Thermoelectric power in quasi-two-dimensional systems with scattering of current carriers by phonons

The thermopower α in electron systems with a quasi-two-dimensional energy spectrum is investigated in the relaxation-time tensor approximation. The longitudinal and transverse components of the thermopower are calculated for scattering of the current carriers by different types of phonons. It is shown that the anisotropy of the thermopower in such systems is substantial. The dependence of a on the ratio of the Fermi level ɛ _F to the half-width ɛ ₀ of the one-dimensional conduction band is considered. For scattering by acoustical and nonpolar optical phonons, the thermopower changes sign: α becomes positive for ɛ _F<ɛ ₀. Comparison of the theory with published experimental data demonstrates good qualitative agreement. Fiz. Tverd. Tela (St. Petersburg) 39, 1857–1858 (October 1997)     

Dielectric properties of single-crystal deuterated triglycine sulfate (DTGS) in ultra-weak low-and infra-low-frequency electric fields

The complex permittivity ɛ* is studied with separate readings for ɛ′ and ɛ″ at low and infralow frequencies and ultraweak fields. The effective conductivity λ is determined. An Arrhenius dependence is observed for ln ɛ′(1/T), ln ɛ″(1/T), and ln λ(1/T), both in the paraphase and in the polar phase. It is proposed that the conductivity of crystalline DTGS in the paraphase is an ion jump conductivity. Fiz. Tverd. Tela (St. Petersburg) 41, 1073–1075 (June 1999)     

Random Homogenization and Singular Perturbations¶in Perforated Domains

The paper considers the singularly perturbed Dirichlet problem −ɛΔu ^ɛ+u ^ɛ=f in a randomly perforated domain Ω^ɛ, which is obtained from a bounded open set Ω in R ^N after removing many holes of size ɛ ^q . The perforated domain is described in terms of an ergodic dynamical system acting on a probability space. Imposing certain conditions on the domain, the behaviour of u ^ɛ when ɛ→ 0 in Lebesgue spaces L ⁿ (Ω) is studied. Test functions together with the Birkhoff ergodic theorem are the main tools of analysis. The Poisson distribution of holes of size ɛ ^p with the intensity λɛ^{− r} is then considered. The above results apply in some cases; other cases are treated by the Wiener sausage approach. Received: 15 December 1999 / Accepted: 14 April 2000     

Dielectric and photoelectric properties of Pb(Mg1/3Ta2/3O3 crystals

The temperature dependence of the dielectric constant ɛ and the spectral dependence of the photoconductivity of Pb(Mg_1/3Ta_2/3)O₃ crystals are investigated. The width of the band gap (3.4 eV) is determined. It is found that above the temperature of the maximum of the dielectric constant, its reciprocal 1/ɛ varies with temperature first quadratically and then according to a linear law, as is characteristic of ferroelectrics with a smeared phase transition. The smearing parameter of the transition estimated from the experimental data is close to the value calculated assuming the absence of long-range order in the arrangement of the Mg and Ta ions. Fiz. Tverd. Tela (St. Petersburg) 40, 109–110 (January 1998)     

Dielectric properties of Sn2P2S6 crystals as a function of their growth conditions

The behavior of the permittivity near a phase transition in Sn₂P₂S₆ crystals of different technological quality is studied. It is established that, in high-resistance crystals, where an internal electric field is formed by the screening of spontaneous polarization in the polar phase, long-time relaxation of ɛ is observed in a temperature range ∼2 K above T _max. This relaxation and change in the form of the maximum of ɛ′(T) at a phase transition are attributed to an internal electric field induced by the volume space charge formed in regions near the surface. It is established that the existing differences in the properties of Sn₂P₂S₆ crystals are due to deviations from stoichiometry, arising during growth and synthesis of the crystals. Fiz. Tverd. Tela (St. Petersburg) 41, 1456–1461 (August 1999)     

Originalarbeiten / Travaux originaux / Original Papers

An account is given of a variational calculation to estimate the amplitudes of resonance factorsɛ in a recent theory to describe the enhancement of crystalline field potentials by conduction electrons in heavy rare earth metals. It is demonstrated that the values ofɛ obtained by minimising the energy of interaction between conduction electrons and rare earth ions are consistent with those previously used to form a comparison with experiment. These latter values were obtained by maximising theA ₂ ⁰ crystal field coefficient with respect toɛ. Consistency is exhibited in both the sign and order of magnitude of the resonance amplitudes and renders the theory parameterless. The values ofɛ show an approximate linear dependence with the number of electrons in the incompletef shell of the rare earth ions.     

