Frequency response of graphene phonons to heating and compression

Abstract

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.

Hydrogen-bond relaxation dynamics: Resolving mysteries of water ice

“…Therefore, the competition between the O:H-O bond angle and its length relaxation determines the density anomalies of water ice. [192,193,241,[291][292][293][294][295]. However, as shown in Figure 30, heating stiffens the stiffer  H phonons and softens the softer  L phonons of liquid water [25,113,[296][297][298][299][300] and ice at temperatures above 80 K [195,298,[301][302][303].…”

“…Phonons of 'normal' materials undergo heat softening because of the thermal lengthening and softening of all bonds involved [191,192,240,[290][291][292][293][294]. However, as shown in Figure 30, heating stiffens the stiffer H phonons and softens the softer L phonons of liquid water [25,113,[295][296][297][298][299] and ice at temperatures above 80 K [194,297,[300][301][302].…”

Number‐of‐layer, pressure, and temperature resolved bond–phonon–photon cooperative relaxation of layered black phosphorus

“…The number‐of‐layer dependence of the Raman shift and electronic bandgap are two of the most powerful tools for probing bond relaxation dynamics of two‐dimensional layered materials . The relationship between bond relaxation and average atomic coordination is as follows: where Δ ω (z) and Δ ω (z B ) denote the phonon frequency difference between the reference wavenumber ω (1) and the measured ω ( z ) or the bulk ω ( z B ).…”

Number-of-layer discriminated graphene phonon softening and stiffening

“…Based on the BOLS theory and the LBA approach, we have recently 18 formulated the thermally softened and the mechanically stiffened graphene phonons 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.…”