Photothermoacoustic oscillations in a solid-piezoelectric layered structure

Photothermoacoustic oscillations in a thin plane-layered structure consisting of an isotropic solid and a piezoelectric crystal of class 6mm (or piezoelectric ceramics) are studied theoretically and experimentally. Expressions for the potential difference across an arbitrary layer of the piezoelectric transducer are derived. For the case of a two-layer transducer, the amplitude-frequency and phase-frequency dependences of the signal are analyzed. It is shown that, from these experimental dependences, one can determine certain elastic and thermal parameters of a solid. An experiment is performed with samples of Cu, Zn, and TsTS-19 piezoceramics in the frequency range within 9–1000 Hz. The experimental data are used to determine the values of the reduced Young’s modulus and the thermal diffusivity of the materials under study.     

Interesting directions in crystals from the aspect of the voigt and Laval-Raman theory of the elastic properties of crystals

In an experiment carried out by Le Corre in ADP crystals [Bull. Soc. Franc. Minér. Cryst.77 (1954), 1963] the validity of the Laval-Raman theory of the elastic properties of crystals was borne out by the experimental finding that different values of the phase velocity correspond to two suitably chosen elastic waves; in the case of the validity of Voigt's theory they would have to agree. The method described in this paper permits systematic examination of the possibility of performing in principle the same experiment for crystals of all classes of symmetry.     

Calculation of the electroelastic Green’s function of the hexagonal infinite medium

The electroelastic 4 × 4 Green’s function of a piezoelectric hexagonal (transversely isotropic) infinitely extended medium is calculated explicitly in closed compact form ((73) ff. and (88) ff., respectively) by using residue calculation. The results can also be derived from Fredholm’s method [2]. In the case of vanishing piezoelectric coupling the derived Green’s function coincides with two well known results: Kröner’s expressions for the elastic Green’s function tensor [4] is reproduced and the electric part then coincides with the electric potential (solution of Poisson equation) which is caused by a unit point charge. The obtained electroelastic Green’s function is useful for the calculation of the electroelastic Eshelby tensor [16].     

Dielectric, piezoelectric and elastic properties of tetragonal BiScO3-PbTiO3 single crystal with single domain

Modified BiScO₃-PbTiO₃ (BSPT) tetragonal single crystals were grown using high temperature solution method. The dielectric, piezoelectric and elastic properties of single domain BSPT crystals, after poling along [001] crystallographic direction, have been determined experimentally using the resonance method. The results showed that the BSPT tetragonal crystals possess good piezoelectric properties, with electromechanical coupling factor about 88% and piezoelectric coefficient over 400 pC/N at room temperature. BSPT tetragonal crystals have high Curie temperature around 436 °C and high coercive field ∼28 kV/cm, also, the crystal exhibited a very good temperature stability of the properties till 380 °C. For comparison, the material constants of tetragonal Pb(Zn_1/3Nb_2/3)O₃-PbTiO₃ (PZNT) single crystals were measured and listed in this paper.     

Crystal growth and dielectric, piezoelectric and elastic properties of Ca3TaGa3Si2O14 single crystal

Single crystals of Ca₃TaGa₃Si₂O₁₄ (CTGS) were successfully grown from stoichiometric melts by the conventional Czochralski technique. The relative dielectric constants, the piezoelectric strain constants and the elastic compliance constants of CTGS single crystal have been determined by an electric bridge and resonance-antiresonance method. At room temperature, the two piezoelectric strain constants d₁₁ and d₁₄ are −4.58×10⁻¹² coulombs per newton (C/N) and 10.43×10⁻¹² coulombs per newton (C/N), respectively. The velocities of the bulk acoustic wave are also calculated.     

Effect of uniaxial stress on the birefringence of triglycine sulphate crystals doped with L threonine

The temperature and spectral dependences of the birefringence ??n _i of triglycine sulphate (TGS) crystals with L-threonine impurity have been investigated. Doping with L-threonine is found to reduce the temperature dependence of ??n _i of TGS crystals. The baric coefficients of shift of the phase-transition (PT) point, ?T _c /???m, are found to be somewhat smaller than those for pure TGS crystals, which is confirmed by the increase in the hardness of TGS crystals after doping. The temperature and spectral dependences of the combined piezoelectric constants ?? _im ⁰ have been calculated. The stepwise changes in all piezoelectric constants at the PT of doped crystals are found to be much smaller than those for pure crystals.     