Effect of gamma irradiation on the dielectric properties and electrical conductivity of the TlInS<Subscript>2</Subscript> single crystal

The effect of gamma irradiation on the dielectric properties and ac conductivity of a TlInS₂ single crystal with a layered structure has been investigated in the frequency range from 5 × 10⁴ to 3.5 × 10⁷Hz. It has been shown that gamma irradiation of the TlInS₂ single crystal with a dose of 10⁴–2.25 × 10⁶ rad leads to a considerable increase in the dielectric loss tangent tanδ, the real part ɛ′ and imaginary part ɛ″ of the complex permittivity, and the ac conductivity σ _ac across the layers. It has been established that, for all gamma irradiation doses, the TlInS₂ single crystal is characterized by the dielectric loss due to electrical conduction up to a frequency of 10⁷ Hz and by the relaxation loss at a higher frequency. Irradiation of the TlInS₂ single crystal results in an increase in the dispersion of tan δ, ɛ′, and ɛ″. It has been demonstrated that, as the gamma irradiation dose is accumulated in the TlInS₂ single crystal, the density of localized states near the Fermi level N _F increases (from 5.2 × 10¹⁸ to 1.9 × 10¹⁹ eV⁻¹ cm⁻³).     

Influence of γ irradiation on the electrical conductivity and dielectric properties of β TlInS2 in the temperature range of the incommensurate phase

The influence of γ irradiation on the electrical conductivity σ, the dielectric permittivity ɛ, and the dielectric loss tangent tanδ of β-TlInS₂ crystals is investigated in the temperature range of the incommensurate phase. It is established that γ irradiation lowers the values of ɛ and tanδ over the entire investigated temperature range and decreases the maxima of the σ(T) and tanδ(T) curves in the vicinity of the transition temperature T _c, but does not alter the transition temperature. Fiz. Tverd. Tela (St. Petersburg) 39, 1088–1090 (May 1997)     

Features of the hydrodynamic pressure field of an electric explosion in an equilibrium gas-liquid medium

The hydrodynamic features of an electric explosion in a bubble gas-liquid mixture are studied in the equilibrium approximation of the medium for the case of fine gas bubbles when the initial size of the latter ranges from units to tens of micrometers, as is observed when actual liquids contain natural gas. In mathematically modeling the electric-explosion processes, the characteristics of the hydrodynamic field were calculated, taking into account the finite size of the plasma piston for which the quasi-wave equation with the nonlinear barotropic equation of state of the mixture was numerically integrated, using an explicit finite-difference scheme in an ellipsoidal coordinate system. It is established that the presence of gaseous inclusions manifests itself when the gas concentration is ɛ ₀≳10⁻⁴, whereas appreciable nonlinear effects appear when ɛ ₀≳5×10⁻³. Zh. Tekh. Fiz. 68, 7–12 (July 1998)     

Thermal boundary layer for non-Newtonian fluid

Summary Analytical and numerical solutions for the momentum and thermal boundary layer equations of a non-Newtonian power law fluid are presented. The flow is assumed to be under the influence of an external magnetic fieldB (x) applied perpendicular to the surface and an electric fieldE(x) perpendicular toB(x) and the direction of the longitudinal velocity in the boundary layer. For the power law fluid it is assumed that the shear stress is proportional to then-th power of the velocity gradient andn is called the flow index. The variations of the velocity fieldf′, the temperature field θ, the shear stress on the surfaceτ _W , the displacement thicknessδ ₁ and the momentum thicknessδ ₂ with the magnetic-field parameter γ, the flow indexn, the heat transfer indexS and the Prandtl number Pr are studied. It is found that, if the outer flow velocityU(x) (potential flow) is proportional to the arc lengthx raised to a powerm, then the similarity solution for the thermal boundary layer equation is possible only whenm=1/3, which represents flow past a wedge of included angle π/2. It is established that the temperature of the wedge increases with the increase of γ, Pr,S and the decrease ofn. In general the magnetic field can be used as a heater for the surface of the wedge.     

