Density Functional Study of Cubic to Rhombohedral Transition in $\alpha$-AlF$_3$

TL;DR

This study uses density functional theory to analyze the structural and electronic properties of $ ext{AlF}_3$ during its phase transition from rhombohedral to cubic, providing insights into the transition mechanism and related properties.

Contribution

It presents a detailed DFT analysis of the phase transition in $ ext{AlF}_3$, including energy surface mapping and property calculations, which are novel for this material.

Findings

The minimum energy structure matches the observed rhombohedral phase.

Calculated phonon modes and dielectric function agree with experimental data.

Evidence suggests possible antiferroelectric behavior in the low-temperature phase.

Abstract

Under heating, $\alpha$-AlF$_3$ undergoes a structural phase transition from rhombohedral to cubic at temperature $T$ around 730 K. The density functional method is used to examine the $T$=0 energy surface in the structural parameter space, and finds the minimum in good agreement with the observed rhombohedral structure. The energy surface and electronic wave-functions at the minimum are then used to calculate properties including density of states, $\Gamma$-point phonon modes, and the dielectric function. The dipole formed at each fluorine ion in the low temperature phase is also calculated, and is used in a classical electrostatic picture to examine possible antiferroelectric aspects of this phase transition.