Measuring the absolute Raman cross section of nanographites as a function of laser energy and crystallite size

In this paper, the dependence of the differential Raman cross section beta of the D, G, D-', and G(') bands of nanographites on the excitation laser energy and also on the crystallite size is reported. We show that beta(G) is proportional to the fourth power of the excitation laser energy (E-l), as predicted by the Raman scattering theory. For the bands which arise from the double-resonance mechanism (D, D-', and G(')), the differential cross section does not depend on E-l, explaining the strong dependence of the ratio I-D/I-G on the excitation laser energy E-l used in the Raman experiment. The L-a dependence of D and D-' band differential cross sections is measured, confirming that the proportionality I-D/I-G proportional to L-a(-1) originates from the strong dependence of beta(D) on the inverse of the crystallite size. In the G(') band case, the data show that its differential cross section increases with the increasing crystallite size L-a, following an opposite behavior when compared with the disorder induced D and D-' bands. An analysis on the dependence of the full width at half maximum (Gamma) of the D, G, D-', and G(') bands on the crystallite size L-a of nanographites is performed, showing that the phonon lifetime is proportional to the crystallite size.