Critical-point phonon frequencies of diamond

The phonon-dispersion curves derived from neutron-scattering experiments performed on diamond [J. Warren et al., Phys. Rev. 158, 805 (1967)] are not accurate enough to yield the exact frequencies of critical-point (CP) phonons and, thus, to provide a satisfactory interpretation of second-order optical spectra. A self-consistent analysis of such spectra [S. Solin and A. Ramdas, Phys. Rev. B 1, 1687 (1970)] was not fully successful because of ambiguities that arise in assigning second-order infrared absorptions and features in the Raman spectra to specific two-phonon summations. A more effective method for obtaining accurate CP phonon frequencies involves investigating defect-activated one-phonon absorptions; in this paper, we take advantage of the availability of chemically vapor-deposited (CVD) diamond for the purpose of locating and assigning infrared (ir) absorption features in the one-phonon region to CP phonons at the Brillouin-zone boundary. Fourier-transform ir absorbance spectra of CVD diamond exhibit a complex structure at wave numbers below the 1332.5-${\mathrm{cm}}^{\mathrm{-}1}$ lattice-mode cutoff, which is induced by impurity-associated defect centers and yields the exact positions of 16 zone-edge CP phonons. In conjunction with the triply degenerate zone-center mode, this set of phonons then provides the basis for predicting the positions of second-order optical features through simple summations. When the selection rules are taken into account, the procedure yields excellent results, not only in terms of CVD-diamond ir spectra, but also in regard to earlier measurements of the intrinsic two-phonon absorption coefficient of type-IIa natural diamond [J. Hardy and S. Smith, Philos. Mag. 6, 1163 (1961)] and the second-order polarization-dependent Raman spectra recorded by Solin and Ramdas.