Investigation of the mass dependence of self-diffusion coefficients by molecular dynamics calculations: binary non-isotopic mixtures of atoms

Extensive molecular dynamics calculations have been used to study systematically for the first time the dependence of the self-diffusion coefficients D_i (i = 1,2) in binary equimolar non-isotopic atomic mixtures (mole fractions x ₁ = x ₂ = 0.5, reduced temperature T? = 1.6) on the particle mass ratio m?₂ = m ₂/m ₁ (1 ≤ m?₂ ≤ 16.5) in the ranges of reduced particle number density 0.15 ≤ n? ≤ 0.85 and reduced length parameter 0.5 ≤ σ?₂₂ ≤ 2.0 for a Lennard-Jones 12-6 potential. The calculated D_i values can be represented quantitatively by an exponential estimate of the form: D_i = D ⁰ _i (m?₂) ^ex _i . D ⁰ _i are the self-diffusion coefficients in reference mixtures with m?₂ = 1. The observed dependence of the exponents ex _i (m?₂, n?, σ?₂₂) on m?₂, n? and σ?₂₂ is discussed in this paper.     

Investigation of the mass dependence of self-diffusion coefficients by molecular dynamics calculations: comparison with the Enskog theory

The dependence of the Enskog self-diffusion coefficients D_i,E on mass ratios m_i* = m_i/m₁ in hard sphere mixtures is described by exponential expressions of the form D_i,E = D⁰ _i,E(m*₂)eX_i,E in the case of binary mixtures and D_i,E = D⁰ _iE (m*₂)eX_i,E(m*₃)eXt_i,E in the case of ternary mixtures. D⁰ _i,E are the self-diffusion coefficients in reference mixtures with m*₂ = m*₃ = 1. ex_i,E (i = 1,2) and ext_i,E (i = 1,2,3) are the so called Enskog exponents of binary and ternary mixtures, respectively. Their dependence on particle mass and diameter, mole fraction, density and temperature is discussed and compared with corresponding results of molecular dynamics calculations.     

Concentration and temperature dependence of the refractive index of ethanol-water mixtures: Influence of intermolecular interactions

The temperature and concentration dependence of the refractive index, n _D(x, T) , in ethanol-water mixtures agrees with previous data in the ethanol-rich concentration range. The refractive index versus concentration x determined at 20 ^° C shows the expected maximum at about 41 mol% water (22 mass% water). The temperature derivative of the refractive index, dn _D /dT, shows anomalies at lower water concentrations at about 10 mol% water but no anomaly at 41 mol% water. Both anomalies are related to intermolecular interactions, the one in n_D seems to be due to molecular segregation and cluster formation while the origin of the second one in dn _D /dT is still not clear.     

Symmetry coupling coefficients for the double groups C n*, D n* and T*

By coupling linear combinations of the |JM ket vectors which transform as irreducible representations of C_n *, D_n * and T*, symmetry coupling coefficients for these groups are calculated. Also, ? coefficients as defined by Golding [1] are evaluated.     

Diffusion of Au in amorphous Zr x Ni100−x alloys studied by Rutherford Backscattering Spectrometry

The diffusion coefficients (D) of Au in three binary amorphous Zr _x Ni_100–x (x=61, 65, and 67) alloys were measured in the temperature range 549–623 K using the technique of the Rutherford Backscattering Spectrometry (RBS). The D values were found to lie in the range 1.0×10^–21–9.0×10^–20 m²s^–1 for different alloys. The activation energy (Q) was calculated in each case on the basis of an observed Arrhenius temperature dependence of D. The activation energy was found to scale with the crystallization temperature (T _x) of the alloy. Other published measurements for Au diffusion in amorphous Zr-Ni alloys also appear to follow the scaling relation between Q and T _x.     

