Percolation Thresholds and Phase Transitions in Binary Composites

The metal–insulator and metal–superconductor phase transitions related to the percolation thresholds in two-component composites are considered. The behavior of effective conductivity σ _e in the vicinity of both thresholds is described in terms of the similarity hypothesis. A one-to-one correspondence between the equations derived for σ _e in both critical regions is found for randomly heterogeneous systems.     

To the theory of conduction of binary composites

The relationship between the local electric field strength in a binary composite, as an example, with its macroscopic characteristics of a nonuniform medium (effective conductivity σ _e and the derivatives of σ _e with respect to the concentrations and conductivities of the individual components) is discussed. It was demonstrated that the determination of all these parameters in a numerical experiment makes it possible to obtain a detailed information on the properties of the effective conductivity σ _e , especially near the percolation threshold, a metal-dielectric phase transition.     

Electric conductivity of inhomogeneous two-component media in two dimensions

The electric conductivity is calculated for regular inhomogeneous two-component isotropic medium in which droplets of one phase with conductivity σ₂ are embedded in another, with conductivity σ₁. An expression is formulated that can be used in many different situations and is of particular relevance in the case where the relative proportion of the components is temperature-dependent and varies over a wide range. Behavior of the effective conductivity depends on the spatial arrangements and the shape of the inclusions.     

Influence of the inclusion shape on the conductivity of two-dimensional models of composites

The conductivity of some two-dimensional models of composites with randomly located and oriented dielectric inclusions of various shapes is considered. Exact analytical expressions are obtained for the effective conductivity σ _e at low concentration N of inclusions. The results are compared with the results of the corresponding computer experiment.     

Thermal conduction through loose and granular two-phase materials at normal pressure

The integrated theory derived for the lattice-type dispersions is modified and extended to estimate the effective thermal conductivity of loose and granular two-phase materials at normal pressure assuming an effective continuous media approximation. A comparison of calculated values ofλ _e with the reported experimental results over a wide range of loose and granular two-phase materials shows a good agreement.     

Conductivity of a “colored” plane

The conductivity of a “colored” plane, i.e., a plane divided into domains differing in conductivity, is calculated. The exact relation between the effective conductivities of the cited and dual (with inverse conductivities) systems is derived for the isotropic case (i.e., the effective conductivity tensor is proportional to the unit matrix). The conductivity of two-colored systems such as a “chessboard” or triangular lattice is exactly calculated to give σ=(σ₁σ₂)^1/2. The particular case of a “hexagon, ” as well as the duality relations for anisotropic systems and for a system in a magnetic field are discussed.     

The influence of phonons on the optical properties and the conductivity of quasi-one-dimensional metals

The frequency dependent conductivity σ(ω) completely taking into account the interaction between electrons is studied. The shape and the temperature dependence of optical absorption near the frequency of a molecular phonon activated due to the interaction with electrons are found. For a system with attractive sign of the e-e backward scattering amplitude g₁<0 an absorption edge near the gap 2Δ in the electronic spectrum is studied. A low frequency conductivity is discussed. The properties under consideration depend essentially on the magnitudes of e-e interactions and are critical to the sign of g₁.     

Rigorous bounds for the complex dielectric constant of a two-component composite

Rigorous bounds are systematically derived for the bulk effective dielectric constant of a two-phase composite material ε_e under various assumptions about the available information. The bounds are drawn for some special cases in the complex ε_e-plane. The question of optimality of the bounds and their connection to solvable microgeometries is discussed. It is shown how linear programming theory can be used to aid in the derivation of these bounds.     

On the two definitions of nuclear surface energy and its calculation in two-component systems

It is shown that when a large nuclear system is in equilibrium there is a minimum in the Gibbs surface energy σ_μ but not generally in the droplet-model surface energy σ_e. Attempts to minimize σ_e result in the non-conservation of neutrons and protons. Nevertheless, σ_e can be calculated from the density distributions that result from the minimization of σ_μ.     

