Formal elasticity of four carbon allotropes: II. The anatomy of the macroscopic elastic constants, compliances, and pressure derivatives and a generalized method of homogeneous deformation

The formal contributions of inner elastic constants to the macroscopic second- and third-order elastic constants of four diamond and graphite allotropes of carbon are analysed. Second- and third-order compliances and compressibilities, effective elastic constants, and pressure derivatives of the second-order constants are also presented. A generalized method of homogeneous deformation is developed to relate the computationally friendly infinitesimal strain approach to the thermodynamically rigorous finite-strain formalism. Computational protocols, involving up to nine distinct shape-changing deformations, are developed to facilitate the determination of all second- and third-order elastic and inner elastic constants, and hence of all derived quantities.