source: Tutorials/Simulation/SimTutorial.htm @ 3552

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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><B>A video version of this tutorial is available at
536<A href="https://anl.box.com/v/SimTutorial" target="_blank">
537https://anl.box.com/v/SimTutorial</A></B></P>
538
539<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
540mso-bidi-font-family:"Times New Roman"'>While GSAS-II provides an environment
541for fitting of diffraction data, it can also be used to simulate diffraction
542experiments, where results are quantitative models for what can be expected,
543provided that an accurate instrument description is used. Here we demonstrate
544how a simulation is done for a two-phase mixture with multiple instrument
545types. <o:p></o:p></span></p>
546
547<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
548"Times New Roman"'>Step 1: Read in Phases<o:p></o:p></span></h2>
549
550<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
551mso-bidi-font-family:"Times New Roman"'>First we will read in two phases, CuCr<sub>2</sub>O<sub>4</sub>
552and <span class=SpellE>CuO</span> from files CuCr2O4.cif and <span
553class=SpellE>CuO.cif</span>, which can be downloaded from <a
554href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/Simulation/data/">directory
555https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/Simulation/data/</a>. <o:p></o:p></span></p>
556
557<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
558mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</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"'>Create a new project by starting GSAS-II
562or by using the File/New Project menu item. Then use the Import/Phase/“from CIF
563file” and select the CuCr2O4.cif for the “Choose Phase input file” dialog window.
564Click “Ok” and “Yes” in the “Is this <span class=SpellE>the</span> file you
565want?” confirmation window. <span style="mso-spacerun:yes"> </span>The default
566Phase name, CuCr2O4 is fine.<o:p></o:p></span></p>
567
568<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
569mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
570
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604style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
605"Times New Roman"'>Repeat this to read in the second phase: use the
606Import/Phase/“from CIF file” and select the <span class=SpellE>CuO.cif</span>
607for the “Choose Phase input file” dialog window. Click “Ok” and “Yes” in the “Is
608this the file you want?” confirmation window. <span
609style="mso-spacerun:yes"> </span>The default Phase name, <span class=SpellE>CuO</span>
610is also fine.<o:p></o:p></span></p>
611
612<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
613mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
614
615<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
616"Times New Roman"'>Step 2: Create Simulation Histograms<o:p></o:p></span></h2>
617
618<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span
619style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
620"Times New Roman"'>Part A</span></b><span style='font-size:12.0pt;mso-fareast-font-family:
621"Times New Roman";mso-bidi-font-family:"Times New Roman"'>: Use the
622Import/Powder Data/“Simulate a dataset” menu item (at bottom of menu list) to
623create a simulation (dummy) histogram. The program then requests an instrument
624parameter file name. Click Cancel and a list of default instrument parameters
625are then displayed, as shown to the right. Select the APS 11-BM instrument
626listing and press OK.</span> <span style='font-size:12.0pt;mso-fareast-font-family:
627"Times New Roman";mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p>
628
629<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
630mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</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"'>A dialog window is then displayed that with
634the name for the histogram, the range of data and the step size. Below, note
635that the name and start angle have been changed from the defaults. Then press
636OK and the “Add to phase(s)” dialog is displayed. <o:p></o:p></span></p>
637
638<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
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645style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
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647
648<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
649mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
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"'>Finally, in this dialog, we need to
653indicate which phases are linked with this histogram. We want to include both
654in the simulation, so use the “Set All” button (or select each phase) and press
655OK.<o:p></o:p></span></p>
656
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666
667<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
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669
670<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
671mso-bidi-font-family:"Times New Roman"'>Note that a new histogram is now added
672to the data tree, as below. (Note the "Edit range" button which can be
673used to change the values entered on the previous dialog).
