Nanocrystalline samples of Ba 1-x Ca x F 2 prepared by high-energy milling show an unusually high Fion conductivity, which exhibit a maximum in the magnitude and a minimum in the activation energy at x = 0.5. Here, we report an X-ray absorption spectroscopy (XAS) at the Ca and Sr K edges and the Ba L 3 edge and a molecular dynamics (MD) simulation study of the pure and mixed fluorides. The XAS measurements on the pure binary fluorides, CaF 2 , SrF 2 and BaF 2 show that high-energy ball-milling

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... roduces very little amorphous material, in contrast to the results for ball milled oxides. XAS measurements of Ba 1-x Ca x F 2 reveal that for 0 < x <1 there is considerable disorder in the local environments of the cations which is highest for x = 0.5. Hence the maximum in the conductivity corresponds to the composition with the maximum level of local disorder. The MD calculations also show a highly disordered structure consistent with the XAS results and similarly showing maximum disorder at x = 0.5.