Influence of isotopic substitution on the diffusion and thermal diffusion coefficient of binary liquids

The mutual mass diffusion coefficient (D) and the thermal diffusion coefficient ( D _T) of the liquids acetone, benzene, benzene-d ₁, benzene-d ₃, benzene-d ₅, benzene-d ₆, benzene- ¹³C₆, n-hexane, toluene, 1, 2, 3, 4-tetrahydronaphtalene, isobutylbenzene, and 1, 6-dibromohexane in protonated and perdeuterated cyclohexane have been measured with a transient holographic grating technique at a temperature of 25 ^°C. The mass diffusion coefficient shows a pronounced concentration dependence. Perdeuteration of cyclohexane only leads to marginal changes of the mass diffusion coefficient. The Stokes-Einstein equation describes the limiting tracer diffusion coefficients well if the solute molecule is smaller than the solvent. It is not capable to describe the small isotope effect of a few percent. On the other hand, the isotope effect, which is independent of concentration, is in agreement with the Enskog theory, that does not provide the absolute value of the mass diffusion coefficient of the liquid mixtures. The thermal diffusion coefficient of all the binary mixtures shows a moderate and almost linear concentration dependence. Its isotope effect, which is the change of D _T upon deuteration of cyclohexane, varies with mole fraction. The thermophoretic force acting on any tracer molecule in cyclohexane changes by the same amount when cyclohexane is perdeuterated, irrespective of the magnitude of the thermophoretic force before deuteration. This change of the thermophoretic force is equal but of opposite sign to the difference between the thermophoretic forces acting on cyclohexane and perdeuterated cyclohexane as tracers in any of the above liquids.     

The gauge transformation of the modified KP hierarchy

In this paper, we firstly investigate the successive applications of three elementary gauge transformation operators T_i with i = 1,2,3 for the mKP hierarchy in Kupershmidt-Kiso version, and find that the gauge transformation operators T_i can not commute with each other. Then two types of gauge transformation operators T_D and T_I constructed from T_i are proved that they can commute with each other. In particular, T_I is introduced for the first time in the literature. And the successive applications of T_D and T_I in the form of T^(n,k), which is the product of n terms of T_D and k terms of T_I, are derived in three cases for different n and k. At last, the corresponding successive applications of T_D and T_I on the eigenfunction Φ, the adjoint eigenfunction Ψ and the tau functions τ₀ and τ₁ are considered.     

Desorption kinetics and surface diffusion of potassium,rubidium and cesium on a silicon(111)7 × 7-surface

Using pulsed atomic beam technique and a surface ionization ion microscope, the desorption kinetics and the surface diffusion of the alkalis potassium, rubidium and cesium were investigated on a Si(111)7 × 7-surface at extremely low alkali coverages. In the temperature range 1120 … 800 K, the mean adsorption lifetime τ(T) = τ₀ · exp(E_desⁱ/kT) and the mean diffusion length x(T) - defined in the equilibrium between adsorption, diffusion and desorption - were measured. From these data the diffusion constant D(T) = D₀ · exp(-E_diff/kT) was obtained as D = x^?2/τ. For temperatures T ? 750 K, the diffusion constant was calculated from nonstationary alkali concentration profiles using the Boltzmann-Matano method. From the temperature dependence of these quantities the parameters of desorption (E_des,ⁱ τ₀) and surface diffusion (E_diff, D₀) for K, Rb and Cs on Si(111) were obtained. The values of E_diff and D₀ are comparably high and may be interpreted by non-localized diffusion according to a model proposed by Bonzel (Surf. Sci. 21 (1970) 45).     

Crystal symmetry groups and their representations I lattice extensions of point groups in R2 and R3

We classify all point groups in R² and R³ according to their decomposition into m-fold semidirect products of cyclic groups. This product is characterized completely by means of m?1 matrices α⁽¹⁾,…, α^(m?1) with non-negative integer elements. For any arithmetic class [Pⁿ_i] in Rⁿ (n=2, 3) we define the set D(Pⁿ_i, T) of representative translations with the following properties: (a) The elements of D(Pⁿ_i, T) are in one-to-one correspondence with defining relations of Pⁿ_i; (b) D(Pⁿ_i, T) determines uniquely all equivalence classes of the factors of Pⁿ_i over T.We present: (i) a construction of all sets D(Pⁿ_i, T) in R² and R³; (ii) a construction of all algebraic classes of space groups and a derivation of all group operations which transform one algebraic class into another; (iii) a derivation of formulas expressing the multiplication table of any space group by means of the representative translations and matrices α⁽¹⁾,…, α^(m?1). The results (i), (ii) and (iii) are obtained without making use of the notion of non-primitive translations.     

