Anharmonicity of lattice vibrations and transverse deformation of crystalline and vitreous solids

This paper reports on the additional data confirming the interrelation between the Grüneisen parameter and Poisson’s ratio in crystalline and vitreous solids. The assumption is made that the ratio between the velocities of longitudinal and transverse acoustic waves can depend on the anharmonicity of lattice vibrations.     

Anharmonicity of short-wavelength acoustic phonons in silicon at high temperatures

Second-order Raman spectra corresponding to transverse acoustic phonons are studied in detail for crystalline Si over the temperature range 20–620°C. The largest relative softening and anharmonicity at the boundaries of the Brillouin zone were observed for the TA(X) mode. Extrapolation of the TA(X) frequency to high temperatures suggests that the Si lattice should be dynamically unstable at temperatures on the order of a doubled melting temperature. It is found that the main contribution to the softening of the transverse acoustic phonons in silicon comes from the anharmonicity and not from the volume expansion.     

Soliton-like propagation modes of picosecond acoustic pulses in a paramagnetic crystal

The nonlinear propagation of picosecond acoustic pulses at an arbitrary angle to an external magnetic field is studied in an elastically isotropic paramagnetic crystal at low temperatures. Various soliton-like propagation modes arising due to spin-phonon interaction and acoustic anharmonicity are revealed, and the stability of these modes with respect to transverse perturbations is analyzed. In the case of defocusing cubic nonlinearity, the crystal can support the propagation of compression pulses, which undergo defocusing, and rarefaction pulses can propagate in the self-channeling mode. In the case of focusing cubic nonlinearity, only compression pulses can propagate if the conditions of stability with respect to self-focusing are satisfied.     

Soliton generation via continuous stokes acoustic self-scattering of hypersonic waves in a paramagnetic crystal

A new mechanism is proposed for continuous frequency down-conversion of acoustic waves propagating in a paramagnetic crystal at a low temperature in an applied magnetic field. A transverse hypersonic pulse generating a carrier-free longitudinal strain pulse via nonlinear effects is scattered by the generated pulse. This leads to a Stokes shift in the transverse hypersonic wave proportional to its intensity, and both pulses continue to propagate in the form of a mode-locked soliton. As the transverse-pulse frequency is Stokes shifted, its spectrum becomes narrower. This process can be effectively implemented only if the linear group velocity of the transverse hypersonic pulse equals the phase velocity of the longitudinal strain wave. These velocities are renormalized by spin-phonon coupling and can be made equal by adjusting the magnitude of the applied magnetic field. The transverse structure of the soliton depends on the sign of the group velocity dispersion of the transverse component. When the dispersion is positive, planar solitons can develop whose transverse component has a topological defect of dark vortex type and longitudinal component has a hole. In the opposite case, the formation of two-component acoustic “bullets” or vortices localized in all directions is possible.     

Temperature variation of phonon frequency distribution in the fast ion conductor lead fluoride

A weighted phonon frequency distribution has been measured in PbF₂ at temperatures 10, 302, 660 and 910 K, using a neutron scattering technique. At 10 K good agreement is found between the measured distribution and the phonon density-of-states calculated from the low temperature dispersion relation of PbF₂. At the higher temperatures, near the ionic conductivity transition temperature, T_c ～ 700 K, the optic modes are observed to broaden into a high energy tail consistent with strong anharmonicity or extensive disorder. A low energy peak arising from transverse acoustic modes remains well defined even at temperatures above T_c.     

Fermi resonance of optical one-phonon and acoustic two-phonon vibrations in light metals

It is shown that the anharmonicity of crystal lattice vibrations in light metals such as beryllium, can give rise to a Fermi resonance of optical one-phonon and acoustic two-phonon vibrations. New hybridized vibrational states are formed as a result of such a resonance interaction: biphonon and quasibiphonon vibrations and renormalized optical vibrations. Depending on the wave vector, these vibrational states can be both damped and stationary. The corresponding dispersion equation is obtained, whose solution made it possible to determine the spectrum of these vibrations (dispersion curves and the wave vector dependence of the damping for damped vibrations). It is shown that ultrafast damping of optical vibrations, similar to the well-known superradiance effect for Frenkel’ and Wannier-Mott excitons, is possible. Fiz. Tverd. Tela (St. Petersburg) 39, 542–546 (March 1997)     

Effect of magnon–phonon interaction on transverse acoustic phonon excitation at finite temperature

A magnon–phonon interaction model is developed on the basis of two-dimensional square Heisenberg ferromagnetic system. By using Matsubara Green function theory transverse acoustic phonon excitation is studied and transverse acoustic phonon excitation dispersion curves is calculated on the main symmetric point and line in the first Brillouin zone. On line Σ it is found that there is hardening for transverse acoustic phonon on small wave vector zone (nearby point Γ), there is softening for transverse acoustic phonon on the softening zone and there is hardening for transverse acoustic phonon near point M. On line Δ it is found there is no softening and hardening for transverse acoustic phonon. On line Z it is found that there is softening for transverse acoustic phonon on small wave vector zone (nearby point X) and there is hardening for transverse acoustic phonon nearby point M. The influences of various parameters on transverse acoustic phonon excitation are also explored and it is found that the coupling of the magnon–phonon and the spin wave stiffness constant play an important role for the softening of transverse acoustic phonon.     

