Long-wavelength Acoustic Modes Research Articles

On the possibility of dust acoustic waves over sunlit lunar surface

ABSTRACTThe photoelectron sheath and floating fine positively charged dust particles constitute two-component dusty plasma in the sunlit lunar regolith’s vicinity. By including the charge fluctuation into photoelectron–dust dynamics, the lunar exospheric plasma is proposed to support the propagation of long-wavelength dust acoustic (DA) modes. Using the standard approach based on the dynamical equations for continuity, momentum, plasma potential, and dust charging along with Fowler's treatment of photoemission and non-Maxwellian nature of the sheath photoelectrons, the wave dispersion is derived. The dust charge variation modifies the usual DA wave dispersion and excites the ultralow frequency modes that propagate with sufficiently low phase speed. Such ultralow frequency modes are predicted as pronounced for smaller values of dust charge and sheath potential. The DA wave dispersion is also depicted as sensitive to the photoelectrons’ energy distribution within the sheath. The quantitative estimates suggest that the nominal exospheric plasma may exhibit DA waves propagating with frequencies of the order of unity.

Non-monotonic double layers and electron two-stream instabilities resulting from intermittent ion acoustic wave growth

Transient characteristics of a current-carrying plasma subjected to ion acoustic instability are studied via Vlasov–Poisson simulations. After saturation of the ion acoustic instability, when a sufficient range of long-wavelength ion acoustic modes is considered, ion acoustic wave packets form and give rise to ion phase space holes. These ion holes grow in magnitude until asymmetric electron reflection, due to the current carrying plasma, results in a potential gradient across the hole known as a non-monotonic double layer. Downstream of the double layer, an electron two-stream instability is generated due to a depletion of forward-streaming electrons by reflection. This secondary instability initiates a plasma wave whose phase velocity is determined by the magnitude of the double layer potential. While the double layer potential depends on the ion mass for a given domain length, the phase velocity of the secondary wave is consistently observed to be greater than the ion acoustic speed. Implications for the presence of these transient phenomena are discussed in the context of experimental plume measurements of hollow cathode devices.

First-principles calculations of electronic, acoustic and anharmonic properties of Mn2RuZ (Z = Si and Ge) Heusler compounds

The electronic, acoustic and anharmonic properties of Mn2RuZ (Z = Si and Ge) Heusler compounds were systematically studied by first-principles calculations combined with homogeneous deformation theory. The calculated lattice constants, electronic, magnetic and elastic properties were found to agree with the available experimental and theoretical values. Based on the obtained elastic properties, the acoustic velocities, Debye temperatures and thermal conductivities were calculated for both compounds. Their acoustic velocities and thermal conductivities were found to exhibit anisotropic behavior. Mn2RuSi has larger acoustic velocities, higher Debye and thermal conductivities for its lower density and larger second-order elastic constants. The pressure derivatives of second-order elastic constants, mode Grüneisen constants of long-wavelength acoustic modes, and nonlinear ultrasonic parameters were also obtained. The predictions on the acoustic and anharmonic properties are useful for further study of the related materials in the near future.

Continuum approach for long-wavelength acoustic phonons in quasi-two-dimensional structures

As an alternative to atomistic calculations of long-wavelength acoustic modes of atomically thin layers, which are known to converge very slowly, we propose a quantitatively predictive and physically intuitive approach based on continuum elasticity theory. We describe a layer, independent of its thickness, by a membrane and characterize its elastic behavior by a $(3\ifmmode\times\else\texttimes\fi{}3)$ elastic matrix as well as the flexural rigidity. We present simple quantitative expressions for frequencies of long-wavelength acoustic modes, which we determine using two-dimensional elastic constants calculated by ab initio density functional theory. The calculated spectra accurately reproduce observed and calculated long-wavelength phonon spectra of graphene and phosphorene, the monolayer of black phosphorus. Our approach also correctly describes the observed dependence of the radial breathing mode frequency on the diameters of carbon fullerenes and nanotubes.

