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

## TL;DR

This study uses density functional theory to calculate the elastic constants of beta-eucryptite, revealing insights into its mechanical properties and thermal expansion behavior, with results aligning closely with some experimental data.

## Contribution

It provides the first DFT-based calculation of all five elastic constants of beta-eucryptite, clarifying discrepancies in experimental measurements of its compressibility.

## Key findings

- Calculated elastic constants agree within 15% of experimental data.
- The c-axis compressibility is positive, contradicting some direct measurements.
- Positive c-axis compressibility has implications for understanding negative thermal expansion.

## Abstract

The five independent elastic constants of hexagonal $\beta$-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 $\beta$-eucryptite parallel to the c-axis, $\chi_c$, and perpendicular to it, $\chi_a$, 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 $\chi_c$ must be positive and discussed the implications of a positive $\chi_c$ in the context of explaining the negative bulk thermal expansion of $\beta$-eucryptite.