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 β 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 βG is proportional to the fourth power of the excitation laser energy (Eₗ), 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 Eₗ, explaining the strong dependence of the ratio ID∕IG on the excitation laser energy Eₗ used in the Raman experiment. The Lₐ dependence of D and D^' band differential cross sections is measured, confirming that the proportionality ID∕IG∝Lₐ^-1 originates from the strong dependence of βD 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 Lₐ, 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 (Γ) of the D, G, D^', and G^' bands on the crystallite size Lₐ of nanographites is performed, showing that the phonon lifetime is proportional to the crystallite size.