BRILLOUIN AND RAMAN-SCATTERING IN NATURAL AND ISOTOPICALLY CONTROLLEDDIAMOND

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 composi tion. The predictions are tested in a study of the elastic moduli (c(i j)) deduced from Brillouin spectra and the zone center optical mode fr equency (omega(0)) from Raman spectra of isotopically controlled diamo nd specimens. On the basis of the anharmonicity parameter of the model associated with bond stretching, deduced from a comparison of the the ory with experimentally reported dependence of the lattice parameter w ith the atomic fraction of C-13 in C-12(1-x), C-13(x) diamond, it is p redicted that the bulk modulus of C-13 diamond exceeds that for C-12 d iamond by one part in a thousand, just below the experimental sensitiv ity accessible with Brillouin measurements; oo exceeds the value expec ted from the M-1/2 dependence, where M is the average atomic mass, by similar to 0.3 cm(-1), consistent with observation. The Gruneisen para meter for omega(0) and the third-order bulk modulus are consistent wit h the theoretical estimates from the present model. The elastic moduli for natural diamond determined in the present study, viz., c(11)=10.8 04(5), c(12)=1.270(10), and c(44)=5.766(5) in units of 10(12)(dyn/cm(2 )) are the most accurate yet obtained.