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

Abstract

From the perspective of bond relaxation and bond vibration, we have formulated the Raman phonon relaxation of graphene, under the stimuli of the number-of-layers, the uni-axial strain, the pressure, and the 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 the Raman shifts, which are due to the number-of-layers reduction, of the G-peak shift and arises from the vibration of a pair of atoms, while the D- and the 2D-peak shifts involve the z-neighbor of a specific atom; (ii) the tensile strain-induced phonon softening and phonon-band splitting arise from the asymmetric response of the C(3v) bond geometry to the C(2v) 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 as well as the length, energy, force constant, Debye temperature, compressibility and elastic modulus of the C-C bond in graphene, which is of instrumental importance in the understanding of the unusual behavior of graphene.

End and Edge States: Entrapment and Polarization

“…Intensive XPS and Raman analyses and numerical calculations confirmed the BOLS prediction on the C-C bond attributes in different situations, see Table 13.1 [47][48][49][50].…”

Anomalous behavior of B1g mode in highly transparent anatase nano-crystalline Nb-doped Titanium Dioxide (NTO) thin films

“…13,[24][25][26] Moreover, the lattice defects and lattice strain also play an important role for softening, stiffening and broadening of Raman phonon modes. [27][28][29] Firstly, to understand our observations the phonon confinement model (PCM) is applied to study the stiffening and broadening of the most intense E g(1) mode. In the bulk, the phonon contribution comes from the center of the Brillouin zone (BZ) corresponding to wave vector, q = 0.…”

Lattice Dynamics: Phonon Relaxation

“…The size-softened phonons arise from the involvement of the interaction between the specific atom and it surrounding neighbors [32,33]. [40] and CdSe [29,41], c CeO 2 [20,42,43] and InP-1 [44], d ZnO [45,46] nanoparticles (Reprinted with permission from [31])…”

“…For instance, for the D and the 2D modes of graphene, z is the number of neighboring atoms, and for the G mode of graphene, and the 141 cm -1 mode of TiO 2 , z = 1 [32,33].…”