有限温度下二维Heisenberg铁磁系统的横向声频支声子激发

在二维正方Heisenberg铁磁系统的基础上建立了磁振子-声子相互作用模型.利用Matsubara格林函数理论研究了系统的横向声频支声子激发，计算了布里渊区的主要对称点线上的横向声频支声子色散曲线，发现在第一布里渊区的Σ线上，小波矢区(Γ附近k_xa＜0.2)横向声频支声子有硬化现象，但是在软化区(0.25＜k_xa＜0.7)有横向声频支声子有软化现象，在M附近(0.75＜k_xa)横向声频支声子有硬化现象.在Δ线上没有发生横向声频支声子有软化与硬化现象.在Z线上小波失区(X附近k_xa＜0.65)横向声频支声子有软化现象，但是在M附近横向声频支声子有硬化现象.并且又讨论了各项参数对横向声频支声子激发的影响，发现磁振子-声子耦合与自旋波劲度常数对横向声频支声子软化起很大的作用. 关键词： 磁振子-声子相互作用 横向声频支声子软化 Matsubara格林函数理论 铁磁系统     

Nonlinear interactions of longitudinal acoustic modes in magnets near the antiferromagnetic-ferromagnetic phase transition

The effective elastic anharmonicity induced by exchange magnetoelastic interaction is investigated for easy plane antiferromagnets, in which an antiferromagnetic-ferromagnetic phase transition takes place. Near the transition point this anharmonicity can be manifested in nonlinear interactions of longitudinal acoustic modes, resulting in magnetoacoustic mode-frequency conversion effects. It is shown that these effects are amplified in the vicinity of the phase transition, because the effective third-order elastic constants increase by several orders of magnitude. The generation of longitudinal acoustic second harmonics is analyzed as an example. Fiz. Tverd. Tela (St. Petersburg) 39, 1432–1436 (August 1997)     

On the propagation of linear transverse acoustic waves in isotropic media with mechanical relaxation phenomena due to viscosity and a tensorial internal variable: II. Some cases of special interest (Poynting-Thomson,Jeffreys, Maxwell,Kelvin-Voigt,Hooke and Newton media)

The propagation of linear transverse acoustic waves in isotropic media in which mechanical relaxation phenomena occur was considered in a previous paper. In particular expressions for the velocity and attenuation of the waves were obtained and the limiting cases of waves with high and low frequencies were discussed. In the present paper we investigate the propagation of linear transverse acoustic waves in Poynting-Thomson, Jeffreys, Maxwell, Kelvin-Voigt, Hooke and Newton media. We show that the dispersion relations for these waves may be considered as degeneracies of the dispersion relation which we derived in the general case of a viscoanelastic medium with memory. In particular we investigate the explicit dependence of the dispersion relations on the thermodynamic parameters and the phenomenological coefficients.     

The influence of transverse perturbations on the propagation of picosecond acoustic pulses in a paramagnetic crystal

The influence of transverse perturbations on the dynamics of a picosecond soliton-like acoustic pulse in a paramagnetic crystal in an external magnetic field is investigated. The nonlinear and dispersion effects are governed by the intrinsic properties of the crystal and the spin-phonon interaction. The effect of different nonlinear mechanisms and an external magnetic field on the stability against transverse perturbations is analyzed. It is shown that, in the absence of paramagnetic impurities, there can exist only a compression pulse that propagates in a defocusing regime. In the presence of paramagnetic ions in the crystal, there can arise rarefaction pulses that, under specific conditions, can propagate in self-focusing and self-channeling regimes.     

Dispersion relation for two-dimensional simple cubic lattices

The linear wave equation for the simple cubic lattice is given in this paper. The dispersion relations of both longitudinal and transverse waves are given analytically for the acoustic mode and the optical mode, respectively.     

Dispersion relation for two-dimensional simple cubic lattices

The linear wave equation for the simple cubic lattice is given in this paper. The dispersion relations of both longitudinal and transverse waves are given analytically for the acoustic mode and the optical mode, respectively.      

