source: Tutorials/Simulation/SimTutorial.htm @ 4627

Last change on this file since 4627 was 4457, checked in by toby, 18 months ago

add data link to tutorials

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531
532<h1><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
533"Times New Roman"'>Simulating Powder Diffraction with GSAS-II<o:p></o:p></span></h1>
534
535<P><BL>
536  <LI><B>A video version of this tutorial is available at
537<A href="https://anl.box.com/v/SimTutorial-" target="_blank">
538https://anl.box.com/v/SimTutorial-</A></B>
539  <LI>Exercise files are found <A href="./data/" target="_blank">here</a>
540</BL></P><P></P>
541
542<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
543mso-bidi-font-family:"Times New Roman"'>While GSAS-II provides an environment
544for fitting of diffraction data, it can also be used to simulate diffraction
545experiments, where results are quantitative models for what can be expected,
546provided that an accurate instrument description is used. Here we demonstrate
547how a simulation is done for a two-phase mixture with multiple instrument
548types. <o:p></o:p></span></p>
549
550<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
551"Times New Roman"'>Step 1: Read in Phases<o:p></o:p></span></h2>
552
553<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
554mso-bidi-font-family:"Times New Roman"'>First we will read in two phases, CuCr<sub>2</sub>O<sub>4</sub>
555and <span class=SpellE>CuO</span> from files CuCr2O4.cif and <span
556class=SpellE>CuO.cif</span>, which can be downloaded from <a
557href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/Simulation/data/">directory
558https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/Simulation/data/</a>. <o:p></o:p></span></p>
559
560<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
561mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
562
563<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
564mso-bidi-font-family:"Times New Roman"'>Create a new project by starting GSAS-II
565or by using the File/New Project menu item. Then use the Import/Phase/“from CIF
566file” and select the CuCr2O4.cif for the “Choose Phase input file” dialog window.
567Click “Ok” and “Yes” in the “Is this <span class=SpellE>the</span> file you
568want?” confirmation window. <span style="mso-spacerun:yes"> </span>The default
569Phase name, CuCr2O4 is fine.<o:p></o:p></span></p>
570
571<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
572mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
573
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607style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
608"Times New Roman"'>Repeat this to read in the second phase: use the
609Import/Phase/“from CIF file” and select the <span class=SpellE>CuO.cif</span>
610for the “Choose Phase input file” dialog window. Click “Ok” and “Yes” in the “Is
611this the file you want?” confirmation window. <span
612style="mso-spacerun:yes"> </span>The default Phase name, <span class=SpellE>CuO</span>
613is also fine.<o:p></o:p></span></p>
614
615<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
616mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
617
618<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
619"Times New Roman"'>Step 2: Create Simulation Histograms<o:p></o:p></span></h2>
620
621<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span
622style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
623"Times New Roman"'>Part A</span></b><span style='font-size:12.0pt;mso-fareast-font-family:
624"Times New Roman";mso-bidi-font-family:"Times New Roman"'>: Use the
625Import/Powder Data/“Simulate a dataset” menu item (at bottom of menu list) to
626create a simulation (dummy) histogram. The program then requests an instrument
627parameter file name. Click Cancel and a list of default instrument parameters
628are then displayed, as shown to the right. Select the APS 11-BM instrument
629listing and press OK.</span> <span style='font-size:12.0pt;mso-fareast-font-family:
630"Times New Roman";mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p>
631
632<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
633mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
634
635<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
636mso-bidi-font-family:"Times New Roman"'>A dialog window is then displayed that with
637the name for the histogram, the range of data and the step size. Below, note
638that the name and start angle have been changed from the defaults. Then press
639OK and the “Add to phase(s)” dialog is displayed. <o:p></o:p></span></p>
640
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650
651<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
652mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
653
654<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
655mso-bidi-font-family:"Times New Roman"'>Finally, in this dialog, we need to
656indicate which phases are linked with this histogram. We want to include both
657in the simulation, so use the “Set All” button (or select each phase) and press
658OK.<o:p></o:p></span></p>
659
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669
670<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
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672
673<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
674mso-bidi-font-family:"Times New Roman"'>Note that a new histogram is now added
675to the data tree, as below. (Note the "Edit range" button which can be
676used to change the values entered on the previous dialog).
