Effect of Crystal Anisotropy on the Thermal Conductivity of Copper Alloys

Abstract

The lattice thermal conductivity of copper alloys has been studied, taking account of the anisotropy of the crystal by using a modified Debye distribution having angular dependence. This is equivalent to replacing the elastic velocities ($V_i$) that occur in the usual Debye distribution by $V_i(\theta , \phi )$ and multiplying by $\frac{d\Omega }{4\pi }$. Lindenfeld and Pennebaker assumed an isotropic crystal and so used the usual Debye distribution in their calculation of the conductivity. Using the expressions for $K_T$ and $K_L$ (the contributions to the conductivity from the transverse and longitudinal modes) employed by Lindenfeld and Pennebaker and the elastic velocities found from elastic-constant data, the angular integration for the anisotropic average of the total conductivity was performed by using a Houston's average over the principal crystalline directions.