Multiphonon Raman and infrared spectra of isotopically controlled diamond

Two-phonon spectra of ¹²C_1-x¹³Cₓ diamonds, $0<~x<~1,$ are measured with a sensitive charge-coupled device-based Raman and a Fourier transform infrared spectrometer. Exploiting the infrared activity and the polarization characteristics of the Raman spectra recorded for a variety of scattering geometries, the two-phonon features are interpreted in terms of the critical points revealed in the phonon dispersion curves determined by inelastic neutron scattering. The occurrence of identical spectroscopic features in both ¹³C and natural diamond, consistent with virtual crystal approximation, proved invaluable in arriving at assignments for them. Space group selection rules for two-phonon combinations/overtones and the wave-vector conservation, all employed in a self-consistent fashion, yield the frequencies of the critical points with improved precision.