677<o:p></o:p></span></p>
678
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688
689<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
690mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
691
692<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span
693style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
694"Times New Roman"'>Part B</span></b><span style='font-size:12.0pt;mso-fareast-font-family:
695"Times New Roman";mso-bidi-font-family:"Times New Roman"'>: Again use the
696Import/Powder Data/“Simulate a dataset” menu item (at bottom of menu list) to
697create a simulation (dummy) histogram. This time when the program then requests
698an instrument parameter file name, supply file BT1.prm, which can also be
699downloaded from <a
700href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/Simulation/data/">directory
701https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/Simulation/data/</a>. <o:p></o:p></span></p>
702
703<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
704mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
705
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715
716<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
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718
719<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
720mso-bidi-font-family:"Times New Roman"'>Click Open and a dialog opens for the
721dataset name and range for this histogram. Change the range to 1 to 120 degrees
722with 0<span class=GramE>.025 degree</span> steps and optionally change the
723name, as below. <o:p></o:p></span></p>
724
725<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
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736
737<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
738mso-bidi-font-family:"Times New Roman"'>Press OK and then the
739“Add to phase(s)” dialog is displayed. As
740before, add link both phases to this histogram. <span
741style="mso-spacerun:yes"> </span>At this point a second histogram is shown in
742the data tree:<o:p></o:p></span></p>
743
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749 <v:imagedata src="SimTutorial_files/image013.png" o:title=""/>
750</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=230
751src="SimTutorial_files/image014.png" v:shapes="Picture_x0020_17"><![endif]></span><span
752style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
753"Times New Roman"'><o:p></o:p></span></p>
754
755<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
756"Times New Roman"'>Step 3: Set Phase Fractions<o:p></o:p></span></h2>
757
758<p class=MsoNormal><!--[if gte vml 1]><v:shape id="Picture_x0020_1" o:spid="_x0000_s1026"
759 type="#_x0000_t75" alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f1.png"
760 style='position:absolute;margin-left:300.4pt;margin-top:70.5pt;width:351.6pt;
761 height:188.1pt;z-index:251658240;visibility:visible;mso-wrap-style:square;
762 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
763 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
764 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
765 mso-position-horizontal-relative:text;mso-position-vertical:absolute;
766 mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0;
767 mso-width-relative:page;mso-height-relative:page'>
768 <v:imagedata src="SimTutorial_files/image015.png" o:title="f1.png"/>
769 <w:wrap type="tight"/>
770</v:shape><![endif]--><![if !vml]><img width=354 height=190
771src="SimTutorial_files/image016.png" align=right hspace=9
772alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f1.png" v:shapes="Picture_x0020_1"><![endif]><span
773style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
774"Times New Roman"'>It is important to understand how the scale factor (found
775each histogram's Sample Parameters tree entry) and phase fractions (found in
776each phase's data tab) are used in GSAS-II. The scattering contribution for
777each phase is set from the product of the histogram scale factor multiplied by
778the phase fraction for each phase in that histogram which multiplies the
779scattering power of each atom in the unit cell. This means that the phase
780fraction effectively represents the relative number of unit cells present for
781each phase. Note that after reading in the two phases in the previous step,
782their phase fractions default to 1 for each. The contents of each phase are
783shown on the General tab. Note that the unit cell contents for each phase are
784Cu<sub>8</sub>Cr<sub>16</sub>O<sub>32</sub> (1852.3 g/<span class=SpellE>mol</span>)
785and Cu<sub>4</sub>O<sub>4</sub> (318.2 g/<span class=SpellE>mol</span>), with
786equal numbers of unit cells, the mass (or equivalently weight) fractions will
787be 1852.3/(318.2+1852.3)=85.3% and 318.2/(318.2+1852.3)=14.7%. This can be
788confirmed on the Data for each phase, as below.<o:p></o:p></span></p>
789
790<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
791mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
792 id="Picture_x0020_3" o:spid="_x0000_i1032" type="#_x0000_t75" alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f2.png"
793 style='width:453pt;height:170pt;visibility:visible;mso-wrap-style:square'>
794 <v:imagedata src="SimTutorial_files/image017.png" o:title="f2.png"/>
