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Brillouin and Raman scattering in natural and isotopically controlled diamond

1996; American Physical Society; Volume: 54; Issue: 6 Linguagem: Inglês

10.1103/physrevb.54.3989

1095-3795

Ralf Vogelgesang, A. K. Ramdas, S. Rodríguez, M. Grimsditch, T. R. Anthony,

Force Microscopy Techniques and Applications

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 (${\mathrm{\ensuremath{\omega}}}_{0}$) 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{\ensuremath{-}}\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; ${\mathrm{\ensuremath{\omega}}}_{0}$ exceeds the value expected from the ${\mathit{M}}^{\mathrm{\ensuremath{-}}1/2}$ dependence, where M is the average atomic mass, by \ensuremath{\sim} 0.3 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, consistent with observation. The Gr\"uneisen parameter for ${\mathrm{\ensuremath{\omega}}}_{0}$ 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. \textcopyright{} 1996 The American Physical Society.