Microscopic theory of second-order and third-order elastic constants for an NaCl crystal

Relations between the second-order and third-order symmetry-independent elastic constants and the energy of interatomic interactions dependent on the mutual arrangement of pairs and triplets of atoms are obtained for crystals belonging to the crystal class O _h. The derived relations and experimental data on the elastic constants are used to calculate four third-order elastic constants and the temperature dependence of the elastic anisotropy factor a(T) for an NaCl crystal. The calculated dependence a(T) is in qualitative agreement with the experimental dependence a _exp(T).     

Specific propagation directions of acoustic waves for piezoelectric and nonpiezoelectric media

I reanalyze the problem of the existence of longitudinal normals inside the symmetry planes of piezoelectric crystals belonging to the symmetry class mm2. The equations determining components of longitudinal normals situated outside the symmetry planes for media of this symmetry are discussed. It is proven that nonpiezoelectric media of rhombic symmetry could have 4 or 8 distinct acoustic axes. Examples of nonpiezoelectric elastic media of monoclinic symmetry without acoustic axes are given. The method of determination of the components of acoustic axes for piezoelectric media of arbitrary symmetry is presented. With the help of this method, I discuss the problem of acoustic axes for piezoelectric media of the symmetry class mm2. The text was submitted by the author in English.     

Effect of pressure on the elastic properties of silicon carbide

The pressure dependences of the second-order elastic constants C _ij and the velocity of sound in 3C-SiC and 2H-SiC crystals are calculated in the framework of the Keating model. The third-order elastic constants C _ijk for 3C-SiC are determined from the dependences of the second-order elastic constants C _ij on the pressure p.     

Quantum-chemical calculations of the piezoelectric characteristics of boron nitride and carbon nanotubes

The piezoelectric characteristics of boron-nitride and carbon nanotubes were calculated. The electronic structure of nanotubes was studied using the quantum-chemical semiempirical MNDO method within a molecular-cluster model. The piezoelectric constants e _zzz, e _xzz, and e _xxx of boron nitride nanotubes of two structural modifications (n, n) (n = 5, 6, ..., 9) and (n, 0) (n = 6, 7, ..., 12) were calculated. The values of the piezoelectric constants e _zzz of tubular boron nitride are found to be close in order of magnitude to the respective values obtained using nonempirical calculation methods. The piezoelectric constant e _xzz of a (6, 6) carbon nanotube doped with substitutional point defects was calculated.     

Determination of elastic constants of trigonal crystals by the rectangular parallelepiped resonance method

We present a theoretical method to calculate the resonance frequencies of a rectangular parallelepiped of a trigonal (D₃, C_3v, D_3d crystal, and apply it to determine the elastic constants of Al₂O₃ by the rectangular parallelepiped resonance (RPR) method. We demonstrate complete agreement between observed and calculated resonance spectra up to the thirty-ninth mode. The determined elastic constants of Al₂O₃ agree well with previous data. This study offers a new tool for the determination of elastic constants of a trigonal crystal.     

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：     

Studying the dielectric, electromechanical, and elastic properties of K1 − x (NH4) x H2PO4 mixed crystals

Temperature dependences of the longitudinal permittivity, piezoelectric coefficient d ₃₆, and elastic constant c ₆₆ ^E of K_{1 ? x} (NH₄) _x H₂PO₄ mixed crystals are studied experimentally. A microscopic model is proposed for crystals of the K_{1 ? x} (NH₄) _x H₂PO₄ type that includes the piezoelectric contribution to the effective pseudospin cluster Hamiltonian. Dielectric elastic and electromechanical properties of these crystals with ammonium concentrations x below 0.40 are calculated in a wide temperature range using the cluster approach. The calculation results are in qualitative agreement with experimental data.     