Application of the van der Pauw method to conductivity measurements on mixed ionic-electronic solid conductors

The analysis of four point dc conductivity measurements by the van der Pauw method is generalized to mixed ionic-electronic solid conductors (MSC) with gas electrodes, e.g. doped and reduced CeO₂ in a controlled oxygen atmosphere. If such measurements are done with non-blocking voltage probes, the electronic and ionic currents at the probes do not vanish. The measurement then yields the total conductivity even if the current carrying electrodes are blocking for ions or electrons. By imposing a difference in the gas pressure at the two reversible voltage probes the ionic conductivity can be determined. The currents through the probes are calculated. If the probes are not reversible, then there exist voltage drops on the probes and the four point measurement cannot be used in the above manner to yield the conductivity. To overcome the difficulty that arises with non-reversible probes a four-point measurement with three blocking electrodes (two of which are the voltage probes) is suggested and analyzed. When the electrodes block ions then the electronic conductivity σ_e is measured and when they block electrons, the ionic conductivity σ_X⁺ is determined.     

Scalar quarks: Higher corrections to σtot (e+e− → hadrons)

The next-to-leading corrections to σ_tot (e⁺e^? → hadrons) are calculated in electro-strong models with spontaneously broken colour symmetry. The effective Λ_eff in the Higgs sector, and presumably the mass scale of bound states with constituent scalars, is fairly large.     

Bounds on the effective thermal conductivity of two-phase systems

The weighted geometric mean of resistors considered for determining the effective thermal conductivityK _E of two-phase systems has been optimised. Solutions of the equations lead to a useful set of bounds. When compared with other bounds the present bounds give the better results in estimating the upper and lower values of the effective thermal conductivity of a two-phase system.     

Proton shielding function for hydrogen chloride

For a diatomic molecule the nuclear shielding constant σ(ξ) of either nucleus can be expanded as a power series in the relative displacement from equilibrium ξ. Thus the nuclear shielding function is

where ξ=(r-r _e)/r _e with r the actual bond length and r _e the equilibrium bond length. The σ_e ⁽ⁱ⁾ are molecular parameters. By experimental observation of the temperature dependence of the proton magnetic shielding of hydrogen chloride gas it is possible, after allowing for intermolecular effects, to obtain the values σ_e ⁽⁰⁾=32·48 (±0·33) p.p.m. and σ_e ⁽¹⁾=-100 (±24) p.p.m. for the coefficients of the proton shielding function. Using this data it is possible to show that the isotope shift between H³⁷Cl and H³⁵Cl is about 0·001 p.p.m. By a comparison with earlier results for molecular hydrogen it would appear that in some instances differences in vibrational and rotational averaging may alter chemical shifts between different compounds by amounts considerably larger than the experimental error in chemical shift measurement.     

Thermal conduction in a homogeneous two-phase system

Assuming a regular geometry of dispersed phase (λ ₂) an integrated theory for the effective thermal conductivityλ _e of all kind of two-phase materials (including loose materials) is developed. The flux modification is carried out by considering the effective neighbouring interactions in the solution of Poisson’s equation. A comparison of calculatedλ _e values with the reported experimental results over a wide range of two-phase materials shows a good agreement.     

Effects of Pauli paramagnetism on superconducting fluctuations

We discuss the effects of the Pauli paramagnetism on the excess conductivity σ^fl due to fluctuations of the superconducting order parameter. We derived a formula for σ^fl for a thin film placed in a magnetic field of an arbitrary orientation α. It was found that σ^fl has a universal behavior as a function of some parameterp which depends on α and ΔH=H-H _c. If ΔH is kept constant and σ^fl is measured as a function of α, in the absence of the Pauli paramagnetism σ^fl is maximum when the field is parallel to the film and is minimum when the field is perpendicular. But in high field superconductors due to the effect of the Pauli paramagnetism σ^fl becomes maximum at some intermediate field orientation. We also discussed the excess conductivity in magnetic alloys in which impurity spins are aligned by an external magnetic field. It was shown that in this case one should expect, with certain strengths of the external field, the excess conductivity which is non-monotonic in temperature.     

