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| 3 | <META NAME="Author" CONTENT="Brian H. Toby"> |
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| 4 | <title>EXPGUI</title> |
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| 5 | <meta name="keywords" content="crystallography, Rietveld, diffraction, |
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| 6 | GSAS, EXPGUI"> |
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| 19 | include("/var/www/include/utility.inc"); |
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| 21 | <blockquote><font face="arial, helvetica, sans-serif"> |
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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 | <HR noshade width="75%" size="2" align="center"> |
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| 30 | EXPGUI, part 1 |
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| 31 | <HR noshade width="75%" size="2" align="center"> |
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| 32 | </h1></center> |
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| 33 | <P> |
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| 34 | <h3>A.1 Least Squares (LS) Controls Pane</h3> |
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| 35 | <DL><DL> |
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| 36 | <p>The LS Controls pane shows information about the |
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| 37 | current experiment, typically found in the EXPEDT "Least |
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| 38 | Squares Controls" options. |
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| 39 | <P> |
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| 40 | Note that the order that histograms appear in this |
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| 41 | pane is determined by the |
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| 42 | <a href="expguic.html#sorthist">"Sort histograms by"</a> option in |
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| 43 | the Options Menu. |
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| 44 | </DL> |
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| 45 | <img SRC="1.gif" align=TEXTTOP alt="EXPGUI Screen snapshot"> |
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| 46 | </DL> |
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| 47 | <DL><DL> |
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| 48 | The entries on the upper part of this pane are overall options for the |
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| 49 | entire experiment. |
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| 50 | <P> |
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| 51 | <DT><B>Last History</B><DD> |
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| 52 | This shows the last history record written into |
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| 53 | the experiment file, showing the last program that modified the file |
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| 54 | and when it was run. |
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| 55 | <DT><B>Title</B><DD> |
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| 56 | This is a title for the refinement. users can specify any information |
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| 57 | they want saved in the experiment file. |
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| 58 | <DT><B>Number of Cycles</B><DD> |
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| 59 | This is the number of refinement cycles to be performed in GENLES. |
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| 60 | If this number is zero when GENLES is run, |
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| 61 | powder diffraction intensities are computed and, when requested |
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| 62 | (<a href="#extract">see below</a>) reflection intensities are estimated |
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| 63 | but parameters are not refined. Note that when a |
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| 64 | <a href="#lebail">LeBail extraction</a> is performed |
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| 65 | with the cycles set at zero, reflection |
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| 66 | intensities are optimized even when though no cycles of refinement are |
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| 67 | performed. |
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| 68 | <DT><B>Print Options</B><DD> |
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| 69 | <img SRC="1a.gif" align=right alt="EXPGUI Screen snapshot"> |
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| 70 | This allows you to control what types of output GENLES provides. The menu of |
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| 71 | options is shown to the right. I recommend including the summary of shifts and |
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| 72 | in most cases the correlation matrix in the output. |
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| 73 | <DT><B>Convergence Criterion</B><DD> |
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| 74 | GENLES stops refinements when the sum of the squares of each |
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| 75 | parameter shifts divided by its standard uncertainty is less than |
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| 76 | this "Convergence Criterion." Since this quantity is the <I>total</I> |
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| 77 | sum of squares, it is reasonable to raise this value for refinements |
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| 78 | where large numbers of parameters will be refined. |
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| 79 | <DT><B>Marquardt Damping</B><DD> |
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| 80 | Marquardt damping increases the weighting of the diagonal elements |
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| 81 | in the Hessian matrix, reducing the impact of parameter correlation |
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| 82 | on the refinement. It increases refinement stability at the cost |
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| 83 | of requiring additional cycles of refinement. A Marquardt term of 1.0 |
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| 84 | corresponds to a standard least-squares refinement with no Marquardt |
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| 85 | damping. The value 1.2 has been recommended to me by Lachlan Cranswick as |
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| 86 | a good choice. |
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| 87 | <P> |
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| 88 | </DL> |
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| 89 | <br clear=all> |
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| 90 | <DL> |
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| 91 | The lower section, labeled "Reflection Intensity Extraction" has options |
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| 92 | for each histogram that determine if reflection intensities will be estimated, |
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| 93 | and if so, how. |
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| 94 | <P> |
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| 95 | <DT><B>Extract Fobs</B><DD> |
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| 96 | When the Extract Fobs option is on, reflection intensities are computed |
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| 97 | using the method developed by Hugo Rietveld. In this method |
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| 98 | the intensity for each reflection is determined by summing the |
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| 99 | appropriate data points, weighed by the ratio of the computed intensity |
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| 100 | from that reflection to the total computed intensity at that point. This means |
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| 101 | that in the case of severely overlapped reflections, "observed" |
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| 102 | intensities are apportioned according to the relative computed reflection |
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| 103 | intensities. This is clearly biased since it invokes the crystallographic |
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| 104 | model, but is about the best that can be done. Turning this option off |
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| 105 | saves a very small amount of computer time. |
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| 106 | <a name="extract"> |
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| 107 | </a><DT><B>Intensity Extraction Methods</B><DD> |
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| 108 | There are two approaches to reflection intensity determination. In the |
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| 109 | conventional <B>Rietveld</B> approach, if the "Extract Fobs" flag is on, |
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| 110 | reflection intensities are determined |