674<o:p></o:p></span></p>
675
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683style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
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685
686<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
687mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
688
689<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span
690style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
691"Times New Roman"'>Part B</span></b><span style='font-size:12.0pt;mso-fareast-font-family:
692"Times New Roman";mso-bidi-font-family:"Times New Roman"'>: Again use the
693Import/Powder Data/“Simulate a dataset” menu item (at bottom of menu list) to
694create a simulation (dummy) histogram. This time when the program then requests
695an instrument parameter file name, supply file BT1.prm, which can also be
696downloaded from <a
697href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/Simulation/data/">directory
698https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/Simulation/data/</a>. <o:p></o:p></span></p>
699
700<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
701mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
702
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712
713<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
714mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
715
716<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
717mso-bidi-font-family:"Times New Roman"'>Click Open and a dialog opens for the
718dataset name and range for this histogram. Change the range to 1 to 120 degrees
719with 0<span class=GramE>.025 degree</span> steps and optionally change the
720name, as below. <o:p></o:p></span></p>
721
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733
734<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
735mso-bidi-font-family:"Times New Roman"'>Press OK and then <span class=GramE>the
736<span class=SpellE>the</span></span> “Add to phase(s)” dialog is displayed. As
737before, add link both phases to this histogram. <span
738style="mso-spacerun:yes"> </span>At this point a second histogram is shown in
739the data tree:<o:p></o:p></span></p>
740
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746 <v:imagedata src="SimTutorial_files/image013.png" o:title=""/>
747</v:shape><![endif]--><![if !vml]><img border=0 width=366 height=230
748src="SimTutorial_files/image014.png" v:shapes="Picture_x0020_17"><![endif]></span><span
749style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
750"Times New Roman"'><o:p></o:p></span></p>
751
752<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
753"Times New Roman"'>Step 3: Set Phase Fractions<o:p></o:p></span></h2>
754
755<p class=MsoNormal><!--[if gte vml 1]><v:shape id="Picture_x0020_1" o:spid="_x0000_s1026"
756 type="#_x0000_t75" alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f1.png"
757 style='position:absolute;margin-left:300.4pt;margin-top:70.5pt;width:351.6pt;
758 height:188.1pt;z-index:251658240;visibility:visible;mso-wrap-style:square;
759 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
760 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
761 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
762 mso-position-horizontal-relative:text;mso-position-vertical:absolute;
763 mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0;
764 mso-width-relative:page;mso-height-relative:page'>
765 <v:imagedata src="SimTutorial_files/image015.png" o:title="f1.png"/>
766 <w:wrap type="tight"/>
767</v:shape><![endif]--><![if !vml]><img width=354 height=190
768src="SimTutorial_files/image016.png" align=right hspace=9
769alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f1.png" v:shapes="Picture_x0020_1"><![endif]><span
770style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
771"Times New Roman"'>It is important to understand how the scale factor (found
772each histogram's Sample Parameters tree entry) and phase fractions (found in
773each phase's data tab) are used in GSAS-II. The scattering contribution for
774each phase is set from the product of the histogram scale factor multiplied by
775the phase fraction for each phase in that histogram which multiplies the
776scattering power of each atom in the unit cell. This means that the phase
777fraction effectively represents the relative number of unit cells present for
778each phase. Note that after reading in the two phases in the previous step,
779their phase fractions default to 1 for each. The contents of each phase are
780shown on the General tab. Note that the unit cell contents for each phase are
781Cu<sub>8</sub>Cr<sub>16</sub>O<sub>32</sub> (1852.3 g/<span class=SpellE>mol</span>)
782and Cu<sub>4</sub>O<sub>4</sub> (318.2 g/<span class=SpellE>mol</span>), with
783equal numbers of unit cells, the mass (or equivalently weight) fractions will
784be 1852.3/(318.2+1852.3)=85.3% and 318.2/(318.2+1852.3)=14.7%. This can be
785confirmed on the Data for each phase, as below.<o:p></o:p></span></p>
786
787<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
788mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
789 id="Picture_x0020_3" o:spid="_x0000_i1032" type="#_x0000_t75" alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f2.png"
