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.

An analytical form connecting the energy shift of Raman modes directly to the bonding identities (order, nature, length, energy) of a specimen and the response of the bonding identities to the applied stimuli of temperature and pressure was presented for a deeper understanding of the atomistic origin of the ZnO Raman shift. Theoretical reproduction based on the BOLS correlation theory [Sun, C. Q. Prog. Solid State Chem. 2007, 35, 1] and the local bond average (LBA) approach [Sun, C. Q. Prog. Mater. Sci. 2009, 54, 179] of the measurements revealed that the thermally softened ZnO Raman modes arise from bond expansion and bond weakening due to vibration and that the pressure-stiffened Raman modes result from bond compression and bond strengthening due to mechanical work hardening. The developed approach could be useful in generalizing the lattice dynamics directly to the process of vibration and relaxation of a representative bond of the specimen under external stimuli.

The thermally softened and the mechanically stiffened graphene phonons have been formulated from the perspective of bond order-length-strength correlation with confirmation of the C-C bond length in the single-layer graphene contracting from 0.154 to 0.125 nm and the binding energy increasing from 0.65 to 1.04 eV. Matching theory to the measured temperature-and pressure-dependent Raman shift has derived that the Debye temperature drops from 2230 to 540 K, the atomic cohesive energy drops from 7.37 to 3.11 eV/atom, and the binding energy density increases from 250 to 320 eV/nm 3 compared with the respective quantities of bulk diamond.