Computation of Mean Debye Temperature of Cubic Crystals from Elastic Constants

An improved method is presented for computing the mean Debye characteristic temperature of cubic crystals from the elastic constants. It is based upon an evaluation of the distribution in solid angle of the roots of the cubic equation which describes the propagation of plane acoustic waves in the crystal, and otherwise employs a device due to Hopf and Lechner. The end result is given in simple closed expressions which present no computational difficulty. The uncertainty in the computed value of the mean Debye temperature due to the approximation made in the method is of the order 0.1 percent when the anisotropy factor of the crystal is as large as 4.