Effective elastic properties of piezoelectric composites with radially polarized cylinders

Effective elastic properties of piezoelectric composites containing an infinitely long, radially polarized cylinder embedded in an isotropic non-piezoelectric matrix are theoretically investigated under an external strain field. Analytical solutions of elastic displacement and electric potentials are exactly derived, and the effective elastic responses are formulated in the dilute limit. Meanwhile, a vanishing piezoelectric response mechanism is revealed in the piezoelectric composite containing radially polarized cylinders. Furthermore, it is shown that the effective elastic properties can be enhanced (or reduced) due to the increase of the piezoelectric (or dielectric) constants of the cylinders.     

Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics

The complete set of self-consistent parameters of nominally undoped LiNbO₃ crystals of congruent composition that describe the electro-optic, piezoelectric, elasto-optic, elastic, and dielectric response has been determined by numerically evaluating available measurements. The parameters were determined at room temperature and consist of the low-frequency clamped dielectric constants ε^S _ij, elastic stiffness constants at constant electric field C^E _ijkl, piezoelectric stress coefficients e_ijk, elasto-optic constants at constant electric field p^E _ijkl, and clamped electro-optic coefficients r^S _ijk. It is shown that the complete set is required for calculating the effective electro-optic coefficients and dielectric constants in photorefractive applications of LiNbO₃. Received: 4 January 2002 / Revised version: 1 February 2002 / Published online: 14 March 2002     

Measurement of elastic constants of nematic liquid crystals with use of hybrid in-plane-switched cell

A new method for quick and pretty accurate measurements of splay, twist and bend elastic constants of nematic liquid crystals is experimentally verified. The main concept relies on exploiting only the electric field and determining magnitudes of nematic elastic constants from threshold fields for Freedericksz transitions in only one hybrid in-plane-switched cell. In such cell the deformations of an investigated liquid crystal are controlled by three separated pairs of electrodes confining measurement domains. In two of them inter-digital electrodes are mounted on one cell cover. Splay, twist and bend elastic constants can be measured by a proper choice of electrodes?? configuration together with orienting cover coatings (without applying magnetic fields). In this paper, we describe layout of our cells and results of experimental tests by using different liquid crystals: 5CB and 6CHBT (with positive dielectric anisotropy), Demus?? esters (with negative dielectric anisotropy) and new liquid crystals mixtures produced in our university.     

One- and two-dimensional deformations in nematic liquid crystals: Influence of the flexoelectric polarization

Summary The elastic deformations in nematic liquid crystals are analysed in one and two dimensions. The influence of the flexoelectric polarization on the elastic properties of the medium is studied. It is shown that for one-dimensional deformations, the presence of the flexoelectric polarization introduces a renormalization of the elastic constants. On the contrary in the bidimensional case, the effect of the flexoelectricity is not a simple renormalization of the elastic constants. The profiles of the electric potential and of the tilt angle are evaluated for the cases in which the substrate is an insulating or conducting material. The validity of the calculations is discussed by considering the value of Debye's screening length of the nematic liquid crystal.     

Effective elastic properties of two-phase composites

Expressions for the effective elastic constants of two-phase composites in the form of series obtained with Fourier transforms have been analyzed. In certain cases, such series are shown to be fully summed up; as a result, one can directly obtain exact expressions for the effective bulk modulus of a composite. It is found that the symmetry of the coefficients in series for the shear modulus and Young’s modulus and the corresponding reciprocal quantities can be used to relate these series to each other. Thus, all well-known exact relations for the effective elastic constants can be derived. A set of equations is proposed to compute the effective constants of a two-dimensional isotropic symmetrical composite with arbitrary properties of its phases.     

α—AlPO4单晶的压电和弹性性质研究

用缓慢升温法在高压釜中生长了α-AlPO₄单晶体;用传输法测量了室温下α-AlPO₄单晶体的压电、弹性和介电常数,研究了晶体中缺陷对电性能的影响。 关键词：     

导电球简立方格子有效介电常数的计算

基于MaxwellWagner模型,推导出有效介电常数关于颗粒体积比的一系列正幂项解析表达式,计算导电球颗粒悬浮于介质或导电液体中构成的简立方格子结构的有效介电常数.数值计算结果表明:在高频条件下(0.1～1.0kHz),有效介电常数主要由导电球颗粒与液体的介电常数比决定,而在低频或直流条件下,导电球颗粒与液体电导率比则起主要作用;有效介电常数的虚数部分有时会很大,即电流变液中的电致损耗有时会相当强,在设计高性能的电流变液时,体系的电导率效应不能忽略.     

