Second-order and third-order elastic properties of diamond: An ab initio study

Diamond's second-order elastic properties, and several third-order properties associated with uniform deformation, were calculated using ab initio all-electron density-functional theory. The predicted second-order elastic properties and equilibrium lattice parameter, in units of GPa and nm, are c11=1043(5), c12=128(5), c44=534(17), bulk modulus B=433(5), shear modulus G=502(10), Poisson ratio μ=0.082(5), and a=0.35569(2), where the parenthetic number is the uncertainty. The second-order force constants, in units of GPa, are kI=3843(108), kII=2346(17), kIII=2847(35), and kIV=5635(45). Here, subscripts I-IV denote four strains whose tensor elements are [ε, ε, ε, 0, 0, 0], [ε, ε, 0, 0, 0, 0], [ε, ε, −ε, 0, 0, 0], and [ε, ε, ε, ε, ε, ε], respectively, using 6-component notation in the format [ε1, ε2, ε3, ε4, ε5, ε6]. Predicted inelastic properties include the third-order force constant corresponding to uniform dilation gI=−55,000(3,500) GPa, the bulk-modulus pressure derivative ∂B/∂P=4.7(3), and the overall Gruneisen parameter γG=0.85(15). Both our second-order and third-order properties agree well with measured values obtained by ultrasonics and by Raman spectroscopy.