Reappraisal of experimental values of third-order elastic constants of some cubic semiconductors and metals

Abstract

The third-order elastic constants of many cubic materials have been determined by measurements of the changes in acoustic velocities under hydrostatic and uniaxial stress. These measurements give, typically, 14 data to determine the six material parameters ${c}_{\mathrm{IJK}}$, related by linear equations. Not least because of the unreliability of uniaxial stress experiments, the resulting ${c}_{\mathrm{IJK}}$ has been considered to be dubious. Multivariate linear regression analysis is applied to the published data for some semiconductors, Si, Ge, GaAs, GaP, and InSb, some elemental metals, Cu, Ag, Au, Al, and Ni, and some miscellaneous materials, to obtain the best estimates of the material parameters and of the errors in them. We find that the published data are remarkably good and many of the published ${c}_{\mathrm{IJK}}$ and errors on them need little adjustment. Some values and errors do require significant adjustment. Uniaxial stress data on metals turns out to be nearly useless, by itself, but we show that in combination with hydrostatic data it gives essential and reliable input.