Inverse problems in the theory of electrostatic energy analyzers. I

General formulas are derived for reconstructing two-dimensional Laplace fields from specified focusing and dispersion characteristics in the plane of symmetry. The electrode configuration is determined for an energy analyzer with ideal focusing of a fan beam. The parameters of the plane trajectories, their shape, and their energy dispersion are determined. Zh. Tekh. Fiz. 69, 128–131 (September 1999)     

Adhesion of metals and semiconductors analyzed by a dielectric formalism

This paper discusses a model of the adhesive interaction of metals and semiconductors, based on a dielectric formalism and using the concepts of collective excitations — plasmons of the electron-ion system. Expressions are obtained in terms of the jellium model in the longwavelength approximation for the adhesion energy and the adhesive interaction force and are determined via the dispersion dependences of the energies of surface plasma oscillations for various materials whose surfaces are separated by a gap of arbitrary magnitude. The adhesion energies and the adhesive interaction forces are calculated for a number of simple and transition metals and semiconductors, and the adhesion characteristics are also obtained for the contact of the given materials with an insulating medium. Fiz. Tverd. Tela (St. Petersburg) 39, 964–967 (June 1997)     

A study of the determination of grain boundary diffusivity and energy through the thermally grown oxide ridges on a Fe-22Cr alloy surface

Abstract

The grain boundaries (GBs) present in polycrystalline materials are important with respect to materials behaviour and properties. During the transient stage of oxidation, the higher GB diffusivity results in heterogeneous oxidation structures in the form of oxide ridges that emerge along the alloy GBs. In an attempt to delve into the more fundamental aspects of the GBs, such as GB energy, the size of the oxide ridges was quantitatively measured by atomic force microscopy on the post oxidation surface of a Fe-22 wt % Cr alloy after an oxidation exposure at 800 °C in dry air. The GB diffusivity was calculated utilising the ridge size data and the relationship between the GB diffusivity and the GB characteristics was determined. Furthermore, the GB energy was calculated from the GB diffusivity data, also to make comparison with the data available in the literature. The absolute value of the calculated GB energy was quite close to the values reported in the literature. However, compared to the extremely low temperature (0 K) data-set from the literature, the data-set obtained from this study showed much less spread. The smaller variation range may be attributed to the higher temperature condition (1073 K) in this study.     

Formation of a high-current discharge plasma in metal vapor

A method of converting the energy of a capacitive store into the energy of a high-current gas discharge in aluminum vapor is investigated. The spatial and temporal characteristics of the gas-discharge plasma are studied. The electron temperature, density of charged particles, and conductivity of the plasma are determined. Zh. Tekh. Fiz. 69, 134–137 (November 1999)     

Calculation of the force characteristics of a multi-coil suspension of a superconducting sphere

The theory presented in the accompanying paper [Ref. 1: Zh. Tekh. Fiz. 67(1), 3 (1997); Tech. Phys. 42, 1 (1997)] for the calculation of the magnetic field and the force characteristics of an electromagnetic suspension for a superconducting body is used to carry out specific calculations of the force characteristics of a multi-coil suspension of a superconducting sphere. Formulas are obtained for the dependence of the force and the stiffness, from which it is possible to approach the problem of the stable suspension of a superconducting sphere in the field of a system of circular currents. The problem of determining the magnetic field at the sphere is analyzed and the conditions are found for which it is less than the critical field. Zh. Tekh. Fiz. 67, 10–16 (January 1997)     

Dispersing of a charged drop in an electrostatic field

The characteristics of the breakup of a charged drop in a uniform electrostatic field are calculated on the basis of Onsager’s principle of minimum dissipation of energy in nonequilibrium processes. The ranges of the physical parameters where daughter droplets are emitted from two tips and from one tip of an unstable parent drop and when emission is completely absent are found. The dimensionless radii, charges, and specific charges of the daughter droplets are determined. Zh. Tekh. Fiz. 69, 26–30 (December 1999)     

Single-particle thermal diffusion of charged colloids: Double-layer theory in a temperature gradient

The double-layer contribution to the single-particle thermal diffusion coefficient of charged, spherical colloids with arbitrary double-layer thickness is calculated and compared to experiments. The calculation is based on an extension of the Debye-Hückel theory for the double-layer structure that includes a small temperature gradient. There are three forces that constitute the total thermophoretic force on a charged colloidal sphere due to the presence of its double layer: i) the force F _W that results from the temperature dependence of the internal electrostatic energy W of the double layer, ii) the electric force F _el with which the temperature-induced non-spherically symmetric double-layer potential acts on the surface charges of the colloidal sphere and iii) the solvent-friction force F _sol on the surface of the colloidal sphere due to the solvent flow that is induced in the double layer because of its asymmetry. The force F _W will be shown to reproduce predictions based on irreversible-thermodynamics considerations. The other two forces F _el and F _sol depend on the details of the temperature-gradient-induced asymmetry of the double-layer structure which cannot be included in an irreversible-thermodynamics treatment. Explicit expressions for the thermal diffusion coefficient are derived for arbitrary double-layer thickness, which complement the irreversible-thermodynamics result through the inclusion of the thermophoretic velocity resulting from the electric- and solvent-friction force.     

