The best RDM model was
proposed to be the NaPbFe_{2}F_{9} crystal structure, disclosed
during the recrystallization study inside the vitreous domain in the NaF/PbF_{2}/FeF_{3}
system.
The crystal structure is built up from linear intercrossed chains of cornerlinked [MF_{6}] 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 Xray one.
The expected isomorphous replacement between Fe^{3+} and V^{3+} is well supported by the crystal chemistry in fluorides in general.
As a rule, when a Fe^{3+} based fluoride exists, the isostructural equivalent V^{3+} 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 FeF and VF atom pairs in octahedra.
These considerations apply exclusively to fluoride compounds, because Fe^{3+} and V^{3+} 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 MF_{6} coordination was constrained to occur with a maximum MF 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 MF_{6} polyhedra should not have necessarily
led to regular octahedra. A model built up from [MF_{6}] trigonal
prisms (unknown for Fe^{3+} and V^{3+} 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 [MF_{6}] entities by a
threedimensional 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
[MF_{6}] (M = Fe, V) polyhedral chains were zigzagging with trans
or cis connections. A few rings with 3, 4, 5 or 6 [MF_{6}] polyhedra
sharing corners were built up by the Monte Carlo process and 92 of the
300 [MF_{6}] 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 [MF_{6}]
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 A_{2}M_{2}F_{9},
none presents any established [MF_{6}] octahedra edge sharing.
However edge sharing occurs as a fraction of the octahedra interlinks in
crystallized compounds as BaZnFeF_{7} , BaCuFeF_{7}
or BaMnFeF_{7} (with larger 3dcation/F ratio) and also BaTiF_{5}
(with smaller ratio), it is thus admittable that edge sharing could occur
in the NaPbM_{2}F_{9} glasses. On another hand, the presence
of [MF_{6}] 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 cornersharing 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 NaPbM_{2}F_{9} (M = Fe, V), starting from the
NaPbFe_{2}F_{9} 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) Xray, M = Fe and
Rp = 1.75 %.
Projection of the RMC model for NaPbM_{2}F_{9} (M = Fe, V) fluoride glasses, starting from the NaPbFe_{2}F_{9}, RDM model. The distorted intercrossed chains of [MF_{6}] octahedra are finger print of the starting model :