Excess molar volumes, viscosities, and refractive indices for binary and ternary mixtures of {cyclohexanone (1) + N,N-dimethylacetamide (2) + N,N-diethylethanolamine (3)} at (298.15, 308.15, and 318.15) K

Densities ρ, viscosities η, and refractive indices n_D, of the binary and ternary mixtures formed by cyclohexanone + N,N-dimethylacetamide + N,N-diethylethanolamine were measured at (298.15, 308.15, and 318.15) K for the liquid region and at ambient pressure for the whole composition ranges. The excess molar volumes V_m^E, viscosity deviations Δη, and refractive index deviations Δn_D, were calculated from experimental densities and refractive indices. The excess molar volumes are positive over the mole fraction range for binary mixtures of cyclohexanone(1) + N,N-dimethylacetamide (2) and N,N-dimethylactamide (2) + N,N-diethylethanolamine (3) and increase with increasing temperatures from (298.15 to 318.15) K. The excess molar volumes of cyclohexanone (1) + N,N-diethylethanolamine (3) are S-shaped dependence on composition with negative values in the N,N-diethylethanolamine rich-region and positive values at the opposite extreme and increase with increasing temperatures from (298.15 to 318.15) K. The excess molar volumes are positive over the whole mole fraction ranges for the ternary mixtures at all temperatures. Viscosity deviations are negative over the mole fraction range for all binary and ternary mixtures and decrease with increasing temperatures from (298.15 to 318.15) K. Refractive index deviations are negative over the mole fraction range for all binary and ternary mixtures and increase with increasing temperatures from (298.15 to 318.15) K. The experimental data of constitute were correlated as a function of the mole fraction by using the Redlich–Kister equation for binary and , Cibulka, Jasinski and Malanowski , Singe et al., Pintos et al., Calvo et al., Kohler, and Jacob–Fitzner for ternary mixture, respectively. McAllister^'s three body, Hind, and Nissan–Grunberg models were used for correlating the kinematic and dynamic viscosity of binary mixtures. The experimental data of the constitute binaries are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures.     

Photoconductivity of Cu x Ag1−x Cd2InTe4

Summary The prominent photoelectric parameters of the semiconducting solid solutions Cu _x Ag_1−x Cd₂InTe₄ are reported. From the spectral dependence of photoconductivity at room temperature and at 77 K the energy gaps and their thermal coefficients are obtained. The detectivityD ^*, the photocurrent gainG and the carrier lifetime are measured and the carrier mobility is deduced. In order to improve theD ^* characteristics, the analysis of its parameters is also performed. Paper presented at the ?V International Conference on Ternary and Multinary Compounds?, held in Cagliari, September 14–16, 1982.     

Correlations betweenT c andn s/m * (carrier density/ effective mass) in high-T c and organic superconductors

We update our muon spin relaxation studies of the magnetic field penetration depth which show the correlations betweenT _c and the relaxation rate σ αn _s/m ^* (carrier density/effective mass) of hole-doped high-T _c cuprate superconductors (La₂, Sr₃)CuO₄, YBa₂Cu₃O₇ (Y_1−xPr_x)Ba₂Cu₃O₇, and other double and triple layer systems. These studies are extended to the organic superconductor (BEDT-TTF)₂Cu(NCS)₂.     