Heat conductivity and the Lorentz number of the Sm1−x GdxS “black” phase

Measurement of the heat conductivity and electrical resistivity of two Sm_1−x Gd_xS compositions with x=0.1 and 0.14 is reported within the 80–300 K interval. An analysis of experimental data on the electronic component of heat conductivity permits a conclusion that the d subband of “heavy” carriers in the conduction band of these materials lies above the s “light”-carrier subband. Fiz. Tverd. Tela (St. Petersburg) 41, 26–29 (January 1999)     

Effect of γ irradiation on the low-temperature electrical conductivity and dielectric properties of TlGaSe2 crystals

Electrical conductivity and dielectric properties of single-crystal TlGaSe₂ have been studied as a function of γ irradiation dose in the 100–280 K range including the existence of an incommensurate phase. Anomalies in the form of maxima have been observed in the σ=f(T), tan δ=f(T), and ɛ=f(T) curves at the points of transition from the paraphase to incommensurate (IC) phase, T _i, and from the IC to commensurate phase, T _c. The increase in the quantities σ, tan δ, and ɛ observed initially with increasing irradiation dose is followed by their strong decrease and disappearance of the anomalies. It has been established that γ irradiation does not affect the phase transition temperatures T _i and T _c. Fiz. Tverd. Tela (St. Petersburg) 40, 1328–1331 (July 1998)     

Effect of infrared radiation on the plasticity of solid hydrogen

This paper reports on the first results obtained from the investigation of the effect of IR radiation on the low-temperature (1.8 ≤ T ≤ 4.2 K) plasticity of solid hydrogen. It has been found that, when the samples are exposed to IR radiation, a drastic increment Δɛ_IR of the elongation per unit length ɛ (which was preliminarily achieved under a continuously applied mechanical stress σ = const) occurs without an increase in the temperature of the samples. It has been revealed that the effect observed both in the case of normal hydrogen (n-H₂, 75% o-H₂) and in the case of parahydrogen (p-H₂, ∼0.2% o-H₂) only for a sufficiently high power of the IR radiation source has a threshold character. The reverse deformation of solid hydrogen is observed after the irradiation with a flux of IR photons is completed: the quantity ɛ rapidly decreases to values provided only by the applied load. The appearance of jumps in the increment of deformation Δɛ_IR ⁱ is interpreted as a consequence of the existence of the fundamental IR absorption band for solid hydrogens. It has been established that, depending on the time t of exposure of the samples to IR radiation, the change in the quantity Δɛ_IR ⁱ (t) obeys the logarithmic law, which is characteristic of the dislocation creep and observed in the case of unirradiated hydrogen. It has also been found that, under multiple relatively long-term exposure to IR radiation, the constant α of the logarithmic creep of n-H₂ abruptly decreases, whereas the strength of both the n-H₂ and p-H₂ samples increases significantly, which indicates their explicit hardening (instead of the expected “superplastic” behavior due to the exposure to IR irradiation).     

Stability range for a flat graphene sheet subjected to in-plane deformation

The effects of the elastic deformation on the mechanical and physical properties of graphene are a subject of intensive current studies. Nevertheless, the stability range for a flat graphene sheet subjected to in-plane deformation is still unknown. Here, this problem is solved by atomistic simulations. In the three-dimensional space corresponding to the ɛ _xx , ɛ _yy , and ɛ _xy components of the planar strain tensor, the surface bounding the stability range for a flat graphene sheet has been constructed disregarding the thermal vibrations and the effects of boundary conditions. For the points of this surface, force components T _x , T _y , and T _xy have been calculated. It is shown that graphene is structurally stable up to strains on the order of 0.3–0.4, but it is unstable with respect to the shear in the absence of stretching forces. In addition, graphene cannot preserve its flat shape under the effect of a compressive force since it has zero flexural stiffness.     

