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 \AA{}. 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.

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

The present synchrotron sources with brilliant x-ray beams, due to high photon fluxes, small source sizes and high collimation, have revolutionized x-ray physics. Enormous progress has been initiated in all established x-ray methods, with the aim of the development of new types of spectroscopy. This is particularly true for the spectroscopy of the dynamics in condensed matter. Meanwhile, there are two powerful x-ray methods with very high-energy resolution available for the study of low energetic excitations like phonons. This review summarizes the developments of these methods focusing on these instrumental developments of the spectrometers using either crystal optics in close-to-backscattering geometry or nuclear resonant techniques. Applications to measurements of phonon dispersion curves and of phonon density of states in ordered and disordered solids and in liquids are presented. It is shown how x-ray results are stimulating improvements in the theoretical approaches to the dynamics. New insights into the dynamics of liquids are discussed. The sensitivities of the spectroscopies allow the study of vibrational behaviour in very small amounts of material even in nanometre-sized thin films or particles. We can already analyse the phonon spectrum of a monolayered nuclear resonant isotope. Prospects of the techniques are also demonstrated.

https://iopscience.iop.org/article/10.1088/0034-4885/63/2/203/pdf

Phonon spectroscopy by inelastic x-ray scattering

Second order Raman spectrum of MoS2

Tomoyuki Sekine

Papers

Raman scattering by silicon

Critical-point analysis of the two-phonon Raman spectrum of silicon

Two-phonon Raman scattering in GaAs

Raman scattering from two-phonon resonance states in SrTiO3