Elastic wave modes in crystals

In summary, in solid state theory, there are three modes for each elastic wave in crystals, one of longitudinal polarization and two of transverse polarization. The Brillouin and Raman scatterings in solids are induced by acoustic and optical phonons, which do not produce regular diffraction gratings due to the random distribution of phases. The transverse wave of the incident light can couple with the transverse optic modes near resonance frequencies, producing a polariton in crystals. This interaction is enhanced at the frequencies of overtones and combination bands of the fundamental lattice vibrations. Plasmons and polaritons are examples of quasi particles, which are particles that are adapted to mimic the interactions of a system of particles.
  • #1
Astronuc
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In solid state theory, there are three modes for each elastic wave in crystals, one of longitudinal polarization and two of transverse polarization [1,2]. In the transverse optic (TO) mode the induced polarization is perpendicular to the wavevector, whereas in the longitudinal optic (LO) mode the electric polarization is parallel to the wavevector [2]. The Brillouin and the Raman scatterings are induced by acoustic and optical phonons in solids. Because of the random distribution of phases, the acoustic and optical phonons do not produce the regular diffraction gratings for the incident light whose frequency is quite different from that of the optic modes in the infrared region [3]. The transverse wave of the incident light couples with the TO modes near resonance frequencies, producing a polariton in crystals [2]. Interaction or coupling of the incident light with the TO modes is enhanced at the frequencies of overtones and combination bands of the fundamental lattice vibrations [2,4]
from C.Z. Tan, Optical interference in overtones and combination bands in [itex]\alpha[/itex]-quartz, Journal of Physics and Chemistry of Solids 64 (2003) 121–125.

[1] M. Born, K. Huang, Dynamical Theory of Crystal Lattices, Clarendon Press, Oxford, 1988.
[2] C. Kittel, Introduction to Solid State Physics, Wiley, New York, 1996.
[3] H. Tanaka, T. Sonehara, S. Takagi, Phys. Rev. Lett. 5 (1997) 881.
[4] C.Z. Tan, J. Arndt, J. Chem. Phys. 112 (2000) 5970.

Relevant to some work I am doing on thermal conductivity.
 
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  • #2
Yes and plasmons are the particles (well quasi particles actually) that are associated with the longitudinal waves of the conduction electrons in a metal that has been submitted to incident EM-radiation. The electrons will start to vibrate longitudinally as a response to the incident EM-radiation (ie as a reaction to the incident oscillating electrical field actually). It is this oscillation of conduction electrons that gives rise to the phase shifted reflected light of a conductor. The plasma frequence is that frequence above which the electrons can no longer 'follow' the oscillating incident E-field. Thus the E-field is no longer reflected but passes through the medium, right ?


Polaritons are particles associated with the interaction between phonons and incident photons. Like astronuc explained, this interaction is expressed by the coupling between transverse optical phonons and the incident photons.

Plasmons and polaritons are good examples of the socalled quasi particles which are particles associated with some interaction. Do not confuse then with gauge bosons though. A quasi particle can be seen as a matter particle plus it's interactions. For example suppose you have many mutually interacting protons. In order to describe the dynamics you will need to solve one set of coupled diff equations.

This is impossible so a way out is to say well put the energies associated with the mutual interactions into the particle (for example in it's mass) and continue the calculations with this adapted particle that now can be treated as being independent of the other particles. This adapted particle is the quasi particle. So instead of looking at 100 interacting protons, you look at 100 adapted protons that do not interact with each other. Now, you just need to solve 100 one-body equations...which is very possible.

This way of working is analogous (conceptually) to the effective mass in solid state physics. This is the adapted mass that mimicks an interacting particle as if it were moving inside a vacuum with no interactions what so ever, so as a free particle. So basically you can apply the easy equations to describe this free particle but you will need to use the adapted mass, ie the effective mass.

The big difference is that in order to define a quasi particle, you will need to lumb in QM energy contributions like the self energy...but let us not get into that.

marlon
 
  • #3


Thank you for sharing this information on elastic wave modes in crystals. As a scientist working on thermal conductivity, this is particularly relevant to my work. The three modes for each elastic wave in crystals, as well as the differences between longitudinal and transverse polarization, are important factors to consider when studying the thermal properties of crystals. The interaction and coupling of these modes with incident light at specific frequencies, as well as the effects of overtones and combination bands, can greatly affect the thermal conductivity of crystals. I will be sure to further explore the literature you have referenced in my research. Thank you again for your contribution to the scientific community.
 

Related to Elastic wave modes in crystals

What are elastic waves and how are they classified?

Elastic waves are a type of mechanical wave that propagate through a medium by causing particles in the medium to vibrate. There are two main types of elastic waves: longitudinal waves, which vibrate in the same direction as the wave propagation, and transverse waves, which vibrate perpendicular to the wave propagation.

What are crystal lattice structures and how do they affect elastic wave modes?

Crystal lattice structures are the regular, repeating arrangement of atoms or molecules in a crystal. These structures can affect the propagation of elastic waves in crystals by influencing the speed and direction of the waves. The anisotropy of the crystal lattice also plays a role in determining the different types of elastic wave modes that can exist in a crystal.

What are the different types of elastic wave modes in crystals?

The different types of elastic wave modes in crystals include longitudinal waves, transverse waves, and surface waves. Longitudinal waves travel through the crystal lattice in the same direction as the wave propagation, while transverse waves travel perpendicular to the wave propagation. Surface waves are a combination of both longitudinal and transverse waves and travel along the surface of the crystal.

How are elastic wave modes in crystals studied and measured?

Elastic wave modes in crystals can be studied and measured using various experimental techniques such as ultrasonic measurements, Brillouin scattering, and X-ray diffraction. These techniques allow for the measurement of the speed, direction, and polarization of elastic waves in crystals, providing valuable information about the crystal's properties.

What applications do elastic wave modes in crystals have?

Elastic wave modes in crystals have a wide range of applications in fields such as materials science, geology, and engineering. They are used to study the structure and properties of crystals, to detect defects and changes in a crystal's structure, and to determine material parameters such as elasticity and anisotropy. They also have practical applications in devices such as ultrasonic sensors, piezoelectric transducers, and acoustic filters.

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