Reverse Monte Carlo Modelling with the RMCA software. The model was generated from 1950 atoms in a cubic box (30.12 Å length). The initial model was built from a random filling of the box by the M atoms first, then the Na, the Pb and the F atoms successively. Positions at the filling stage were accepted if minimal predefined interatomic distances were respected. Then the RMC was made by using M-F distance and coordination constraints against the neutron diffraction patterns of NaPbFe2F9 and NaPbV2F9 glasses (wavelength 0.703 Å), assuming isomorphous replacement of Fe by V atoms (hypothesis well supported by fluoride crystal chemistry). Moves were stopped at 100% of the 3d cations in octahedral sites. Partial view of the MF6 final octahedra network is online as a gif file prepared from a three-dimensional polyhedral view in VRML. The 3D view with a wireframe rendering is also available.
Modelling by the Rietveld method with the ARITVE software. Several models selected among the ABM2F9 crystal structures were tested. The best agreement between observed and calculated neutron diffraction patterns was for models deriving from the crystalline forms of NaPbFe2F9, KCaAl2F9 and NaBaFe2F9. The first two structures are polytypes with linear octahedral chains loosely interconnected (the NaPbFe2F9 glass recrystallizes into the NaPbFe2F9 crystal structure type on heating) whereas the third structure-type is quite different with staircase double octahedral chains. Analogous views as above are also available for the NaPbFe2F9-derived model (gif, 3D with polyhedral and wireframe rendering) as well as for the KCaAl2F9-derived model (gif, polyhedral and wireframe) and the NaBaFe2F9 one (gif, polyhedral and wireframe).
Discussion. 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 octahedra. It is amazing to observe the agreement quality on the neutron data associated to such small boxes : 690, 2093 and 720 Å3 respectively for the models derived from crystalline NaPbFe2F9 (neutron data fits for M = Fe, M = V), KCaAl2F9 (M = Fe, M = V) and NaBaFe2F9 (M = Fe, M = V). At first glance, the RMC model (27325 Å3) does not present two identical polyhedra and the octahedral chains are zig-zaging with trans or cis connections. Moreover, a few rings with 3, 4 or 5 (to be checked) octahedra sharing corners have been built by the Monte Carlo process and some of the 300 octahedra share an edge.
Conclusion. The short and medium range order govern diffraction patterns of glasses. From this study, expectations for a unique structure representation for the NaPbM2F9 (M = Fe, V) fluoride glasses are disappointed. Several models which may seem very different to crystallographer eyes lead to similar mean short and medium range order. The RMCA model may be considered as combining the various special arrangements (plus others) characterizing the crystalline-derived models tested by the ARITVE software.
Copyright © 1997 - Armel
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RMC Modelling Internet Conference 1997