Comparing RMC and RDM methods

One can think about what would happen if the ten partial structure factors had been available. It is not possible to assert that the actual models proposed by either the RMC or the RDM methods would lead necessarily to low R factors on the lacking structure factors. Fitting without the X-ray data by the RDM method has clearly shown that the less the data, the best the fit and the less the model is reliable. The RMC final result produces a closest approach to the three datasets than the RDM which has difficulties to model the X-ray data. There are large differences in model size and consequently in the number of free parameters in the two methods. Obtaining the quality of the fits as shown in figure 3 by the Rietveld refinement of only 14 atomic coordinate parameters may be considered as convincing that the model reflects some local reality in the glass, owing to the fact that the glass truly recrystallizes into it. The first Rietveld method application to glass structure modelling [15] was published 12 years ago, well before the first RMC one [19]. The Reverse Monte Carlo method was considered as "no different in principle to the method of Rietveld refinement" [19]. Both methods are based on models using periodic boundary conditions (leading thus to some sort of "triperiodic glasses"). The model for the RMC method is usually described with the P1 space group and the cell is large otherwise no acceptable fit can be expected. The model for the RDM method has to be generally much smaller in volume and can use space groups with any symmetry. A powder diffraction pattern from the RMC result could be calculated exactly in the same way as by the RDM method. The problem is to build a special program for the simulation of powder patterns in case of P1 space group with cell parameters of 30 Å or more. The reflection number for Q up to 25 Å-1 would be probably larger than 106. There is no serious difficulty to code a program doing that, but this was not realized in the present study (30000 reflections maximum are allowed per pattern in the present RDM ARITVE software [37]).

Is it possible to take the best RDM model and to build a starting RMC model with it, extending the size by doubling (or more) the cell dimensions ? In the present case and if the sixfold constraint is introduced, the response is no : the effect of the constraint is so drastic that the model will not move from this starting position. Will the agreement R factor corresponding to this starting model be of the same order with RMC and RDM ? The response is no again, because RMC does not simulate a statistical disorder as does RDM by applying line broadening to the reflections following the microstrain rules. If a RMC configuration was used in a standard powder diffraction pattern calculation, then depending on either the instrumental resolution is low or high, the pattern will look like to that of a crystalline compound or to that of a glass.

Is it excluded that two different users will obtain different results trying to model the same glass from the same data ? This cannot be excluded. By the RMC method, various strategies are possible for building the starting model but generally a random number generator is used so that it is excluded that two starting configurations could be identical so that the final results will never be exactly the same. By the RDM method, it is easy to fall down various false minima by using different strategies (in fact, even the "best" final results presented here are to be considered as the lowest false minima I have found).

At the present stage, we are able to fit without to be very sure that the model really represents a possible local arrangement for the glass. In the present study, full data would have consisted in 10 partial structure factors and we had only three really independent ones. This study is thus highly contestable. Are we more happy with a ~2000 atoms model by RMC modelling than with a 50 or 150 atoms model of which 9 or 20 only are really crystallographycally independent by the RDM method ? Well, the truth is that the modeller may be embarrassed with both of them. All that can be concluded is that both are quite different but fit as well (an advantage has to be given to the RMC method which usually is able to fit perfectly), this should discredit all further attempts of modelling glass structures but in fact this simply reflects the impossibility to propose a unique model for a material by definition built up from much more different configurations than we could reasonably introduce. If a large number of these arrangements lead to quite similar short and medium range order, then testing some of them will produce relatively good fits. It was emphasized in the RDM study of glassy SiO2 [23] that reliability factors RI which may seem low (1-2%) when estimated from the I(Q) = [F(Q) + 1] data, may become less satisfying when estimated from the F(Q) data which oscillate around zero. For the present study, the RMC RF values drop to 11.1, 7.3 and 13.6 % whereas the RDM best model gives 14.1, 12.9 and 43.9 % respectively for the Fe and V-based neutron data and Fe-based X-ray data. From such values it is clear that modelling has progress to make, requiring accuracy better than 1% on the experimental data. Such accuracy was certainly not attained for the X-ray pattern, much more difficult to normalize than neutrons patterns. It has to be noted that the neutron patterns, in addition to the usual data reduction, were corrected for paramagnetism as a consequence of the Fe3+ and V3+ presence in the glasses.

Armel Le Bail - June 1997