Transferability of Empirical Force Fields in Silicates: Lattice-Dynamical Evaluation of Atomic Displacement Parameters and Thermodynamic Properties for the Al₂OSiO₄ Polymorphs

A Born-von Karman rigid-ion lattice-dynamical model, using empirical atomic charges and valence force fields derived from the best fit to the vibrational frequencies of a group of silicates and oxides, has been applied to andalusite, kyanite and sillimanite, the three naturally occurring Al₂OSiO₄ polymorphs. For andalusite there is good agreement with the atomic anisotropic displacement parameters (ADP's) derived from accurate crystal structure refinement at different temperatures and with the values of thermodynamic functions, such as the specific heat and entropy. For kyanite, our calculations are successful in reproducing the values of thermodynamic functions, but not the ADP's, almost certainly due to the poor quality of the crystals used in the structure determination. For sillimanite, imaginary frequencies are obtained in a region of the Brillouin zone: such an inadequacy might be ascribed to the presence of fourfold coordinated Al, whose properties are considerably different from those of higher-coordinated Al present in andalusite and kyanite.

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