source: Tutorials/FPAfit/FPAfit.htm @ 4271

Last change on this file since 4271 was 3780, checked in by toby, 3 years ago

fix typos; error in CIF Dij reporting; improve generalized restraint GUI

  • Property svn:mime-type set to text/html
File size: 61.2 KB
Line 
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25  <o:Author>Brian Toby</o:Author>
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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:
665  14.0pt'>The FPA peak shapes are computed with the NIST FPA Python code
666  </span>
667  (<A
668  HREF="http://dx.doi.org/10.6028/jres.120.014.c">http://dx.doi.org/10.6028/jres.120.014.c</A>),
669  <span style='font-size:14.0pt'>which should be cited using "Mendenhall, Marcus H.;
670Mullen, Katharine; &amp; Cline, James P.; <B>(2015)</B>. <i>
671An Implementation of the Fundamental
672Parameters Approach for Analysis of X-ray Powder Diffraction Line Profiles</i>.<Journal of Research of the National Institute of Standards
673and Technology.
674<b style='mso-bidi-font-weight:normal'>120</b> 223-251. <a
675href="http://dx.doi.org/10.6028/jres.120.014"
676title="Link to Mendenhall et al paper">10.6028/jres.120.014</a>," if this
677capability is used within GSAS-II. This code is used to generate a pattern with
678isolated peaks. The profile of these peaks is fit using profile parameters U,
679V, W, X, Y and SH/L. </span><span style='font-family:Times;mso-fareast-font-family:
680"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:
681Times;color:black'><o:p></o:p></span></p>
682
683<h2><span style='mso-bidi-font-weight:normal'>1.</span> Open the FPA module</h2>
684
685<p class=MsoNormal><o:p>&nbsp;</o:p></p>
686
687<p class=MsoNormal><span style='font-size:14.0pt'>To invoke this capability,
688the "Import/Powder Data/Fit instr. profile from fundamental <span class=SpellE>parms</span>É"
689menu command is used. This opens a dialog, as below <o:p></o:p></span></p>
690
691<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
692
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718
719<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
720
721<p class=MsoNormal><span style='font-size:14.0pt'>This describes how a pattern
722will be generated. The computation should be done over the angular range at
723least as large as the data range for analysis of samples. Since we will fit
724several profile terms, at least double that number of peaks should be computed.
725The default of 13 peaks, to space them 10 degrees apart, works well here and
726would not need to be increased if a larger data range were used. Lowering this
727number might be needed to keep peaks from overlapping, if very broad peaks and
728a small data range are used. The pattern step size should allow at least 10 points
729above the half-intensity point in each peak, which would need to be made
730smaller with narrow peaks. As will be shown, this is checked, so leaving this
731as the default value is fine. Computing each peak over a 2-degree range is
732likely way more than what is needed in this example, but also does not slow the
733computation noticeably.<span style="mso-spacerun:yes">&nbsp; </span>This might
734need to be changed with very broad or very narrow peaks. For this example, we
735will not change any parameters.<o:p></o:p></span></p>
736
737<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
738
739<h2><span style='mso-bidi-font-weight:normal'>2.</span> Input FPA parameters<o:p></o:p></h2>
740
741<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
742
743<p class=MsoNormal><span style='font-size:14.0pt'>The FP parameters can be
744input in one of two ways. They can be read from a file, which can be
745hand-edited to access the full range of capabilities in the NIST FPA Python
746code (discussed further in "7. Supplying NIST FPA input manually" below) or can
