Convergence in the Evolution of Nanodiamond Raman Spectra with Particle Size: A Theoretical Investigation
Structural characterization of nanodiamonds by vibrational spectroscopy requires knowledge of the factors determining the spectra. Raman spectroscopy is widely used to detect the diamond phase in nanodiamond powders and films, but several spectral features are still poorly understood. Here we present a theoretical study of the evolution of diamond hydrocarbon Raman spectra with increasing size, from the adamantane molecule to ?3 nm large tetrahedral and octahedral particles of Td symmetry, containing up to about 1000 carbon atoms. The self-consistent-charge density functional tight-binding method (SCC-DFTB) was used for the calculation of harmonic first-order Raman spectra. We demonstrate very good agreement with Raman spectra computed by standard density functional theory (DFT) for the smaller model systems. The evolution of the Raman patterns is smooth, and convergence to the bulk limit could clearly be observed in case of the acoustic vibrational modes (?A = 0 cm?1). We found a simple relationship between nanodiamond size and vibrational frequency, which is analogous to the corresponding equation for the radial breathing mode of single-walled carbon nanotubes. The T2 modes of octahedral diamond hydrocarbons coalesce faster to the bulk optical vibrational mode (in experiment, ?O = 1332 cm?1) than those of tetrahedral particles, consistent with the fact that the bulk/surface ratio is more favorable for octahedral particles. Our simulations unequivocally show that controversial Raman features around 500 and 1150 cm?1 do not originate from the nanodiamond crystals, and that the nanocrystal shape plays an important role in the appearance of the Raman spectra even in the 3 nm domain.