Modelling the NaPbM₂F₉ (M = Fe, V) Fluoride Glass Structures

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Full paper now available (June 1997)

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 ų 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 ų) 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.