Nonlinear elastic response and anharmonic properties of MgO single crystal: First-principles investigation

Knowledge of the nonlinear elastic response and anharmonic properties of MgO single crystal is important for interpreting the seismically observed velocity variations in the Earth’s mantle and constructing reliable mineralogical modes of the Earth’s interior. However, investigations on these properties of it have not been performed sufficiently to date. So the nonlinear elastic response of the MgO is first studied by calculating the second-, third-, and fourth-order elastic constants. Results show that our predications on the high-order elastic constants exhibit excellent agreement with the available experimental ones and other theoretical values, which indicates that the present computational approach is suitable for the calculations of the high-order elastic constants and it can be expanded into other complex systems. Then on the basis of the elastic constants, the related anharmonic properties such as the first-order pressure derivatives of the second- and third-order elastic constants, Grüneisen constants of the long-wavelength acoustic modes, and ultrasonic nonlinear parameters are also investigated. The predications on the anharmonic properties first given in the present work are hoped to serve as a valuable guidance or reference for further related investigations.

Equation of State, Nonlinear Elastic Response, and Anharmonic Properties of Diamond-Cubic Silicon and Germanium: First-Principles Investigation

Abstract Nonlinear elastic properties of diamond-cubic silicon and germanium have not been investigated sufficiently to date. Knowledge of these properties not only can help us to understand nonlinear mechanical effects but also can assist us to have an insight into the related anharmonic properties, so we investigate the nonlinear elastic behaviour of single silicon and germanium by calculating their second- and third-order elastic constants. All the results of the elastic constants show good agreement with the available experimental data and other theoretical calculations. Such a phenomenon indicates that the present values of the elastic constants are accurate and can be used to further study the related anharmonic properties. Subsequently, the anharmonic properties such as the pressure derivatives of the second-order elastic constants, Grüneisen constants of long-wavelength acoustic modes, and ultrasonic nonlinear parameters are explored. All the anharmonic properties of silicon calculated in the present work also show good agreement with the existing experimental results; this consistency not only reveals that the calculation method of the anharmonic properties is feasible but also illuminates that the anharmonic properties obtained in the present work are reliable. For the anharmonic properties of germanium, since there are no experimental result and other theoretical data till now, we hope that the anharmonic properties of germanium first offered in this work would serve as a reference for future studies.

Nonlinear Elastic Properties of Superconducting Antiperovskites MNNi3 (M =Zn, Cd, Mg, Al, Ga, and In) from First Principles

We present theoretical studies for the third-order elastic constants (TOECs) of superconducting antiperovskites MNNi 3 (M = Zn, Cd, Mg, Al, Ga, and In) using the density functional theory (DFT) and homogeneous deformation method. From the nonlinear least-square fitting, the elastic constants are extracted from a polynomial fit to the calculated strain-energy data. Calculated second-order elastic constants (SOECs) are compared with the previous theoretical calculations, and a very good agreement was found. The nonlinear effects often play an important role when the finite strains are larger than approximately 2.5 %. Besides, we have computed the pressure derivatives of SOECs and provided rough estimations for the Gruneisen constants of long-wavelength acoustic modes by using the calculated TOECs.

High-Order Elastic Constants and Anharmonic Properties of NaBH4: First-Principles Calculations

We present theoretical studies for second- and third-order elastic constants in NaBH4 based on ab initio calculations. Our calculated second-order elastic constants agree well with available experimental results. The anharmonic properties of NaBH4, such as pressure derivative of the second-order elastic constants and the Grüneisen constants for long-wavelength acoustic mode γ(q, j), are characterized using the third-order elastic constants.

First-principles effective Hamiltonian for ferroelectric polarization inBaTiO3/SrTiO3 superlattices

We present an effective Hamiltonian for the description of ferroelectric polarizations in perovskite oxide superlattices. To understand the ferroelectric behavior of (BaTiO3)n/(SrTiO3)m superlattices, we constrained the local distortion modes along the c direction only and set up the effective Hamiltonian based on the local modes that capture the physics of long-wavelength acoustic modes (strain) and lowest energy transverse optical phonon modes (soft modes) as prescribed by the localized Wannier functions. All the parameters in this effective Hamiltonian were predetermined from the first-principles density-functional theory calculations of each BaTiO3 and SrTiO3 components. As an application of the model parameters, we calculated the polarizations of (BaTiO3)n/(SrTiO3)m with n+m=5, the results of which are in good agreement with those of the previous first-principles calculations of average polarizations as well as local polarizations. This effective Hamiltonian procedure can provide guidance for developing ferroelectric model of other kinds of oxide superlattices.

