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Elastic constants of beta-eucryptite: A density functional theory study

The five independent elastic constants of hexagonal $β$-eucryptite have been determined using density functional theory (DFT) total energy calculations. The calculated values agree well, to within 15%, with the experimental data. Using the calculated elastic constants, the linear compressibility of $β$-eucryptite parallel to the c-axis, $χ_c$, and perpendicular to it, $χ_a$, have been evaluated. These values are in close agreement to those obtained from experimentally known elastic constants, but are in contradiction to the direct measurements based on a three-terminal technique. The calculated compressibility parallel to the c-axis was found to positive as opposed to the negative value obtained by direct measurements. We have demonstrated that $χ_c$ must be positive and discussed the implications of a positive $χ_c$ in the context of explaining the negative bulk thermal expansion of $β$-eucryptite.