source: Tutorials/Simulation/SimTutorial.htm @ 3235

Last change on this file since 3235 was 3235, checked in by toby, 4 years ago

New simulation tutorial

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530<div class=WordSection1>
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 class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
536mso-bidi-font-family:"Times New Roman"'>While GSAS-II provides an environment
537for fitting of diffraction data, it can also be used to simulate diffraction
538experiments, where results are quantitative models for what can be expected,
539provided that an accurate instrument description is used. Here we demonstrate
540how a simulation is done for a two-phase mixture with multiple instrument
541types. <o:p></o:p></span></p>
542
543<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
544"Times New Roman"'>Step 1: Read in Phases<o:p></o:p></span></h2>
545
546<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
547mso-bidi-font-family:"Times New Roman"'>First we will read in two phases, CuCr<sub>2</sub>O<sub>4</sub>
548and <span class=SpellE>CuO</span> from files CuCr2O4.cif and <span
549class=SpellE>CuO.cif</span>, which can be downloaded from <a
550href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimTut/data/">directory
551https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimTut/data/</a>. <o:p></o:p></span></p>
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"'><o:p>&nbsp;</o:p></span></p>
555
556<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
557mso-bidi-font-family:"Times New Roman"'>Create a new project by starting GSAS-II
558or by using the File/New Project menu item. Then use the Import/Phase/“from CIF
559file” and select the CuCr2O4.cif for the “Choose Phase input file” dialog window.
560Click “Ok” and “Yes” in the “Is this <span class=SpellE>the</span> file you
561want?” confirmation window. <span style="mso-spacerun:yes"> </span>The default
562Phase name, CuCr2O4 is fine.<o:p></o:p></span></p>
563
564<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
565mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
566
567<p class=MsoNormal><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600"
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599src="SimTutorial_files/image002.png" align=right hspace=9 v:shapes="Picture_x0020_7"><![endif]><span
600style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
601"Times New Roman"'>Repeat this to read in the second phase: use the
602Import/Phase/“from CIF file” and select the <span class=SpellE>CuO.cif</span>
603for the “Choose Phase input file” dialog window. Click “Ok” and “Yes” in the “Is
604this the file you want?” confirmation window. <span
605style="mso-spacerun:yes"> </span>The default Phase name, <span class=SpellE>CuO</span>
606is also fine.<o:p></o:p></span></p>
607
608<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
609mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
610
611<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
612"Times New Roman"'>Step 2: Create Simulation Histograms<o:p></o:p></span></h2>
613
614<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span
615style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
616"Times New Roman"'>Part A</span></b><span style='font-size:12.0pt;mso-fareast-font-family:
617"Times New Roman";mso-bidi-font-family:"Times New Roman"'>: Use the
618Import/Powder Data/“Simulate a dataset” menu item (at bottom of menu list) to
619create a simulation (dummy) histogram. The program then requests an instrument
620parameter file name. Click Cancel and a list of default instrument parameters
621are then displayed, as shown to the right. Select the APS 11-BM instrument
622listing and press OK.</span> <span style='font-size:12.0pt;mso-fareast-font-family:
623"Times New Roman";mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p>
624
625<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
626mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
627
628<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
629mso-bidi-font-family:"Times New Roman"'>A dialog window is then displayed that with
630the name for the histogram, the range of data and the step size. Below, note
631that the name and start angle have been changed from the defaults. Then press
632OK and the “Add to phase(s)” dialog is displayed. <o:p></o:p></span></p>
633
634<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
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643
644<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
645mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
646
647<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
648mso-bidi-font-family:"Times New Roman"'>Finally, in this dialog, we need to
649indicate which phases are linked with this histogram. We want to include both
650in the simulation, so use the “Set All” button (or select each phase) and press
651OK.<o:p></o:p></span></p>
652
653<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
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660style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
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662
663<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
664mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
665
666<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
667mso-bidi-font-family:"Times New Roman"'>Note that a new histogram is now added
668to the data tree, as below. <o:p></o:p></span></p>
669
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677style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
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679
680<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
681mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
682
683<p class=MsoNormal><b style='mso-bidi-font-weight:normal'><span
684style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
685"Times New Roman"'>Part B</span></b><span style='font-size:12.0pt;mso-fareast-font-family:
686"Times New Roman";mso-bidi-font-family:"Times New Roman"'>: Again use the
687Import/Powder Data/“Simulate a dataset” menu item (at bottom of menu list) to
688create a simulation (dummy) histogram. This time when the program then requests
689an instrument parameter file name, supply file BT1.prm, which can also be
690downloaded from <a
691href="https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimTut/data/">directory
692https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/SimTut/data/</a>. <o:p></o:p></span></p>
693
694<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
695mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
696
697<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
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706
707<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
708mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
709
710<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
711mso-bidi-font-family:"Times New Roman"'>Click Open and a dialog opens for the
712dataset name and range for this histogram. Change the range to 1 to 120 degrees
713with 0<span class=GramE>.025 degree</span> steps and optionally change the
714name, as below. <o:p></o:p></span></p>
715
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717mso-bidi-font-family:"Times New Roman"'><span style="mso-spacerun:yes"> </span></span><span
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727
728<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
729mso-bidi-font-family:"Times New Roman"'>Press OK and then <span class=GramE>the
730<span class=SpellE>the</span></span> “Add to phase(s)” dialog is displayed. As
731before, add link both phases to this histogram. <span
732style="mso-spacerun:yes"> </span>At this point a second histogram is shown in
733the data tree:<o:p></o:p></span></p>
734
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745
746<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
747"Times New Roman"'>Step 3: Set Phase Fractions<o:p></o:p></span></h2>
748
749<p class=MsoNormal><!--[if gte vml 1]><v:shape id="Picture_x0020_1" o:spid="_x0000_s1026"
750 type="#_x0000_t75" alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f1.png"
751 style='position:absolute;margin-left:300.4pt;margin-top:70.5pt;width:351.6pt;
752 height:188.1pt;z-index:251658240;visibility:visible;mso-wrap-style:square;
753 mso-width-percent:0;mso-height-percent:0;mso-wrap-distance-left:9pt;
754 mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
755 mso-wrap-distance-bottom:0;mso-position-horizontal:right;
756 mso-position-horizontal-relative:text;mso-position-vertical:absolute;
757 mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0;
758 mso-width-relative:page;mso-height-relative:page'>
759 <v:imagedata src="SimTutorial_files/image015.png" o:title="f1.png"/>
760 <w:wrap type="tight"/>
761</v:shape><![endif]--><![if !vml]><img width=354 height=190
762src="SimTutorial_files/image016.png" align=right hspace=9
763alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f1.png" v:shapes="Picture_x0020_1"><![endif]><span
764style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
765"Times New Roman"'>It is important to understand how the scale factor (found
766each histogram's Sample Parameters tree entry) and phase fractions (found in
767each phase's data tab) are used in GSAS-II. The scattering contribution for
768each phase is set from the product of the histogram scale factor multiplied by
769the phase fraction for each phase in that histogram which multiplies the
770scattering power of each atom in the unit cell. This means that the phase
771fraction effectively represents the relative number of unit cells present for
772each phase. Note that after reading in the two phases in the previous step,
773their phase fractions default to 1 for each. The contents of each phase are
774shown on the General tab. Note that the unit cell contents for each phase are
775Cu<sub>8</sub>Cr<sub>16</sub>O<sub>32</sub> (1852.3 g/<span class=SpellE>mol</span>)
776and Cu<sub>4</sub>O<sub>4</sub> (318.2 g/<span class=SpellE>mol</span>), with
777equal numbers of unit cells, the mass (or equivalently weight) fractions will
778be 1852.3/(318.2+1852.3)=85.3% and 318.2/(318.2+1852.3)=14.7%. This can be
779confirmed on the Data for each phase, as below.<o:p></o:p></span></p>
780
781<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
782mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