Synthesis, structure, and dielectric properties of KH2PO4 fractal aggregates

Macroscopic fractal aggregates of KH₂PH₄ (KDP) measuring up to 500 μm have been obtained. The fractal structure forms as a result of the precipitation of KDP particles from a supersaturated aqueous solution in the presence of a temperature gradient followed by a diffusioncontrolled mechanism of aggregation. The electron-microscopic analysis performed has shown that the fractals are formed predominantly from crystallites of the tetragonal modification measuring ∼1 μm. The dielectric constant (ɛ) of fractal KH₂PO₄ has been measured in the temperature range 80–300 K. A characteristic anomaly has been discovered on the ɛ(T) curve in the vicinity of 122 K, which attests to a ferroelectric phase transition. The absolute value of ɛ is significantly smaller than the components ɛ ₁₁ and ɛ ₃₃ for KH₂PO₄. Fiz. Tverd. Tela (St. Petersburg) 41, 2059–2061 (November 1999)     

Investigation of the electromagnetic fields at a jump in the dielectric constant

The passage of a plane wave through an inhomogeneous flat insulator layer of arbitrary thickness without absorption is considered. A method is given for solving the problem in terms of elementary functions, which reduces the number of independent parameters of the layer. A similarity principle for layers having equivalent reflectivities is described. It is shown that the electric field intensity can increase to infinity near the critical point where ɛ=0. Zh. Tekh. Fiz. 69, 5–9 (August 1999)     

Regularities in the variation of the rate of stepped creep in polyethylene with different supermolecular structure

The study of stepped creep, previously discovered with micron-size deformation increments (ɛ) of polymers, in the form of a variation of the rate near the average value is continued. A scheme based on a laser interferometer was used to record the creep; this made it possible to perform precise measurements. Attention was focused on the degree of scatter of the rate h in the process of deformation of polyethylene fibers. It is shown that the creep rate of textured fibers is extremely nonuniform and pulsates continuously, forming beats of different periods, i.e., deformation jumps of different height. The ratio of h of the highest to the lowest rate for arbitrarily chosen small increments of the deformation has a maximum near the start of the “flow” stage and prior to fracture. The h-ɛ curve shifts along the deformation scale as the polymer structure changes, but the form of the curve and the overall level of h change very little. It is also established that the value of h for identical deformations is higher in more highly oriented polymers, and the value of h is higher in cross-linked structures than in unmodified structures. It is proposed that h reflects not only the deformation heterogeneity, but also influences crack formation during the creep process. Fiz. Tverd. Tela (St. Petersburg) 39, 580–585 (March 1997)     

Reduction of Quantum Systems with Arbitrary First Class Constraints and Hecke Algebras

We propose a method for reduction of quantum systems with arbitrary first-class constraints. An appropriate mathematical setting for the problem is the homology of associative algebras. For every such algebra A and subalgebra B with augmentation ɛ there exists a cohomological complex which is a generalization of the BRST one. Its cohomology is an associative graded algebra Hk ^*(A,B) which we call the Hecke algebra of the triple (A,B,ɛ). It acts in the cohomology space H ^*(B,V) for every left A module V. In particular the zeroth graded component $Hk^{0}(A,B)$ acts in the space of B invariants of $V$ and provides the reduction of the quantum system. Received: 15 June 1998 / Accepted: 25 January 1999     

Relaxation of the conductivity of CsI-Tl after excitation by subnanosecond electron pulses

The pulsed conductivity is investigated for a CsI-Tl crystal having a Tl⁺ concentration N=8×10¹⁷cm⁻³ and excited by an electron beam (0.2 MeV, 50 ps, 10²–10⁴ A/cm ²). It is shown that the amplitude of the conduction current pulse is almost an order of magnitude lower than for “pure” CsI crystals irradiated under like conditions. The conduction current relaxation time is preserved up to τ=100 ps in this case. Under the experimental conditions, therefore, the lifetime of electrons in the conduction band is controlled by trapping at Tl⁺ centers. The electron capture cross section at a Tl⁺ center is determined: σ=7×10⁻¹⁶ cm², which agrees in order of magnitude with estimates of the capture cross section for a neutral trapping center. Fiz. Tverd. Tela (St. Petersburg) 40, 66–67 (January 1998)