Raman spectroscopic determination of the length, energy, Debye temperature, and compressibility of the C–C bond in carbon allotropes

Raman phonon relaxation dynamics in carbon allotropes including graphene, carbon nanotube, C60, carbon nanobud, graphite, and diamond has been formulated in terms of the bond order–length–strength (BOLS) correlation. The length and energy responses of the representative bond to the change of coordination environment, pressure, and temperature determine intrinsically the Raman shifts. Reproduction of the measured results in quantitative information of the bond length, bond energy, mode cohesive energy, binding energy density, Debye temperature, and the compressibility of the C–C bond in each phase without needing involvement of the phonon scattering resonant processes or the mode Grüneisen constants.