CRYSTAL BINDING AND ELASTIC CONSTANTS — Charles Kittel
Physics — Solid State · elastic-waves-cubic-crystals
Problem
General propagation direction. (a) By substitution in (57) find the determinantal equation which must be satisfied for plane waves to propagate in a crystal of cubic symmetry in a direction with direction cosines (l,m,n) with respect to the cube edges. (b) The sum of the roots of the determinantal equation is equal to the sum of the diagonal elements of the matrix. Show from part (a) that the sum of the squares of the three elastic wave velocities in any propagation direction in a cubic crystal is (C11+2C44)/ρ. Recall that l2+m2+n2=1.