Solid state chemistry considerations on models

At first glance, the RMC model (figure 2) does not present two identical polyhedra and the [MF6] (M = Fe, V) polyhedral chains are zigzagging with trans or cis connections. A few rings with 3, 4, 5 or 6 [MF6] polyhedra sharing corners have been built up by the Monte Carlo process and 92 of the 300 [MF6] units share at least one edge with another such unit (12 of them share 2 edges and 2 share 3 edges). It should be kept in mind that the RMC constraint to have [MF6] polyhedra should not have necessarily led to regular octahedra. A model built up from [MF6] trigonal prisms (unknown for Fe3+ and V3+ in fluorides) could have been proposed by the RMC method as well. Indeed, a large majority of more or less distorted octahedra have been built but a few trigonal prisms have occurred (figure 5).

Fig. 5. Selected [MF6] polyhedra. Some (10%) of the most regular octahedra and trigonal prisms are shown together with the most irregular ones built by the RMC process. At the bottom are the two different [MF6] octahedra of the RDM model derived from the NaPbFe2F9 crystal structure.

A visual examination of each of the 300 [MF6] entities by a three-dimensional capable VRML (Virtual Reality Modelling Language) viewer, allows to estimate that 20 of them are near of trigonal prisms (TP), 25 are quite irregular polyhedra (intermediate between TP and octahedra), the rest being acceptable more or less distorted octahedra (very few being really regular). The way octahedra are linked in the RMC model is dominantly by corners. In fact among fluoride crystal structures with formulation A2M2F9, none presents any established [MF6] octahedra edge sharing. However edge sharing occurs as a fraction of the octahedra interlinks in crystallized compounds as BaZnFeF7 [33], BaCuFeF7 [34] or BaMnFeF7 [35] (with larger 3d-cation/F ratio) and also BaTiF5 [30] (with smaller ratio), it is thus admittable that edge sharing could occur in the title glasses. Rings delimited by F-F edges with 3, 4, 5 and 6 octahedra sharing corners are the only known in 3d transition metal fluoride crystal chemistry. One can find some of them in the RMC model but zigzagging chains are the main arrangement. A strange cluster of five edge sharing octahedra has been built (figure 6) which is really unknown for 3+ charged 3d cations in fluorides which show only binuclear edge sharing whereas a trinuclear unit has been described for Cu2+ in Ba6Cu11F34 [36]. The counterpart of such a denser zone is that 5 isolated octahedra exist in the RMC model.

Fig. 6. Five [MF6] polyhedra linked by edges as found in the RMC model.

The Na and Pb coordinations are much less strict than the Fe and V ones in fluorides with respectively 6 to 9 and 7 to 12 fluorine neighbours, with various possible polyhedra shapes for each coordination, regular or not. Thus there could not have been any constraint on the Na-F and Pb-F atom pairs. Table IV gives the details of the Na-F, Pb-F and Fe-Fe statistics of neighbours for the RMC and first RDM models.

Table IV. Neighbours (N) statistics of Na-F, Pb-F and Fe-Fe pairs as obtained by RMC and RDM methods.

















1 88-----------4


7 38


17 2 8


39 16 1


42----------4 38


30 38


12 42----------4


2 12


Total 150---------4 150---------4 300---------8
Cutoff (A) 3.2--------3.2 3.5--------3.5 4.3--------4.3
Average N 7.75---------8 8.97-------10 3.44---------4

The RDM best model is of course consistent with crystal chemistry. The [MF6] polyhedra, which are all octahedra contrarily to the RMC model, present the expected mean M-F distance and are not excessively distorted (figure 5). If we accept the idea that obtaining low R discrepancy factors by RDM fits could indicate that the glass may present locally a distorted but analogous arrangement as in the crystalline model, then we should conclude that several such different models may be present in the glass because similar fits have been obtained with quite different models. Models from RMC and Rietveld studies present similitudes in the sense that one observes predominantly chains of [MF6] octahedra sharing corners. The Rietveld models are limited by the existence of only two or three different types of crystallographycally independent octahedra. It is amazing to observe the agreement quality on the neutron data associated to such small box volumes (see Table II).

Armel Le Bail - June 1997