783 id="Picture_x0020_3" o:spid="_x0000_i1032" type="#_x0000_t75" alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f2.png"
784 style='width:453pt;height:170pt;visibility:visible;mso-wrap-style:square'>
785 <v:imagedata src="SimTutorial_files/image017.png" o:title="f2.png"/>
786</v:shape><![endif]--><![if !vml]><img border=0 width=455 height=172
787src="SimTutorial_files/image018.png"
788alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f2.png" v:shapes="Picture_x0020_3"><![endif]></span><span
789style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
790"Times New Roman"'><o:p></o:p></span></p>
791
792<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
793mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
794
795<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
796mso-bidi-font-family:"Times New Roman"'>For this tutorial, we will choose to
797set the mass fractions to give 90% CuCr<sub>2</sub>O<sub>4</sub> and 10% <span
798class=SpellE>CuO</span>, so 90/1852.3=</span><span style='font-size:12.0pt;
799font-family:"Times New Roman";mso-fareast-font-family:"Times New Roman";
800color:black'>0.04859 and 10/</span><span style='font-size:12.0pt;mso-fareast-font-family:
801"Times New Roman";mso-bidi-font-family:"Times New Roman"'>318.2=0.03143. Equivalently,
802we can normalize the phase fractions sum to 1 or so that either phase fraction is
8031. We will use 1 for CuCr<sub>2</sub>O<sub>4</sub>, and </span><span
804style='font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-family:
805"Times New Roman";color:black'>10*</span><span style='font-size:12.0pt;
806mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'>1852.3</span><span
807style='font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-family:
808"Times New Roman";color:black'>/(</span><span style='font-size:12.0pt;
809mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'>318.2*90)=0.6468
810for <span class=SpellE>CuO</span>. Enter 0.6468 for the <span class=SpellE>CuO</span>
811Phase fraction. <span style="mso-spacerun:yes"> </span>When the mouse is moved
812out of the box, the mass fraction to be recomputed and appears as 10%, as
813expected:<o:p></o:p></span></p>
814
815<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
816mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
817 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"
818 style='width:451pt;height:238pt;visibility:visible;mso-wrap-style:square'>
819 <v:imagedata src="SimTutorial_files/image019.png" o:title="Untitled.png"/>
820</v:shape><![endif]--><![if !vml]><img border=0 width=453 height=240
821src="SimTutorial_files/image020.png"
822alt="Description: BHT14 HD:Users:toby:Library:Mobile Documents:com~apple~Preview:Documents:Untitled.png"
823v:shapes="Picture_x0020_18"><![endif]></span><span style='font-size:12.0pt;
824mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:"Times New Roman"'><o:p></o:p></span></p>
825
826<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
827mso-bidi-font-family:"Times New Roman"'>This must be set for both histograms.
828Clicking on the second histogram allows that phase fraction to be edited. Even easier
829is to use the “Edit Phase”/“Copy data” menu item to copy all <span
830class=SpellE>CuO</span> data settings from histogram 1 to histogram 2. Note
831that if the CuCr<sub>2</sub>O<sub>4 </sub>Data tab is selected for either phase,
832the mass fraction is now shown as 90%. <o:p></o:p></span></p>
833
834<h2><span style='mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
835"Times New Roman"'>Step 4: Turn off Optimization<o:p></o:p></span></h2>
836
837<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
838mso-bidi-font-family:"Times New Roman"'>A refinement computation is needed to
839cause the pattern to be simulated. When a pattern is first simulated, the
840observed pattern is set to the computed pattern. This means that it is actually
841possible to optimize any parameters that are selected to be refined. There is
842no reason to actually do this, so we will turn off optimization by setting the
843number of cycles to zero. Click on the Controls data tree entry and set the Max
844cycles value to 0 using the pull-down menu:<o:p></o:p></span></p>
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";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
848 id="Picture_x0020_5" o:spid="_x0000_i1030" type="#_x0000_t75" alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f4.png"
849 style='width:442pt;height:114pt;visibility:visible;mso-wrap-style:square'>
850 <v:imagedata src="SimTutorial_files/image021.png" o:title="f4.png"/>
851</v:shape><![endif]--><![if !vml]><img border=0 width=444 height=116
852src="SimTutorial_files/image022.png"
853alt="Description: BHT14 HD:Users:toby:Scratch:SimTutorial:f4.png" v:shapes="Picture_x0020_5"><![endif]></span><span
854style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
855"Times New Roman"'><o:p></o:p></span></p>
856
857<h2>Step 5: Change Histogram Scale Factor</h2>
858
859<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
860mso-bidi-font-family:"Times New Roman"'>As discussed earlier, the range of
861intensities is determined by the histogram scale factor. For x-rays, a
862histogram scale factor with the default value of 1 produces a reasonable
