Quasi-transverse Phonons Research Articles

The effect of phonon focusing on the electron-phonon relaxation and electron transport in potassium crystals

The influence of anisotropy of elastic energy on electron-phonon relaxation and the role of shear waves in the electrical resistance of potassium crystals are investigated. It is shown that, at temperatures much lower than the Debye temperature (T<< θD), the contribution of slow quasi-transverse phonons to the electrical resistance of potassium crystals exceeds that of longitudinal phonons by an order of magnitude. Earlier, the Bloch-Grüneisen theory left aside this component under the above conditions. At the same time, at high temperatures(T>>θD), the contribution of longitudinal phonons to the electrical resistance turns out to be 4 times greater than the total contribution of electron relaxation by fast and slow transverse modes. The role of shear waves in the electrical resistance of potassium crystals is analyzed. It is shown that, at low temperatures, this mechanism provides 32% of the total electrical resistance. It is 4 times higher than the contribution of longitudinal phonons to the electrical resistance and should be taken into account when analyzing the electrical resistance of alkali metals. The distribution function of the most effective phonons for electrical resistance is defined, and the inelasticity of electron-phonon scattering is analyzed. It is shown that the calculated results of the electrical resistance of potassium in the temperature range from 40 to 400 K, taking into account the anisotropy of elastic energy, are in good agreement with the experimental data without the use of fitting parameters.

Effect of Anisotropy of Elastic Energy on the Electron–Phonon Drag and Temperature Dependences of Thermal EMF in Potassium Crystals at Low Temperatures

The effect of anisotropy of elastic energy on electron–phonon drag and thermoelectric phenomena in potassium crystals is studied. The temperature dependences of the thermal conductivity, thermal emf, and contributions to them from phonons of different polarizations are calculated. The calculation results are matched to the experimental data by varying the electron–phonon interaction constant for quasi-transverse phonons. It is established that the contribution of slow quasi-transverse phonons to the drag thermal emf of bulk potassium crystals is by an order of magnitude greater than the contribution of quasi-longitudinal phonons. The maximum values of the drag thermal emf in perfect potassium crystals are determined. It is shown that they do not depend on the electron–phonon interaction constants, but are determined by the second-order elastic moduli and the electron density.

Drag thermopower in nanowires and bulk potassium crystals under the conditions of competition between the boundary and bulk mechanisms of phonon relaxation

At low temperatures, the influence of anisotropy of elastic energy on the electron–phonon drag and thermopower in square cross-section single crystals of potassium has been studied. Change in the role of quasi-longitudinal and quasi-transverse phonons in the anisotropy of the drag thermopower under the conditions of transition from nanowires to bulk single crystals has been analyzed. In the regime of the Knudsen phonon gas flow, slow quasi-transverse phonons are shown to predominantly contribute to the drag thermopower in the nanowires but only in the directions close to the focusing of longitudinal phonons. Change in the drag thermopower anisotropy under the conditions of competition between the boundary and bulk phonon relaxation mechanisms has been investigated. As the sample’s cross-section increases, the drag thermopower anisotropy varies non-monotonically. This occurs due to stronger scattering of longitudinal phonons by electrons. When transitioning from the Knudsen phonon gas flow regime to the bulk relaxation mechanisms, the drag thermopower anisotropy first rises, then reaches a maximum and afterward disappears. The contribution of quasi-transverse phonons in bulk potassium crystals exceeds that of longitudinal phonons by an order of magnitude. This result evidences that the model of an isotropic medium cannot properly describe the electron–phonon drag in metals.

Role of Quasi-Longitudinal and Quasi-Transverse Phonons in the Drag Thermopower of Potassium Crystals at Low Temperatures

We have analyzed the effect of elastic energy anisotropy on the electron–phonon drag and thermoelectric phenomena in potassium crystals. It is shown that focusing leads to drag thermopower anisotropy at low temperatures; when diffuse phonon scattering at the boundaries is the predominant relaxation mechanism, focusing leads to drag thermopower anisotropy. With increasing sample cross section, the competition of the boundary and bulk phonon relaxation mechanisms leads to a nonmonotonic variation of drag thermopower anisotropy: upon a transition from the Knudsen regime of the phonon gas flow, it first increases from 16% to 30%, and then vanishes upon a transition to bulk samples. We have studied the role of quasi-longitudinal and quasi-transverse phonons in the drag thermopower of potassium crystals at low temperatures. It is shown that the contribution of slow quasi-transverse phonons to the drag thermopower of bulk potassium crystals is an order of magnitude larger than the contribution of quasi-longitudinal phonons. For this reason, the isotropic medium model cannot provide a correct description of the electron–phonon drag in metals. The effect of inelastic energy anisotropy on the spectrum and of the phonon polarization vector must be taken into account.

