Sign inversion of the rotatory power and topology of the surface of gyration of αNiSO4·6H2O

The sign inversion point of the rotatory power of the gyrotropic crystals α-NiSO₄·6H₂O (λ _l=503 nm at 300 K) has been established. The topology of the gyration surface varies greatly in the vicinity of λ _l. We have demonstrated the possibility of using this method of spectrophotometric polarimetry for precise monitoring of the mounting of a gyrotropic crystal in the system “polarizer-crystal-analyzer.” Fiz. Tverd. Tela (St. Petersburg) 40, 1608–1609 (September 1998)     

Role of surface phenomena in the magnetoresistivity of polycrystalline manganites La1−x CaxMnO3

The dc electrical resistivity and magnetoresistivity of polycrystalline manganites La_1−x Ca_xMnO₃ (x=0–0.3) are investigated as functions of the temperature, magnetic field and electric field, along with the microwave surface resistance. The investigations show that the dc electrical resistivity and magnetoresistivity are governed by the surface properties of the intergranular boundaries. The dc electrical resistivity is observed to decrease substantially (tenfold) for a comparatively small electric field (E⋟100 V/cm). Estimates are obtained for the internal electrical resistivity of the granules, the thickness of the contact layer (which depends on the temperature and the magnetic field), and the height of the potential barrier between the interfaces separating the surface layer and inner layer of a granule. Fiz. Tverd. Tela (St. Petersburg) 40, 1881–1884 (October 1998)     

Growth of crystallites consisting of C60 molecules on heated (100)Mo

The initial stages of growth of films of C₆₀ molecules on a (100)Mo surface are studied by high-resolution Auger spectroscopy and atomic force microscopy under ultrahigh vacuum conditions. It is shown that at T<750 K, after a specific coating with molecular density 1.5×310¹⁴ cm⁻², which the authors term a high-temperature (HT) monolayer, has formed on the surface, crystallites in the form of “towers” with flat tops grow on the surface. The fraction of the area occupied by towers depends strongly on the substrate temperature and the flux density of the molecules on the surface but is virtually independent of the exposure time. At temperatures _T>760 K the C₆₀ molecules making up the crystallites desorb, while the molecules making up the HT monolayer decompose, and the carbon released is dissolved in the interior of the substrate. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 12, 969–972 (25 June 1998)     

Donaldson Invariants of Product Ruled Surfaces¶and Two-Dimensional Gauge Theories

Using the u-plane integral of Moore and Witten, we derive a simple expression for the Donaldson invariants of product ruled surfaces Σ _g ×S ², where Σ _g is a Riemann surface of genus g. This expression generalizes a theorem of Morgan and Szabó for g=1 to any genus g. We give two applications of our results: (1) We derive Thaddeus' formulae for the intersection pairings on the moduli space of rank two stable bundles over a Riemann surface. (2) We derive the eigenvalue spectrum of the Fukaya–Floer cohomology of Σ _g ×S ¹. Received: 22 July 1999 / Accepted: 12 June 2000     

Polymorphism of biperiodic stripe domain structures

Magnetic-field-induced polymorphism of biperiodic stripe domain structures of films with a positive anisotropy constant and easy axis parallel to the normal to the surface is studied. A symmetry classification of the observed types of domain structures is performed, and the phase diagram of the films in the (H _⊥, H _∥) plane, where H _⊥ and H _∥ are, respectively, the components of the magnetic field vector perpendicular and parallel to the normal to the surface, is determined. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 701–706 (10 May 1998)     

Thermal expansion of thin C60 films

The thermal expansion coefficient a and structure of C₆₀ films with thickness t∼3–10 nm were investigated in the temperature interval from room to liquid-nitrogen temperature by electron-optical methods. The thermal expansion coefficient was determined from the temperature shift of the diffraction maxima in the electron diffraction patterns. The objects of investigation were epitaxial C₆₀ films condensed in vacuum on a (100) NaCl cleavage surface and oriented in the (111) plane. A surface-induced size effect in the thermal expansion coefficient was observed. It was established that as t decreases α _f increases and is described well by the relation α _f=17·10⁻⁶ K⁻¹+8.3·10⁻⁵ nm K⁻¹ t ⁻¹. This relation was used to estimate the linear expansion coefficient α _s of the C₆₀ surface in the (111) plane as α _s=60·10⁻⁶K⁻¹, which is several times larger than the bulk value. The experimental results agree satisfactorily with the theoretical calculations of the mean-square displacements of molecules located in a region near the surface. Zh. éksp. Teor. Fiz. 114, 1868–1875 (November 1998)     

