The best RDM model was proposed to be the NaPbFe₂F₉ crystal structure, disclosed during the recrystallization study inside the vitreous domain in the NaF/PbF₂/FeF₃ system.
 
 

The crystal structure is built up from linear intercrossed chains of corner-linked [MF₆] octahedra. It is worth noting that some Na/Pb disorder was suggested to be present in the crystalline phase.

Data presented here for the RMC/RDM study are two neutron patterns (for M = Fe and V) and an X-ray one.

The expected isomorphous replacement between Fe³⁺ and V³⁺ is well supported by the crystal chemistry in fluorides in general.

As a rule, when a Fe³⁺ -based fluoride exists, the isostructural equivalent V³⁺ material can be prepared too, with generally no more than 1% variation in cell dimension.

The mean usual interatomic distances are 1.935 and 1.950 Å respectively for Fe-F and V-F atom pairs in octahedra.

These considerations apply exclusively to fluoride compounds, because Fe³⁺ and V³⁺ cations may present a quite different behaviour in oxydes having a less pronounced ionic character than fluorides.

The random RMC model consisted in 1950 atoms in a cubic box (30.12 Å length for corresponding to the number density r_o = 0.07135 as determined from the glass density).

The initial positions were generated from a random filling of the box by the M atoms first, then the Na, the Pb and the F atoms successively were inserted. Positions at this filling stage were accepted if minimal predefined interatomic distances were respected. The MF₆ coordination was constrained to occur with a maximum M-F distance equal to 2.15 Å.

The RMC model did not presented two identical polyhedra. 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 (this is not the same for distorted tetrahedra which continue to look like tetrahedra, or possibly square plane if distances allow it). Indeed, a large majority of more or less distorted octahedra were built, but a few trigonal prisms have occurred. A visual examination of each of the 300 [MF₆] entities by a three-dimensional capable VRML (Virtual Reality Modelling Language) viewer, allowed to estimate that 20 of them were near of trigonal prisms (TP), 25 were quite irregular polyhedra (intermediate between TP and octahedra), the rest being acceptable more or less distorted octahedra (very few being really regular) :
 

The RDM model had only two similar ones :
 
 
 

In the RMC model, the [MF₆] (M = Fe, V) polyhedral chains were zigzagging with trans or cis connections. A few rings with 3, 4, 5 or 6 [MF₆] polyhedra sharing corners were 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).
 

A cluster of five [MF₆] polyhedra linked by edges as found in the RMC model :

The way octahedra were linked in the RMC model was 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 , BaCuFeF₇  or BaMnFeF₇  (with larger 3d-cation/F ratio) and also BaTiF₅  (with smaller ratio), it is thus admittable that edge sharing could occur in the NaPbM₂F₉ glasses. On another hand, the presence of [MF₆] trigonal prisms in the RMC result is theoretically a nonsense regarding fluoride crystal chemistry
(but who knows really glass structures ?).
 
 

So that a RMC modelling based on the selected RDM model, showing exclusively corner-sharing octahedra, seemed appropriate, in order to validate it by a modelling involving a much larger atom number. The RDM model was extended to 936 atoms, and the RMC application produced soon acceptable Rp values.
 

Observed (+++) and calculated (¾¾ ) interference functions corresponding to the RMC modelling of glassy NaPbM₂F₉ (M = Fe, V), starting from the NaPbFe₂F₉ RDM model.
The difference functions are in the lower parts.

a) Neutron, M = Fe and Rp = 0.81 % ;
b) Neutron, M = V and Rp = 1.22 % ;
c) X-ray, M = Fe and Rp = 1.75 %.
 

Projection of the RMC model for NaPbM₂F₉ (M = Fe, V) fluoride glasses, starting from the NaPbFe₂F₉, RDM model. The distorted intercrossed chains of [MF₆] octahedra are finger print of the starting model :