Isotope effect on diamond's elastic-stiffness coefficients: An ab initio study

Abstract The effects of isotopic substitution on diamond's elastic-stiffness coefficients are studied theoretically by analyzing the zero-point motion and anharmonicity associated with lattice vibrations. Coefficients c 11 , c 12 , c 44 , and bulk modulus B are reported as purely theoretical functions of x, where x denotes the atomic fraction of 13 C in 12 C (1−x) 13 C x . Second-order and third-order force constants are computed at the ab initio level and used as input to these expressions. As x increases, the predicted values of c 11 , c 12 , c 44 , and B undergo essentially linear increases: c 11 ( x ) = c 11 ( 0 ) ( 1 + 0.000049 x ) , c 12 x = c 12 0 1 + 0.00025 x , c 44 x = c 44 0 1 + 0.000021 x and B x = B 0 1 + 0.000088 x . Thus, compared to the values at x = 0, the values of c 11 , c 12 , c 44 , and B are predicted to change by only 0.0049%, 0.025%, 0.0021%, and 0.0088%, respectively, at x = 1. Our calculations also resolve a large discrepancy between two reported measurements of c 12 , and provide a general method that can be used for arbitrary crystals having diamond's space group.