790 style='width:453pt;height:170pt;visibility:visible;mso-wrap-style:square'>
791 <v:imagedata src="SimTutorial_files/image017.png" o:title="f2.png"/>
792</v:shape><![endif]--><![if !vml]><img border=0 width=455 height=172
793src="SimTutorial_files/image018.png"
794alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f2.png" v:shapes="Picture_x0020_3"><![endif]></span><span
795style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
796"Times New Roman"'><o:p></o:p></span></p>
797
798<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
799mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</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"'>For this tutorial, we will choose to
803set the mass fractions to give 90% CuCr<sub>2</sub>O<sub>4</sub> and 10% <span
804class=SpellE>CuO</span>, so 90/1852.3=</span><span style='font-size:12.0pt;
805font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
806color:black'>0.04859 and 10/</span><span style='font-size:12.0pt;mso-fareast-font-family:
807"Times New Roman";mso-bidi-font-family:"Times New Roman"'>318.2=0.03143. Equivalently,
808we can normalize the phase fractions sum to 1 or so that either phase fraction is
8091. We will use 1 for CuCr<sub>2</sub>O<sub>4</sub>, and </span><span
810style='font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-family:
811"Times New Roman";color:black'>10*</span><span style='font-size:12.0pt;
812mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'>1852.3</span><span
813style='font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-family:
814"Times New Roman";color:black'>/(</span><span style='font-size:12.0pt;
815mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'>318.2*90)=0.6468
816for <span class=SpellE>CuO</span>. Enter 0.6468 for the <span class=SpellE>CuO</span>
817Phase fraction. <span style="mso-spacerun:yes"> </span>When the mouse is moved
818out of the box, the mass fraction to be recomputed and appears as 10%, as
819expected:<o:p></o:p></span></p>
820
821<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
822mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
823 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"
824 style='width:451pt;height:238pt;visibility:visible;mso-wrap-style:square'>
825 <v:imagedata src="SimTutorial_files/image019.png" o:title="Untitled.png"/>
826</v:shape><![endif]--><![if !vml]><img border=0 width=453 height=240
827src="SimTutorial_files/image020.png"
828alt="Description: BHT14 HD:Users:toby:Library:Mobile Documents:com~apple~Preview:Documents:Untitled.png"
829v:shapes="Picture_x0020_18"><![endif]></span><span style='font-size:12.0pt;
830mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p>
831
832<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
833mso-bidi-font-family:"Times New Roman"'>This must be set for both histograms.
834Clicking on the second histogram allows that phase fraction to be edited. Even easier
835is to use the “Edit Phase”/“Copy data” menu item to copy all <span
836class=SpellE>CuO</span> data settings from histogram 1 to histogram 2. Note
837that if the CuCr<sub>2</sub>O<sub>4 </sub>Data tab is selected for either phase,
838the mass fraction is now shown as 90%. <o:p></o:p></span></p>
839
840<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
841"Times New Roman"'>Step 4: Turn off Optimization<o:p></o:p></span></h2>
842
843<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
844mso-bidi-font-family:"Times New Roman"'>A refinement computation is needed to
845cause the pattern to be simulated. When a pattern is first simulated, the
846observed pattern is set to the computed pattern (this can be reset by
847using the "Edit range" button when the histogram data tree item is
848selected. This means that it is actually
849possible to optimize any parameters that are selected to be refined,
850which can be used to test the sensitivity of different models refined
851against a
852simulated dataset. In this case we only need to compute the simulated
853pattern, so we will turn off optimization by setting the
854number of cycles to zero. Do this by clicking on the Controls data tree entry and set the Max
855cycles value to 0 using the pull-down menu:<o:p></o:p></span></p>
856
857<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
858mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
859 id="Picture_x0020_5" o:spid="_x0000_i1030" type="#_x0000_t75" alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f4.png"
860 style='width:442pt;height:114pt;visibility:visible;mso-wrap-style:square'>
861 <v:imagedata src="SimTutorial_files/image021.png" o:title="f4.png"/>
862</v:shape><![endif]--><![if !vml]><img border=0 width=444 height=116
863src="SimTutorial_files/image022.png"
864alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f4.png" v:shapes="Picture_x0020_5"><![endif]></span><span
865style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
866"Times New Roman"'><o:p></o:p></span></p>
867
868<h2>Step 5: Change Histogram Scale Factor</h2>
869
870<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
871mso-bidi-font-family:"Times New Roman"'>As discussed earlier, the range of
872intensities is determined by the histogram scale factor. For x-rays, a
