Resolving the structure of TiBe$_{12}$

TL;DR

This study uses density functional theory to determine that the tetragonal phase of TiBe$_{12}$ is more stable than the hexagonal phase, resolving longstanding structural controversy.

Contribution

The paper provides the first comprehensive computational analysis confirming the tetragonal structure as the ground state of TiBe$_{12}$, clarifying previous experimental ambiguities.

Findings

Tetragonal phase is more stable across all temperatures.

Hexagonal phase shows an unstable phonon mode indicating a transition to tetragonal.

Predicted elastic constants and thermal properties for the tetragonal phase.

Abstract

There has been considerable controversy regarding the structure of TiBe$_{12}$, which is variously reported as hexagonal and tetragonal. Lattice dynamics simulations based on density functional theory show the tetragonal phase space group $I4/mmm$ to be more stable over all temperatures, while the hexagonal phase exhibits an imaginary phonon mode, which, if followed, would lead to the cell adopting the tetragonal structure. We then report the predicted ground state elastic constants and temperature dependence of the bulk modulus and thermal expansion for the tetragonal phase.