Ab initiocalculations of third-order elastic constants and related properties for selected semiconductors

We present theoretical studies for the third-order elastic constants ${C}_{ijk}$ in zinc-blende nitrides AlN, GaN, and InN. Our predictions for these compounds are based on detailed ab initio calculations of strain-energy and strain-stress relations in the framework of the density functional theory. To judge the computational accuracy, we compare the ab initio calculated results for ${C}_{ijk}$ with experimental data available for Si and GaAs. We also underline the relation of the third-order elastic constants to other quantities characterizing anharmonic behavior of materials, such as pressure derivatives of the second-order elastic constants ${c}_{ij}^{\ensuremath{'}}$ and the mode Gr\"uneisen constants for long-wavelength acoustic modes $\ensuremath{\gamma}(\mathbf{q},\mathbf{j})$.

Polarons in quantum chains with XY exchange and Dzyaloshinsky-Moriya interaction

Excitations of the polaron types are investigated in the spin-1/2 quantum chain with XY exchange and Dzyaloshinsky-Moriya interaction, both coupled to acoustic vibrations of the substrate lattice. The study is carried out via Jordan-Wigner transformation with the help of which the spin chain is mapped onto a chain of spinless fermions. From the resulting effective fermion-lattice Hamiltonian, the discrete equations of motion are derived. These equations are solved in the continuum limit for self-trapped states near the bottom of the fermion spectrum interacting with long-wavelength acoustic lattice modes. The associate polaron solution, which has a pulse shape, is shown to propagate bound to the induced lattice kink distortion by translation along the chain at a constant velocity v. The pair can also experience an additional acceleration ϑ0 when the free fermion charge is excited above its groundstate. The polaron binding energy is strongly reduced, depending quadratically on the ratio D/J of the Dzyaloshinsky-Moriya interaction strength D to the isotropic XY exchange interaction J. It is also found that polaron parameters depend only on the XY spin-lattice coupling but not on the Dzyaloshinsky-Moriya contribution.

Envelope solitons of acoustic plate modes and surface waves

The problem of the existence of evelope solitons in elastic plates and at solid surfaces covered by an elastic film is revisited with special attention paid to nonlinear long-wave short-wave interactions. Using asymptotic expansions and multiple scales, conditions for the existence of envelope solitons are established and it is shown how their parameters can be expressed in terms of the elastic moduli and mass densities of the materials involved. In addition to homogeneous plates, weak periodic modulation of the plate's material parameters are also considered. In the case of wave propagation in an elastic plate, modulations of weakly nonlinear carrier waves are governed by a coupled system of partial differential equations consisting of evolution equations for the complex amplitude of the carrier wave (the nonlinear Schrödinger equation for envelope solitons and the Mills-Trullinger equations for gap solitons), and the wave equation for long-wavelength acoustic plate modes. In contrast to this situation, envelope solitons of surface acoustic waves in a layered structure are normally described by the nonlinear Schrödinger equation alone. However, at higher orders of the carrier wave amplitude, the envelope soliton is found to be accompanied by a quasistatic long-wavelength strain field, which may be localized at the surface with penetration depth into the substrate of the order of the inverse amplitude or which may radiate energy into the bulk. A new set of modulation equations is derived for the resonant case of the carrier wave's group velocity being equal to the phase velocity of long-wavelength Rayleigh waves of the uncoated substrate.

Model Hessian for accelerating first-principles structure optimizations

We present two methods to accelerate first-principles structural relaxations, both based on the dynamical matrix obtained from a universal model of springs for bond stretching and bending. Despite its simplicity, the normal modes of this model Hessian represent excellent internal coordinates for molecules and solids irrespective of coordination, capturing not only the long-wavelength acoustic modes of large systems, but also the short-wavelength low-frequency modes that appear in complex systems. In the first method, the model Hessian is used to precondition a conjugate gradients minimization, thereby drastically reducing the effective spectral width and thus obtaining a substantial improvement of convergence. The same Hessian is used in the second method as a starting point of a quasi-Newton algorithm (Broyden's method and modifications thereof), reducing the number of steps needed to find the correct Hessian. Results for both methods are presented for geometry optimizations of clusters, slabs, and biomolecules, with speed-up factors between 2 and 8.

