Superconductivity of ternary rare-earth compounds. III. An analysis of experimental data on the rhodium boride system

In earlier papers by the same authors a theory which discussed the effects of ferromagnetic spin fluctuations on superconductivity was presented. In this paper it is shown that experimental measurements of the phase diagrams and upper critical fields of several pseudo-ternary rare-earth rhodium boride compounds can be explained using the theory. The rare-earth atoms behave magnetically like free 3⁺ ions, and couple weakly to the conduction electrons with a strength that is nearly independent of their atomic number. The rare-earth compounds are typically quite dirty and have very short spin-orbit scattering times. It is predicted that the jump in specific heat in most of these compounds will exceed the BCS value.This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Sciences Division.     

A theory of the upper critical field in quasi-zero-dimensional superconductors

A microscopic theory describing the upper critical field in quasi-zero-dimensional superconductors is presented. The model is applicable to materials in which the superconducting electrons form clusters which are spatially separated from each other. It is argued that in quasi-zero-dimensional superconductors the orbital upper critical field is apt to be very high, and it is predicted that in highly zero-dimensional superconductors the Hinc2 (T) curve will exhibit structure not yet seen experimentally.This work was supported by the U.S. Department of Energy, contract No. W-7405-Eng-82, Division of Materials Sciences, budget code AK-01-02-02-1.     

A possible explanation for the discrepancy in electron persistent current amplitudes: A superfluid persistent current analog

Recently there has been considerable interest in normal electron persistent currents which result from the wave nature of electrons in a normal metal ring for which inelastic electron-phonon scattering has been reduced so that the electron maintains phase coherence around the ring. The application of the current theory of electron transport, which includes the effects of elastic scattering in a disordered potential field, produces an expression which disagrees with the experimental measurements by Webb, et al. In this paper we present an acoustic analog of wave mechanical electrons in a disordered circular waveguide and derive an expression which agrees with the results of the electron persistent current measurements. The acoustic analog shows that the expression derived from electron transport is also correct, but only under conditions which do not correspond to the actual method used in measuring the electron persistent currents. A proposed experiment to test the model using superfluid helium in a disordered scattering field will be presented.     

Influence of multiple scattering on energy loss stragglings for electrons

Elastic multiple scattering for electrons transmitted through carbon foils was studied. The probability distribution for single-nuclear scattering was evaluated using the Born approximation and the electron densities were calculated using the Hartree-Fock approach with the Wigner-Seitz boundary condition. An estimate of the average increase in path length over the depth of penetration was made. Energy loss stragglings for electrons transmitted through carbon foils were calculated and compared with experimental data.     

Generalized debye series for acoustic scattering from objects of separable geometric shape

Summary In a classical paper of 1908, Debye has resolved the electromagnetic field scattered by a dielectric cylinder into a series of waves multiply internally reflected in the cylinder. For acoustic scattering by elastic cylinders, a corresponding series was derived from the conventional solution (obtained by satisfying the overall or global continuity conditions) by Brill and Überall, taking into account mode conversions of longitudinal (L) into transverse (T, shear) waves, or vice versa, upon internal scattering in a some-what involved fashion. In a series of papers, Gérard has shown that this approach could be greatly simplified by introducing local reflection and transmission coefficients at each interface, which is suitable for generalizing the Debye series to the case of elastic waves coupled by the continuity conditions at the external and each of any possible (multiple) internal interfaces of the scattering object. The approach is then applicable to all elastic objects for which surface and interfaces form coordinate surfaces of any separable geometry; the corresponding derivation is given here in the most general fashion, and is concretely illustrated by the examples of an elastic plate, infinite cylinder and sphere.     

Untersuchungen zum Nachweis der Nutzbarkeit elastischer Wechselwirkungsprozesse zwischen niederenergetischen Elektronen und Gasteilchen zur Druckmessung

In the rough and partly in the medium vacuum range collisions and scattering processes of electrons with gas particles influence the motion of slow electrons in an electric field between anode and cathode significantly. After a sufficient number of elastic collisions the electrons move nearly randomly in the electric field with a mean constant drift velocity to their collecting electrode. Using a suitable electrode configuration these interaction processes between electrons and gas particles can be used for the pressure measurement in the upper vacuum pressure range. A gauge construction using this principle is characterised by of a simple electrode structure and electronic equipment. Experimental investigations and numerical calculations are described in this paper.     

Superconductivity of ternary rare-earth compounds

A theoretical discussion of ternary rare-earth compounds which enter the superconducting state at a temperature T _c 1, then ferromagnetically order at T _M < T _c1,is given. The local moments of the rare-earth elements couple to the superconducting electrons so that as T _M is approached from above, the growth of spin fluctuations suppresses the superconductivity, then completely destroys it at T _c2(>T _M ).Expressions for the phase diagram, several thermodynamic quantities, the upper critical field, and the dilution effect are derived.This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Science Division.     