Effect of constant-energy surface anisotropy on the thermoelectric figure-of-merit of the n-Bi2 (Te,Se,S)3 solid solutions

A study is reported of the thermoelectric and galvanomagnetic properties of n-Bi₂Te_3−x−y Se_xSe_y solid solutions for 0.12⩽x⩽0.36 and 0.12⩽y⩽0.21 within the 80–300 K temperature region. The thermoelectric figure-of-merit Z has been found to correlate with the parameters of the many-valley energy-band model including anisotropic carrier scattering. It is shown that a decrease in the constant-energy surface anisotropy and scattering anisotropy results in a growth of Z for optimum carrier concentrations in the solid solution. Fiz. Tverd. Tela (St. Petersburg) 41, 187–192 (February 1999)     

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.     

Dynamic magnetic permeability of a thin, high-T c superconducting wafer

The field dependence of the vibrational contribution to the dynamic magnetic permeability μ _V(H) is calculated for a thin (of thickness d∼λ) high-T _c superconducting wafer in a magnetic field parallel to the surface. The resulting curves are plotted on the basis of an exact numerical analysis of the vortex structures both for the thermodynamic-equilibrium vortex lattice and in the presence of pinning forces and the Bean-Livingston surface barrier. It is shown that the μ _V(H) curves are highly sensitive to the size factor (d/λ) and exhibit abrupt changes corresponding to a change in the number of vortex rows. The equilibrium μ _V(H) curve is found to be similar in its general behavior and absolute value (obtained with allowance for the distribution of grain sizes and with appropriate values of λ and ϰ) to the experimental μ _V(H) curve plotted at nitrogen temperature for fine-grained YBa₂Cu₃O_x with grain diameters 〈D〉∼λ in an increasing magnetic field. It is established that the main cause of the experimentally observed irreversible behavior of the μ _V(H) curves during cyclic variation of the applied magnetic field is the existence of a surface barrier to the exit of vortices from the superconductor. The lower limit H _min(B) of stability of the mixed state in the presence of an ideal surface barrier in a thin, high-T _c superconducting wafer (d∼λ) is determined, along with the range of the vortex state (H _max-H _min) for a fixed number of vortices in micrometer-size grains of the investigated YBaCuO samples. Fiz. Tverd. Tela (St. Petersburg) 39, 1943–1947 (November 1997)     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Use of surface acoustic waves for analysis of gases and surface processes induced by them

An analytical expression for the magnitude of the “response” of surface acoustic waves (SAWs) to gases is obtained. It is tested experimentally. The main features of the detection of gases by means of SAWs are predicted theoretically and confirmed experimentally. The SAWs in coated and uncoated gas sensors are compared. A technique for using SAWs to determine the relative changes in the density (Δρ/ρ) and the elastic moduli (ΔC ₁₁/C ₁₁ and ΔC ₄₄/C ₄₄) of films upon the adsorption (desorption) of gases is proposed. The possibility of using this technique to analyze adsorption and desorption processes is demonstrated. The adsorption properties of polycrystalline, thermally deposited palladium films before and after low-temperature vacuum annealing, as well as unannealed Pd and Pd:Ni films, are compared. The prospects of using SAWs to detect gases and to study surface processes induced by them are discussed. Zh. Tekh. Fiz. 68, 73–81 (February 1998)     

Luminescence detection of multiphoton ionization-fragmentation of the molecular CrO 4 2− anions adsorbed on the surface of dispersed SiO2

It is shown that luminescence detection of multiphoton ionization-fragmentation of the molecular CrO ₄ ²⁻ anions adsorbed on the surface of dispersed SiO₂ is possible under excitation with the fundamental frequency of a Nd:YAG pulsed laser (λ=1.064 μm). The structure and the process of formation of the adsorbed complexes under thermal activation of the surface and the nature of luminescence transitions in CrO ₄ ²⁻ anions are studied in detail. It is shown that luminescence is excited as a result of the recombination of photoelectrons and ionized chromate ions. Multiphoton ionization of the ions occurs under three-photon resonance conditions. The resonance level is an antibonding state of the adsorption complex formed with the participation of an oxygen vacancy on the SiO₂ surface. The dynamics of the multiphoton luminescence excitation process includes autoionization (stimulated by intercomplex electronic excitation) in superexcited states, fragmentation of chromate anions, and annealing of surface oxygen vacancies. The rate equations for three-photon-resonance multiphoton ionization are studied. The cross sections for two-and one-photon transitions on the nonresonance steps of multiphoton absorption are obtained. It is concluded that the nonlinear polarizability of the donor-acceptor adsorption bond in “chromate anion-oxygen vacancy” complexes is very important. Zh. éksp. Teor. Fiz. 111, 1748–1774 (May 1997)     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Diffusion and surface energy barrier for labile oxygen in YBa2Cu3O7−δ

