We present a tight-binding potential based on the moment expansion of the density of states, which includes up to the fifth moment. The potential is fitted to bcc and hcp Zr and it is applied to the computation of vibrational properties of bcc Zr. In particular, we compute the isothermal elastic constants in the temperature range $1200\hspace{0.5em}\mathrm{K}<T<\mathrm{}2000\mathrm{}\hspace{0.5em}\mathrm{K}$ by means of standard Monte Carlo simulation techniques. The agreement with experimental results is satisfactory, especially in the case of the stability of the lattice with respect to the shear associated with $C^{\prime }.$ However, the temperature decrease of the Cauchy pressure is not reproduced. The $T=0\mathrm{}$ K phonon frequencies of bcc Zr are also computed. The potential predicts several instabilities of the bcc structure, and a crossing of the longitudinal and transverse modes in the (001) direction. This is in agreement with recent ab initio calculations in Sc, Ti, Hf, and La.

• Received 18 September 2000

DOI:https://doi.org/10.1103/PhysRevB.63.134104