Theory of neutron scattering on local spin fluctuation systems

The cross section for inelastic neutron scattering on local spin fluctuations in dilute alloys likeA1Mn is calculated in the framework of a semiphenomenological theory. It is found that resonance scattering of the conduction electrons strongly enhances the spin fluctuations near (and at) the impurity sites, leading to a peak in the equal-time spin correlation function, the width of which is determined by the spin fluctuation temperature.Most of this work was done during the author's stay at the Institut Max von Laue-Paul Langevin, Grenoble, France.     

Theoretical and experimental study of nanopore drilling by a focused electron beam in transmission electron microscopy

Sub-10 nm nanopores drilled by a focused electron beam in a transmission electron microscope are widely used in solid-state nanopore devices for DNA translocation. However, there still remains much controversy surrounding the drilling mechanism. In order to explain the drilling of nanopores by electrons, we undertook a theoretical consideration of the energy transfer from the fast electrons to the solid through such mechanisms as elastic and inelastic scattering. According to the calculations based on the scattering cross-section, the direct atomic displacement cross-section induced by elastic scattering increases with increasing incident electron energy, while the ionization cross-section and temperature increment decrease. We performed nanopore drilling in a Si3N4 membrane using two different electron energies, 200 and 300 kV, to identify the drilling mechanism. The dependence of the nanopore drilling on the incident electron energy was well matched with the direct atomic displacement.     

Electron emission from condensed phase material induced by fast protons

Monte Carlo track simulation has become an important tool in radiobiology. Monte Carlo transport codes commonly rely on elastic and inelastic electron scattering cross sections determined using theoretical methods supplemented with gas-phase data; experimental condensed phase data are often unavailable or infeasible. The largest uncertainties in the theoretical methods exist for low-energy electrons, which are important for simulating electron track ends. To test the reliability of these codes to deal with low-energy electron transport, yields of low-energy secondary electrons ejected from thin foils have been measured following passage of fast protons. Fast ions, where interaction cross sections are well known, provide the initial spectrum of low-energy electrons that subsequently undergo elastic and inelastic scattering in the material before exiting the foil surface and being detected. These data, measured as a function of the energy and angle of the emerging electrons, can provide tests of the physics of electron transport. Initial measurements from amorphous solid water frozen to a copper substrate indicated substantial disagreement with MC simulation, although questions remained because of target charging. More recent studies, using different freezing techniques, do not exhibit charging, but confirm the disagreement seen earlier between theory and experiment. One now has additional data on the absolute differential electron yields from copper, aluminum and gold, as well as for thin films of frozen hydrocarbons. Representative data are presented.     

Comparative Investigation of Elastic Diffuse Neutron Scattering in C60 Powder

Abstract

C₆₀ powder samples of varying impurity content have been investigated by neutron scattering techniques. For Q > 2.5 Å^?1 (Q = transferred momentum) strong elastic diffuse scattering is found below T_c ~ 260 K providing evidence of static disorder in the low temperature phase. The elastic scattering increases on cooling from T_c to 150 K but remains virtually constant below this temperature. There is no marked dependence on the impurity level. For Q > 2.5 Å^?1 elastic diffuse scattering obeying a sin(QR)/(QR) law is observed both above and below the phase transition (R= radius of C₆₀ molecule). This scattering is nearly independent of temperature, however, depends strongly on the amount of impurities in the sample. In order to account for the unusually strong elastic diffuse scattering intensity model calculations have been performed which relate orientational disorder in C₆₀ to the elastic scattering observed in powder samples.     

Low-frequency expansions for a penetrable ellipsoidal scatterer in an elastic medium

In this paper the scattering of a plane longitudinal or transverse wave by a penetrable ellipsoid in an isotropic and homogeneous elastic medium in the low-frequency region is examined. Using low-frequency expansions the scattering problem is reduced to a sequence of potential problems. Explicit closed-form solutions for the zeroth and first-order approximations are obtained. The solution of the problem was made possible by using an analytical technique based on Papkovich-Grodski-Neuber potentials. The normalized scattering amplitudes and the scattering cross-section are evaluated up to k ³-order terms, respectively.The author would like to thank the Greek Ministry of Research and Technology for partially supporting the present work.     

Information on Surface Structure by Low Energy Electron Diffraction

During the last decades the investigation of surface structures has become an important and interesting subject of solid state physics. One of the most powerful methods of this surface crystallography is Low Energy Electron Diffraction (LEED). By the analysis of LEED patterns and intensities the size and shape of the surface unit cell, the degree of order and the atomic structure can be determined. Sophisticated video based measurement techniques allow the fast and reliable acquisition of data. The dynamical analysis of intensities, which fully accounts for the multiple scattering of electrons, yields the structure of the surface with a precision of the order of 10^?12 m for atomic positions.     

