The Young's modulus E' can be expressed as a function of the longitudinal acoustic phonon frequency f obtained by Brillouin spectroscopy:
Inelastic light scattering from a crystal can be as an inelastic scattering of a photon from acoustic phonons. In terms of particle description, it is seen as a photon--phonon interaction, where energy and momentum are conserved.
The exact expression for <[v.sup.3]> is found in , while, in long wave approximation, <[v.sup.3]> approximates the cube of acoustic phonon speed of the material.
This indicates that the gap between optical and acoustic modes becomes so larger that the acoustic phonon can hardly be scattered by optical phonons.
Here n is refractive index, [v.sub.ac] is the velocity of acoustic phonons
, [rho] is the average medium density, and [[GAMMA].sub.B] is the Brillouin linewidth angular frequency.
Mukohyama, "Hot Electron Cooling by Acoustic Phonons
in Graphene," Physical Review Letters, vol.
The acoustic phonons
were produced due to disorder (entropy) in the crystalline phase.
The study is the first ever to prove that acoustic phonons
-- the elemental particles that transmit both heat and sound -- have magnetic properties.
The elastic continuum model provides an adequate description of acoustic phonons in nanostructures [2, 9].
In the longwave limit, the dispersion law of acoustic phonons is well approximated by a linear dependence , so the expansion will retain only the first two terms:
Figure 6 shows that the relaxation rate for T + T [left right arrow] L is much larger than those for T + L [left right arrow] L and L + T [left right arrow] L, since the number of transverse acoustic phonons
participating in U scattering is much larger than that of longitudinal acoustic phonons
, according to the Bose-Einstein distribution.
This periodic oscillation in reflectivity (or transmissivity), so-called coherent acoustic phonons
, is caused by interference between the reflected probe beams from sample surface and the wave front of the propagating strain pulse generated upon the pump pulse [75, 76].