Brillouin and Raman scattering in natural and isotopically controlled diamond

The effects of zero-point motion and the anharmonicity of the lattice vibrations of diamond have been explored theoretically in the context of a valence force model explicitly incorporating the isotopic composition. The predictions are tested in a study of the elastic moduli (${\mathit{c}}_{\mathit{ij}}$) deduced from Brillouin spectra and the zone center optical mode frequency (${\mathrm{\omega }}_0$) from Raman spectra of isotopically controlled diamond specimens. On the basis of the anharmonicity parameter of the model associated with bond stretching, deduced from a comparison of the theory with experimentally reported dependence of the lattice parameter with the atomic fraction of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}_{1\mathrm{-}\mathit{x}}^{13}{}_{}{}^{}$ ${\mathrm{C}}_{\mathit{x}}$ diamond, it is predicted that the bulk modulus of ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ diamond exceeds that for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ diamond by one part in a thousand, just below the experimental sensitivity accessible with Brillouin measurements; ${\mathrm{\omega }}_0$ exceeds the value expected from the ${\mathit{M}}^{\mathrm{-}1/2}$ dependence, where M is the average atomic mass, by ∼ 0.3 ${\mathrm{cm}}^{\mathrm{-}1}$, consistent with observation. The Grüneisen parameter for ${\mathrm{\omega }}_0$ and the third-order bulk modulus are consistent with the theoretical estimates from the present model. The elastic moduli for natural diamond determined in the present study, viz., ${\mathit{c}}_{11}$=10.804(5), ${\mathit{c}}_{12}$=1.270(10), and ${\mathit{c}}_{44}$=5.766(5) in units of ${10}^{12}$(dyn/${\mathrm{cm}}^2$) are the most accurate yet obtained. © 1996 The American Physical Society.