20.2 Significance of Multifield Lattice Oscillation
373
size is reduced to 3.8 nm, the peak frequency shifts to a lower frequency by about
3 cm
−1 [23].
Considerable effort has also been paid to the study of bulk compounds due to their
intriguing thermal and mechanical properties and to the promise that they offer potential applications in optoelectronics, waveguides, laser frequency doubling devices,
high capacity computer memory cells, sensors, actuators, etc. [24, 25]. Materials
under mechanical and thermal perturbation vary their structures and properties such
as phase transition or mechanical hardness [26]. Compression hardens globally a substance and raises the vibration frequency and the critical pressure for phase transition
of regular substance. Heating and stretching have a contrasting effect of compression
to narrow the band gap and lower the work function. The volume concentration of
nanopores below a certain value can harden the substance but above the critical value
causes detrimental to the yield strength of the porous materials [7].
In conjunction to the Raman shift, the bulk modulus B or the inverse expansibility
is related to the performance of a material such as acoustic transmission, Debye
temperature, specific heat capacity, and thermal conductivity of the specimen, which
keep constant at the ambient atmospheres. However, the B becomes tunable with
the applied T and P stimuli [27–30]. Atomistic simulations have revealed that the B
of a substance is softened under elevated temperature and stiffened under increased
pressure [28].
The macroscopic properties of a substance depend functionally on the bond length,
bond energy, and valence electron configuration. For instance, the band gap and
dielectrics varies with the interatomic bond energy and the electronic occupancy in
the conduction and in the valence bands [31]. Likewise, the local binding energy
density determines material’s elastic modulus and yield strength [32] and the atomic
cohesive energy [26] determines the critical temperatures of phase transitions, catalytic activation, interatomic diffusion, etc. The competition of binding energy density and atomic cohesive energy determines the inverse Hall-Petch relationship and
the maximal hardness of a crystal at the nanometer scale [33].
The curvature of the bond potentials at equilibrium r = d determines the frequency
of vibration ω in the form of μω
2 x
2
= [U
(d) + U
(d)x/3]x
2 where the nonlinear
term can be omitted in the harmonic approximation that is proper at the equilibrium.
According to the dimensional analysis, the ω is proportional to the bond length d
and energy E in the form of (ω)
2
∝ E/(μd
2 ) [34] with μ being the reduced mass
of the vibrating dimer. Any perturbation will relax the bond and shift the phonon
frequency. Therefore, external stimulus mediates the properties of a substance by
relaxing the bond length and energy and the crystal potentials which provides one
with opportunities to calibrate and control the property change of a substance.
373
size is reduced to 3.8 nm, the peak frequency shifts to a lower frequency by about
3 cm
−1 [23].
Considerable effort has also been paid to the study of bulk compounds due to their
intriguing thermal and mechanical properties and to the promise that they offer potential applications in optoelectronics, waveguides, laser frequency doubling devices,
high capacity computer memory cells, sensors, actuators, etc. [24, 25]. Materials
under mechanical and thermal perturbation vary their structures and properties such
as phase transition or mechanical hardness [26]. Compression hardens globally a substance and raises the vibration frequency and the critical pressure for phase transition
of regular substance. Heating and stretching have a contrasting effect of compression
to narrow the band gap and lower the work function. The volume concentration of
nanopores below a certain value can harden the substance but above the critical value
causes detrimental to the yield strength of the porous materials [7].
In conjunction to the Raman shift, the bulk modulus B or the inverse expansibility
is related to the performance of a material such as acoustic transmission, Debye
temperature, specific heat capacity, and thermal conductivity of the specimen, which
keep constant at the ambient atmospheres. However, the B becomes tunable with
the applied T and P stimuli [27–30]. Atomistic simulations have revealed that the B
of a substance is softened under elevated temperature and stiffened under increased
pressure [28].
The macroscopic properties of a substance depend functionally on the bond length,
bond energy, and valence electron configuration. For instance, the band gap and
dielectrics varies with the interatomic bond energy and the electronic occupancy in
the conduction and in the valence bands [31]. Likewise, the local binding energy
density determines material’s elastic modulus and yield strength [32] and the atomic
cohesive energy [26] determines the critical temperatures of phase transitions, catalytic activation, interatomic diffusion, etc. The competition of binding energy density and atomic cohesive energy determines the inverse Hall-Petch relationship and
the maximal hardness of a crystal at the nanometer scale [33].
The curvature of the bond potentials at equilibrium r = d determines the frequency
of vibration ω in the form of μω
2 x
2
= [U
(d) + U
(d)x/3]x
2 where the nonlinear
term can be omitted in the harmonic approximation that is proper at the equilibrium.
According to the dimensional analysis, the ω is proportional to the bond length d
and energy E in the form of (ω)
2
∝ E/(μd
2 ) [34] with μ being the reduced mass
of the vibrating dimer. Any perturbation will relax the bond and shift the phonon
frequency. Therefore, external stimulus mediates the properties of a substance by
relaxing the bond length and energy and the crystal potentials which provides one
with opportunities to calibrate and control the property change of a substance.