Elastic waves and the Landau-Rumer mechanism of relaxation of quasi-transverse phonons in GaAs crystals

The dependences of the relaxation rate and the absorption coefficient of ultrasound in GaAs crystals on the direction of the wave vector of quasi-transverse phonons for the Landau-Rumer mechanism are analyzed in the framework of the anisotropic-continuum model. The calculations are performed with two sets of second-order and third-order elastic moduli experimentally measured by different authors. It is demonstrated that the angular dependences of the relaxation rates of quasi-transverse phonons and the ultrasonic absorption coefficients calculated from these data differ qualitatively. The correctness of the determination of the third-order elastic moduli available in the literature can be checked by measuring the ultrasonic absorption coefficients for GaAs crystals.     

Anharmonic relaxation of phonons

Using the Ziman scheme of considering a drifting Planck’s distribution, as the eigenvector of the linearized phonon collision operator, the anharmonic relaxation of phonons is discussed. The earlier arbitrariness in the phonon-phonon coupling parameters is removed by formulating explicit expressions for different allowed processes in terms of measurable quantities. Low and high temperature approximations of relaxation rates are also discussed: the results differ from earlier calculations. At low temperatures superthermal or high frequency phonons, which have temperature-independent and equal N- and U-relaxation rates, play important roles in thermal conduction in pure insulators. Presently working as University of Wales Fellow in the Applied Physics Department, UWIST Cathays Park, Cardiff CF1 3NU, U.K.     

Relaxation of quasi-transverse phonons in the Herring mechanism and ultrasound absorption in cubic crystals with positive and negative anisotropies of the second-order elastic moduli

The phonon relaxation and quasi-transverse ultrasound absorption in the course of Herring and Landau-Rumer anharmonic scattering processes in cubic crystals with positive (Ge, Si, diamond, InSb, LiF, MgO) and negative (KCl, NaCl, CaF₂) anisotropies of the second-order elastic moduli have been investigated. A new mechanism of transverse phonon relaxation, according to which the fusion of a transverse (slow or fast) phonon with a slow phonon generates a fast transverse phonon, has been considered in the long-wave-length approximation. This mechanism is similar to the Herring relaxation mechanism for longitudinal phonons. It has been demonstrated that, for crystals of the first group with a considerable anisotropy of the elastic energy (Ge, Si, InSb, LiF, MgO), “anomalous” relaxation processes in which the fusion of a slow transverse phonon with a fast phonon generates a slow transverse phonon are possible in contrast to the Herring relaxation mechanism for longitudinal phonons. These relaxation processes appear to be impossible for all crystals of the second group (KCl, NaCl, CaF₂), as well as for crystals of the first group with a small anisotropy of the elastic energy, such as diamond. The angular dependences of the ultrasound absorption coefficient for the Herring and Landau-Rumer mechanisms have been analyzed using the anisotropic-continuum model. It has been shown that, for the crystals of the first group under consideration, the contribution of the Herring mechanism to the long-wavelength ultrasound absorption is small compared to the contribution of the Landau-Rumer mechanism. However, for the KCl and NaCl crystals of the second group in directions of the [001] type, the contribution of the Herring mechanism can significantly exceed the contribution of the Landau-Rumer mechanism.     

General behavior of longitudinal optical phonons in cubic diatomic crystals

A general relationship for longitudinal optical (LO) phonons in diatomic cubic crystals is introduced. The analysis of spectroscopic data of diatomic cubic crystals reveals that LO frequencies correlate directly with bulk moduli in a nearest-neighbor fashion. The proportionality constant is found to be dependent only on lattice geometries. Transverse effective charges can be obtained when the Lyddane-Sachs-Teller is incorporated into the model. Our calculations are in excellent agreement with experimental values and theoretical calculations. Some interesting implications of the model are discussed.     

The mechanism of Landau-Rumer relaxation of thermal and high-frequency phonons in cubic crystals of germanium,silicon, and diamond

Transverse phonon relaxation according to the Landau-Rumer mechanism is considered for an isotropic medium and crystals of germanium, silicon, and diamond possessing a cubic symmetry. The energy of elastic deformation caused by the anharmonicity of vibrations of the cubic crystal lattice is expressed via the second-and third-order moduli of elasticity. Using the known values of these elastic moduli, parameters determining the frequencies of the transverse phonon relaxation in the Landau-Rumer mechanism are evaluated for the germanium, silicon, and diamond crystals. It is shown that the dependence of the relaxation frequency on the wavevector of thermal and high-frequency phonons sharply differs from the classical Landau-Rumer relationship both in the isotropic medium and in the cubic crystals. It is established that the observed peculiarities in the relaxation frequency are related to the angular dependence of the probability of anharmonic scattering and the anisotropy of elastic properties of the germanium, silicon, and diamond crystals. A new method is proposed for the experimental determination of the relaxation frequency of high-frequency phonons as a function of the wavevector using the temperature dependence of the coefficient of absorption of high-frequency ultrasound.     

Anharmonic phonons and structural phase transitions

Exact results for the order parameter and the meansquare displacement as functions of temperature are given for a quantum interacting phonon Hamiltonian with quartic anharmonicities. Upper bounds for the transition temperature are also derived. Approximate theories including the mean field approximation, the random phase approximation (or quasiharmonic approximation) and the self consistent approach (using Blume-Hubbard scheme) are compared with our exact results. The mean field approximation for the meansquare displacement is found to violate our bounds.The classical value is shown to form a lower bound for the kinetic energy. Upper bounds for the kinetic energy are obtained showing the region of temperature in which the use of the high temperature expansion of the fluctuation-dissipation theorem is justified. Comparison of the Hamiltonian and our results with electron-paramagnetic-resonance measurements are discussed.     

