Brillouin and Raman scattering in natural and isotopically controlled diamond.

Abstract

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 ({ital c}{sub {ital ij}}) deduced from Brillouin spectra and the zone center optical mode frequency ({omega}{sub 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 {sup 13}C in {sup 12}C{sub 1{minus}{ital x}}{sup 13}C{sub {ital x}} diamond, it is predicted that the bulk modulus of {sup 13}C diamond exceeds that for {sup 12}C diamond by one part in a thousand, just below the experimental sensitivity accessible with Brillouin measurements; {omega}{sub 0} exceeds the value expected from the {ital M}{sup {minus}1/2} dependence, where {ital M} is the average atomic mass, by {approximately} 0.3 cm{sup {minus}1}, consistent with observation. The Gr{umlt u}neisen parameter for {omega}{sub 0} and the third-order bulk modulus are consistent with the theoretical estimates from the present model. The elastic moduli for natural diamondmore » determined in the present study, viz., {ital c}{sub 11}=10.804(5), {ital c}{sub 12}=1.270(10), and {ital c}{sub 44}=5.766(5) in units of 10{sup 12}(dyn/cm{sup 2}) are the most accurate yet obtained. {copyright} {ital 1996 The American Physical Society.}« less