Low-frequency dispersion of the effective transverse conductivity in inhomogeneous media in strong magnetic field

On crystalline silicon specimens with a nonuniform carrier concentration distribution produced by an optical method, a dispersion of the effective transverse conductivity σ _⊥ ^eff (ω) is observed near the frequency ω≈ω_c=τ _⊥ ^?1 ≡ε/4πσ _⊥ ^eff . At ω<ω_c, an anomalous transverse effective conductivity is observed: σ _⊥ ^eff (ω) is greater than the transverse conductivity of a homogeneous specimen σ _⊥ ^h (ω) (in the frequency range studied in the experiment σ _⊥ ^h (ω) = const). Near ω≈ω_c, the conductivity σ _⊥ ^eff decreases, and, at ω>ω_c it coincides with σ _⊥ ^h .     

SAXD studies on bulk crystallization of nylon 6.I. Changes in crystal structure,heat of fusion,and surface free energy of lamellar crystals with crystallization temperature

Measurements of small-angle x-ray diffraction (SAXD) were performed for nylon 6 samples quenched from the melt at various crystallization temperatures T (°K). The spacing estimated from the position of maximum intensity in a SAXD diagram, which is assumed to be equal to the thickness of lamellar crystals ?, decreases with the decrease of T. The behavior was analyzed in terms of nucleation theory. In applying the theory. the contribution of γ-form crystals for the samples crystallized at lower T was considered. For this purpose wide-angle x-ray diffraction and infrared data obtained for the same samples used in SAXD measurements were used. It was shown that the relation of ? versus T deviates remarkably from the theoretical prediction under the premise that the surface free energy σ_e (ergs/square centimeter) is constant with T. We present an approach to the analysis of the data from the standpoint that σ_e is a parameter changing with T, where σ_e should be interpreted as related to the degree of irregularity of the fold surface of lamellar crystals. The values of σ_e thus obtained increase with increasing undercooling δT, where δT = T_m ? T, with T_m (°K) being the melting point. SAXD data of polyethylene reported earlier by Mandelkern et al. were analyzed from the same standpoint, and it was found that the values of σ_e increase with δT/T_m in a similar manner for both nylon 6 and polyethylene.     

On the fermi velocity and static conductivity of epitaxial graphene

The models of the energy density of states of a metallic or semiconductor substrate, which does not further lead to divergences, have been proposed to calculate the characteristics of epitaxial graphene. The Fermi velocity of epitaxial graphene formed on a metal has been shown to be greater than that in free-standing graphene irrespective of the position of the Fermi level. On the contrary, the Fermi velocity of graphene formed on a semiconductor is lower so that the lower is the Fermi velocity, the closer is the Fermi level to the center of the band gap of the semiconductor. The zero-temperature static conductivity σ of epitaxial graphene has been calculated according to the Kubo-Greenwood formula. The quantity σ_m of undoped graphene on metal has been shown to decrease with an increase in the deviation of the Dirac point ?_D (which coincides with the Fermi level of the system) from the center of the conduction band of the substrate. In the case of the semiconductor substrate, the static conductivity σ_sc turns out to be nonzero and amounts to σ_sc = 2e ²/π?-only under the condition ?_F =?′_D, where ?′_D is the Dirac-point energy renormalized by the interaction with the substrate.     

Theory of the transverse static magnetoconductivity in a two-dimensional electron-phonon system

The theory of the transverse static magnetoconductivity (σ_xx) in a two-dimensional system under the simultaneous influence of electron-phonon and electron-impurity interactions is presented. The memory function technique is employed to obtain explicit expression for σ_xx under conditions appropriate for typical Shubnikov-deHaas measurements. It is shown that σ_xx involves two different effective masses and scattering times, of which one is the scattering time in the absence of the magnetic field. In addition, the Landau level width appears in σ_xx, thus providing an experimental means for extracting the same from a study of the background conductivity.