X-Sender: firstname.lastname@example.org Date: Mon, 27 Apr 1998 18:45:12 +0200 >How many parameters are being refined when doing a Le Bail >and what about the intensities? Does this mean that each intensity >is a separate refinable parameter that has to go into the least squares? Intensities are refined in the Pawley method. They are not in the Le Bail method in which only profile (U,V, W, eta, zero...) and cell parameters are refined (maximum 6 to 12 parameters). With the Pawley method, you should add 1000 parameters if you have 1000 reflections, that explains the speed difference and also the stability difference.
The information Pawley method gives you over Le Bail method is the co-varience matrix on how the extracted peak intensities correlate with each other which can then (in theory) be used in the structure solution program for reliable structure solution from extracted intensities. Most (all?) readily available structure solution programs do not have the ability to use the co-varience matrix and are at presently optimised for Le Bail extracted data where the ESDs are pretty much meaningless, and are artifically set to a small amount most of the time to stop software ignoring nearly all the peaks (i.e., Shelxs). (Refer: Le Bail Method for Extracting Intensities)
"3.2.2 Whole pattern refinement with cell constraint
A revolution came with the Pawley method as described in a paper entitled Unit-cell refinement from powder diffraction scans, (G.S. Pawley J. Appl. Cryst. 14 (1981) 357-361). The main purpose was thus clearly to refine cell parameters from the whole pattern, however the possibility to use the extracted intensities as the starting point for the application of direct methods was offered. As well as for the Rietveld method, the Pawley method was not recognized as a revolution for a long time. In the Pawley method, profiles are analytical, their width is constrained to follow a Caglioti law with the three refinable parameters U, V, W as defined in most of the Rietveld-derived softwares. The main difference with the Rietveld method is that the intensities are considered as refinable parameters. Slack constraints were introduced for stabilization of the intensities of those reflections overlapping too much. So, the reflection positions are constrained by the cell knowledge. The cell parameters being themselves refined during the process if the user chooses to do so. Taking the case of 1000 reflections as an example, the number of parameters to be refined when applying the Pawley method is near of 1010 (1000 intensities + one to six parameters for the cell + the zeropoint + one or two profile parameters + the U,V,W ones). This leads to a pretty matrix which should be reversed in the refinement process (and consider 10010 for the 10000 reflections of the dreamed synchrotron pattern). The version I tried several years ago was limited to a maximum of 300 reflections on a pattern. I had to cut the pattern into several pieces for complicated crystal structures. Current versions have been improved. "