863intensity range, but with CW neutrons, a much larger scale factor value is
864needed to produce a pattern with non-negligible intensity values. Note that
865GSAS-II adds simulated noise to patterns, so if the scale factor is too small,
866only random counts are seen. Select the Sample Parameters tree item for the
867second histogram and change the scale factor to 1000, as below. </span></p>
868
869<p class=MsoNormal><span style='mso-no-proof:yes'><!--[if gte vml 1]><v:shape
870 id="Picture_x0020_20" o:spid="_x0000_i1029" type="#_x0000_t75" style='width:370pt;
871 height:232pt;visibility:visible;mso-wrap-style:square'>
872 <v:imagedata src="SimTutorial_files/image023.png" o:title=""/>
873</v:shape><![endif]--><![if !vml]><img border=0 width=372 height=234
874src="SimTutorial_files/image024.png" v:shapes="Picture_x0020_20"><![endif]></span></p>
875
876<h2>Step 6: Simulate the Pattern</h2>
877
878<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
879mso-bidi-font-family:"Times New Roman"'>Use the Calculate/Refine menu item to
880compute the simulated pattern. Clicking on the histogram entry in the data tree
881causes the pattern to be displayed as below. This has the reflection <span
882class=SpellE>tickmarks</span> and the difference curve located at zero. While
883both can be dragged to new positions, this is hard to do when they are obscured
884by the “observed” and computed patterns. (The observed pattern has been set to
885the computed pattern with the addition of simulated noise, which is why the
886difference curve is non-zero.)<o:p></o:p></span></p>
887
888<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
889mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
890 id="Picture_x0020_11" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:285pt;
891 height:243pt;visibility:visible;mso-wrap-style:square'>
892 <v:imagedata src="SimTutorial_files/image025.png" o:title=""/>
893</v:shape><![endif]--><![if !vml]><img border=0 width=287 height=245
894src="SimTutorial_files/image026.png" v:shapes="Picture_x0020_11"><![endif]></span><span
895style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
896"Times New Roman"'><o:p></o:p></span></p>
897
898<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
899mso-bidi-font-family:"Times New Roman"'>A nice trick for resetting the <span
900class=SpellE>tickmarks</span> to their usual default positions is to press “s”
901to scale to <span class=SpellE><span class=GramE>sqrt</span></span><span
902class=GramE>(</span>I) and press it again to return to normal scaling, as shown
903below. These changes in scaling can also be done via the “K” (keyboard) button
904on the bottom toolbar. <o:p></o:p></span></p>
905
906<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
907mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
908 id="Picture_x0020_12" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:285pt;
909 height:220pt;visibility:visible;mso-wrap-style:square'>
910 <v:imagedata src="SimTutorial_files/image027.png" o:title=""/>
911</v:shape><![endif]--><![if !vml]><img border=0 width=287 height=222
912src="SimTutorial_files/image028.png" v:shapes="Picture_x0020_12"><![endif]></span><span
913style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
914"Times New Roman"'><o:p></o:p></span></p>
915
916<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
917mso-bidi-font-family:"Times New Roman"'>Note that the Commands menu offers menu
918items for moving the difference curve and <span class=SpellE>tickmarks</span>,
919as well as using drag and drop. Use of this, as well as using the rescaling graphics
920toolbar item (the home button indicated by small house on the lower left)
921allows more fine arrangement of locations. Exporting the plot (using the “floppy
922disk” button allows the plots below to be created. Note the very big
923differences in intensities, data range and resolution between the two
924simulations. <o:p></o:p></span></p>
925
926<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
927mso-bidi-font-family:"Times New Roman";mso-no-proof:yes'><!--[if gte vml 1]><v:shape
928 id="Picture_x0020_22" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:335pt;
929 height:214pt;visibility:visible;mso-wrap-style:square'>
930 <v:imagedata src="SimTutorial_files/image029.png" o:title=""/>
931</v:shape><![endif]--><![if !vml]><img border=0 width=337 height=216
932src="SimTutorial_files/image030.png" v:shapes="Picture_x0020_22"><![endif]><!--[if gte vml 1]><v:shape
933 id="Picture_x0020_21" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:335pt;
934 height:214pt;visibility:visible;mso-wrap-style:square'>
935 <v:imagedata src="SimTutorial_files/image031.png" o:title=""/>
936</v:shape><![endif]--><![if !vml]><img border=0 width=337 height=216
937src="SimTutorial_files/image032.png" v:shapes="Picture_x0020_21"><![endif]></span><span
938style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";mso-bidi-font-family:
939"Times New Roman"'><o:p></o:p></span></p>
940
941<p class=MsoNormal><span style='font-size:12.0pt;mso-fareast-font-family:"Times New Roman";
942mso-bidi-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p>
943
944</div>
945
946</body>
947
948</html>
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