Determination of elastic properties of Si/Ge superlattices and Si1-xGex films from surface acoustic modes by Brillouin scattering

Surface acoustic waves (SAW) have been measured by means of Brillouin scattering (BS) both as a function of k×h and the direction of k in the sample plane (k is the wavevector of the surface acoustic mode and h the thickness of the film). The velocity of the Rayleigh wave on sufficiently thick films (h > 4000 Å) has been experimentally found to ve uneffected by the elastic properties of the substrate material. Thus the directional dependence of the hypersonic surface wave is completely determined by the elastic properties of the layer material alone and reflects its crystallographic symmetry. The SL's can be treated as media with effective elastic constants because the wavelength of the thermally excited Rayleigh wave is much longer than the SL period. Furthermore, the angular dispersion of the SAW can be used to calculate the elastic constants of each film separately.     

Elestic constants in the interfacial layer at the nematic-liquid-crystal-vapour interface

Summary Close to the interface between a nematic liquid crystal (NLC) and another medium, the elastic constants become functions of distancez from the interface and of angle θ between the directorn and the unit vectork orthogonal to the interface. Furthermore, due to the breaking of the translation symmetry at the interface, a lot of new subsurface elastic contributions can appear. In a previous paper we investigated these subsurface anomalies by using a simple molecular model based on induced-dipole-induced-dipole interactions and by making numerical calculations in the special case of a planar director distortion. In this way, only the numerical values of some effective subsurface elastic constants that characterise planar director distortions could be obtained. In this paper we make a more complete analytical calculation of all the subsurface elastic constants by using a microscopic model and a more general theoretical procedure. The microscopic interaction energy is written in a general form that allows us to investigate different kinds of intermolecular interactions (induced diple-induced dipole, quadrupole-quadrupole and so on). Both thez-dependence and the θ-dependence of the subsurface elastic constants are obtained in a closed analytical form. In the special case of induced-dipole-induced-dipole interactions and for planar director distortions, our analytical results are shown to agree with the previous numerical results. The important macroscopic effect of these elastic subsurface anomalies is discussed.     

Effective dielectric and photoelastic tensor components in thin layered superlattices

The effective photoelastic constants of a superlattice composed of thin alternating layers of orthorhombic symmetry are calculated as functions of dielectric, elastic and photoelastic constants of the constituents. In a preliminary step to this calculation, we also obtain the effective dielectric tensor for any symmetry of the layers. It is shown that appropriate combinations of these effective constants are arithmetic averages of the corresponding quantities in the constituents, each layer having a weight equal to its relative thickness.     

An ab initio study of the structural,elastic, electronic and optical properties of the newly synthesized nitridoaluminate LiCaAlN2

The structural parameters, elastic constants, electronic structure and optical properties of the recently reported monoclinic quaternary nitridoaluminate LiCaAlN₂ are investigated in detail using the ab initio plane-wave pseudopotential method within the generalized gradient approximation. The calculated equilibrium structural parameters are in excellent agreement with the experimental data, which validate the reliability of the applied theoretical method. The chemical and structural stabilities of LiCaAlN₂ are confirmed by calculating the cohesion energy and enthalpy of formation. Chemical band stiffness is calculated to explain the pressure dependence of the lattice parameters. Through the band structure calculation, LiCaAlN₂ is predicted to be an indirect band gap of 2.725 eV. The charge-carrier effective masses are estimated from the band structure dispersions. The frequency-dependent dielectric function, absorption coefficient, refractive index, extinction coefficient, reflectivity coefficient and electron energy loss function spectra are calculated for polarized incident light in a wide energy range. Optical spectra exhibit a noticeable anisotropy. Single-crystal and polycrystalline elastic constants and related properties, including isotropic sound velocities and Debye temperatures, are numerically estimated. The calculated elastic constants and elastic compliances are used to analyse and visualize the elastic anisotropy of LiCaAlN₂. The calculated elastic constants demonstrate the mechanical stability and brittle behaviour of the considered material.     

The static and elastic properties of mixed diatomic crystals

An interionic potential model has been proposed to study the static and elastic properties of mixed diatomic crystals. The interaction system of this potential consists of the long-range Coulomb and three-body interaction and the short-range overlap repulsion. This potential has been used to calculate the cohesive energy, phase-transition pressure and volume, third-order elastic constants and pressure derivatives of the effective second-order elastic constants for NaCl-NaBr mixed crystals. These results agree reasonably well with the available experimental results on the host crystals and allow us to draw some meaningful conclusions for the mixed alkali halide crystals.     

The second and third order elastic constants of alkali metals

The second and third order elastic constants of the alkali metals have been calculated on the long wave method using the Heine-Abarenkov lacal model potential with different exchange-correlation corrections. It is found that the use of an exchange correlation correction which satisfies the compressibility sum rule leads to a good agreement between the calculated and measured second order elastic constants of the alkali metals Na, K, Rb and Cs. The shear elastic constants however come out correct even if the compressibility sum rule is violated by the exchange-correlation correction. The third order elastic constants and the pressure derivatives of the second order elastic constants and the pressure derivatives of the second order elastic constants calculated on the HA local potential are lower than the experimental values at room temperature. The discrepancy is pronounced for the heavier alkali metals. Similar calculations using the Wallace potential for Li, Na and K and the Schneider-Stoll potential for Rb give the pressure derivative in good agreement with experiment. In view of the important role by the exchange correlation correction, Suzuki's results calculated without taking this correction into account can only be accepted with some reservation.     

