We derive third-order anharmonic coupling constants between various phonon modes in a zinc-blende crystal of a binary compound using a valence force field model extended by adding Coulomb interactions between polarizable ions. We find and compare the anharmonic coupling between the zone-center LO phonon and other phonon modes along principal directions of a GaAs crystal.
Zinc oxide (ZnO) is a very promising material for optoelectrical devices operating at the short-wavelength end of the visible spectral range and at the near UV. The Raman scattering studies of ZnO heterolayers formed by isothermal annealing show sharp phonon lines. In addition to the A_1(TO), E_1(TO), E_2^{H}, and E_1(LO) one-phonon lines, we observed two-phonon lines identified as: E_2^{H} - E_2^{L}, E_2^{H} + E_2^{L}, and 2LO at 332, 541, and 1160 cm^{-1}, respectively (at room temperature). The identification of the E_2^{H} - E_2^{L} peak was confirmed by its thermal dependence. Temperature dependent measurements in the range 6-300 K show that the phonon frequencies decrease with temperature. The E_2^{H} peak is at energy 54.44 meV (439.1 cm^{-1}), at 4 K and due to phonon-phonon anharmonic interaction, its energy decreases to 54.33 meV (438.2 cm^{-1}) at room temperature. The Grüneisen parameter found for this oscillation mode was γ_{E} 2H = 1.1 at about 300 K. The intensity of the E_2^{H} - E_2^{L} peak increases strongly with temperature and this dependence can be described by the Bose-Einstein statistics with activation energy of 13.8 meV (nearly equal to the energy of the E_2^{L} phonon).
In this paper 1D crystal lattice is analyzed within harmonic approximation, with one atom per elementary cell and nearest neighbor interaction included. For this type of crystal lattice dispersion relations are well known. Thermodynamic functions (specific heat and phonon thermal conductivity) are calculated via phonon density of states given in exact form. Thermodynamic variables are calculated for a whole temperature range. In limiting cases of low and high temperatures these thermodynamic variables can be found in analytic forms. For thermal conductivity the results of Callaway model for exact phonon density of states are compared with the results of Callaway model for Debye approximation of phonon density of states.
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