Raman spectroscopic determination of the length, strength, compressibility, Debye temperature, elasticity, and force constant of the C-C bond in graphene

TL;DR

This study uses Raman spectroscopy to analyze how various stimuli affect the C-C bonds in graphene, providing detailed insights into bond properties and their influence on vibrational characteristics.

Contribution

It offers a theoretical framework unifying Raman shift responses to different stimuli, revealing detailed bond parameters and their effects on graphene's vibrational behavior.

Findings

Quantitative bond length, strength, and force constant data for graphene.

Understanding of Raman shift mechanisms under strain, pressure, and temperature.

Insights into the elastic and thermal properties of graphene bonds.

Abstract

From the perspective of bond relaxation and vibration, we have reconciled the Raman shifts of graphene under the stimuli of the number-of-layer, uni-axial-strain, pressure, and temperature in terms of the response of the length and strength of the representative bond of the entire specimen to the applied stimuli. Theoretical unification of the measurements clarifies that: (i) the opposite trends of Raman shifts due to number-of-layer reduction indicate that the G-peak shift is dominated by the vibration of a pair of atoms while the D- and the 2D-peak shifts involves z-neighbor of a specific atom; (ii) the tensile strain-induced phonon softening and phonon-band splitting arise from the asymmetric response of the C3v bond geometry to the C2v uni-axial bond elongation; (iii) the thermal-softening of the phonons originates from bond expansion and weakening; and (iv) the pressure- stiffening of the phonons results from bond compression and work hardening. Reproduction of the measurements has led to quantitative information about the referential frequencies from which the Raman frequencies shift, the length, energy, force constant, Debye temperature, compressibility, elastic modulus of the C-C bond in graphene, which is of instrumental importance to the understanding of the unusual behavior of graphene.