DEBYE-TEMPERATURE-ELASTIC-CONSTANTS RELATIONSHIP FOR MATERIALS WITH HEXAGONAL AND TETRAGONAL SYMMETRY

In the literature a relation is often used that correlates Debye tempe rature and bulk modulus by a square-root law. It was recently shown th at, for different cubic crystal structures, such a law is only fulfill ed within relatively large error limits. If one takes, however, the av erage of the elastic constants of the transversal acoustic phonon mode s as elastic modulus instead of the bulk modulus, the square-root law is established with high precision. It is demonstrated that the same p rocedure may also be applied successfully to materials with hexagonal crystal symmetry such as hexagonal close-packed metals and semiconduct ing 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. Th e difference between the various structures of a crystal system is qua ntitatively described by the different number of atoms in the crystall ographic unit cell. (C) 1996 American Institute of Physics.