First- and second-order Raman scattering from finite-size crystals of graphite

First- and second-order Raman scattering from graphite has been studied. The second-order spectra of single crystals and of highly oriented pyrolytic graphite are continuous and exhibit several well-defined bands which can be attributed to features in the density of vibrational states as determined from current lattice-dynamics models. The density of states deduced from the lattice-dynamics model of Nicklow, Wakabayashi, and Smith provides the best replication of the second-order Raman spectrum, but is nevertheless somewhat deficient in this regard, and in need of improvement. The dependence of the first- and second-order graphite Raman spectra on crystallite size has also been studied for a series of samples with typical dimensions $L_c$ and $L_a$ as small as 30 Å. With decreasing crystal size the features in the second-order spectrum broaden noticeably and additional broad features appear in both the first- and second-order spectra. The additional first- and second-order features are also attributed to structure in the vibrational density of states and arise from the wave-vector selection-rule relaxation that results from finite-crystal-size effects. Evidence is presented to demonstrate that the above described spectral features are intrinsic and not associated with impurity excitations.