Lattice dynamics of wurtzite-type crystals—II

We evaluated, in the preceding paper, the effective ionic charge and electronic polarizability for wurtzite-type crystals on the basis of the polarizable-ion model given by Born and Huang. With use of the quantities so evaluated, we here estimated the short-range force constants from observed frequencies, elastic constants, and piezoelectric constants after simplifying Born and Huang's procedures. The resulting set of force constants can reproduce the observed data except for the piezoelectric constants. This poor reproduction of the piezoelectric constants is due to the fact that the long-range force is emphasized in the polarizable-ion model.     

Elasticity of globular proteins measured from the ac susceptibility

We introduce a new method to measure the elastic constants of globular proteins. Gold nanoparticles, tethered to a gold surface by the protein, are driven by an ac electric field while their displacement is synchronously detected by evanescent wave scattering, yielding the mechanical response function of the macromolecular sample in the frequency domain. We apply the method to measure the stiffening of an enzyme upon binding its substrate.     

Variational treatment of the elastic constants of disordered materials

Using the method of Hill a variational principle is derived to obtain upper and lower bounds for the effective elastic constants of disordered materials, such as polycrystals or multiphase materials. All bounds previously known are rederived and especially new bounds are given being closer than the ones of Hashin and Shtrikman. In detail the elastic constants of polycrystals built of cubic single crystals and of multiphase materials are considered. The analogous bounds for the dielectric constant of polycrystals are also given.     

BRILLOUIN LIGHT-SCATTERING INVESTIGATION OF ELASTIC ANOMALY FROM SUPERLATTICES

In this paper we report some new experimental results concerning the elastic properties of periodic and quasiperiodic superlattices studied by means of Brillouin spectroscopy. The observation of both bulk and surface acoustic phonons as well as the fitting using effective medium approximation on the phonon spectrum enables us to extract accurately some rele-vant effective elastic constants in both structures. We have verified that the elastic anomaly which occurs in the periodic structures is also present in quasiperiodic ones. These results imply that the interaction mechanism of Fermi electrons with reduced Brillouin zone bound-ary is not responsible for the observed elastic anomalies, The comparative study of these superlattices proves that the elastic anomaly is relevant directly to interfacial effects.     

Piezoelectricity and ferroelectricity in polyvinylidene fluoride

The dielectric, elastic and electrostrictive constants of polyvinylidene fluoride (pvdf) are influenced by thermal molecular motion, particularly at the glass transition temperature. High temperature poling is caused by both dipolar orientation and space-charge redistribution. Low temperature poling and dielectric hysteresis under a strong electric field are caused by crystalline dipolar orientation. The ferroelectric nature of pvdf is confirmed by x-ray and infrared analyses. The piezoelectric constants for a single crystal are theoretically calculated in agreement with experimental values. The piezoelectricity in poled films originates from the intrinsic piezoelectricity of the crystal and the residual polarization in the crystal coupled with electrostriction and dimensional change in the non-crystalline phase.     

The effect of polymer type on electric breakdown strength on a nanosecond time scale

Based on the concepts of fast polarization,effective electric field and electron impact ionization criterion,the effect of polymer type on electric breakdown strength(E BD) on a nanosecond time scale is investigated,and a formula that qualitatively characterizes the relation between the electric breakdown strength and the polymer type is derived.According to this formula,it is found that the electric breakdown strength decreases with an increase in the effective relative dielectric constants of the polymers.By calculating the effective relative dielectric constants for different types of polymers,the theoretical relation for the electric breakdown strengths of common polymers is predicted.To verify the prediction,the polymers of PE(polyethylene),PTFE(polytetrafluoroethelene),PMMA(organic glass) and Nylon are tested with a nanosecond-pulse generator.The experimental result shows E BD(PTFE) > E BD(PMMA) > E BD(Nylon) > E BD(PE).This result is consistent with the theoretical prediction.     

Equivalent circuit with complex physical constants and equivalent-parameters-expressed dissipation factors of piezoelectric materials

The equivalent circuit with complex physical constants for a piezoelectric ceramic in thickness mode is established. In the equivalent circuit, electric components (equivalent circuit parameters) are connected to real and imaginary parts of complex physical coefficients of piezoelectric materials. Based on definitions of dissipation factors, three of them (dielectric, elastic and piezoelectric dissipation factors) are represented by equivalent circuit parameters. Since the equivalent circuit parameters are detectable, the dissipation factors can be easily obtained. In the experiments, the temperature and the stress responses of the three dissipation factors are measured.