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3 | <META NAME="Author" CONTENT="Brian H. Toby"> |
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4 | <title>EXPGUI</title> |
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21 | <br clear=all><hr> |
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22 | |
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23 | <TABLE BORDER BGCOLOR="#FFFF40" ALIGN=RIGHT> |
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24 | <TR><TH><A Href="expgui.html">EXPGUI top</A> |
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25 | </TH><TH><A Href="expgui2.html">Next page</A> |
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26 | </TH></TR></TABLE><BR CLEAR=ALL> |
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27 | |
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28 | <center><h1> |
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29 | EXPGUI, part 1 |
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30 | </h1></center> |
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31 | <P> |
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32 | <h3>A.1 Least Squares (LS) Controls Pane</h3> |
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33 | <DL><DL> |
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34 | <p>The LS Controls pane shows information about the |
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35 | current experiment, typically found in the EXPEDT "Least |
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36 | Squares Controls" options. |
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37 | <P> |
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38 | Note that the order that histograms appear in this |
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39 | pane is determined by the |
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40 | <a href="expguic.html#sorthist">"Sort histograms by"</a> option in |
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41 | the Options Menu. |
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42 | </DL> |
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43 | <img SRC="1.gif" align=TEXTTOP alt="EXPGUI Screen snapshot"> |
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44 | </DL> |
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45 | <DL><DL> |
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46 | The entries on the upper part of this pane are overall options for the |
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47 | entire experiment. |
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48 | <P> |
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49 | <DT><B>Last History</B><DD> |
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50 | This shows the last history record written into |
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51 | the experiment file, showing the last program that modified the file |
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52 | and when it was run. |
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53 | <DT><B>Title</B><DD> |
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54 | This is a title for the refinement. users can specify any information |
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55 | they want saved in the experiment file. |
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56 | <DT><B>Number of Cycles</B><DD> |
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57 | This is the number of refinement cycles to be performed in GENLES. |
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58 | If this number is zero when GENLES is run, |
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59 | powder diffraction intensities are computed and, when requested |
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60 | (<a href="#extract">see below</a>) reflection intensities are estimated |
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61 | but parameters are not refined. Note that when a |
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62 | <a href="#lebail">LeBail extraction</a> is performed |
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63 | with the cycles set at zero, reflection |
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64 | intensities are optimized even when though no cycles of refinement are |
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65 | performed. |
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66 | <DT><B>Print Options</B><DD> |
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67 | <img SRC="1a.gif" align=right alt="EXPGUI Screen snapshot"> |
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68 | This allows you to control what types of output GENLES provides. The menu of |
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69 | options is shown to the right. I recommend including the summary of shifts and |
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70 | in most cases the correlation matrix in the output. |
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71 | <DT><B>Convergence Criterion</B><DD> |
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72 | GENLES stops refinements when the sum of the squares of each |
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73 | parameter shifts divided by its standard uncertainty is less than |
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74 | this "Convergence Criterion." Since this quantity is the <I>total</I> |
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75 | sum of squares, it is reasonable to raise this value for refinements |
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76 | where large numbers of parameters will be refined. |
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77 | <DT><B>Marquardt Damping</B><DD> |
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78 | Marquardt damping increases the weighting of the diagonal elements |
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79 | in the Hessian matrix, reducing the impact of parameter correlation |
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80 | on the refinement. It increases refinement stability at the cost |
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81 | of requiring additional cycles of refinement. A Marquardt term of 1.0 |
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82 | corresponds to a standard least-squares refinement with no Marquardt |
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83 | damping. The value 1.2 has been recommended to me by Lachlan Cranswick as |
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84 | a good choice. |
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85 | <P> |
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86 | </DL> |
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87 | <br clear=all> |
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88 | <DL> |
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89 | The lower section, labeled "Reflection Intensity Extraction" has options |
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90 | for each histogram that determine if reflection intensities will be estimated, |
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91 | and if so, how. |
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92 | <P> |
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93 | <DT><B>Extract Fobs</B><DD> |
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94 | When the Extract Fobs option is on, reflection intensities are computed |
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95 | using the method developed by Hugo Rietveld. In this method |
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96 | the intensity for each reflection is determined by summing the |
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97 | appropriate data points, weighed by the ratio of the computed intensity |
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98 | from that reflection to the total computed intensity at that point. This means |
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99 | that in the case of severely overlapped reflections, "observed" |
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100 | intensities are apportioned according to the relative computed reflection |
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101 | intensities. This is clearly biased since it invokes the crystallographic |
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102 | model, but is about the best that can be done. Turning this option off |
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103 | saves a very small amount of computer time. |
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104 | <a name="extract"> |
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105 | </a><DT><B>Intensity Extraction Methods</B><DD> |
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106 | There are two approaches to reflection intensity determination. In the |
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107 | conventional <B>Rietveld</B> approach, if the "Extract Fobs" flag is on, |
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108 | reflection intensities are determined |
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109 | as part of the Rietveld refinement, reflection R-factors are |