747be input from another dialog window. Press the "Input FP <span class=SpellE>vals</span>"
748button, which opens the window shown below:<o:p></o:p></span></p>
749
750<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
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759style='font-size:14.0pt'><o:p></o:p></span></p>
760
761<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
762
763<p class=MsoNormal><span style='font-size:14.0pt'>The top section of the dialog
764window specifies the details of the radiation source, where any number of
765components can be given. Two common default settings with Cu K</span><span
766style='font-family:"Lucida Grande";color:black'>&#945;</span><span
767style='font-size:14.0pt'> radiation modeled as a 2-line or 5-line spectrum.<span
768style="mso-spacerun:yes">&nbsp; </span>The input can also be switched from
769Point-detector mode (as is shown above) to position-sensitive-detector mode, by
770pressing the PSD button. Note that parameters are named similar to their use in
771the <span class=SpellE>Topas</span> program with the same units. <o:p></o:p></span></p>
772
773<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
774
775<h2><span style='mso-bidi-font-weight:normal'>3.</span> Plot the peak shape and
776convolution contributions (optional)<o:p></o:p></h2>
777
778<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
779
780<p class=MsoNormal><span style='font-size:14.0pt'>The "Plot peak" button at the
781bottom of the window can be used to visualize the resulting peak shape at any
782position in 2-theta, as well as all the contributions to <span class=GramE>the</span>
783peak shape, like this:<o:p></o:p></span></p>
784
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799
800<p class=MsoNormal><span style='font-size:14.0pt'>Note that distinguishing the
801components in the peak convolution functions plot can be difficult. Clicking on
802an entry in the legend changes the display of that component, as shown below
803where "emission" in the legend was clicked:<o:p></o:p></span></p>
804
805<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
806mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_5" o:spid="_x0000_i1032"
807 type="#_x0000_t75" style='width:324pt;height:226pt;visibility:visible;
808 mso-wrap-style:square'>
809 <v:imagedata src="FPAfit_files/image009.png" o:title=""/>
810</v:shape><![endif]--><![if !vml]><img border=0 width=326 height=228
811src="FPAfit_files/image010.png" v:shapes="Picture_x0020_5"><![endif]></span><span
812style='font-size:14.0pt'><o:p></o:p></span></p>
813
814<h2><span style='mso-bidi-font-weight:normal'><o:p>&nbsp;</o:p></span></h2>
815
816<h2><span style='mso-bidi-font-weight:normal'>4.</span> Accept the FPA values,
817correct the step size</h2>
818
819<p class=MsoNormal><span style='font-size:14.0pt'>For this example, we will not
820change any of the default FPA parameters. Press OK to accept the displayed values
821and to close the dialog window. The pattern step size is then checked,
822producing the following warning: <o:p></o:p></span></p>
823
824<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
825mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_6" o:spid="_x0000_i1031"
826 type="#_x0000_t75" style='width:4in;height:105pt;visibility:visible;
827 mso-wrap-style:square'>
828 <v:imagedata src="FPAfit_files/image011.png" o:title=""/>
829</v:shape><![endif]--><![if !vml]><img border=0 width=290 height=107
830src="FPAfit_files/image012.png" v:shapes="Picture_x0020_6"><![endif]></span><span
831style='font-size:14.0pt'><o:p></o:p></span></p>
832
833<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
834
835<p class=MsoNormal><span style='font-size:14.0pt'>Note that the Pattern step
836size is changed, as below. <span style="mso-spacerun:yes">&nbsp;</span><o:p></o:p></span></p>
837
838<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
839mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_7" o:spid="_x0000_i1030"
840 type="#_x0000_t75" style='width:324pt;height:275pt;visibility:visible;
841 mso-wrap-style:square'>
842 <v:imagedata src="FPAfit_files/image013.png" o:title=""/>
843</v:shape><![endif]--><![if !vml]><img border=0 width=326 height=277
844src="FPAfit_files/image014.png" v:shapes="Picture_x0020_7"><![endif]></span><span
845style='font-size:14.0pt'><o:p></o:p></span></p>
846
847<p class=MsoNormal><span style='font-size:14.0pt'>Also note that after values
848have been entered, the "Save FPA <span class=SpellE>dict</span>" button is now
849available. <o:p></o:p></span></p>
850
851<h2><span style='mso-bidi-font-weight:normal'>5.</span> Perform the computation<o:p></o:p></h2>
852
853<p class=MsoNormal><span style='font-size:14.0pt'>Press OK to start the
854computation. A "please wait" message is displayed<o:p></o:p></span></p>
855
856<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
857mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_8" o:spid="_x0000_i1029"
858 type="#_x0000_t75" style='width:262pt;height:161pt;visibility:visible;
859 mso-wrap-style:square'>
860 <v:imagedata src="FPAfit_files/image015.png" o:title=""/>
861</v:shape><![endif]--><![if !vml]><img border=0 width=264 height=163
862src="FPAfit_files/image016.png" v:shapes="Picture_x0020_8"><![endif]></span><span
863style='font-size:14.0pt'><o:p></o:p></span></p>
864
865<p class=MsoNormal><span class=GramE><span style='font-size:14.0pt'>as</span></span><span
866style='font-size:14.0pt'> the fitting may take a few minutes (output can be
867seen in the console window as the fit progresses). When the fit is complete,
868you will be provided with a window to save the instrument parameters to <span
869class=GramE>an .<span class=SpellE>instparm</span></span> file. After the
870parameters have been saved, the fit will be plotted (here I have switched to
871the main PWDR tree entry and dragged the difference curve down so that it can
872be seen better.) <o:p></o:p></span></p>
873
874<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
875mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_9" o:spid="_x0000_i1028"
876 type="#_x0000_t75" style='width:364pt;height:262pt;visibility:visible;
877 mso-wrap-style:square'>
878 <v:imagedata src="FPAfit_files/image017.png" o:title=""/>
879</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=264
880src="FPAfit_files/image018.png" v:shapes="Picture_x0020_9"><![endif]></span><span
881style='font-size:14.0pt'><o:p></o:p></span></p>
882
883<p class=MsoNormal><span style='font-size:14.0pt'>Clicking on the Instrument Parameters
884tree entry causes the powder profile terms to be plotted: <o:p></o:p></span></p>
885
886<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
887mso-no-proof:yes'><!--[if gte vml 1]><v:shape id="Picture_x0020_10" o:spid="_x0000_i1027"
888 type="#_x0000_t75" style='width:324pt;height:236pt;visibility:visible;
889 mso-wrap-style:square'>
890 <v:imagedata src="FPAfit_files/image019.png" o:title=""/>
891</v:shape><![endif]--><![if !vml]><img border=0 width=326 height=238
892src="FPAfit_files/image020.png" v:shapes="Picture_x0020_10"><![endif]></span><span
893style='font-size:14.0pt'><span style="mso-spacerun:yes">&nbsp;</span><o:p></o:p></span></p>
894
895<h2><span style='mso-bidi-font-weight:normal'><o:p>&nbsp;</o:p></span></h2>
896
897<h2><span style='mso-bidi-font-weight:normal'>6.</span> Improve the profile
898parameters. </h2>
899
900<p class=MsoNormal><span style='font-size:14.0pt'>Note that due to correlation
901between the peak asymmetry parameter (SH/L) and the <span class=SpellE>Lorentzian</span>
902broadening terms, the Gamma (Lorentz width) terms refine to negative values for
903the first few low angle peaks. This can be addressed by setting X to 0.0 and
904refining U, V, W, Y and SH/L but not X in the "Instrument Parameters" tree item.
