Brillouin spectroscopy
The technique uses inelastic scattering of light when it encounters acoustic phonons in a crystal, a process known as Brillouin scattering, to determine phonon energies and therefore interatomic potentials of a material.
Information relating to modes of vibration, such as the six normal modes of vibration of the carbonate ion, (CO3)2−, can be obtained through a Raman spectroscopy study shedding light on structure and chemical composition,[2] whereas Brillouin scattering involves the scattering of photons by low frequency phonons providing information regarding elastic properties.
Applying conservation of energy also sheds light upon the frequency regime in which Brillouin scattering occurs.
[clarification needed][4] Given an approximate frequency of visible light, ~1014 Hz, it is easy to see that Brillouin scattering generally lies in the GHz regime.
[citation needed] The second equation describes the application of conservation of momentum to the system.
The equations describe both the constructive (Stokes) and destructive (anti-Stokes) interactions between a photon and phonon.
This peak is generally quite intense and is not of direct interest for Brillouin spectroscopy.
In order to adjust for this, most spectrum are plotted with the Rayleigh peak either filtered out or suppressed.
The second noteworthy aspect of the figure is the distinction between Brillouin and Raman peaks.
[1] As Brillouin and Raman spectroscopy probe two fundamentally different interaction regimes this is not too large of an inconvenience.
The fact that Brillouin interactions are such low frequency however creates technical challenges when performing experiments for which a Fabry-Perot interferometer are usually used in order to overcome.
A Raman spectroscopy system is generally less technically complicated and can be performed with a diffraction grating–based spectrometer.
[citation needed] In some cases a single grating–based spectrometer has been used to collect both Brillouin and Raman spectra from a sample.
The locations of peaks are symmetric about the Rayleigh line because they correspond to the same energy level transition but of a different sign.
Solids can be considered nearly incompressible, within an appropriate pressure regime, as a result, longitudinal waves, which are transmitted via compression parallel to the propagation direction, can transmit their energy through the material easily and thus travel quickly.
As a result, transverse wave signals are not found in Brillouin spectra of fluids.
The equation shows the relationship between acoustic wave velocity, V, angular frequency Ω, and phonon wavenumber, q.
In isotropic solids, the two transverse waves will be degenerate, as they will be traveling along elastically identical crystallographic planes.
Brillouin spectroscopy is a valuable tool for determining the complete elastic tensor,
The elastic tensor is an 81 component 3x3x3x3 matrix which, through Hooke's Law, relates stress and strain within a given material.
[citation needed] It is possible to determine elastic properties of materials such as the adiabatic bulk modulus,
, without first finding the complete elastic tensor through techniques such as the determination of an equation of state through a compression study.
In order to obtain the elastic tensor the Christoffel Equation needs to be applied:
The Christoffel Equation is essentially an eigenvalue problem which relates the elastic tensor,
, whose eigenvalues are equal to ρV2, where ρ is density and V is acoustic velocity.
Equation 5 shows the complete elastic tensor for a cubic material.
In order make the above calculations the phonon wavevector, q, must be pre-determined from the geometry of the experiment.
[citation needed] The frequency shift of the incident laser light due to Brillouin scattering is given by[8] where
