src="FPAfit_files/image021.png" o:title=""/>
916</v:shape><![endif]--><![if !vml]><img border=0 width=434 height=211
917src="FPAfit_files/image022.png" v:shapes="Picture_x0020_12"><![endif]></span><span
918style='font-size:14.0pt'><o:p></o:p></span></p>
919
920<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
921mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_11" o:spid="_x0000_i1025"
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923 mso-wrap-style:square'>
924 <v:imagedata src="FPAfit_files/image023.png" o:title=""/>
925</v:shape><![endif]--><![if !vml]><img border=0 width=362 height=262
926src="FPAfit_files/image024.png" v:shapes="Picture_x0020_11"><![endif]></span><span
927style='font-size:14.0pt'><o:p></o:p></span></p>
928
929<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
930
931<h2><span style='mso-bidi-font-weight:normal'>7.</span> Supplying NIST FPA input
932manually. <o:p></o:p></h2>
933
934<p class=MsoNormal><span style='font-size:14.0pt'>Once FPA values have been
935entered, the ÒSave FPA <span class=SpellE>dict</span>Ó button can be pressed. <span
936style="mso-spacerun:yes">&nbsp;</span>The <span class=GramE>contents of this
937file, slightly reformatted for more easy reading, is</span> shown below. Note
938that the <span class=SpellE>dict</span> keys and values use the naming and SI units
939from <span class=SpellE>convolutors</span> the NIST FPA program. By editing
940this file, it is possible to use all of the convolution features within the
941NIST program, beyond the values that can be edited from the GUI. <o:p></o:p></span></p>
942
943<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
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992 <v:textbox>
993  <![if !mso]>
994  <table cellpadding=0 cellspacing=0 width="100%">
995   <tr>
996    <td><![endif]>
997    <div>
998    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
999    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1000    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1001    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'># <span
1002    class=GramE>parameters</span> to be used in the NIST XRD Fundamental
1003    Parameters program<o:p></o:p></span></p>
1004    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1005    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1006    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1007    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'>{<o:p></o:p></span></p>
1008    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1009    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1010    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1011    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1012    style="mso-spacerun:yes">&nbsp;&nbsp; </span><span class=GramE>'' :</span>
1013    {'<span class=SpellE>diffractometer_radius</span>': 0.22, '<span
1014    class=SpellE>equatorial_divergence_deg</span>': 0.5, <o:p></o:p></span></p>
1015    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1016    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1017    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1018    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1019    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1020    </span>'<span class=GramE>oversampling'</span>: 8, <o:p></o:p></span></p>
1021    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1022    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1023    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1024    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1025    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1026    </span>'<span class=SpellE><span class=GramE>dominant</span>_wavelength</span>':
1027    1.540596e-10},<span style="mso-spacerun:yes">&nbsp; </span># global
1028    parameters<o:p></o:p></span></p>
1029    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1030    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1031    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1032    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><o:p>&nbsp;</o:p></span></p>
1033    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1034    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1035    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1036    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1037    style="mso-spacerun:yes">&nbsp;&nbsp; </span>'<span class=GramE>axial'</span>
1038    : {'<span class=SpellE>angI_deg</span>': 2.0, '<span class=SpellE>axDiv</span>':
1039    'full', '<span class=SpellE>angD_deg</span>': 2.0,<o:p></o:p></span></p>
1040    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1041    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1042    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1043    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1044    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1045    </span><span style="mso-spacerun:yes">&nbsp;</span><span
1046    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;</span>'<span
1047    class=SpellE><span class=GramE>n</span>_integral_points</span>': 10,
1048    'slit_length_target':0.01200012,<o:p></o:p></span></p>
1049    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1050    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1051    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1052    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1053    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1054    </span><span style="mso-spacerun:yes">&nbsp;</span><span
1055    style="mso-spacerun:yes">&nbsp;&nbsp;</span>'<span class=SpellE><span
1056    class=GramE>length</span>_sample</span>': 0.012, '<span class=SpellE>slit_length_source</span>':
1057    0.012},<o:p></o:p></span></p>
1058    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1059    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1060    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1061    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><o:p>&nbsp;</o:p></span></p>
1062    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1063    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1064    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1065    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1066    style="mso-spacerun:yes">&nbsp;&nbsp; </span>'<span class=GramE>emission'</span>
1067    : {'<span class=SpellE>emiss_lor_widths</span>': array([<span
1068    style="mso-spacerun:yes">&nbsp; </span>5.01844e-14,<span
1069    style="mso-spacerun:yes">&nbsp;&nbsp; </span>6.26579e-14]),<o:p></o:p></span></p>