905Then return to the "Peak List" tree item to use the Peak Fitting/<span
906class=SpellE>Peakfit</span> menu command. Finally, return to "Instrument
907Parameters" and use Operations/Save Profile to write the improved values to <span
908class=GramE>an .<span class=SpellE>instparm</span></span> file.<o:p></o:p></span></p>
909
910<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
911
912<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
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915 mso-wrap-style:square'>
916 <v:imagedata src="FPAfit_files/image021.png" o:title=""/>
917</v:shape><![endif]--><![if !vml]><img border=0 width=434 height=211
918src="FPAfit_files/image022.png" v:shapes="Picture_x0020_12"><![endif]></span><span
919style='font-size:14.0pt'><o:p></o:p></span></p>
920
921<p class=MsoNormal><span style='font-size:14.0pt;mso-fareast-language:EN-US;
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924 mso-wrap-style:square'>
925 <v:imagedata src="FPAfit_files/image023.png" o:title=""/>
926</v:shape><![endif]--><![if !vml]><img border=0 width=362 height=262
927src="FPAfit_files/image024.png" v:shapes="Picture_x0020_11"><![endif]></span><span
928style='font-size:14.0pt'><o:p></o:p></span></p>
929
930<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
931
932<h2><span style='mso-bidi-font-weight:normal'>7.</span> Supplying NIST FPA input
933manually. <o:p></o:p></h2>
934
935<p class=MsoNormal><span style='font-size:14.0pt'>Once FPA values have been
936entered, the "Save FPA <span class=SpellE>dict</span>" button can be pressed. <span
937style="mso-spacerun:yes">&nbsp;</span>The <span class=GramE>contents of this
938file, slightly reformatted for more easy reading, is</span> shown below. Note
939that the <span class=SpellE>dict</span> keys and values use the naming and SI units
940from <span class=SpellE>convolutors</span> the NIST FPA program. By editing
941this file, it is possible to use all of the convolution features within the
942NIST program, beyond the values that can be edited from the GUI. <o:p></o:p></span></p>
943
944<p class=MsoNormal><span style='font-size:14.0pt'><o:p>&nbsp;</o:p></span></p>
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994  <![if !mso]>
995  <table cellpadding=0 cellspacing=0 width="100%">
996   <tr>
997    <td><![endif]>
998    <div>
999    <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;
1000    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1001    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1002    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'># <span
1003    class=GramE>parameters</span> to be used in the NIST XRD Fundamental
1004    Parameters program<o:p></o:p></span></p>
1005    <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;
1006    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1007    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1008    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'>{<o:p></o:p></span></p>
1009    <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;
1010    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1011    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1012    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1013    style="mso-spacerun:yes">&nbsp;&nbsp; </span><span class=GramE>'' :</span>
1014    {'<span class=SpellE>diffractometer_radius</span>': 0.22, '<span
1015    class=SpellE>equatorial_divergence_deg</span>': 0.5, <o:p></o:p></span></p>
1016    <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;
1017    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1018    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1019    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1020    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1021    </span>'<span class=GramE>oversampling'</span>: 8, <o:p></o:p></span></p>
1022    <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;
1023    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1024    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1025    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1026    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1027    </span>'<span class=SpellE><span class=GramE>dominant</span>_wavelength</span>':
1028    1.540596e-10},<span style="mso-spacerun:yes">&nbsp; </span># global
1029    parameters<o:p></o:p></span></p>
1030    <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;
1031    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1032    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1033    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><o:p>&nbsp;</o:p></span></p>
1034    <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;
1035    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1036    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1037    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1038    style="mso-spacerun:yes">&nbsp;&nbsp; </span>'<span class=GramE>axial'</span>
1039    : {'<span class=SpellE>angI_deg</span>': 2.0, '<span class=SpellE>axDiv</span>':
1040    'full', '<span class=SpellE>angD_deg</span>': 2.0,<o:p></o:p></span></p>
1041    <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;
1042    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1043    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1044    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1045    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1046    </span><span style="mso-spacerun:yes">&nbsp;</span><span
1047    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;</span>'<span
1048    class=SpellE><span class=GramE>n</span>_integral_points</span>': 10,
1049    'slit_length_target':0.01200012,<o:p></o:p></span></p>
1050    <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;
1051    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1052    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1053    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1054    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1055    </span><span style="mso-spacerun:yes">&nbsp;</span><span
1056    style="mso-spacerun:yes">&nbsp;&nbsp;</span>'<span class=SpellE><span
1057    class=GramE>length</span>_sample</span>': 0.012, '<span class=SpellE>slit_length_source</span>':
1058    0.012},<o:p></o:p></span></p>
1059    <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;
1060    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1061    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1062    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><o:p>&nbsp;</o:p></span></p>