Phonon Focusing and Anisotropy of the Lattice Thermal Conductivity of Potassium Crystals at Low Temperatures

This work studies the influence of the anisotropy of elastic energy on the lattice thermal conductivity of potassium crystals. Our results have shown that, at sufficiently low temperatures, when diffuse scattering at the boundaries is the dominant mechanism of phonon relaxation, focusing leads to anisotropy of the phonon density of states (PDS) and lattice thermal conductivity. Crystallographic directions providing the maximum and minimum values of the lattice thermal conductivity have been determined. The phonon relaxation mechanisms are analyzed, and conditions under which Knudsen phonon gas flow can be realized in potassium crystals are determined. The role of the relaxation of quasi-longitudinal and quasi-transverse phonons on electrons in the thermal resistance of potassium crystals at low temperatures is studied.

Phonon focusing and electron–phonon drag in semiconductor crystals with degenerate charge-carrier statistics

We study the effect of anisotropy in elastic properties on the electron–phonon drag and thermoelectric phenomena in gapless semiconductors with degenerate charge-carrier statistics. It is shown that phonon focusing leads to a number of new effects in the drag thermopower at low temperatures, when diffusive phonon scattering from the boundaries is the predominant relaxation mechanism. We analyze the effect of phonon focusing on the dependences of the thermoelectromotive force (thermopower) in HgSe:Fe crystals on geometric parameters and the heat-flow directions relative to the crystal axes in the Knudsen regime of the phonon gas flow. The crystallographic directions that ensure the maximum and minimum values of the thermopower are determined and the role of quasi-longitudinal and quasi-transverse phonons in the drag thermopower in HgSe:Fe crystals at low temperatures is analyzed. It is shown that the main contribution to the drag thermopower comes from slow quasi-transverse phonons in the directions of focusing in long samples.

Elastic and elasto-optical properties of triglycine-zinc chloride crystal

The behaviours of bulk phonons propagating in triglycine-zinc chloride (Gly3-ZnCl2) single crystal for different polarizations of the incident and scattered beams were studied by Brillouin spectroscopy. All components of the elastic and elasto-optical tensors were determined at room temperature. Dependences of the velocities of quasi-longitudinal, transverse, and quasi-transverse phonons propagating in the planes (110), (101), and (011) on the direction of propagation are presented.

10.1007/s11451-008-3018-4

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.

Phase transition in tetragonal hen egg-white lysozyme crystals

Lattice dynamics of tetragonal hen egg-white lysozyme crystals was studied by Brillouin light scattering and differential ac-nanocalorimetry with controlled relative humidity from 298 to 330 K. Temperature dependences of fast quasitransverse phonon velocity and integral intensity were found to exhibit anomalies in the vicinity of 306 K. An anomaly in the temperature behavior of heat capacity was also observed near this temperature. It is concluded that the anomalies point to a structural phase transition. Possible mechanisms of phase transition in lysozyme crystals are discussed.

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.

Anharmonic processes of scattering and relaxation of slow quasi-transverse phonons in cubic crystals

Relaxation of slow quasi-transverse phonons in anharmonic processes of scattering in cubic crystals with positive (Ge, Si, diamond) and negative (KCl, NaCl) anisotropies of the second-order elastic moduli has been considered. The dependences of the relaxation rates on the direction of the wave vector of phonons in scattering processes with the participation of three quasi-transverse phonons (the TTT relaxation mechanisms) are analyzed within the anisotropic continuum model. It is shown that the TTT relaxation mechanisms in crystals are associated with their cubic anisotropy, which is responsible for the interaction between noncollinear phonons. The dominant contribution to the phonon relaxation comes from large-angle scattering. For crystals with significant anisotropy of the elastic energy (Ge, Si, KCl, NaCl), the total contribution of the TTT relaxation mechanisms to the total relaxation rate exceeds the contribution of the Landau-Rumer mechanism either by several factors or by one to two orders of magnitude depending on the direction. The dominant role of the TTT relaxation mechanisms as compared to the Landau-Rumer mechanism is governed, to a considerable extent, by the second-order elastic moduli. The total relaxation rates of slow quasi-transverse phonons are determined. It is demonstrated that, when the anharmonic processes of scattering play the dominant role, the inclusion of one of the relaxation mechanisms (the Landau-Rumer mechanism or the mechanisms of relaxation of the slow quasi-transverse mode by two slow or two fast modes) is insufficient for describing the anisotropy of the total relaxation rates in cubic crystals.

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.