Superconductivity of ternary rare earth compounds. IV. Coexistence of antiferromagnetism and superconductivity

The possibility of the coexistence of antiferromagnetic order and superconductivity in ternary rare earth compounds is examined within the framework of our previous papers on the ferromagnetic case. It is demonstrated that antiferromagnetic ordering does not destroy the superconducting state, which coincides with recent experimental facts. The phase diagram and several thermodynamic properties are investigated. We calculate the upper critical fieldH _c2 in the dirty limit, and compare it with the experimental data on Gd_1.2Mo₆S₈. Some of the characteristic features ofH _c2 can be explained qualitatively.This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Sciences Division.     

Range and stopping power for slowing down of electrons in matter

Some problems of slowing down of radiation due to the interaction with matter can be studied by an approximate method of solution of the transport equation. In this work we describe energy-range and energy-stopping-power relationships for Coulomb elastic scattering of electrons (test particles) interacting with the electrons (field particles) of a medium. For test particles we assume a Maxwellian energy spectrum in the peculiar velocity, thus taking straggling into account. A comparison with the case when no energy spread of electrons is assumed is also reported.     

4He Atoms Incident on a Superfluid 4He Slab: Quantum Sticking, Scattering and Transmission

We present the results of a microscopic theory of the scattering, transmission, and sticking of ⁴ He atoms impinging on a zero temperature ⁴ He slab at near normal incidence. The theory includes coupling between different modes and allows for inelastic processes. The present work focuses on the elastic reflection and transmission of a ⁴ He atom in the sense that we examine these intensities for atoms which have the same energy as the incident atoms. We find a considerable loss of total intensity due to scattering into multiple excitations. The reflected signal is in qualitative and semi-quantitative agreement with experimental results for ⁴ He atoms scattered from the surface of bulk helium. The transmission intensity — which has not been measured — shows a very strong energy dependence. Moreover, we show that this dependence is substantially different from the Feynman level theory, which doesn't permit the decay of the single excitation into multiple excitations, and thus cannot describe a reduction in total intensity. In our theory, the major source of decay of elastic transmission and reflection (i.e., sticking) is from the production of ripplons at the liquid-vacuum interfaces.     

Scattering of electrons in beta-spectroscopy sources

Experimental spectra of the¹⁶⁹Yb conversion lines having kinetic energies of 3.7–18.4 keV and the beta spectrum from the decay of²⁴¹Pu are compared with calculations by the Monte Carlo method which take into account the individual elastic and inelastic scattering processes of the electrons in the source, in the substrate, and in a carbon layer contaminating the source. Good agreement is obtained between the theoretical and experimental results. It is also shown that the scattering of the electrons depends on their emission angle. Translated from Izmeritel'naya Tekhnika, No. 8, pp. 63–65, August. 1997.     

Scattering of Elementary Excitations at the Surface of Superfluid 4He

We study the scattering of atoms, rotons and phonons at the free surface of superfluid ⁴ He. We calculate the evaporation, condensation and reflection probabilities in the framework of linearized time dependent density functional theory accounting for elastic one-to-one processes. We explore the angular dependence of the scattering probabilities showing that most results are independent of the incidence angle and can be expressed in terms of a single energy dependent parameter.     

Inelastic scattering on spherical microparticles with inclusions

The subject of the paper is scattering at spherical microparticles with inclusions. The inclusions are represented as dipoles for both elastic and inelastic scattering. For elastic scattering the dipoles are computed iteratively, and sequence transformations are used to accelerate this iteration. Mie theory is used to calculate the cross sections for scattering on spherical microparticles with inclusions as well as on agglomerates.     

基于快速多极子基本解方法(FMM-MFS)的弹性波二维散射模拟研究

针对弹性波二维散射问题,发展一种新的快速多极子基本解方法（FMM-MFS）。方法基于单层位势理论,通过在虚边界上设置膨胀波线源和剪切波线源以构造散射波场,从而避免了奇异性的处理和边界单元离散;结合快速多极子展开技术（FMM）,大幅度降低了计算量和存储量,突破了传统方法难以处理大规模散射问题的瓶颈。以全空间孔洞对P、SV波的二维散射为例,给出了具体求解步骤,并在个人计算机上实现了上百万自由度问题的快速精确计算。在方法效率和精度检验基础上,分别以单孔洞和随机孔洞群对平面波（P、SV波）的散射为例进行计算模拟,揭示了孔洞（群）周围弹性波散射的若干重要规律。