Resolving the structure of TiBe$_{12}$

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.