The elastic dielectric

Macroscopic field equations, boundary conditions and equations of state are derived for the non-linear, macroscopic elastic and dielectric response of an insulator. A centrosymmetric polynomial representation of order four is introduced for the energy density; the equations of state for the electric field and stress tensor are then deduced as polynomials of degree three in the displacement gradients and electric displacement field. The results are applied to the special case of m3m material symmetry.

A finite, point-charge model of a centrosymmetric ionic crystal is introduced and used to determine 0°K microscopic expressions for the electric field and stress tensor equation of state coefficients introduced in the macroscopic analysis. The results are used to calculate the full set of second and third-order non-linear coefficients for NaI, based on a Born-Mayer potential and the 4·2°K elastic stiffness data of Claytor and Marshall.     

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.     

Dielectric and anelastic relaxation of crystals containing point defects

A theory is developed which describes the linear, reversible, time-dependent response of a crystal containing point defects to stress or electric fields, respectively known as anelastic and dielectric relaxation. Such relaxation occurs because of the redistribution of the defects among sites which are initially equivalent, but which becomes inequivalent in the presence of the external field. The macroscopic behaviour of such a crystal is found to be describable in terms of the symmetry which can be assigned to the defect. This defect symmetry determines whether or not the crystal will undergo dielectric or anelastic relaxation and, if relaxation can occur, which specific coefficients of elastic compliance or electric susceptibility show the relaxation effect. The latter information, called the ‘selection rules’ tells, in effect, which combination of stress or electric field components is capable of redistributing the defects. Tables are given for these selection rules for all possible defect symmetries in each of the 32 crystal classes. It is also shown that a hitherto unobserved phenomenon of piezoelectric relaxation may occur; the selection rules for this effect are also given.

Aside from its symmetry, the defect can be described as an electric dipole in terms of a suitable dipole moment vector μ, and as an ‘elastic dipole’ in terms of a tensor λ. It is shown that the defect symmetry determines the number of independent components of μ and λ. Finally, a thermodynamic theory is developed which permits calculation of the relaxation strengths for those compliance, susceptibility, and piezoelectric coefficients which undergo relaxation, in terms of the independent components of μ and λ. Applications of the theory to specific cases are then reviewed.     

Investigation of covalency in CrI3 using Mössbauer spectroscopy of129I

The principal components of the electric field gradient tensor, the transferred hyperfine magnetic field and the isomer shift have been measured in ferromagnetic CrI₃ using the 27.8 keV Mössbauer resonance in¹²⁹I. From these hyperfine parameters we have determined the electron transfer and spin transfer coefficients for CrI₃ and compared these with the ones deduced for other Cr compounds.     

Electric field gradient for interstitial positive muons in fcc metals: An AB Initio calculation of size effect

The electric field gradients (EFGs) resulting from interstitial point defects in fcc metals have been investigated. The defect induced charge density, used to evaluate the valence effect EFG, is calculated self-consistently in the density functional formalism. An ab initio calculation of the size effect EFG is carried out for a positive muon at an octahedral site in the fcc lattice in the elastic continuum model. The components of the strain field tensor are evaluated assuming the lattice of dressed point ions interacting through the screened Coulomb potential. No adjustable parameter has been used. The theoretical results are in good agreement with the experimental values within experimental uncertainties. It is emphasized that both the strain and conduction electron contributions are equally important in the estimation of the electric field gradient.     

Verification of the interpretation of the polarizing effect with piezoelectric cuts

The change in resonant frequency of piezoelectric cuts caused by a d.c. electrical voltage applied to the exciting electrodes of the cuts has been interpreted as brought about mainly by the change in the values of elastic constants due to the d.c. polarizing field. The present paper shows that the agreement between the theoretical and experimental values of the polarizíng effect is reasonably good and thus verifies the suggested interpretation. The new values of some tensor components representing the change in the values of elastic compliances of -quartz in the d.c. electric field are also presented.The authors are greatly indebted to Mr. A. Houry of the Computer Centre of the University of Khartoum for his kind assistance in the necessary calculations.     

Wave processes in elastic-viscoplastic media with dislocations

The mechanisms of plane harmonic wave propagation in homogeneous and interfaced elastic-viscoplastic media are considered using the field theory of defects with kinematic identities of a dislocation-containing elastic continuum and dynamic equations of the gauge theory of dislocations. The reflection and refraction coefficients were determined for displacement waves and defect field waves with the defect field characterized by the dislocation density tensor and flux density tensor. The dependence of the coefficients on the parameters of the interfaced media is analyzed.     

Second-order electroelastic tensor of cubic KAl(SO4)2·12H2O

The second-order electroelastic tensor {Z_ijklmn}, which describes the variation of the elasticity tensor under the influence of an electric field in centrosymmetric crystals, has been completely determined on cubic KAl(SO₄)₂·12H₂O by measuring the electric-field-induced shift of ultrasonic resonance frequencies. The state of resonance was detected by diffraction of light through the standing ultrasonic grating formed in the state of resonance. The necessary resolution of 10^-9 for the relative frequency change was achieved employing a phase-sensitive amplification of the modulated part of the diffracted light.All main components of the second-order electroelastic tensor possess values of about -15·10^-10 NV^-2. The negative sign indicates a general weakening of the elastic bonds by an electric field. A distinct anisotropy is observed in accordance with point symmetry m3.     