795</v:shape><![endif]--><![if !vml]><img border=0 width=455 height=172
796src="SimTutorial_files/image018.png"
797alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f2.png" v:shapes="Picture_x0020_3"><![endif]></span><span
798style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
799"Times New Roman"'><o:p></o:p></span></p>
800
801<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
802mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
803
804<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
805mso-bidi-font-family:"Times New Roman"'>For this tutorial, we will choose to
806set the mass fractions to give 90% CuCr<sub>2</sub>O<sub>4</sub> and 10% <span
807class=SpellE>CuO</span>, so 90/1852.3=</span><span style='font-size:12.0pt;
808font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
809color:black'>0.04859 and 10/</span><span style='font-size:12.0pt;mso-fareast-font-family:
810"Times New Roman";mso-bidi-font-family:"Times New Roman"'>318.2=0.03143. Equivalently,
811we can normalize the phase fractions sum to 1 or so that either phase fraction is
8121. We will use 1 for CuCr<sub>2</sub>O<sub>4</sub>, and </span><span
813style='font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-family:
814"Times New Roman";color:black'>10*</span><span style='font-size:12.0pt;
815mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'>1852.3</span><span
816style='font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-family:
817"Times New Roman";color:black'>/(</span><span style='font-size:12.0pt;
818mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'>318.2*90)=0.6468
819for <span class=SpellE>CuO</span>. Enter 0.6468 for the <span class=SpellE>CuO</span>
820Phase fraction. <span style="mso-spacerun:yes"> </span>When the mouse is moved
821out of the box, the mass fraction to be recomputed and appears as 10%, as
822expected:<o:p></o:p></span></p>
823
824<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
825mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
826 id="Picture_x0020_18" o:spid="_x0000_i1031" type="#_x0000_t75" alt="Description: BHT14 HD:Users:toby:Library:Mobile Documents:com~apple~Preview:Documents:Untitled.png"
827 style='width:451pt;height:238pt;visibility:visible;mso-wrap-style:square'>
828 <v:imagedata src="SimTutorial_files/image019.png" o:title="Untitled.png"/>
829</v:shape><![endif]--><![if !vml]><img border=0 width=453 height=240
830src="SimTutorial_files/image020.png"
831alt="Description: BHT14 HD:Users:toby:Library:Mobile Documents:com~apple~Preview:Documents:Untitled.png"
832v:shapes="Picture_x0020_18"><![endif]></span><span style='font-size:12.0pt;
833mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p>
834
835<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
836mso-bidi-font-family:"Times New Roman"'>This must be set for both histograms.
837Clicking on the second histogram allows that phase fraction to be edited. Even easier
838is to use the “Edit Phase”/“Copy data” menu item to copy all <span
839class=SpellE>CuO</span> data settings from histogram 1 to histogram 2. Note
840that if the CuCr<sub>2</sub>O<sub>4 </sub>Data tab is selected for either phase,
841the mass fraction is now shown as 90%. <o:p></o:p></span></p>
842
843<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
844"Times New Roman"'>Step 4: Turn off Optimization<o:p></o:p></span></h2>
845
846<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
847mso-bidi-font-family:"Times New Roman"'>A refinement computation is needed to
848cause the pattern to be simulated. When a pattern is first simulated, the
849observed pattern is set to the computed pattern (this can be reset by
850using the "Edit range" button when the histogram data tree item is
851selected. This means that it is actually
852possible to optimize any parameters that are selected to be refined,
853which can be used to test the sensitivity of different models refined
854against a
855simulated dataset. In this case we only need to compute the simulated
856pattern, so we will turn off optimization by setting the
857number of cycles to zero. Do this by clicking on the Controls data tree entry and set the Max
858cycles value to 0 using the pull-down menu:<o:p></o:p></span></p>
859
860<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
861mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
862 id="Picture_x0020_5" o:spid="_x0000_i1030" type="#_x0000_t75" alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f4.png"
863 style='width:442pt;height:114pt;visibility:visible;mso-wrap-style:square'>
864 <v:imagedata src="SimTutorial_files/image021.png" o:title="f4.png"/>
865</v:shape><![endif]--><![if !vml]><img border=0 width=444 height=116
866src="SimTutorial_files/image022.png"
867alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f4.png" v:shapes="Picture_x0020_5"><![endif]></span><span
868style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
869"Times New Roman"'><o:p></o:p></span></p>
870
871<h2>Step 5: Change Histogram Scale Factor</h2>
872
873<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
874mso-bidi-font-family:"Times New Roman"'>As discussed earlier, the range of
875intensities is determined by the histogram scale factor. For x-rays, a