Calculations of potential of mean force: application to ion-pairs and host–guest systems

ABSTRACT

We report the calculation of the potential of mean force (PMF) of different types of associations by various techniques: two no biased methods (thermodynamic integration and finite difference thermodynamic integration), a constraint biased technique (adaptive biasing force) and an umbrella biased method (umbrella sampling). We apply these methodologies to the association between two methane molecules in water, to the formation of an ion pair in water and to the formation of an insertion complex between a macrocycle and a cation. The different PMFs are compared to each other on the basis of the depth of the free energy minimum and on the location of different specific points.     

Current-voltage characteristics of extended Josephson junctions with viscous magnetic-flux transport

A theory that describes the current-voltage characteristics of extended Josephson junctions is built. The width of the junctions is much larger than the mean free path of a single fluxon, with the length of the path determined by energy dissipation in the junction. Explicit analytic expressions are derived for the maximum supercurrent in the junction and the low-voltage asymptotic behavior of the current-voltage characteristics. Zh. éksp. Teor. Fiz. 112, 910–925 (September 1997)     

On a Mathematical Framework for the Constitutive Equations of Anisotropic Dielectric Relaxation

Three classes of time-domain non-relativistic anisotropic dielectric constitutive equations of increasing generality are discussed. In each class dissipativity is ensured by the choice of a class of convolution kernels in the D-to-E constitutive equation expressing the electric field E in terms of the electric displacement field D. Defining properties of the inverse (E-to-D) kernels and their Fourier-Laplace transforms (complex dielectric functions) are determined by inversion of the D-to-E constitutive equation. By this procedure it is shown that dielectric functions of the dipolar dielectrics are tensor-valued Bernstein functions while the dielectric functions of the Drude-Lorentz type are tensor-valued negative definite functions. The properties of the complex dielectric permittivities are also determined for either class. The theory is applied to an exhaustive review of empirical response functions of real dielectric materials encountered in the literature. Each class of convolution kernels is consistent with existence of a conserved energy, but in one case a strictly dissipative energy can be constructed.     

Some effects of the electrostatic interaction of water drops in the atmosphere

The electric field at the surface of two conducting spherical charged particles and their interaction force are calculated. It is shown that as particles carrying like charge approach each other, the force changes sign and becomes attractive. The case where the charge on each particle varies as the square of its radius is an exception (repulsion at any distance between the particles). Self-similar asymptotic solutions for the interaction force and energy are found for particles of identical size. For a pair of charged water drops falling simultaneously in the atmosphere, a numerical simulation shows that a drop formed by coalescence of the pair may be subject to the Rayleigh instability. Zh. Tekh. Fiz. 69, 12–17 (December 1999)     

Using an atomic force microscope in the surface modification regime to determine the migration energy of surface defects

The lines of constant force and the profiles of the horizontal force component are calculated for the scanning of the tip of an atomic force microscope over a surface vacancy in a closepacked lattice with allowance for atomic displacements. The character of the lines of force is studied in all three scanning regimes that arise for different values of the force: without modification of the surface by the tip, migration of a single vacancy by a single interatomic distance in the direction opposite to the motion of the tip, and “dragging” of a vacancy by the tip. It is shown that the profiles of the horizontal force component can be used to calculate the activation energy for surface migration of a vacancy. An estimate is made of the scanning force for which these effects may be observed experimentally. Zh. Tekh. Fiz. 69, 104–110 (August 1999)     

Exact matrix elements for general two-body central-force interactions,expressed as sums of products

ABSTRACT

In a manner similar to but distinct from concurrent tensor efforts in electronic structure, it is shown that the Laplace transform can serve as a generator for a sum-of-products (SOP) form that allows one to write essentially any function of distance between two particles (i.e. any central force potential) as an exact two-body matrix. In particular, exact expressions for the Coulomb, Yukawa and long-range Ewald two-body operators are evaluated in a band-limited (Sinc function) basis. The resultant exact, full-basis, SOP representations for these interaction potentials – acting in conjunction with an external harmonic confining field – are validated via comparison with energy eigenstate solutions obtained via an independent calculation based on separation of variables. The new two-body matrix representations may have substantial impact in any of the many disciplines in which pair-wise central force interactions are relevant – especially, electronic structure and dynamics.     

