Computation of Mean Debye Temperature of Cubic Crystals from Elastic Constants. II

Quimby and Sutton have presented, in an array of equations, an improved, accurate method for computing the mean Debye characteristic temperature of cubic crystals from the elastic constants. The present paper gives an equivalent, simplified, explicit equation. The pertinent integral is also expanded in a Taylor series to the fifth term by a special device and a method of getting the general term made evident. The first two terms of this series constitute Born's equation which is shown to be usually inaccurate since the series is slowly convergent. This series is useful, however, in estimating the correction to the simple equation first mentioned. This correction is analyzed in more detail and extended to values of the anisotropy factor less than unity. Graphs are given permitting rapid calculation of Debye temperatures with an uncertainty due to the approximation made in the method of about 0.1 percent.