876histogram scale factor with the default value of 1 produces a reasonable
877intensity range, but with CW neutrons, a much larger scale factor value is
878needed to produce a pattern with non-negligible intensity values. Note that
879GSAS-II adds simulated noise to patterns, so if the scale factor is too small,
880only random counts are seen. Select the Sample Parameters tree item for the
881second histogram and change the scale factor to 1000, as below. </span></p>
882
883<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
884 id="Picture_x0020_20" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:370pt;
885 height:232pt;visibility:visible;mso-wrap-style:square'>
886 <v:imagedata src="SimTutorial_files/image023.png" o:title=""/>
887</v:shape><![endif]--><![if !vml]><img border=0 width=372 height=234
888src="SimTutorial_files/image024.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
889
890<h2>Step 6: Simulate the Pattern</h2>
891
892<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
893mso-bidi-font-family:"Times New Roman"'>Use the Calculate/Refine menu item to
894compute the simulated pattern. Clicking on the histogram entry in the data tree
895causes the pattern to be displayed as below. This has the reflection <span
896class=SpellE>tickmarks</span> and the difference curve located at zero. While
897both can be dragged to new positions, this is hard to do when they are obscured
898by the “observed” and computed patterns. (The observed pattern has been set to
899the computed pattern with the addition of simulated noise, which is why the
900difference curve is non-zero.)<o:p></o:p></span></p>
901
902<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
903mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
904 id="Picture_x0020_11" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:285pt;
905 height:243pt;visibility:visible;mso-wrap-style:square'>
906 <v:imagedata src="SimTutorial_files/image025.png" o:title=""/>
907</v:shape><![endif]--><![if !vml]><img border=0 width=287 height=245
908src="SimTutorial_files/image026.png" v:shapes="Picture_x0020_11"><![endif]></span><span
909style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
910"Times New Roman"'><o:p></o:p></span></p>
911
912<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
913mso-bidi-font-family:"Times New Roman"'>A nice trick for resetting the <span
914class=SpellE>tickmarks</span> to their usual default positions is to press “s”
915to scale to <span class=SpellE><span class=GramE>sqrt</span></span><span
916class=GramE>(</span>I) and press it again to return to normal scaling, as shown
917below. These changes in scaling can also be done via the “K” (keyboard) button
918on the bottom toolbar. <o:p></o:p></span></p>
919
920<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
921mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
922 id="Picture_x0020_12" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:285pt;
923 height:220pt;visibility:visible;mso-wrap-style:square'>
924 <v:imagedata src="SimTutorial_files/image027.png" o:title=""/>
925</v:shape><![endif]--><![if !vml]><img border=0 width=287 height=222
926src="SimTutorial_files/image028.png" v:shapes="Picture_x0020_12"><![endif]></span><span
927style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
928"Times New Roman"'><o:p></o:p></span></p>
929
930<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
931mso-bidi-font-family:"Times New Roman"'>Note that the Commands menu offers menu
932items for moving the difference curve and <span class=SpellE>tickmarks</span>,
933as well as using drag and drop. Use of this, as well as using the rescaling graphics
934toolbar item (the home button indicated by small house on the lower left)
935allows more fine arrangement of locations. Exporting the plot (using the “floppy
936disk” button allows the plots below to be created. Note the very big
937differences in intensities, data range and resolution between the two
938simulations. <o:p></o:p></span></p>
939
940<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
941mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
942 id="Picture_x0020_22" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:335pt;
943 height:214pt;visibility:visible;mso-wrap-style:square'>
944 <v:imagedata src="SimTutorial_files/image029.png" o:title=""/>
945</v:shape><![endif]--><![if !vml]><img border=0 width=337 height=216
946src="SimTutorial_files/image030.png" v:shapes="Picture_x0020_22"><![endif]><!--[if gte vml 1]><v:shape
947 id="Picture_x0020_21" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:335pt;
948 height:214pt;visibility:visible;mso-wrap-style:square'>
949 <v:imagedata src="SimTutorial_files/image031.png" o:title=""/>
950</v:shape><![endif]--><![if !vml]><img border=0 width=337 height=216
951src="SimTutorial_files/image032.png" v:shapes="Picture_x0020_21"><![endif]></span><span
952style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
953"Times New Roman"'><o:p></o:p></span></p>
954
955<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
956mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
957
958</div>
959
960</body>
961
962</html>
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