1063    <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;
1064    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1065    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1066    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1067    style="mso-spacerun:yes">&nbsp;&nbsp; </span>'<span class=GramE>emission'</span>
1068    : {'<span class=SpellE>emiss_lor_widths</span>': array([<span
1069    style="mso-spacerun:yes">&nbsp; </span>5.01844e-14,<span
1070    style="mso-spacerun:yes">&nbsp;&nbsp; </span>6.26579e-14]),<o:p></o:p></span></p>
1071    <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;
1072    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1073    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1074    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1075    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1076    </span><span style="mso-spacerun:yes">&nbsp;</span>'<span class=SpellE><span
1077    class=GramE>emiss</span>_intensities</span>': array([ 1.<span
1078    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1079    </span>,<span style="mso-spacerun:yes">&nbsp; </span>0.52947996]),<o:p></o:p></span></p>
1080    <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;
1081    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1082    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1083    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1084    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1085    </span><span style="mso-spacerun:yes">&nbsp;</span><span
1086    style="mso-spacerun:yes">&nbsp;&nbsp;</span>'<span class=SpellE><span
1087    class=GramE>crystallite</span>_size_lor</span>': 0.001, <o:p></o:p></span></p>
1088    <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;
1089    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1090    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1091    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1092    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
1093    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>'<span
1094    class=SpellE><span class=GramE>emiss</span>_wavelengths</span>':
1095    array([<span style="mso-spacerun:yes">&nbsp; </span>1.540596e-10,<span
1096    style="mso-spacerun:yes">&nbsp;&nbsp; </span>1.544493e-10]),<o:p></o:p></span></p>
1097    <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;
1098    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1099    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1100    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1101    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><span
1102    style="mso-spacerun:yes">&nbsp;</span><span
1103    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span>'<span
1104    class=SpellE><span class=GramE>emiss</span>_gauss_widths</span>':
1105    array([<span style="mso-spacerun:yes">&nbsp; </span>1.0e-16,<span
1106    style="mso-spacerun:yes">&nbsp;&nbsp; </span>1.0e-16]),<o:p></o:p></span></p>
1107    <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;
1108    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1109    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1110    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1111    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1112    </span><span style="mso-spacerun:yes">&nbsp;</span>'<span class=SpellE><span
1113    class=GramE>crystallite</span>_size_gauss</span>': 0.001},<o:p></o:p></span></p>
1114    <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;
1115    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1116    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1117    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><o:p>&nbsp;</o:p></span></p>
1118    <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;
1119    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1120    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1121    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1122    style="mso-spacerun:yes">&nbsp;&nbsp; </span>'<span class=SpellE><span
1123    class=GramE>receiver</span>_slit</span>' : {'<span class=SpellE>slit_width</span>':
1124    0.0002},<o:p></o:p></span></p>
1125    <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;
1126    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1127    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1128    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><o:p>&nbsp;</o:p></span></p>
1129    <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;
1130    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1131    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1132    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1133    style="mso-spacerun:yes">&nbsp;&nbsp; </span>'<span class=SpellE><span
1134    class=GramE>tube</span>_tails</span>' : {'<span class=SpellE>tail_intens</span>':
1135    0.001, '<span class=SpellE>tail_left</span>': 0.001, <o:p></o:p></span></p>
1136    <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;
1137    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1138    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1139    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'><span
1140    style="mso-spacerun:yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
1141    </span>'<span class=SpellE><span class=GramE>main</span>_width</span>':
1142    4e-05, '<span class=SpellE>tail_right</span>': 0.001},<o:p></o:p></span></p>
1143    <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;
1144    mso-layout-grid-align:none;text-autospace:none'><span style='font-family:
1145    Courier;mso-fareast-font-family:"\FF2D\FF33 \660E\671D";mso-fareast-theme-font:
1146    minor-fareast;mso-bidi-font-family:"Menlo Regular";color:black'>}<o:p></o:p></span></p>
1147    <p class=MsoNormal><span style='font-family:Courier'><o:p>&nbsp;</o:p></span></p>
1148    </div>
1149    <![if !mso]></td>
1150   </tr>
1151  </table>
1152  <![endif]></v:textbox>
1153 <w:wrap type="square"/>
1154</v:shape><![endif]--><![if !vml]><img width=575 height=293
1155src="FPAfit_files/image025.png" align=left hspace=9
1156alt="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;"
1157v:shapes="Text_x0020_Box_x0020_13"><![endif]><span style='font-size:14.0pt'><o:p></o:p></span></p>
1158
1159</div>
1160
1161</body>
1162
1163</html>
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