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 c11,c12,c44, and bulk modulus B are reported as purely theoretical functions of x, where x denotes the atomic fraction of 13C in 12C(1−x)13Cx. 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 c11, c12, c44, and B undergo essentially linear increases: c11(x)=c11(0)(1+0.000049x),c12x=c1201+0.00025x,c44x=c4401+0.000021x and Bx=B01+0.000088x. Thus, compared to the values at x = 0, the values of c11, c12, c44, 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 c12, and provide a general method that can be used for arbitrary crystals having diamond's space group.