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 (cij) deduced from Brillouin spectra and the zone center optical mode frequency (ω0) 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 13C in 12C1-x13Cx diamond, it is predicted that the bulk modulus of 13C diamond exceeds that for 12C diamond by one part in a thousand, just below the experimental sensitivity accessible with Brillouin measurements; ω0 exceeds the value expected from the M-1/2 dependence, where M is the average atomic mass, by ∼ 0.3 cm-1, consistent with observation. The Grueneisen parameter for ω0 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., c11=10.804(5), c12=1.270(10), and c44=5.766(5) in units of 1012(dyn/cm2) are the most accurate yet obtained. copyright 1996 The American Physical Society