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 c(11) = 1043(5), c(12) = 128(5), c(44) = 534(17), bulk modulus B = 433(5), shear modulus G = 502(10), Poisson ratio mu = 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 k(1) = 3843(108), k(II) = 2346(17), k(III) = 2847(35), and k(IV) = 5635(45). Here, subscripts I-IV denote four strains whose tensor elements are [epsilon, epsilon, epsilon, 0, 0, 0], [epsilon, epsilon, 0, 0, 0, 01, [epsilon, epsilon, -epsilon, 0, 0, 0], and [epsilon, epsilon, epsilon, epsilon, epsilon, epsilon], respectively, using 6-component notation in the format [epsilon(1), epsilon(2), epsilon(3), epsilon(4), epsilon(5), epsilon(6)]. Predicted inelastic properties include the third-order force constant corresponding to uniform dilation g(1) = -55,000(3,500) GPa, the bulk-modulus pressure derivative delta B/delta P=4.7(3), and the overall Gruneisen parameter gamma(G) =0.85(15). Both our second-order and third-order properties agree well with measured values obtained by ultrasonics and by Raman spectroscopy. (c) 2005 Elsevier Ltd. All rights reserved.