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| 111 | as part of the Rietveld refinement, reflection R-factors are |
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| 112 | computed, and the reflection intensities |
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| 113 | are saved on disk file for use in Fourier or other computations. |
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| 114 | <P> |
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| 115 | In the extraction method developed by Armel <B>LeBail</B>, |
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| 116 | reflection intensities are "optimized" by treating the setting the F<sub>calc</sub> value |
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| 117 | for each reflection to the F<sub>obs</sub> value extracted |
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| 118 | during the previous cycle. |
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| 119 | By iterating, the F<sub>calc</sub> values slowly converge to a |
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| 120 | set of reflection |
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| 121 | intensities that yields a best fit to the pattern. |
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| 122 | The F<sub>obs</sub> values are determined every time GENLES is run, |
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| 123 | or a least squares |
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| 124 | refinement cycle is run. This it is possible to improve the LeBail fit, by |
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| 125 | running GENLES with the "Number of Cycles" set to zero. |
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| 126 | <P> |
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| 127 | Note that due to reflection |
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| 128 | overlap, there are usually many different ways to apportion intensities with |
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| 129 | fits of comparable quality, depending on what starting values are used for |
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| 130 | F<sub>obs</sub>. Any time POWPREF is run, the reflection list |
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| 131 | is regenerated and the first time that GENLES is run, the |
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| 132 | starting F<sub>calc</sub> values are set one of two ways: |
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| 133 | <P><DL> |
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| 134 | <a name="lebail"> |
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| 135 | <DT><B>F(calc) weighted</B><DD> |
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| 136 | In a "F(calc) weighted" LeBail extraction the initial F<sub>calc</sub> values are computed |
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| 137 | from the crystal structure model. If the model is fairly close to being |
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| 138 | correct, it will likely apportion intensity for overlapping reflections in |
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| 139 | a manner that is fairly close to correct. Thus, the F<sub>calc</sub> values obtained |
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| 140 | from a "F(calc) weighted" LeBail extraction are about as good as can be |
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| 141 | done for the case where the structure is pretty close to correct. |
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| 142 | <DT><B>Equally weighted</B><DD> |
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| 143 | On the other hand, if one has no good structural model, but would like to |
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| 144 | use LeBail extraction as a way to obtain F<sub>obs</sub> values for use in structure |
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| 145 | solution, for example, by direct methods, then it is best to assume that all |
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| 146 | reflections are equally likely to contain intensity. In the "Equally weighted" |
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| 147 | mode, all reflections are given an identical F<sub>obs</sub> starting value. Thus, if |
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| 148 | two reflections are completely overlapped, in this methods, they will |
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| 149 | be assigned equal F<sub>obs</sub> values through the LeBail fit. |
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| 150 | </DL> |
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| 151 | <P> |
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| 152 | It is possible to refine unit cell, background, profile and other |
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| 153 | non-structural parameters at the same time as a LeBail extraction is |
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| 154 | performed. I often do this, for two reasons. One is that the final LeBail |
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| 155 | R<sub>wp</sub> and Chi<sup>2</sup> provides a better measure of the |
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| 156 | best possible fit |
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| 157 | than the statistical values, particularly if the material has non-ideal |
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| 158 | peak shapes or other factors that cannot modeled. The second reason is the |
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| 159 | LeBail fit provides excellent starting values for the unit cell, background |
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| 160 | and profile parameters, so these terms need not be refined again |
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| 161 | until all structural terms have been fit well. |
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| 162 | <P> |
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| 163 | These LeBail refinements, alas, are prone to diverge |
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| 164 | if the the extracted intensities are changing rapidly and |
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| 165 | other parameters, such as unit cell parameters are compensating. It is |
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| 166 | a good practice to run GENLES several times with |
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| 167 | the "Number of Cycles" set to zero each time POWPREF is run -- to allow the |
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| 168 | reflection intensities to converge before refining parameters. |
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| 169 | <P> |
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| 170 | Note that extraction different methods can be used for different phases |
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| 171 | in a histogram. |
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| 172 | It can be convenient to use LeBail extraction for an impurity phase, |
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| 173 | in the case where the impurity has preferred orientation or has a known |
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| 174 | unit cell, but an unknown structure. I have also used LeBail fits to |
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| 175 | obtain precise lattice constants via profile fits of materials where the |
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| 176 | exact structure is not known, so a Rietveld refinement cannot be performed. |
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| 177 | <DT><B>LeBail Damping</B><DD> |
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| 178 | The shifts to the reflection intensities can damped. This is useful when |
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| 179 | refining lattice constants or other terms that might otherwise cause the |
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| 180 | reflection intensities to shift dramatically and in turn cause the refinement |
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| 181 | to diverge. |
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| 182 | </DL></DL> |
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| 183 | <hr> |
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| 184 | <TABLE BORDER BGCOLOR="#FFFF40" ALIGN=RIGHT> |
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| 185 | <TR><TH><A Href="expgui.html">EXPGUI top</A> |
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| 186 | </TH><TH><A Href="expgui2.html">Next page</A> |
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| 187 | </TH></TR></TABLE> |
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| 188 | |
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| 189 | <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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| 190 | <br> |
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| 191 | $Revision: 505 $ $Date: 2009-12-04 23:07:17 +0000 (Fri, 04 Dec 2009) $ |
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| 192 | </blockquote> |
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| 193 | </body> |
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| 194 | </html> |
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