Gravitational Waves Interacting with a Spinning Charged Particle in the Presence of a Uniform Magnetic Field

The equations which determine the response of a spinning charged particle moving in a uniform magnetic field to an incident gravitational wave are derived in the linearized approximation to general relativity. We verify that 1) the components of the 4-momentum, 4-velocity and the components of the spinning tensor, both electric and magnetic moments, exhibit resonances and 2) the co-existence of the uniform magnetic field and the GW are responsible for the resonances appearing in our equations. In the absence of the GW, the magnetic field and the components of the spin tensor decouple and the magnetic resonances disappear.     

Complete elastic tensor through the first-order transformation in U2Rh3Si5

The complete elastic tensor of U(2)Rh(3)Si(5) has been determined over the temperature range of 5-300 K, including the dramatic first-order transition to an antiferromagnetic state at 25.5 K. Sharp upward steps in the elastic moduli as the temperature is decreased through the transition reveal the first-order nature of the phase change. In the antiferromagnetic state the temperature dependence of the elastic moduli scales with the square of the ordered moment on the uranium ion, demonstrating strong spin-lattice coupling. The temperature dependence of the moduli well above the transition indicates coupling of the ultrasonic waves to the crystal electric field levels of the uranium ion where the lowest state is a singlet. The elastic constant data suggest that the first-order phase change is magnetically driven by a bootstrap mechanism involving the ground state singlet and a magnetically active crystal electric field level.     

Structure of elastic and electric fields induced near the boundary of a LiNbO3 crystal in the course of recording of photorefractive gratings through the photovoltaic mechanism

This paper reports on the results of the investigation into the structure of elastic and electric fields induced near the boundary of the X cut of a lithium niobate crystal during the formation of a photorefractive grating with a wave vector K parallel to the threefold symmetry axis due to the photovoltaic effect. The elastic and electric fields induced by the photorefractive grating and the changes in the components of the dielectric impermeability tensor of the lithium niobate crystal at the frequency of the light wave are calculated using numerical analysis. It is demonstrated that light waves with orthogonal polarizations can effectively interact at a photorefractive grating formed near the electrically short-circuited boundary of a lithium niobate crystal.     

Orientational Relaxation in Ferroelectrics of Tetragonal Symmetry

The energy absorption caused by rotation of the spontaneous and induced polarization vectors in external longitudinal alternating-sign stress field is calculated for the barium titanate ferroelectric of tetragonal symmetry. The acoustic absorption coefficient, the internal friction, and the E effect together with their frequency and orientational dependences are derived in terms of elastic and piezoelastic constants, components of the electrostriction tensor, and rotational dissipation coefficients. The given dissipation type can dominate in ferroelectric magnets with strong coupling of their elastic, electrical, and magnetic subsystems.     

Vacuum correlators of the electromagnetic field and the Casimir-Polder forces in the field of a cosmic string

Vacuum correlators of the electric and magnetic fields are calculated in the geometry of a cosmic string. Formulas for the vacuum expectation values for the squares of field components are derived. The forces acting on an atom due to the vacuum fluctuations (Casimir-Polder forces) are investigated. For atoms with isotropic tensor of polarizability these forces are attractive with respect to the string. In the anisotropic case, depending on the eigenvalues of the polarizability tensor, the Casimir-Polder forces can be either attractive or repulsive.     

57Fe Mössbauer spectra for tetrahedral cage hopping with correlated electric field gradient reorientation

Mössbauer relaxation spectra are calculated for tetrahedral cage hopping of ⁵⁷Fe with correlated jumps of an axial electric field gradient. We give an analytical solution allowing a separation of elastic and quasielastic contributions. Asymmetric powder patterns arise from quasielastic contributions due to anisotropic hopping with respect to the electric field gradient tensor.     

Frequency addition in crystals having an inversion center

A nonlinear-effect tensor is obtained on the basis of microscopic theory for crystals having an inversion center in a constant electric field. The form of this tensor and the dependence of its components on the direction of the applied field are studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 12, No. 6, pp. 107–110, June, 1969.     

Elastic dipoles in the model of single-crystal and amorphous copper

The characteristic values of the elastic polarizability tensor components of point defects in crystalline and amorphous copper, which determine changes in the elasticity tensor components upon introduction of defects, have been found using the molecular dynamics method. A relation of the elastic polarizability tensor with the main parameter of the interstitialcy theory, i.e., shear susceptibility, has been established. An analysis of the elastic polarizability tensors of defects in crystalline and amorphous copper has demonstrated that, in a noncrystalline structure, there are specific atomic configurations that under deformation manifest themselves similarly to elastic dipoles (interstitial atoms in a dumbbell configuration) in single-crystal copper.     

The signature of the nuclear quadrupole interaction in continuous phase transitions

A correlation between the largest component of the electric field gradient (EFG) tensor, V_zz, and its asymmetry parameter η is discovered in a series of compounds which exhibt phase transitions. It is shown that all the EFG tensor components depend linearly on a single control parameter. A convenient way to unravel this correlation from V_zz, η-data is presented.     

Nonlinear anisotropic thermal expansion in problems of crystal growth from the melt

The paper considers the influence of the temperature dependence of the coefficients of thermal expansion of a single crystal on thermoelastic stresses arising during crystal growth from the melt. We obtain zero stress conditions in an axisymmetric temperature field of axial symmetry and derive approximate expressions for the components of the stress tensor in a cylindrical crystal when this dependence is taken into account.