Relative contribution of various factors to the formation of the energy spectrum of fast, medium-energy, charged particles and ions transmitted through a thin target with fluctuations of the target thickness

The characteristics of the energy spectra of kiloelectron-volt protons transmitted through a free-standing foil are investigated theoretically and experimentally as functions of the angle of incidence of the beam on the target. Analytical expressions for the average characteristics of the transmitted-particle energy spectrum are determined for the case of small-angle scattering. The combined influence of various factors affecting the formation of the energy spectra is taken into account: systematic stopping of particles in the medium, fluctuations of the particle energy losses in inelastic collisions, bending of the particle trajectories due to multiple elastic scattering, and fluctuations of the target thickness. It is shown that the contributions of these factors to the width of the transmitted-particle energy spectrum depend differently on the angle of incidence of the beam on the target surface. On the basis of this differentiation it is inferred from the experimental dependence of the width of the energy spectra of kiloelectron-volt protons transmitted through a free-standing foil on the angle of incidence of the beam that fluctuations of the particle energy losses in inelastic collisions are the predominant factor in the formation of the proton energy spectra. Zh. Tekh. Fiz. 67, 81–93 (May 1997)     

Anisotropic momentum transfer in low-dimensional electron systems in a magnetic field

In low-dimensional systems with an asymmetric quantizing potential, an asymmetric electron energy spectrum ε(p)≠ε(−p), where p is the electron momentum, arises in the presence of a magnetic field. A consequence of such an energy spectrum is that momentum transfer to the electron system in mutually opposite directions in the presence of an external perturbation is different. Therefore, in the presence of a standing electromagnetic wave momentum is transferred from the wave to the electrons, which gives rise to a new type of electromotive force. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 8, 551–555 (25 October 1997)     

Topological characteristics of electronic spectra of single crystals

The paper considers the topological characteristics of dispersion functions ɛ_s(p) in energy bands in single crystals related to classical electron trajectories in uniform magnetic fields. Specifically, the topological properties of open trajectories in p-space on various energy levels within one energy band and related physical effects are described. Zh. éksp. Teor. Fiz. 112, 371–378 (July 1997)     

Anomalous electron emission spectra and polarization phenomena in a lead magnesium niobate single crystal

The time dependences of the intensity and the energy positions of fine-structure of the spectra of anomalous electron emission from a polarized lead magnesium niobate (PMN) single crystal irradiated with soft x-rays are investigated experimentally. It is shown that the relaxation time of the electret charge can be determined from the graphs of these dependences, and the depth distribution of the potential in the surface layer of the sample can be determined from the profile of the anomalous electron emission spectrum. Estimates of the fields in the surface layers of a polarized PMN single crystal, obtained from the characteristics of the anomalous electron emission spectra, agree with data obtained by electrophysical research techniques. Fiz. Tverd. Tela (St. Petersburg) 39, 1446–1451 (August 1997)     

Definitions and units in mechanics

With displacement, time, and force as basic undefined physical quantities, other physical quantities are defined as combinations of two vector quantities and one scalar quantity. Combinations include multiplication and division of vectors by vectors, scalars by vectors, and scalars by scalars. Defined quantities are vectors, scalars or quaternions, depending on directions of vectors in the definitions. Division of a vector by a vector is equivalent to multiplication of vectors divided by a scalar. The unit of a vector (or scalar) is itself a vector (or scalar) quantity. Thesquare meter (a vector) differs from meter ² (a scalar), and the cubic meter (a scalar) is different frommeter ³ . The characteristics of displacement, time, and force are considered known from experience.     

Short-wavelength asymptotic behavior of the Burgers turbulence spectrum

Using a third-order structure function, an asymptotic expression is obtained for the stationary energy spectrum in the dissipative region of Burgers turbulence excited by a random external force. It is shown that in contrast to the case of turbulence described by a homogeneous Burgers equation, the spectrum contains a parameter characterizing energy transfer into the small-scale region. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 6, 383–386 (25 March 1998)     

Inverse problems of magnetostatics and the design of double-focusing electron magnetic spectrometers

A method is proposed for the design of double-focusing electron magnetic spectrometers by using direct methods of solving inverse problems of magnetostatics. The conditions for double-focusing electron magnetic spectrometers in a system with two pairs of electromagnetic coils are determined for the first time in a third-order model, which appreciably improves the main optical characteristics of the device: the resolution and the luminosity. This system is used to design a real energy analyzer with a free toric chamber in the third-order model. Zh. Tekh. Fiz. 67, 66–69 (November 1997)