Formal elasticityof four carbon allotropes: II. The anatomy of the macroscopic elasticconstants, compliances, and pressure derivatives and a generalizedmethod of homogeneous deformation

Abstract

The formal contributions of inner elastic constants to themacroscopic second- and third-order elastic constants of fourdiamond and graphite allotropes of carbon are analysed. Second-and third-order compliances and compressibilities, effectiveelastic constants, and pressure derivatives of the second-orderconstants are also presented. A generalized method ofhomogeneous deformation is developed to relate thecomputationally friendly infinitesimal strain approach to thethermodynamically rigorous finite-strain formalism.Computational protocols, involving up to nine distinctshape-changing deformations, are developed to facilitate thedetermination of all second- and third-order elastic and innerelastic constants, and hence of all derived quantities.