  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.