A study is made of the isotope exchange kinetics of tracer oxygen atoms between the gas phase and the CuO_1−δ plane in the YBa₂Cu₃O_7−δ crystal under isochronous and isothermal annealing. The parameters of the surface energy barrier for oxygen atoms are found. Fiz. Tverd. Tela (St. Petersburg) 39, 42–48 (January 1997)     

Observation of a correlation between the dependences of the radiative decay time and intensity of the impurity core-valence luminescence on excitation energy in K1−x CsxCl and Rb1−x CsxCl mixed crystals

A study of the spectral and kinetic parameters of impurity core-valence luminescence (CVL) excited by synchrotron radiation in K_1−x Cs_xCl and Rb_1−x Cs_xCl mixed crystals is reported. The dependences of the intensity and radiative decay time τ of impurity CVL on exciting photon energy hν have been found to be correlated. It is concluded that the observed τ = f(hv) relation originates from nonradiative decay of core excitations near the surface, which govern also the excitation spectral features in this spectral region. Fiz. Tverd. Tela (St. Petersburg) 41, 1973–1975 (November 1999)     

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.     

Field-induced phase transitions in magnetooptical films with a small positive anisotropy constant

We study phase transitions induced by a static magnetic field in magnetically uniaxial films with a small positive anisotropy constant. The phase diagram of these objects is determined in the H _∥-H _⊥ plane, where H _∥ and H _⊥ are, respectively, the components of the magnetizing field along and perpendicular to the surface normal. The stability boundary is located for all of the main types of domain configurations observed: a simple stripe domain structure, a stripe domain structure with periodic bending by surface distortions in the profile of the domain walls, and hexagonal lattices of cylindrical magnetic bubbles. Zh. éksp. Teor. Fiz. 111, 283–297 (January 1997)     

Backscattering of low-energy (0–8 eV) electrons by a silicon surface

An experimental apparatus and method for investigating elastic and inelastic backscattering (180°) of low-energy (0–8 eV) monoenergetic electrons by a solid surface are described and the first results are presented for the reflection of electrons by samples of pure single-crystalline silicon with a polished surface (Si), doped p-type single-crystalline silicon with a porous surface (Si-p) as well as H₂O and H₂O₂ passivated porous samples, Si-p + H₂O and Si-p + H₂O₂. A structure due to the excitation of surface plasmons has been observed for the first time in the loss spectra. Features corresponding to a resonance excited state of molecular nitrogen adsorbed on the surface of porous silicon have been observed in the constant residual energy spectra. Zh. Tekh. Fiz. 67, 103–108 (May 1997)     

Quantum deformation of lorentz group

A one parameter quantum deformationS _μ L(2,ℂ) ofSL(2,ℂ) is introduced and investigated. An analog of the Iwasawa decomposition is proved. The compact part of this decomposition coincides withS _μ U(2), whereas the solvable part is identified as a Pontryagin dual ofS _μ U(2). It shows thatS _μ L(2,ℂ) is the result of the dual version of Drinfeld's double group construction applied toS _μ U(2). The same construction applied to any compact quantum groupG _c is discussed in detail. In particular the explicit formulae for the Haar measures on the Pontryagin dualG _d ofG _c and on the double groupG are given. We show that there exists remarkable 1-1 correspondence between representations ofG and bicovariant bimodules (“tensor bundles”) overG _c . The theory of smooth representations ofS _μ L(2,ℂ) is the same as that ofSL(2,ℂ) (Clebsh-Gordon coefficients are however modified). The corresponding “tame” bicovariant bimodules onS _μ U(2) are classified. An application to 4D ₊ differential calculus is presented. The nonsmooth case is also discussed.     

Inequalities for a unified family of Voigt functions in several variables

The classical Voigt functions occur frequently in a wide variety of problems in astrophysical spectroscopy, emission, absorption and transfer of radiation in heated atmosphere, and plasma dispersion, and indeed also in the theory of neutron reactions. Here, in the present paper, by applying several known upper bounds for the first-kind Bessel function J _ν (x) given recently by (for example) Landau, Olenko and Krasikov, sharp bounding inequalities are obtained for the unified multivariable Voigt function V _μ,ν (x; y) in terms of the confluent Fox-Wright function ₁ψ₀ and its incomplete variant ₁ψ₀. Connections of the unified multivariable Voigt function V _μ,ν (x; y) with other unifications and generalizations of the classical Voigt function are also briefly pointed out.