二维声子晶体同质位错结缺陷态特性

利用平面波展开法结合超原胞的方法研究了二维声子晶体同质位错结的缺陷态.分别研究了横向位错和纵向位错两种情况，研究结果表明：横向位错效应与线缺陷相似，它可以使处于禁带频率范围内的声波沿位错通道进行传播，形成声波导；纵向位错效应则类似于点缺陷，位错线两边三个最接近的散射子形成腔，因而能够产生局域模.另外，横向位错距离和纵向位错距离的大小将影响缺陷带的位置和数量，因此，可以通过调节横向位错距离或纵向位错距离来人为的控制同质位错结中的缺陷带. 关键词： 声子晶体 同质位错结 缺陷态     

Estimation of dispersion curve of transverse acoustic phonons in CdI2 by Raman scattering

Shear type rigid layer modes in various polytypes of CdI₂ have been measured by Raman scattering. The dispersion curve of transverse acoustic phonons in the [0 0 ξ] direction is estimated from the observed frequencies of the rigid layer modes. The analysis of the estimated dispersion curve indicates that interlayer forces in CdI₂ are mainly short range ones.     

Phonons and periodons in IV–VI semiconductor superlattices

We have calculated the phonon and periodon dispersion relations in IV–VI semi-conducting bulk PbTe and SnTe and their superlattice structure. The model used here is a one-dimensional lattice which includes harmonic interactions up to second neighbours as well as on-site nonlinear electron-ion interactions at the anion site. We calculate the phonon and periodon dispersion relations in bulk and PbTe-SnTe superlattice for the transverse optic and acoustic modes using the transfer matrix method. Our analysis has predicted correct nature of the folding of acoustic and confinement of optical phonons at various frequency intervals corresponding to pass and stop bands of the superlattices.     

平面波与线性粘弹海底的反射和折射

采用基于广义标准线性体Boltzmann叠加原理的固体流变模型来描述粘弹性海底底质结构,分析了沉积层和基岩的纵、横波速度频散和衰减的特点,计算了海水沉积层界面和沉积层基岩界面位移势反射和折射系数和能量反射和折射系数。结果表明,采取本模型的粘弹性海底的速度频散、衰减和已有文献的实验数据符合较好,能准确的描述海底底质的主要性质,反射和折射系数和声波的频率有关。      

Nonlinear picosecond acoustics of low-temperature paramagnetic crystals

The interaction of transverse picosecond deformation pulses with a system of S=1/2 spins, forming a paramagnetic crystal, is investigated theoretically. The influence of acoustic dispersion, owing to the lattice structure, and the anharmonicity of atomic vibrations on the formation of stationary soliton-like video pulses, interacting with the spins of paramagnetic atoms, is studied for the example of a cubic crystal. The phenomenon of total reflection of deformation pulses from the paramagnetic crystal is predicted. The amplification and self-compression of nonresonant pulses in nonequilibrium paramagnetics is studied, and it is shown that generation of higher-order (up to tenth-order) harmonics of the frequency of the initial signal is possible. It is concluded that for appropriate crystal parameters, a limiting solition with a duration of one period of the oscillations, corresponding to spatial size of the order of the lattice constant of the crystal, is possible at the final stage of amplification.V. V. Kuibyshev Tomsk State University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 94–113, July, 1993.     

Propagation behavior of two transverse surface waves in a three-layer piezoelectric/piezomagnetic structure

Propagation of transverse surface waves in a three-layer system consisting of a piezoelectric/piezomagnetic (PE/PM) bi-layer bonded on an elastic half-space is theoretically investigated in this paper. Dispersion relations and mode shapes for transverse surface waves are obtained in closed form under electrically open and shorted boundary conditions at the upper surface. Two transverse surface waves related both to Love-type wave and Bleustein–Gulyaev (B–G) type wave propagating in corresponding three-layer structure are discussed through numerically solving the derived dispersion equation. The results show that Love-type wave possesses the property of multiple modes, it can exist all of the values of wavenumber for every selected thickness ratios regardless of the electrical boundary conditions. The presence of PM interlayer makes the phase velocity of Love-type wave decrease. There exist two modes allowing the propagation of B–G type wave under electrically shorted circuit, while only one mode appears in the case of electrically open circuit. The modes of B–G type wave are combinations of partly normal dispersion and partly anomalous dispersion whether the electrically open or shorted. The existence range of mode for electrically open case is greatly related to the thickness ratios, with the thickness of PM interlayer increasing the wavenumber range for existence of B–G type wave quickly shortened. When the thickness ratio is large enough, the wavenumber range of the second mode for electrically shorted circuit is extremely narrow which can be used to remove as an undesired mode. The propagation behaviors and mode shapes of transverse surface waves can be regulated by the modification of the thickness of PM interlayer. The obtained results provide a theoretical prediction and basis for applications of PE–PM composites and acoustic wave devices.     

Acoustic rectification and generation of the second hypersonic harmonic in the resonant parametric soliton regime

A resonant parametric mechanism of generation of the zeroth and second harmonics of acoustic pulses propagating in a crystal involving resonance Zeeman transitions is proposed. The analysis performed has made it possible to determine the conditions for the effective acoustic rectification and excitation of the second harmonics in the resonant parametric soliton regime. The advantage of the proposed mechanism of acoustic harmonic generation over the conventional mechanism associated with the acoustic anharmonicity is that the degree of conversion is controlled by a change in the external magnetic field strength and the direction of propagation of the input pulse.