Theories of elastic properties and elastic waves of equal phase velocities in crystals

A survey is made of pairs of heteronormal planar elastic waves, which can propagate in an unlimited crystal medium and have equal theoretical values of the phase velocity, using Voigt elastic moduli. Such pairs are chosen for which it is possible that the theoretical equality of velocities will be disturbed when using another theory of the elastic properties of crystals with generally different tensors of material constants (for example Kuvshinskij J. V., Aero E. L.: Fiz. tv. tela5 (1963), 2591). In such a case, a comparison of the measured velocities of a suitable pair of waves can help to decide between the two theories. Pairs of waves are found for 12 non-piezoelectric crystal classes. Among such pairs it is easy to find pairs of waves of the same properties for piezoelectric crystal classes.     

Optical and acoustic properties of 33PbIn1/2Nb1/2O3-35PbMg1/3Nb2/3O3-32PbTiO3 single crystals in an electric field

The influence of different conditions of applying a dc electric field (0 < E < 4 kV/cm) on the behavior of optical transmission and on the acoustic parameters (sound velocity and attenuation) in the [001]- and [011]-oriented single crystals 33Pb(In_1/2Nb_1/2)O₃-35PbMg_1/3Nb_2/3O₃-32PbTiO₃ existing near the morphotropic phase boundary has been investigated. It has been found that the optical transmission, sound velocity, and attenuation sharply change near the phase transition in a narrow range of electric fields for any method of their applying. In the field applied along [001], the change in the sound velocity due to the phase transition is 1.5 times greater than that in the field applied along [011]. This is caused by a larger contribution of the piezoelectric effect to the elastic modulus determining the sound velocity along [001] as compared to [011]. It has been shown that the number, symmetry, and stability of the phases formed in the field depend on the conditions of applying the field.     

Grüneisen parameter and thermal expansion of V3Si and V3Ge

The Grüneisen parameter and lattice thermal expansion of the A-15 compounds V₃Si and V₃Ge at room temperature are evaluated on the basis of the method due to Brugger and Fritz [1] from the third order elastic constants reported earlier [2]. The calculated values are compared with available experimental values and are found to fit satisfactorily.     

Determination of the elastic constants by coherent neutron scattering in polycrystals

It is shown that elastic constants which usually can be determined in single crystals only may be measured in polycrystals by inelastic coherent neutron scattering. Measurements are reported for polycrystalline samples of aluminium, copper and stainless steel. The method is best suited for the determination of the elastic constants connected with transverse phonons.     

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     

Construction of a dynamical matrix for an HCP crystal using phonon data at the symmetry points of the Brillouin zone and elastic constants

General analytical expressions are obtained for the dynamical matrix D(k) and the elastic constants C _ik in an HCP crystal in terms of the Born-von Karman (BvK) parameters. An analytical method is proposed for constructing D(k) on the basis of data about the phonon frequencies ω _i (N) at the symmetry points of the Brillouin zone and the elastic constants C _ik . A number of relations between the values of ω _i (N) and C _ik are presented for conventional interaction models. It is shown that the standard method for determining BvK parameters by fitting them to experimental phonon spectra in HCP lattices is, as a rule, ambiguous, whereas the analytical method proposed allows one to find all the solutions of the problem. The methods developed are illustrated by the construction of dynamical matrices for Tb, Sc, Ti, and Co.     

Ligand hyperfine interaction in Gd<Superscript>3+</Superscript> tetragonal centers in CaF<Subscript>2</Subscript> and SrF<Subscript>2</Subscript> and the structure of the impurity nearest surroundings

ENDOR experimental spectra of Gd³⁺ tetragonal impurity centers in CaF₂ and SrF₂ crystals were used to determine the superhyperfine interaction (SHFI) constants of the impurity with ¹⁹F nuclear spins of its first coordination sphere and the compensator ion. The distances in the Cd³⁺F₉ complex were estimated within the model of isotropic SHFI constants suggested in [1]. An analysis of the data on the SHFI and spin-Hamiltonian constants [2] in terms of the superposition model indicates significant changes in the contributions (due to the Gd³⁺ mixed states) to these parameters for the tetragonal centers in comparison with the corresponding contributions for the cubic and trigonal centers in the same crystals.