873histogram scale factor with the default value of 1 produces a reasonable
874intensity range, but with CW neutrons, a much larger scale factor value is
875needed to produce a pattern with non-negligible intensity values. Note that
876GSAS-II adds simulated noise to patterns, so if the scale factor is too small,
877only random counts are seen. Select the Sample Parameters tree item for the
878second histogram and change the scale factor to 1000, as below. </span></p>
879
880<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
881 id="Picture_x0020_20" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:370pt;
882 height:232pt;visibility:visible;mso-wrap-style:square'>
883 <v:imagedata src="SimTutorial_files/image023.png" o:title=""/>
884</v:shape><![endif]--><![if !vml]><img border=0 width=372 height=234
885src="SimTutorial_files/image024.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
886
887<h2>Step 6: Simulate the Pattern</h2>
888
889<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
890mso-bidi-font-family:"Times New Roman"'>Use the Calculate/Refine menu item to
891compute the simulated pattern. Clicking on the histogram entry in the data tree
892causes the pattern to be displayed as below. This has the reflection <span
893class=SpellE>tickmarks</span> and the difference curve located at zero. While
894both can be dragged to new positions, this is hard to do when they are obscured
895by the “observed” and computed patterns. (The observed pattern has been set to
896the computed pattern with the addition of simulated noise, which is why the
897difference curve is non-zero.)<o:p></o:p></span></p>
898
899<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
900mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
901 id="Picture_x0020_11" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:285pt;
902 height:243pt;visibility:visible;mso-wrap-style:square'>
903 <v:imagedata src="SimTutorial_files/image025.png" o:title=""/>
904</v:shape><![endif]--><![if !vml]><img border=0 width=287 height=245
905src="SimTutorial_files/image026.png" v:shapes="Picture_x0020_11"><![endif]></span><span
906style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
907"Times New Roman"'><o:p></o:p></span></p>
908
909<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
910mso-bidi-font-family:"Times New Roman"'>A nice trick for resetting the <span
911class=SpellE>tickmarks</span> to their usual default positions is to press “s”
912to scale to <span class=SpellE><span class=GramE>sqrt</span></span><span
913class=GramE>(</span>I) and press it again to return to normal scaling, as shown
914below. These changes in scaling can also be done via the “K” (keyboard) button
915on the bottom toolbar. <o:p></o:p></span></p>
916
917<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
918mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
919 id="Picture_x0020_12" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:285pt;
920 height:220pt;visibility:visible;mso-wrap-style:square'>
921 <v:imagedata src="SimTutorial_files/image027.png" o:title=""/>
922</v:shape><![endif]--><![if !vml]><img border=0 width=287 height=222
923src="SimTutorial_files/image028.png" v:shapes="Picture_x0020_12"><![endif]></span><span
924style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
925"Times New Roman"'><o:p></o:p></span></p>
926
927<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
928mso-bidi-font-family:"Times New Roman"'>Note that the Commands menu offers menu
929items for moving the difference curve and <span class=SpellE>tickmarks</span>,
930as well as using drag and drop. Use of this, as well as using the rescaling graphics
931toolbar item (the home button indicated by small house on the lower left)
932allows more fine arrangement of locations. Exporting the plot (using the “floppy
933disk” button allows the plots below to be created. Note the very big
934differences in intensities, data range and resolution between the two
935simulations. <o:p></o:p></span></p>
936
937<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
938mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
939 id="Picture_x0020_22" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:335pt;
940 height:214pt;visibility:visible;mso-wrap-style:square'>
941 <v:imagedata src="SimTutorial_files/image029.png" o:title=""/>
942</v:shape><![endif]--><![if !vml]><img border=0 width=337 height=216
943src="SimTutorial_files/image030.png" v:shapes="Picture_x0020_22"><![endif]><!--[if gte vml 1]><v:shape
944 id="Picture_x0020_21" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:335pt;
945 height:214pt;visibility:visible;mso-wrap-style:square'>
946 <v:imagedata src="SimTutorial_files/image031.png" o:title=""/>
947</v:shape><![endif]--><![if !vml]><img border=0 width=337 height=216
948src="SimTutorial_files/image032.png" v:shapes="Picture_x0020_21"><![endif]></span><span
949style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
950"Times New Roman"'><o:p></o:p></span></p>
951
952<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
953mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
954
955</div>
956
957</body>
958
959</html>
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