Armel Le Bail came up with another implementation for pattern-fitting in the late 1980’s that avoids use of least-squares refinement for reflection intensities and cleverly takes advantage of Hugo Rietveld’s intensity extraction method. He wanted \(|F_{obs, hkl}|\) values for materials where he wanted to determine the structure, and thus had no idea for information to provide approximate \(F_{calc, hkl}\) values, but did have a known unit cell. He ran a Rietveld fit where instead of computing all the \(F_{calc, hkl}\) from the structure, he overrode the computed values and set them all to a constant. After this was done, computing the powder pattern was done and as expected the match to the pattern was terrible. Hugo’s intensity extraction method could still be used to come up with estimates for the \(|F_{obs, hkl}|\) values. They would be imperfect, but certainly far better than the constant values he started with for \(F_{calc, hkl}\). He then replaced the previously constant \(|F_{calc, hkl}|\) values with the just-extracted \(|F_{obs, hkl}|\) values and then recomputed the diffraction pattern. The match between the observed and computed patterns would now be much closer. Likewise, repeating the intensity extraction gave even better values than those from before. This process would be cycled a few times resulting in a pattern is that is well-fit and a good set of \(|F_{obs, hkl}|\) values is obtained, though the intensities for overlapping peaks will be apportioned a bit differently than in the Pawley method. Once the intensities have been fairly-well fit, it is also possible to refine background, peak positions and peak shape parameters rather than simply recomputing the pattern.
It should be understood what this Le Bail process is doing. The Le Bail extraction process is effectively a steepest descent fitting method for reflection intensities while if any parameters are being fit, that is being done via Levenberg-Marquardt damped Gauss-Newton fitting, but that fitting process is completely disconnected from the intensity fitting process. This type of fitting is not very stable if the parameters are undergoing large changes, which is why it is wise to approach Le Bail fitting with a “soft touch.”
Bob Von Dreele came up with an alternate approach to Le Bail fitting, where instead of setting all \(F_{calc, hkl}\) values to a constant, they remain at whatever values they have been computed at, based on the structural information in the model. This is useful when a partial structure is known. In this case, the \(F_{calc, hkl}\) values from the partial structure are likely to be better starting guesses than setting all values to a constant.
You should understand that Le Bail intensities are optimized in GSAS-II when the powder profile is computed, even if no least-squares optimization cycles are performed. Setting the number of least-squares cycles (in the Controls data tree entry) to 0 and then using the Calculate/Refine menu command will optimize the Le Bail intensities. Doing this twice is usually enough to bring the intensities pretty close to optimum values. At this point the number of cycles can be set to a non-zero value, but it is wise to add parameters to the fit slowly due to the potential instability of the fitting process.
Note that unlike the Pawley fitting, which is a phase property, Le Bail fitting is a HAP setting, so that Le Bail fitting can be done for only for selected histograms associated with a phase. Also, each histogram for each phase has an independent reflection table, so Le Bail intensities are not shared across histograms.
To perform a Le Bail fit, go to the Phase’s Data tab (or in “SeparateHistPhaseTreeItem” mode, in the Hist/Phase data tree entry – see §14.8.1) and press the “Start Le Bail extraction” button, just under the plot selection options. When the Calculate/Refine menu command is first used after Le Bail is selected, the window seen in Fig. 20.7 is displayed, where you are offered a choice for how the Le Bail extraction is initialized. When “Yes” is selected here, all reflection intensities are initialized (as in the original Le Bail method), but if “No” is used, the Von Dreele approach is used, where the previous \(F_{calc, hkl}\) are used as starting values. A Le Bail-only fit is then performed, where the powder diffraction pattern is computed, but no parameters are optimized. A window will be opened with results from this fit and you will be asked if the fit should continue with refinement of parameters. Note that these two steps are only performed when Le Bail mode is initially turned on. In subsequent refinement steps, the reflection intensities are not reset and no “Le Bail-only fit” is performed, but should the latter be wanted, this can be done by setting the number of least-squares cycles to 0.
