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

Abstract

In this paper, the dependence of the differential Raman cross section $\ensuremath{\beta}$ of the $D$, $G$, ${D}^{\ensuremath{'}}$, and ${G}^{\ensuremath{'}}$ bands of nanographites on the excitation laser energy and also on the crystallite size is reported. We show that ${\ensuremath{\beta}}_{G}$ 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 ($D$, ${D}^{\ensuremath{'}}$, and ${G}^{\ensuremath{'}}$), 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 ${D}^{\ensuremath{'}}$ band differential cross sections is measured, confirming that the proportionality ${I}_{D}∕{I}_{G}\ensuremath{\propto}{L}_{a}^{\ensuremath{-}1}$ originates from the strong dependence of ${\ensuremath{\beta}}_{D}$ on the inverse of the crystallite size. In the ${G}^{\ensuremath{'}}$ 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 ${D}^{\ensuremath{'}}$ bands. An analysis on the dependence of the full width at half maximum $(\ensuremath{\Gamma})$ of the $D$, $G$, ${D}^{\ensuremath{'}}$, and ${G}^{\ensuremath{'}}$ bands on the crystallite size ${L}_{a}$ of nanographites is performed, showing that the phonon lifetime is proportional to the crystallite size.