Anisotropic attenuation of transverse ultrasound in cubic crystals of Ge, Si, and diamond with various isotopic compositions

The attenuation of transverse ultrasound in germanium, silicon, and diamond crystals is considered with allowance for competing isotopic and anharmonic scattering processes. The dependence of the attenuation of transverse ultrasound on the direction of the wave vector of quasi-transverse phonons is analyzed within an anisotropic continuum model. The Landau—Rumer mechanism is considered for anharmonic scattering processes. Given the second-and third-order elastic moduli, the parameters are found determining ultrasonic absorption in the above crystals with various degrees of isotopic disorder. The attenuation coefficients of transverse ultrasound associated with isotopic and anharmonic scattering processes are shown to have qualitatively different angular dependences. Therefore, from studying the anisotropic attenuation of ultrasound in cubic crystals, one can determine the dominant mechanism of ultrasonic absorption in isotopically modified crystals.

Anharmonic scattering processes and relaxation of quasi-transverse modes in cubic crystals with positive or negative anisotropy of second-order elastic moduli

Relaxation of long-wavelength quasi-transverse modes due to anharmonic scattering processes is considered. An anisotropic continuum model is used to analyze the dependence of the relaxation in cubic crystals on the direction of the wave vector of quasi-transverse phonons for the Landau-Rumar mechanism both in the quasi-isotropic approximation and in the case where the cubic anisotropy is rigorously taken into account. The quasi-isotropic approximation is shown to be inadequate for quantitative description of the anisotropy in the relaxation rates of quasi-transverse phonons. It is found that not only the spectra and polarization vectors of phonons but also the angular dependences of the relaxation rates of quasi-transverse vibrational modes are different in cubic crystals with positive and negative anisotropy in the second-order elastic moduli.

Anomalous temperature behavior of hypersonic acoustic phonons in a lysozyme crystal

The behavior of acoustic phonons in tetragonal lysozyme crystals is studied using Brillouin scattering over a temperature range from 298 to 330 K. Around 307 K, anomalies in the temperature dependence of the velocity and integral intensity of a quasi-transverse phonon and in the velocity of a quasi-longitudinal phonon are detected. The experimental results are discussed in terms of the current concepts of the dynamics of proteins. The observed anomalies in the behavior of hypersonic acoustic phonons are indicative of a structural phase transition occurring in a lysozyme crystal at 307 K.

Spectroscopic properties of KGd(WO4)2: (Er, Yb) single crystals studied by Brillouin scattering method

The study of KGW: (Er, Yb) was performed for the acoustic phonons [100], [001], [−101], [101], [110] and [011]. In some Brillouin spectra obtained at room temperature we observed additional modes connected with mixed polarization modes propagating as quasi-longitudinal or quasi-transverse phonons which is characteristic for low symmetry crystals. Moreover, it has been revealed, that the value of Brillouin shift and integral intensity of the longitudinal phonon [101] propagating in KGW: (Er, Yb) show the anomaly at about 175K.

Erratum: “Dispersion of the Acoustic Phonon and New Dynamic Central Peak of Piezoelectric DKDP in the Paraelectric Phase Studied by Light Scattering”

The V V scattering spectra in the a b plane were measured with various scattering angles. It is shown that the elastic stiffness constant C 66 shows clear dispersion near the transition temperature T tr just in the frequency region of GHz. A dynamic central peak (DCP) was observed in the spectra of quasitransverse acoustic phonon near q //[100] in the very vicinity of T tr . From the observed angular dependence of the linewidth of DCP it is revealed that this central peak scattering is caused by the piezoelectric interaction between the z -component of the polarization fluctuation and the x y shear component in the quasitransverse phonon.

Dispersion of the Acoustic Phonon and New Dynamic Central Peak of Piezoelectric DKDP in the Paraelectric Phase Studied by Light Scattering

The V V scattering spectra in the a b plane were measured with various scattering angles. It is shown that the elastic stiffness constant C 66 shows clear dispersion near the transition temperature T tr just in the frequency region of GHz. A dynamic central peak (DCP) was observed in the spectra of quasitransverse acoustic phonon near q //[100] in the very vicinity of T tr . From the observed angular dependence of the linewidth of DCP it is revealed that this central peak scattering is caused by the piezoelectric interaction between the z -component of the polarization fluctuation and the x y shear component in the quasitransverse phonon.

Excitations in commensurate and incommensurate BaMnF4: a light scattering study

Brillouin and Raman spectroscopy have been used to characterise the zone-centre phonons of BaMnF4 and to elucidate the dynamics of the commensurate-incommensurate transition at Ti=247K. The experiments for T<Ti have revealed three low-frequency temperature-dependent modes and these are interpreted in terms of the phase and amplitude excitations of the ground state (phasons and amplitudons) predicted by theory. In particular, the c(aa)b Brillouin spectrum contains scattering localised at approximately 0.6 cm-1 that is attributed to the phason. There is also a critical central peak, which appears to be static in origin. Above Ti, all quasi-transverse acoustic phonons in 90 degrees scattering show critical behaviour in intensity with an exponent of approximately 0.55. All of the elastic and piezoelectric constants and most of the elasto-optic constants have been determined for commensurate BaMnF4 at 295K.