Scattering of Infraparticles

In the hope of getting some new insight into the infrared problem we study the space-time aspects of electron scattering events in quantum electrodynamics. Localization of electrons is provided by „counters”︁ described by a quasilocal field. An initial n-electron state, prepared in a specified bounded region of space-time, is obtained by applying n electron field operators, smeared over suitable test functions, to the vacuum. The probability that m counters localized in bounded four-dimensional neighbourhoods of the points x₁, …, x_m are triggered, is the vacuum expectation value of a product of two time-ordered products of n electron fields and m counter fields each. These vacuum expectation values are closely related to the Green's functions of the theory. For macroscopic counter separations x_i–x_i we can evaluate the triggering probability with the help of asymptotic methods, starting from the p-space singularities of the Green's functions. We assume the singularity structure of perturbation theory summed over soft photons. As typical examples we analyze one and two electron initial states. The results are those expected for classical particles. For a one-particle state with momentum p, prepared in a neighbourhood of the origin, the probability that counters in x₁. …, x_m are triggered is measurably non-zero only if x₁, …,x_m lie on a ray through O in direction p. The dependence of the probability on the distances ∥x_i – x_i∥ is as given by geometry. Similar results hold for two- particle states, in which case scattering events are seen. Only elastic scattering is considered. The dependence of the scattering probability on the momenta of the four particles involved is given by a factor |M(p, p₂, q₁, q₂)|². M replaces the S-matrix element of the familiar case without infrared problems. The definition of M is a generalization of the reduction formula expression of S in terms of Green's functions. The properties of M are not discussed. Processes involving photons as observed particles are not considered.     

Study of spin-wave dynamics in Fe65Ni35 ferromagnetic via small-angle polarized-neutron scattering

The results of studying the spin dynamics of a classical Fe₆₅Ni₃₅ invar alloy are presented and analyzed. The investigations are performed via small-angle polarized-neutron scattering in the oblique geometry of a magnetic field at various temperatures (T < T _C). This approach is based on the analysis of left-right asymmetry in the magnetic scattering of polarized neutrons. The asymmetry effect arises when the magnetization direction of a sample is inclined with respect to the wave vector of the incident beam. The spin-wave scattering is concentrated within a range bounded by the cutoff angle θ_c determined by the magnetic field: θ _c ² (H) = θ ₀ ² ?(gμ_B H)θ₀/E, where \(\theta _0 = \hbar ^2 \frac{1} {{2Dm_n }}\) , H is the external magnetic field, E is the initial neutron energy, D is the spin-wave stiffness constant, and m _n is the neutron mass. The scattering is blurred by spinwave damping in the vicinity of the cutoff angle. The spin-wave stiffness constant can be obtained from a comparison of the asymmetric contribution to scattering and a model function. The temperature dependence D = D(T) is well defined by the expression D = D ₀ |τ| ^x , where \(\tau = 1 - \frac{T} {{T_C }}\) , x = 0.47 ± 0.01, D ₀ = 137 ± 3 meVŲ, and τ > 0.1 in the entire temperature range. The given method enables us to construct the temperature dependence of the spin-wave stiffness constant with a high accuracy and a small step.     

Capacity of Multivariate Channels with Multiplicative Noise: Random Matrix Techniques and Large-N Expansions (2)

We study memoryless, discrete time, matrix channels with additive white Gaussian noise and input power constraints of the form Y i = ∑ _j H _ij X _j + Z _i , where Y _i , X _j and Z _i are complex, i = 1… m, j = 1… n, and H is a complex m× n matrix with some degree of randomness in its entries. The additive Gaussian noise vector is assumed to have uncorrelated entries. Let H be a full matrix (non-sparse) with pairwise correlations between matrix entries of the form E[H ik H ^* jl] = 1/n C ij D kl, where C, D are positive definite Hermitian matrices. Simplicities arise in the limit of large matrix sizes (the so called large-n limit) which allow us to obtain several exact expressions relating to the channel capacity. We study the probability distribution of the quantity f(H) = log (1+PH ^† SH) . S is non-negative definite and hermitian, with TrS = n and P being the signal power per input channel. Note that the expectation E[f(H)], maximised over S, gives the capacity of the above channel with an input power constraint in the case H is known at the receiver but not at the transmitter. For arbitrary C, D exact expressions are obtained for the expectation and variance of f(H) in the large matrix size limit. For C = D = I, where I is the identity matrix, expressions are in addition obtained for the full moment generating function for arbitrary (finite) matrix size in the large signal to noise limit. Finally, we obtain the channel capacity where the channel matrix is partly known and partly unknown and of the form α; I+ β H, α,β being known constants and entries of H i.i.d. Gaussian with variance 1/n. Channels of the form described above are of interest for wireless transmission with multiple antennae and receivers.     

