Effect of isotopic constitution of diamond on its elastic constants:C13diamond, the hardest known material

Elastic moduli of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ diamond, deduced from the Brillouin shifts experienced by inelastically scattered monochromatic radiation, are ∼0.5% higher than the corresponding values for natural diamond. This suggests ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ diamond is harder than natural diamond. A simple model incorporating the zero-point motion and the anharmonicity of the interatomic forces is proposed; it explains quantitatively the increase in the elastic moduli, the decrease in the lattice parameter, and a correction to the Raman frequency beyond its ${\mathit{M}}^{\mathrm{-}1/2}$ dependence (where M is the average atomic mass) observed for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ diamond with respect to their values for natural diamond.