Calculation of the debye temperatures of hexagonal crystals from elastic constants

Hexagonal crystals are less symmetric than cubic crystals, but the integrations to calculate debye temperatures from single crystal elastic constants are simpler and easier for hexagonal crystals. Houston's method actually works for hexagonal crystals in contrast to cubic crystals where it fails. The literature on these calculations for hexagonal crystals is reviewed and checked against modern computer calculations, and errors both small and substantial have been found in the use of Houston's method for hexagonal crystals in published papers. Examples of correct calculations of transverse, longitudinal, and overall debye temperatures are given for eleven different hexagonal crystals of interest, and for a number of arbitrary sets of elastic constants in the Wolcott tables. Mixing of longitudinal and transverse modes is a major problem for some cubic crystals, but appears to be less for known hexagonal crystals. The mixing of modes was examined for a particular case of C44 greater than C11 for one set of values covering hexagonal, tetragonal, and cubic symmetries. The one integration for any hexagonal crystal that can be performed analytically is also reviewed.