Nonlinear modulation of multidimensional lattice waves.

The equations governing weakly nonlinear modulations of N-dimensional lattices are considered using a quasidiscrete multiple-scale approach. It is found that the evolution of a short wave packet for a lattice system with cubic and quartic interatomic potentials is governed by the generalized Davey-Stewartson (GDS) equations, which include mean motion induced by the oscillatory wave packet through cubic interatomic interaction. The GDS equations derived here are more general than those known in the theory of water waves because of the anisotropy inherent in lattices. The generalized Kadomtsev-Petviashvili equations describing the evolution of long-wavelength acoustic modes in two- and three-dimensional lattices are also presented. Then the modulational instability of an N-dimensional Stokes lattice wave is discussed based on the N-dimensional GDS equations obtained. Finally, the one- and two-soliton solutions of two-dimensional GDS equations are provided by means of Hirota's bilinear transformation method.

Structural evidence for Ta-tetramerization displacements in the charge-density-wave compound (TaSe4)2I from x-ray anomalous diffraction.

We use the anomalous x-ray diffraction technique to investigate the nature of the tantalum displacement pattern in the modulated phase of the charge-density-wave compound (TaSe4)2I. In addition to the known acousticlike modulation, we find the first direct evidence for the condensation of opticlike Ta displacements along the metallic chains corresponding to an LLSS pattern of long and short in-chain Ta-Ta distances (Ta-tetramerization modes). This result confirms a previous model in which the interaction of the electronically coupled optic modes with long-wavelength acoustic shear modes leads to the condensation of a modulation of mixed character.

Phonon instabilities in high-pressure bcc-fcc and the isostructural fcc-fcc phase transitions of Cs

The phonon instabilities of cesium related to its pressure-induced $\mathrm{bcc}\ensuremath{-}\mathrm{to}\ensuremath{-}{\mathrm{fcc}}^{(1)}\ensuremath{-}\mathrm{to}\ensuremath{-}{\mathrm{fcc}}^{(2)}$ phase transitions are studied using the density-functional perturbation theory. It is found that at low pressure, both the bcc and fcc Cs are dynamically stable, but fcc is thermodynamically metastable. The high-pressure phase transitions of Cs from bcc to ${\mathrm{fcc}}^{(1)}$ and from ${\mathrm{fcc}}^{(1)}$ to ${\mathrm{fcc}}^{(2)}$ are related to the phonon instabilities of the long-wavelength acoustic modes resulted from the negative tetragonal shear elastic constant ${C}^{\ensuremath{'}}=\frac{1}{2}{(C}_{11}\ensuremath{-}{C}_{12}).$ During the ${\mathrm{fcc}}^{(1)}\ensuremath{-}\mathrm{to}\ensuremath{-}{\mathrm{fcc}}^{(2)}$ phase transition, all the phonon modes become soft, making it the most striking feature of this isostructural phase transition.

Lattice stability and martensitic transition in β -phase Cu-based shape memory alloys: long-wavelength acoustic mode anharmonicity

Abstract We report measurements of the complete set of third-order elastic constants of β-phase Cu—Al—Ni and Cu—Al—Be alloys as a function of temperature. These data provide the experimental information needed for the study of the vibrational anharmonicity of long-wavelength acoustic modes in Cu-based alloys. The long-wavelength acoustic mode Grüneisen parameters have been computed for different families of Cu-based alloys. The modes associated with the two shears necessary to accomplish the lattice distortion from the β phase to the close-packed martensite structure have been found to exhibit the largest anharmonicity. It has also been found that the Grüneisen parameters of these two relevant modes take fixed values (independent of alloy composition and structure of the martensitic phase) at the transition temperature. Based on the results, the mechanical stability of the β phase and the nucleation mechanism is discussed in terms of the vibrational anharmonicity.