1070    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1071    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1072    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1073    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1074    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1075    </span><span style="mso-spacerun:yes">&nbsp;</span>'<span class=SpellE><span
1076    class=GramE>emiss</span>_intensities</span>': array([ 1.<span
1077    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1078    </span>,<span style="mso-spacerun:yes">&nbsp; </span>0.52947996]),<o:p></o:p></span></p>
1079    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1080    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1081    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1082    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1083    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1084    </span><span style="mso-spacerun:yes">&nbsp;</span><span
1085    style="mso-spacerun:yes">&nbsp;&nbsp;</span>'<span class=SpellE><span
1086    class=GramE>crystallite</span>_size_lor</span>': 0.001, <o:p></o:p></span></p>
1087    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1088    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1089    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1090    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1091    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
1092    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>'<span
1093    class=SpellE><span class=GramE>emiss</span>_wavelengths</span>':
1094    array([<span style="mso-spacerun:yes">&nbsp; </span>1.540596e-10,<span
1095    style="mso-spacerun:yes">&nbsp;&nbsp; </span>1.544493e-10]),<o:p></o:p></span></p>
1096    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1097    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1098    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1099    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1100    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
1101    style="mso-spacerun:yes">&nbsp;</span><span
1102    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>'<span
1103    class=SpellE><span class=GramE>emiss</span>_gauss_widths</span>':
1104    array([<span style="mso-spacerun:yes">&nbsp; </span>1.0e-16,<span
1105    style="mso-spacerun:yes">&nbsp;&nbsp; </span>1.0e-16]),<o:p></o:p></span></p>
1106    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1107    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1108    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1109    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1110    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1111    </span><span style="mso-spacerun:yes">&nbsp;</span>'<span class=SpellE><span
1112    class=GramE>crystallite</span>_size_gauss</span>': 0.001},<o:p></o:p></span></p>
1113    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1114    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1115    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1116    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><o:p>&nbsp;</o:p></span></p>
1117    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1118    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1119    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1120    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1121    style="mso-spacerun:yes">&nbsp;&nbsp; </span>'<span class=SpellE><span
1122    class=GramE>receiver</span>_slit</span>' : {'<span class=SpellE>slit_width</span>':
1123    0.0002},<o:p></o:p></span></p>
1124    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1125    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1126    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1127    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><o:p>&nbsp;</o:p></span></p>
1128    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1129    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1130    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1131    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1132    style="mso-spacerun:yes">&nbsp;&nbsp; </span>'<span class=SpellE><span
1133    class=GramE>tube</span>_tails</span>' : {'<span class=SpellE>tail_intens</span>':
1134    0.001, '<span class=SpellE>tail_left</span>': 0.001, <o:p></o:p></span></p>
1135    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1136    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1137    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1138    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1139    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1140    </span>'<span class=SpellE><span class=GramE>main</span>_width</span>':
1141    4e-05, '<span class=SpellE>tail_right</span>': 0.001},<o:p></o:p></span></p>
1142    <p class=MsoNormal style='mso-pagination:none;tab-stops:28.0pt 56.0pt 84.0pt 112.0pt 140.0pt 168.0pt 196.0pt 224.0pt 3.5in 280.0pt 308.0pt 336.0pt;
1143    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1144    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1145    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'>}<o:p></o:p></span></p>
1146    <p class=MsoNormal><span style='font-family:Courier'><o:p>&nbsp;</o:p></span></p>
1147    </div>
1148    <![if !mso]></td>
1149   </tr>
1150  </table>
1151  <![endif]></v:textbox>
1152 <w:wrap type="square"/>
1153</v:shape><![endif]--><![if !vml]><img width=575 height=293
1154src="FPAfit_files/image025.png" align=left hspace=9
1155alt="Text Box: # parameters to be used in the NIST XRD Fundamental Parameters program&#13;{&#13;   '' : {'diffractometer_radius': 0.22, 'equatorial_divergence_deg': 0.5, &#13;          'oversampling': 8, &#13;          'dominant_wavelength': 1.540596e-10},  # global parameters&#13;&#13;   'axial' : {'angI_deg': 2.0, 'axDiv': 'full', 'angD_deg': 2.0,&#13;              'n_integral_points': 10, 'slit_length_target':0.01200012,&#13;              'length_sample': 0.012, 'slit_length_source': 0.012},&#13;&#13;   'emission' : {'emiss_lor_widths': array([  5.01844e-14,   6.26579e-14]),&#13;                 'emiss_intensities': array([ 1.        ,  0.52947996]),&#13;                 'crystallite_size_lor': 0.001, &#13;                 'emiss_wavelengths': array([  1.540596e-10,   1.544493e-10]),&#13;                 'emiss_gauss_widths': array([  1.0e-16,   1.0e-16]),&#13;                 'crystallite_size_gauss': 0.001},&#13;&#13;   'receiver_slit' : {'slit_width': 0.0002},&#13;&#13;   'tube_tails' : {'tail_intens': 0.001, 'tail_left': 0.001, &#13;                    'main_width': 4e-05, 'tail_right': 0.001},&#13;}&#13;&#13;"
1156v:shapes="Text_x0020_Box_x0020_13"><![endif]><span style='font-size:14.0pt'><o:p></o:p></span></p>
1157
1158</div>
1159
1160</body>
1161
1162</html>
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