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EXPGUI, part 1

## A.1 Least Squares (LS) Controls Pane

The LS Controls pane shows information about the current experiment, typically found in the EXPEDT "Least Squares Controls" options.

Note that the order that histograms appear in this pane is determined by the "Sort histograms by" option in the Options Menu.

The entries on the upper part of this pane are overall options for the entire experiment.

Last History- This shows the last history record written into the experiment file, showing the last program that modified the file and when it was run.
Title- This is a title for the refinement. users can specify any information they want saved in the experiment file.
Number of Cycles- This is the number of refinement cycles to be performed in GENLES. If this number is zero when GENLES is run, powder diffraction intensities are computed and, when requested (see below) reflection intensities are estimated but parameters are not refined. Note that when a LeBail extraction is performed with the cycles set at zero, reflection intensities are optimized even when though no cycles of refinement are performed.
Print Options- This allows you to control what types of output GENLES provides. The menu of options is shown to the right. I recommend including the summary of shifts and in most cases the correlation matrix in the output.
Convergence Criterion- GENLES stops refinements when the sum of the squares of each parameter shifts divided by its standard uncertainty is less than this "Convergence Criterion." Since this quantity is the
totalsum of squares, it is reasonable to raise this value for refinements where large numbers of parameters will be refined.Marquardt Damping- Marquardt damping increases the weighting of the diagonal elements in the Hessian matrix, reducing the impact of parameter correlation on the refinement. It increases refinement stability at the cost of requiring additional cycles of refinement. A Marquardt term of 1.0 corresponds to a standard least-squares refinement with no Marquardt damping. The value 1.2 has been recommended to me by Lachlan Cranswick as a good choice.

The lower section, labeled "Reflection Intensity Extraction" has options for each histogram that determine if reflection intensities will be estimated, and if so, how.

Extract Fobs- When the Extract Fobs option is on, reflection intensities are computed using the method developed by Hugo Rietveld. In this method the intensity for each reflection is determined by summing the appropriate data points, weighed by the ratio of the computed intensity from that reflection to the total computed intensity at that point. This means that in the case of severely overlapped reflections, "observed" intensities are apportioned according to the relative computed reflection intensities. This is clearly biased since it invokes the crystallographic model, but is about the best that can be done. Turning this option off saves a very small amount of computer time.
Intensity Extraction Methods- There are two approaches to reflection intensity determination. In the conventional
Rietveldapproach, if the "Extract Fobs" flag is on, reflection intensities are determined as part of the Rietveld refinement, reflection R-factors are computed, and the reflection intensities are saved on disk file for use in Fourier or other computations.In the extraction method developed by Armel

LeBail, reflection intensities are "optimized" by treating the setting the F_{calc}value for each reflection to the F_{obs}value extracted during the previous cycle. By iterating, the F_{calc}values slowly converge to a set of reflection intensities that yields a best fit to the pattern. The F_{obs}values are determined every time GENLES is run, or a least squares refinement cycle is run. This it is possible to improve the LeBail fit, by running GENLES with the "Number of Cycles" set to zero.Note that due to reflection overlap, there are usually many different ways to apportion intensities with fits of comparable quality, depending on what starting values are used for F

_{obs}. Any time POWPREF is run, the reflection list is regenerated and the first time that GENLES is run, the starting F_{calc}values are set one of two ways:

F(calc) weighted- In a "F(calc) weighted" LeBail extraction the initial F
_{calc}values are computed from the crystal structure model. If the model is fairly close to being correct, it will likely apportion intensity for overlapping reflections in a manner that is fairly close to correct. Thus, the F_{calc}values obtained from a "F(calc) weighted" LeBail extraction are about as good as can be done for the case where the structure is pretty close to correct.Equally weighted- On the other hand, if one has no good structural model, but would like to use LeBail extraction as a way to obtain F
_{obs}values for use in structure solution, for example, by direct methods, then it is best to assume that all reflections are equally likely to contain intensity. In the "Equally weighted" mode, all reflections are given an identical F_{obs}starting value. Thus, if two reflections are completely overlapped, in this methods, they will be assigned equal F_{obs}values through the LeBail fit.It is possible to refine unit cell, background, profile and other non-structural parameters at the same time as a LeBail extraction is performed. I often do this, for two reasons. One is that the final LeBail R

_{wp}and Chi^{2}provides a better measure of the best possible fit than the statistical values, particularly if the material has non-ideal peak shapes or other factors that cannot modeled. The second reason is the LeBail fit provides excellent starting values for the unit cell, background and profile parameters, so these terms need not be refined again until all structural terms have been fit well.These LeBail refinements, alas, are prone to diverge if the the extracted intensities are changing rapidly and other parameters, such as unit cell parameters are compensating. It is a good practice to run GENLES several times with the "Number of Cycles" set to zero each time POWPREF is run -- to allow the reflection intensities to converge before refining parameters.

Note that extraction different methods can be used for different phases in a histogram. It can be convenient to use LeBail extraction for an impurity phase, in the case where the impurity has preferred orientation or has a known unit cell, but an unknown structure. I have also used LeBail fits to obtain precise lattice constants via profile fits of materials where the exact structure is not known, so a Rietveld refinement cannot be performed.

LeBail Damping- The shifts to the reflection intensities can damped. This is useful when refining lattice constants or other terms that might otherwise cause the reflection intensities to shift dramatically and in turn cause the refinement to diverge.

Brian Toby (Brian.Toby@NIST.GOV)

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$Revision: 505 $ $Date: 2009-12-04 23:07:17 +0000 (Fri, 04 Dec 2009) $