Temperature dependence of the electrical resistivity of R6(Fe1-xMnx)23 compounds in the temperature range 4.2 to 300 K

The temperature dependence of the electrical resistivity of binary R₆Mn₂₃, R₆Fe₂₃ (R = Y, Dy, Ho, Er, Tm) and pseudobinary R₆(Fe_1-xMn_x)₂₃ (R = Y, Er, Ho) compounds has been determined by a four-probe measuring technique in the temperature range 4 to 400 K.The binary compounds exhibit a prop. T² dependence at low temperatures, while above 100 K a negative curvature of the -T-curves is observed.These experimental results are discussed on the basis of electron-spin wave scattering in the low temperature range and on the basis of s-d scattering in the high temperature range, taking explicitly into account the temperature dependence of the chemical potential.The pseudobinary compounds generally exhibit a decreasing resitivity with increasing temperature, combined with a high residual resistivity. These facts are explained by the so-called strong scattering mechanism and the appearance of “quasilocalized” states.     

Current-voltage characteristics of YBa2Cu3O7−x single crystals and Kosterlitz-Thouless transition

The nonlinear I-V characteristic (V(I)) of YBa₂Cu₃O_7−x single crystal was investigated near the transition from the resistive to the superconducting state in the absence of a magnetic field. A modulation Fourier analysis at temperature T* (the maximum of the amplitudes of the higher (n>1) harmonics of the response voltage) was used to determine an analytic dependence V(I) which accurately describes the experimental results (direct measurements and harmonics) in the range of currents I<30 mA (j<310 A/cm²). It is shown that at T* the power approximation of the I-V characteristic V∼I ³ is only found in the low current density limit (j≪j ₀=140 A/cm²). The results are interpreted in terms of the Kosterlitz-Thouless (KT) transition model. It is established that T* corresponds to the temperature of the KT transition T _KT, which means that T _KT can be determined directly. The deviation of V(I) from a power dependence is caused by the nonlogarithmic variation of the vortex interaction energy as a function of the distance between them. Fiz. Tverd. Tela (St. Petersburg) 40, 202–204 (February 1998)     

ESR Investigation of Gd3+ Ion Introduction into the Structure of Simple and Double Tungstates

In this paper the spectra of Gd³⁺ ions studied by electron spin resonance (ESR) in four types of tungstate crystals KY(WO₄)₂, CdWO₄, CsLa(WO₄)₂ and La₂(WO₄)₃ are discussed. The tungstate crystals were grown by the low-temperature gradient Czochralski technique with Gd₂O₃ addition in melt. The estimation of spin Hamiltonian (SH) parameters was realized using an original simulation program developed. The parameters of crystalline field in oxide crystals are comparable with Zeeman interaction so the solution of the Schr?dinger equation was realized numerically. We have estimated 36 SH parameters from ESR angular diagrams of Gd³⁺, including g _x , g _y , g _z , g _i (where i = 1, …, 6), B _m ⁿ , C _m ⁿ (where m = 2, …, 6, n = 0 (or 1 for C _m ⁿ ), …, m), and the Euler angles. The positions of Gd³⁺ ions in the crystal structures, the charge compensation and the influence of lattice parameters on the SH parameters B ₂ ⁰ and B ₂ ² are discussed in this paper as well. Authors' address: Nikolay V. Cherney, Institute of Inorganic Chemistry, Russian Academy of Sciences, Lavrentyev av. 3, Novosibirsk 630090, Russian Federation     

标定粉末照相指数的一个新图解法

本文叙述了标定德拜-谢乐照相指数的一个新图解法。利用三条低角度衍射线的sin²θ值和该晶体的密度,在A-C空间画一系列条件直线及等原子曲线。三条条件直线和一条等原子曲线的交点直接决定了晶胞的大小和晶胞内所含的原子数或位形单位数。这个方法可应用于四方晶系和六角晶系。 关键词：