Generalized Grüneisen parameters and low temperature limit of lattice thermal expansion of cadmium and zirconium

The generalized Grüneisen parameters (γ′ _j ) and (γ″ _j ) for cadmium and zirconium were calculated from the second- and third-order elastic constants to determine the low temperature limit of the volume thermal expansion of these metals of hexagonal symmetry. The low temperature limit of cadmium and zirconium was calculated to be positive values indicating a positive volume expansion down to 0 K even though many Grüneisen gammas were found to be negative.