Reliable non-linear elastic constants

The values given in the literature for the third-order elastic constants c(IJK) of the standard semiconductors have long been suspect. We have applied modem statistical analysis to the raw data from which the databook c(IJK) were obtained, and we give revised values with reliable error estimates for Si, Ge and GaAs. The databook c(IJK) are appropriate for an expansion of the elastic energy of a body as a Taylor series in Lagrangian strain eta(IJ), but there are formidable mathematical difficulties in using Lagrangian strain in the analysis of physical problems. To facilitate such analysis, we introduce effective second-order elastic constants for materials under finite strain. From these, strain, stress and pressure derivatives are readily calculated. The pressure derivatives are given for Si, Ge and GaAs. Using the stress derivatives, the relationships between physical observables such as acoustic velocities and the databook c(IJK) can be obtained by simple algebra.