Lattice stability and martensitic transition in β-phase Cu-based shape memory alloys: Long-wavelength acoustic mode anharmonicity

Abstract We report measurements of the complete set of third-order elastic constants of β-phase Cu—Al—Ni and Cu—Al—Be alloys as a function of temperature. These data provide the experimental information needed for the study of the vibrational anharmonicity of long-wavelength acoustic modes in Cu-based alloys. The long-wavelength acoustic mode Gruneisen parameters have been computed for different families of Cu-based alloys. The modes associated with the two shears necessary to accomplish the lattice distortion from the β phase to the close-packed martensite structure have been found to exhibit the largest anharmonicity. It has also been found that the Gruneisen parameters of these two relevant modes take fixed values (independent of alloy composition and structure of the martensitic phase) at the transition temperature. Based on the results, the mechanical stability of the β phase and the nucleation mechanism is discussed in terms of the vibrational anharmonicity.

Ultrasonic study of the temperature and pressure dependences of the elastic properties of a single-crystal Heusler structure Cu41Mn20Al39 alloy

Pulse-echo-overlap measurements of ultrasonic wave velocity have been used to determine the elastic-stiffness tensor components Cu and the adiabatic bulk modulus, BS, of a ferromagnetic Heusler structure Cu41Mn20Al39 at % alloy single crystal as functions of temperature in the range 14–300 K and hydrostatic pressure up to 0.2 GPa at room temperature. At 295 K the elastic stiffnesses are: C11=133 GPa, C44=92 GPa, C′ (=(C11−C12)/2)=17 GPa, C12=99 GPa, CL(=C11+C44−C′)=205 GPa, and BS (=C11−4C′/3)=106 GPa. Cu41Mn20Al39 is a comparatively soft material elastically because its elastic properties are influenced strongly by magnetoelastic effects. The results of measurements of the effects of hydrostatic pressure on the ultrasonic wave velocity have been used to obtain the hydrostatic-pressure derivatives of the elastic – stiffness tensor components. At 295 K (∂C11/∂P)P=0, (∂C44/∂P)P=0, (∂C′/∂P)P=0, (∂C12/∂P)P=0, (∂CL/∂P)P=0, and (∂BS/∂P)P=0 are 5.0±0.1, 3.0±0.1, 1.0±0.2, 3.0±0.3, 7.7±0.4 and 3.7±0.4, respectively. Application of hydrostatic pressure does not induce acoustic-mode softening: the pressure derivatives (∂CIJ/∂P)P=0 and (∂BS/∂P)P=0 and the acoustic-mode Gruneisen parameters are positive. An interesting feature of the non-linear acoustic behaviour of this alloy is that the value obtained for (∂C′/∂P)P=0, associated with the softer shear mode propagated along the [1 1 0] direction and polarized along the [1 1 0] direction, is small in comparison with those of the other shear and longitudinal modes. The Gruneisen parameter of this mode, and hence its vibrational anharmonicity, is much larger than those of the other long-wavelength acoustic phonon modes. © 1998 Kluwer Academic Publishers

Ultrasonic study of the elastic and nonlinear acoustic properties of the paramagnetic Cr-5 at.% V single-crystal alloy

Abstract To assist understanding the effects of pressure on the magnetoelastic interactions in antiferromagnetic Cr alloys, the elastic and nonlinear acoustic properties of single-crystal Cr-5 at. %V alloy, which is paramagnetic at all temperatures, have been studied by the ultrasonic pulse-echo-overlap technique. Measurements of the hydrostatic-pressure dependences of the velocities of ultrasonic modes, propagated along the [100] and [110] directions, have been used to obtain the hydrostatic-pressure derivatives (∂CIJ∂P)P=0 of the elastic-stiffness tensor components CIJ . At 296 K, (∂CIJ/∂P}P=0 , (∂CL/∂P)P=0 , (∂C44/∂P)P=0 , (∂C1/∂P)P=0 and (∂B2/∂P)P=0 are 9·1 ± 0·1, 8·7 ± 0·1, 1·0 ± 0.02, 1·74 ± 0·02 and 6·8 ± 0·1 respectively. To establish the vibrational anharmonicity of the long-wavelength acoustic modes, the results obtained for CIJ and (∂CIJ/∂P)P=0 have been used to calculate the corresponding Gruneisen parameters. The mean long-wavelength acoustic Gruneisen parameter γd(= 1·43) is similar to the t...