Lattice instabilities of cubic NiTi from first principles

Abstract

The phonon dispersion relation of NiTi in the simple cubic $B2$ structure is computed using first-principles density-functional perturbation theory with pseudopotentials and a plane-wave basis set. The structure is shown not to be a local energy minimum, so that its observation at high temperatures must be due to entropic stabilization by large fluctuations around the average atomic positions. Lattice instabilities are observed to occur across nearly the entire Brillouin zone, excluding three interpenetrating tubes of stability along the (001) directions and small spheres of stability centered at R. The strongest instability is that of the doubly degenerate ${M}_{{5}^{\ensuremath{'}}}$ mode. The distorted structure produced by freezing a particular choice of unstable ${M}_{{5}^{\ensuremath{'}}}$ eigenvector into the reference cubic structure yields, with an appropriate choice of overall amplitude, an excellent approximation to the observed ground-state ${B19}^{\ensuremath{'}}$ structure.