Internal strain parameter of silicon and GaAs and planar force constants

We show that the internal strain parameter ζ and elastic constants of the tetrahedral semiconductors can be determined from the force constants between planes of atoms. These have been computed recently for Si and GaAs from self-consistent electronic calculations using the Hellmann-Feynman theorem. The theoretical results are ζ = 0.72 for GaAs and ～0.57 for Si compared to experimental values of 0.76 and 0.73.