After demonstrating inconsistencies in some of the better known elasticity calculations, an alternative method of imposing the necessary invariance conditions on the strain energy of a crystal is presented. The new method is equivalent to the Born-Huang procedure but, in addition to providing further insight, also offers one or two operational advantages. For example, it demonstrates that all purely first-neighbor interactions are central only. The method is applied to the calculation of the elasticity of a two-constant model of the diamond type of crystal, and this predicts the relation $2c_{44}(c_{11}+c_{12})=(c_{11}-c_{12})(c_{11}+3\mathrm{}{c}_{12})$, which is very well satisfied by the experimental data for diamond, silicon, and germanium.

• Received 17 December 1965

DOI:https://doi.org/10.1103/PhysRev.145.637