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20 Wonders of Multifield Lattice Oscillation
20.1 Scope
This part starts with an overview in this chapter on the significance of bond relaxation, lattice oscillation, available experimental database, and theoretical approaches
to naming challenges and potential opportunities. Focus is given on generalizing the
trends of phonon frequency shift due to multifield activation in terms of atomic
undercoordination, mechanical activation, thermal excitation and available theoretical descriptions. Thus, one can discriminate the intrinsic effects from those extrinsic artifacts and specify rooms for theoretical unification to gain consistent insight
and information on bond relaxation by perturbations. It is exciting to find out that
crystal size reduction creates three types of phonon frequency shifts unseen in the
bulk—size-reduction induced E 2g blueshift, A 1g redshift, and the emerging of the
low-frequency Raman (LFR) mode in the THz frequencies that undergo blueshift
with the inverse of size. The Raman shift, bandgap, and elastic modulus follows a
Debye thermal decay—drops nonlinearly and then linearly as temperature rises in a
way of 1 − U(T)/E con with U(T) and E con being the integral of the Debye specific
heat and the atomic cohesive energy, respectively. Compression stiffens the phonon
frequency nonlinearly and the mechanical compression enhances the effect of atomic
undercoordination on the phonon relaxation. However, it is inspiring to note the large
gap to be filled for the bond-phonon-property correlation. Overwhelming debating
approaches exist from various, intrinsic and extrinsic, perspectives for a specific phenomenon. The conventional spectral peak decomposition and evolution simulation
with freely-adjustable parameters with limited information hindered the progress in
understanding the nature behind observations. It is urgent to develop a theory to
reconcile the perturbation-bond-property correlation and to derive information on
bonding dynamics, which drove the presented dedication made in past decade.
Chapter 21 is dedicated to developing the average-bond oscillating dynamics to
incorporate the quantum approaches and Fourier transformation. Conventionally, the
phonon relaxation is described from the perspective of Gibbs free energy, Grüneisen
parameters, ∂ω/∂x i , or their similarities, with x i being the specific degree of freedom.
In contrast, one may consider the Hamiltonian, Schrödinger equation, Lagrangian
oscillation mechanics, Fourier transformation, and Taylor series of potentials with
focus on the bond relaxation by external perturbation. The function dependence of a
detectable quantity Q(x i ) on the bond length and energy is necessary. To seeks for the
relative change of a detectable quantity, Q(x i )/Q(x i0 ) = f(x i , d(x i ), E(x i )) with x i
being any stimulus taken as a hidden factor driving bond relaxation. The Q(x i ) can be
phonon frequency, bandgap, elastic modulus, etc. This way of approach reconciles
the perturbations of atomic and molecular undercoordination, temperature, strain,
pressure, electric polarization, etc., into one equation.
Chapter 22 examined the two-dimensional layered graphene, black phosphorus,
and (W, Mo)(S, Se) 2 structures by theoretically reproducing their Raman shifts due
the number-of-layers, orientational strain, compression, and thermal activation with
derivative of new kind of information. The information includes the bond length
and energy, band nature index, the dimer vibration frequency of reference, Debye
20 Wonders of Multifield Lattice Oscillation
20.1 Scope
This part starts with an overview in this chapter on the significance of bond relaxation, lattice oscillation, available experimental database, and theoretical approaches
to naming challenges and potential opportunities. Focus is given on generalizing the
trends of phonon frequency shift due to multifield activation in terms of atomic
undercoordination, mechanical activation, thermal excitation and available theoretical descriptions. Thus, one can discriminate the intrinsic effects from those extrinsic artifacts and specify rooms for theoretical unification to gain consistent insight
and information on bond relaxation by perturbations. It is exciting to find out that
crystal size reduction creates three types of phonon frequency shifts unseen in the
bulk—size-reduction induced E 2g blueshift, A 1g redshift, and the emerging of the
low-frequency Raman (LFR) mode in the THz frequencies that undergo blueshift
with the inverse of size. The Raman shift, bandgap, and elastic modulus follows a
Debye thermal decay—drops nonlinearly and then linearly as temperature rises in a
way of 1 − U(T)/E con with U(T) and E con being the integral of the Debye specific
heat and the atomic cohesive energy, respectively. Compression stiffens the phonon
frequency nonlinearly and the mechanical compression enhances the effect of atomic
undercoordination on the phonon relaxation. However, it is inspiring to note the large
gap to be filled for the bond-phonon-property correlation. Overwhelming debating
approaches exist from various, intrinsic and extrinsic, perspectives for a specific phenomenon. The conventional spectral peak decomposition and evolution simulation
with freely-adjustable parameters with limited information hindered the progress in
understanding the nature behind observations. It is urgent to develop a theory to
reconcile the perturbation-bond-property correlation and to derive information on
bonding dynamics, which drove the presented dedication made in past decade.
Chapter 21 is dedicated to developing the average-bond oscillating dynamics to
incorporate the quantum approaches and Fourier transformation. Conventionally, the
phonon relaxation is described from the perspective of Gibbs free energy, Grüneisen
parameters, ∂ω/∂x i , or their similarities, with x i being the specific degree of freedom.
In contrast, one may consider the Hamiltonian, Schrödinger equation, Lagrangian
oscillation mechanics, Fourier transformation, and Taylor series of potentials with
focus on the bond relaxation by external perturbation. The function dependence of a
detectable quantity Q(x i ) on the bond length and energy is necessary. To seeks for the
relative change of a detectable quantity, Q(x i )/Q(x i0 ) = f(x i , d(x i ), E(x i )) with x i
being any stimulus taken as a hidden factor driving bond relaxation. The Q(x i ) can be
phonon frequency, bandgap, elastic modulus, etc. This way of approach reconciles
the perturbations of atomic and molecular undercoordination, temperature, strain,
pressure, electric polarization, etc., into one equation.
Chapter 22 examined the two-dimensional layered graphene, black phosphorus,
and (W, Mo)(S, Se) 2 structures by theoretically reproducing their Raman shifts due
the number-of-layers, orientational strain, compression, and thermal activation with
derivative of new kind of information. The information includes the bond length
and energy, band nature index, the dimer vibration frequency of reference, Debye