Chapter 21
Theory: Multifield Oscillation Dynamics
Abstract A physical perturbation mediates intrinsically the performance of a substance through relaxing the length and energy of the chemical bonds and associated
electrons in various energy bands. From the perspective of Fourier transformation,
one can formulate the bond oscillation frequency ω (z, d, E, μ) for a variety of materials by perturbing the Hamiltonian. Reproduction of the excited ω by a perturbation
x i such as bond-order-imperfection, electric polarization, compression, tension, and
thermal activation turns out information on the bond length d(x i ), bond energy E(x i ),
single-bond force-constant, binding energy density, mode cohesive energy, Debye
temperature, elastic modulus, etc., complementing the electron spectrometrics. Exercises proved the immense power of the phonon spectrometrics in revealing the nature
behind the lattice vibration in terms of multifield single-bond oscillation dynamics in
liquid and solid phases.
Highlights
• Bond order, length, and strength stem the phonon frequency, bandgap, and
elasticity.
• Perturbation relaxes the bond and evolves the phonon frequency and related
properties.
• Phonon relaxation fingerprints the intrinsic manner of bond response to stimulus.
• Spectrometrics enables the unprecedented information on bond-phonon-property
cooperativity.
21.1 Lattice Oscillation Dynamics
21.1.1 Single-Body Hamiltonian
There are three major approaches to the oscillation dynamics of a bond that relaxes
in length and energy by perturbing its crystal potential through applying an external
force: resolution to the Schrödinger equation [1], monatomic and diatomic chain
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2020
C. Q. Sun, Electron and Phonon Spectrometrics,
https://doi.org/10.1007/978-981-15-3176-7_21
393
Theory: Multifield Oscillation Dynamics
Abstract A physical perturbation mediates intrinsically the performance of a substance through relaxing the length and energy of the chemical bonds and associated
electrons in various energy bands. From the perspective of Fourier transformation,
one can formulate the bond oscillation frequency ω (z, d, E, μ) for a variety of materials by perturbing the Hamiltonian. Reproduction of the excited ω by a perturbation
x i such as bond-order-imperfection, electric polarization, compression, tension, and
thermal activation turns out information on the bond length d(x i ), bond energy E(x i ),
single-bond force-constant, binding energy density, mode cohesive energy, Debye
temperature, elastic modulus, etc., complementing the electron spectrometrics. Exercises proved the immense power of the phonon spectrometrics in revealing the nature
behind the lattice vibration in terms of multifield single-bond oscillation dynamics in
liquid and solid phases.
Highlights
• Bond order, length, and strength stem the phonon frequency, bandgap, and
elasticity.
• Perturbation relaxes the bond and evolves the phonon frequency and related
properties.
• Phonon relaxation fingerprints the intrinsic manner of bond response to stimulus.
• Spectrometrics enables the unprecedented information on bond-phonon-property
cooperativity.
21.1 Lattice Oscillation Dynamics
21.1.1 Single-Body Hamiltonian
There are three major approaches to the oscillation dynamics of a bond that relaxes
in length and energy by perturbing its crystal potential through applying an external
force: resolution to the Schrödinger equation [1], monatomic and diatomic chain
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2020
C. Q. Sun, Electron and Phonon Spectrometrics,
https://doi.org/10.1007/978-981-15-3176-7_21
393