22.3 Numerical Reproduction of Phonon Relaxation
437
entrapped core and bonding electrons may scatter the incident radiation substantially
and hence lowers the Raman D band reflectivity at the zigzag-edge compared with
that at the arm-chaired edge [56, 57].
22.4 Summary
The notion of multifield bond oscillation has reconciled the following thrusts:
(1) One can join the continuum approaches to the quantum theory by focusing on
the perturbed bond relaxation to the phonon frequency.
(2) Phonon frequency shift under various perturbations could be reproduced from
the perspective of bond relaxation.
(3) Results improve the understanding about the multifield driven bond-phononproperty correlation of a substance.
(4) Theoretical reproduction results in quantitative information on bonding dynamics derived from the combination of the multifield bond oscillation framework
and its driven phonon spectrometrics.
Being able to connect the continuum to quantum premises, the combination
of the BOLS-LBA notion for the multifield oscillation dynamics and the enabled
Raman phonon spectrometrics has enabled the quantitative information about
the perturbation-relaxation-property that is beyond the scope of other available
approaches. The practice of the average-bond bond oscillating dynamics has reconciled (z, ε, P, T) effects on the Raman shifts of BP, GNR, and MX 2 with not only
clarification of the intrinsic phonon relaxation origin but also information on the
bonding dynamics and their properties to the 2-D structures. Consistency between
theory expectations and Raman measurements clarified and quantified the following:
(1) The undercoordination induced bond contraction and bond strength gain govern
the number-of-layer resolved phonon frequency shift. The collective vibration
of bonds between a certain atom and its z neighbors dictates phonon frequency
redshift while the dimer interaction dictates the phonons undergoing blueshift
occurred when the number-of-layer decreases. Matching the number-of-layer
reduction induced phonon frequency shift offers the local bond length, bond
energy, band nature index, referential wavenumber ω(1) and its bulk shift, and
the effective coordination numbers for the layered 2-D structures.
(2) Bond stretching by the directional strain resolves the phonon red-shifting and
phonon band splitting. Reproduction of the strain effect on phonon relaxation
gives rise to the average-bond force constant and the relative direction between
a certain bond and the strain.
(3) Bond thermal expansion softens all phonons—Debye thermal decay. One
can derive the mode cohesive energy E coh and Debye temperature θ D from
reproducing the Debye thermal decay of phonon frequencies.
437
entrapped core and bonding electrons may scatter the incident radiation substantially
and hence lowers the Raman D band reflectivity at the zigzag-edge compared with
that at the arm-chaired edge [56, 57].
22.4 Summary
The notion of multifield bond oscillation has reconciled the following thrusts:
(1) One can join the continuum approaches to the quantum theory by focusing on
the perturbed bond relaxation to the phonon frequency.
(2) Phonon frequency shift under various perturbations could be reproduced from
the perspective of bond relaxation.
(3) Results improve the understanding about the multifield driven bond-phononproperty correlation of a substance.
(4) Theoretical reproduction results in quantitative information on bonding dynamics derived from the combination of the multifield bond oscillation framework
and its driven phonon spectrometrics.
Being able to connect the continuum to quantum premises, the combination
of the BOLS-LBA notion for the multifield oscillation dynamics and the enabled
Raman phonon spectrometrics has enabled the quantitative information about
the perturbation-relaxation-property that is beyond the scope of other available
approaches. The practice of the average-bond bond oscillating dynamics has reconciled (z, ε, P, T) effects on the Raman shifts of BP, GNR, and MX 2 with not only
clarification of the intrinsic phonon relaxation origin but also information on the
bonding dynamics and their properties to the 2-D structures. Consistency between
theory expectations and Raman measurements clarified and quantified the following:
(1) The undercoordination induced bond contraction and bond strength gain govern
the number-of-layer resolved phonon frequency shift. The collective vibration
of bonds between a certain atom and its z neighbors dictates phonon frequency
redshift while the dimer interaction dictates the phonons undergoing blueshift
occurred when the number-of-layer decreases. Matching the number-of-layer
reduction induced phonon frequency shift offers the local bond length, bond
energy, band nature index, referential wavenumber ω(1) and its bulk shift, and
the effective coordination numbers for the layered 2-D structures.
(2) Bond stretching by the directional strain resolves the phonon red-shifting and
phonon band splitting. Reproduction of the strain effect on phonon relaxation
gives rise to the average-bond force constant and the relative direction between
a certain bond and the strain.
(3) Bond thermal expansion softens all phonons—Debye thermal decay. One
can derive the mode cohesive energy E coh and Debye temperature θ D from
reproducing the Debye thermal decay of phonon frequencies.