Phonon focusing in piezoelectric crystals

Striking changes are predicted in acoustic wave propagation and the phonon-focusing properties of piezoelectric crystals as a result of the piezoelectric stiffening of the elastic constants. Phase and group velocities and phonon enhancement factors have been calculated using a general method appli- cable to crystals of any symmetry. Monte Carlo phonon-focusing patterns are presented for a number of the more strongly piezoelectric crystals on which the required material constants are available. The effects of piezoelectric stiffening are generally only pronounced when one or more of the electromechanical coupling constants exceeds 0.1, but become important at much smaller values of the coupling if the elastic anisotropy is small. An important consequence of piezoelectric stiffening is that the degree of the equation of the slowness surface is raised from 6 to 12. As a result the innermost sheet of this surface need not be entirely convex, and fast phonon-branch focusing caustics are permitted. Rochelle salt and ${\mathrm{Ba}}_2$ ${\mathrm{NaNb}}_5$ ${\mathrm{O}}_{15}$ are two crystals which possess this property.