Debye-temperature-elastic-constants relationship for materials with hexagonal and tetragonal symmetry

In the literature a relation is often used that correlates Debye temperature and bulk modulus by a square-root law. It was recently shown that, for different cubic crystal structures, such a law is only fulfilled within relatively large error limits. If one takes, however, the average of the elastic constants of the transversal acoustic phonon modes as elastic modulus instead of the bulk modulus, the square-root law is established with high precision. It is demonstrated that the same procedure may also be applied successfully to materials with hexagonal crystal symmetry such as hexagonal close-packed metals and semiconducting compounds with the wurtzite structure, and to different structures of the tetragonal system. The adequate moduli are G(h)={c(44)[c(44)(c(11)-c(12))/2](1/2)}(1/2) and G(t) = [c(44)c(66)(c(11)-c(12))/2](1/3) for materials with hexagonal and tetragonal symmetry, respectively. The difference between the various structures of a crystal system is quantitatively described by the different number of atoms in the crystallographic unit cell. (C) 1996 American Institute of Physics.