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110 | computed, and the reflection intensities |
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111 | are saved on disk file for use in Fourier or other computations. |
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112 | <P> |
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113 | In the extraction method developed by Armel <B>LeBail</B>, |
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114 | reflection intensities are "optimized" by treating the setting the F<sub>calc</sub> value |
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115 | for each reflection to the F<sub>obs</sub> value extracted |
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116 | during the previous cycle. |
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117 | By iterating, the F<sub>calc</sub> values slowly converge to a |
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118 | set of reflection |
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119 | intensities that yields a best fit to the pattern. |
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120 | The F<sub>obs</sub> values are determined every time GENLES is run, |
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121 | or a least squares |
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122 | refinement cycle is run. This it is possible to improve the LeBail fit, by |
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123 | running GENLES with the "Number of Cycles" set to zero. |
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124 | <P> |
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125 | Note that due to reflection |
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126 | overlap, there are usually many different ways to apportion intensities with |
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127 | fits of comparable quality, depending on what starting values are used for |
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128 | F<sub>obs</sub>. Any time POWPREF is run, the reflection list |
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129 | is regenerated and the first time that GENLES is run, the |
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130 | starting F<sub>calc</sub> values are set one of two ways: |
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131 | <P><DL> |
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132 | <a name="lebail"> |
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133 | <DT><B>F(calc) weighted</B><DD> |
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134 | In a "F(calc) weighted" LeBail extraction the initial F<sub>calc</sub> values are computed |
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135 | from the crystal structure model. If the model is fairly close to being |
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136 | correct, it will likely apportion intensity for overlapping reflections in |
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137 | a manner that is fairly close to correct. Thus, the F<sub>calc</sub> values obtained |
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138 | from a "F(calc) weighted" LeBail extraction are about as good as can be |
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139 | done for the case where the structure is pretty close to correct. |
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140 | <DT><B>Equally weighted</B><DD> |
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141 | On the other hand, if one has no good structural model, but would like to |
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142 | use LeBail extraction as a way to obtain F<sub>obs</sub> values for use in structure |
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143 | solution, for example, by direct methods, then it is best to assume that all |
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144 | reflections are equally likely to contain intensity. In the "Equally weighted" |
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145 | mode, all reflections are given an identical F<sub>obs</sub> starting value. Thus, if |
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146 | two reflections are completely overlapped, in this methods, they will |
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147 | be assigned equal F<sub>obs</sub> values through the LeBail fit. |
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148 | </DL> |
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149 | <P> |
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150 | It is possible to refine unit cell, background, profile and other |
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151 | non-structural parameters at the same time as a LeBail extraction is |
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152 | performed. I often do this, for two reasons. One is that the final LeBail |
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153 | R<sub>wp</sub> and Chi<sup>2</sup> provides a better measure of the |
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154 | best possible fit |
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155 | than the statistical values, particularly if the material has non-ideal |
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156 | peak shapes or other factors that cannot modeled. The second reason is the |
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157 | LeBail fit provides excellent starting values for the unit cell, background |
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158 | and profile parameters, so these terms need not be refined again |
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159 | until all structural terms have been fit well. |
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160 | <P> |
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161 | These LeBail refinements, alas, are prone to diverge |
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162 | if the the extracted intensities are changing rapidly and |
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163 | other parameters, such as unit cell parameters are compensating. It is |
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164 | a good practice to run GENLES several times with |
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165 | the "Number of Cycles" set to zero each time POWPREF is run -- to allow the |
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166 | reflection intensities to converge before refining parameters. |
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167 | <P> |
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168 | Note that extraction different methods can be used for different phases |
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169 | in a histogram. |
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170 | It can be convenient to use LeBail extraction for an impurity phase, |
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171 | in the case where the impurity has preferred orientation or has a known |
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172 | unit cell, but an unknown structure. I have also used LeBail fits to |
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173 | obtain precise lattice constants via profile fits of materials where the |
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174 | exact structure is not known, so a Rietveld refinement cannot be performed. |
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175 | <DT><B>LeBail Damping</B><DD> |
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176 | The shifts to the reflection intensities can damped. This is useful when |
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177 | refining lattice constants or other terms that might otherwise cause the |
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178 | reflection intensities to shift dramatically and in turn cause the refinement |
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179 | to diverge. |
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180 | </DL></DL> |
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181 | <hr> |
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182 | <TABLE BORDER BGCOLOR="#FFFF40" ALIGN=RIGHT> |
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183 | <TR><TH><A Href="expgui.html">EXPGUI top</A> |
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184 | </TH><TH><A Href="expgui2.html">Next page</A> |
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185 | </TH></TR></TABLE> |
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186 | |
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187 | <a href="http://www.ncnr.nist.gov/staff/toby/">Brian Toby</a> (<a href="mailto:brian.toby@nist.gov">Brian.Toby@NIST.GOV</a>) |
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188 | <br> |
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189 | $Revision: 401 $ $Date: 2009-12-04 23:05:33 +0000 (Fri, 04 Dec 2009) $ |
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190 | </body> |
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191 | </html> |
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