Nonradiative relaxation processes in molecular crystals

Internal conversion is the dominant relaxation channel from higher lying excited states in molecular crystals and involves the transfer of energy from the electronic system to the lattice. In this work, we present results from simulations of the nonradiative relaxation process with an emphasis on both intra- and interband transitions. We find the internal conversion process to be strongly nonadiabatic and the associated relaxation time in the case of large energy excitations to be limited by the transitions made between states of different bands.     

On the role of umklapp processes in the scattering of delocalized positronium by acoustic phonons in ionic crystals

The effect of umklapp processes in the scattering of delocalized positronium atoms by acoustic phonons in ionic crystals is analyzed. It is shown that at temperatures above which this effect becomes large, umklapp scattering renormalizes the constant of the deformation potential of positronium. This renormalization has recently been observed in experiments measuring the momentum distribution of delocalized positronium in a MgF₂ crystal. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 215–219 (10 February 1999)     

Clebsch-Gordan coefficients and two-phonon resonance Raman scattering in cubic crystals

The intensity of two-phonon resonance Raman scattering in cubic crystals is expressed in terms of Clebsch-Gordan coefficients. A plot of the scattering intensity against the direction angles of the polarization vectors of the incident and scattered radiation is obtained. Several useful polarization relations are obtained for the scattering intensities in experiments with different geometries.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 75–80, August, 1978.     

Energy estimates of twinning processes in cubic single crystals

The role of twinning processes giving rise to the fragmentation and rotation of a structure caused by single-crystal deformation, as well as the joining of grains during the manufacturing of optical ceramics, is investigated. Models describing the twins in the single crystals under study, which are formed by rotating a cubic lattice about the threefold symmetry axis through an angle of 60°, are constructed. The twin formation energies are estimated.     

Anharmonic effects of phonons with Kohn anomalies

In a quasi-one-dimensional conductor, the phonons with anomaly at the Fermi diameter, 2k_F, cause the phonons at 4k_F to soften via the three-phonon coupling, mainly due to the phonon modulation of the Coulomb interaction between tight-binding electrons on different sites. The 2k_F phonons also cause strong second-order scatterings of X-rays or neutrons. These results may explain the recent observations of phonon anomalies at 4k_F in TTF-TCNQ.     

Anharmonic phonons and central peaks at structural phase transitions

Recent light scattering studies of solids undergoing structural phase transitions clearly demonstrate that the “central peak” phenomenon is not one, but several processes (both static and dynamic) contributing in different degrees to the spectra observed for different types of transition. Our own work on Pb₅Ge₃O₁₁, SrTiO₃, K₂SeO₄ and BaMnF₄ is reviewed and the studies by other on KDP, KH₃(SeO₃)₂, KD₃(SeO₃)₂ are discussed briefly.     

Longitudinal-phonon relaxation mechanisms in cubic crystals of germanium,silicon, and diamond

The relaxation rates of thermal and high-frequency longitudinal phonons are calculated using an anisotropic-continuum model. Three-phonon scattering mechanisms (L ? L + L, L ? T + L) for the phonon relaxation are considered. Anisotropic anharmonic phonon scattering in cubic crystals is described in terms of the second-and third-order elastic moduli. The parameters determining the longitudinal-phonon relaxation rates are found for germanium, silicon, and diamond crystals. The long-wavelength limit and the transition to the isotropic-medium model are considered, and the dependences of the relaxation rates of thermal and high-frequency phonons on temperature and phonon wave vector are analyzed for these crystals.     

Anharmonic effects in crystals with vacancies

On the basis of the dynamic model proposed in [1] for a crystal with vacancies, the following are calculated: the contribution of anharmonic lattice oscillations at high temperatures, the elastic modulus and the thermal expansion coefficient as functions of the temperature and the vacancy concentration.     

A Raman scattering study of long-wavelength optical phonons in hexagonal ammonium fluoride single crystals

All the predicted Raman active translatory vibrations of wurtzite ammonium fluoride (space group C⁴_6v are observed and assigned on the basis of their polarization selections obtained with single crystals. The fundamental ammonium ion librations could not be detected, but a frequency of about 545 cm^?1 is deduced from the analysis of the observed second order Raman spectrum.The TO-LO splitting for the A₁ and E₁ polar phonons is a lot more important than the A₁ — E₁ splitting (125 cm^?1 compared to 1–3 cm^?1); thus, the effect of long-range electric forces strongly dominates over that of the anisotropy of the shortrange interatomic forces. Only very weak directional dispersion could be detected on the quasi-mode spectra. From the observed TO and LO frequencies, one evaluates ?₀ ? 3.95 in good agreement with dielectric experimental data.     

Anharmonic renormalization and non-Markovian decay of coherent optical phonons in polar semiconductors

The influence of anharmonic renormalization effects on the decay dynamics of coherent longitudinal optical phonons is investigated from a microscopic point of view. Time-resolved coherent anti-Stokes Raman signals are calculated for GaP on the basis of a full phonon dispersion calculation, and the relevant decay channels are identified and compared. Anharmonic renormalization effects are found to induce non-Markovian behaviour of the decay dynamics and lead to a decrease of the decay time. The renormalization effects only depend on the special properties of the phonon dispersion of the given material. This underlines the intrinsic nature of the non-Markovian decay dynamics of phonons for any material. Non-Markovian dynamics of the decay of coherent LO-phonons is calculated for GaP and result in a 30% faster decay signal than the corresponding Markovian dynamics.