Showing papers in "Reports on Progress in Physics in 1966"

The fluctuation-dissipation theorem

Abstract: The linear response theory has given a general proof of the fluctuation-dissipation theorem which states that the linear response of a given system to an external perturbation is expressed in terms of fluctuation properties of the system in thermal equilibrium. This theorem may be represented by a stochastic equation describing the fluctuation, which is a generalization of the familiar Langevin equation in the classical theory of Brownian motion. In this generalized equation the friction force becomes retarded or frequency-dependent and the random force is no more white. They are related to each other by a generalized Nyquist theorem which is in fact another expression of the fluctuation-dissipation theorem. This point of view can be applied to a wide class of irreversible process including collective modes in many-particle systems as has already been shown by Mori. As an illustrative example, the density response problem is briefly discussed.

Covalent bonding and magnetic properties of transition metal ions

Abstract: This review is mainly concerned with octahedrally co-ordinated ions with an unfilled d shell. The wave functions of the magnetic electrons are considered first, the covalency being taken into account by admixing ligand s and p orbits into the central ion d orbits. The origin of these admixtures is discussed in a simple way, and a short survey is given of recent developments in the theory. The experimental evidence for the admixtures is described. This evidence includes the ligand hyperfine structures observed in electron and nuclear magnetic resonance experiments and also effects found in neutron-scattering experiments. Some of the available data are tabulated and discussed. The consequences of these covalent admixtures on the properties of the magnetic ions are outlined and illustrated with examples. These include the reduction in orbital magnetic moment of the d electrons, the contribution to the crystal field splitting, and the contribution to the superexchange interaction between neighbouring magnetic ions.

The physics of high temperature creep in metals

Abstract: The slow deformation of metals, known as creep, first came clearly into focus about half a century ago As a problem in metal use it has grown steadily in importance because engineers have persistently raised their operating temperatures in many fields, until now it is one of the half-dozen most important of these problems Besides the abundance of technical data that has necessarily been accumulated, there have been many studies in the last fifteen years of the physics of creep, and it is with these that this article is concerned These physical studies have shown that there are several different creep r?gimes depending mainly on the temperature If TM is the melting point of the metal in question, the different r?gimes roughly cover the temperature ranges 0-0?3 TM, 0?3-0?5 TM, 0?5-0?9 TM and 0?9-1?0 TM The bottom range includes the so-called logarithmic creep and the top range creep by diffusion, which is somewhat similar to flow in liquids Both are quite well understood but neither is particularly important and they are dealt with briefly It is the middle two temperature ranges in which creep worries engineers; they have therefore received much more attention and the creep behaviour in them is described more fully in this article In both of these temperature bands the rate of creep strain is very dependent on temperature, stress applied and composition of the metal The temperature dependence is no surprise, since it is quite clear that creep is a thermally activated phenomenon and its rate is therefore governed by an Arrhenius factor In many pure metals the temperature dependence is quantitatively close to that of self-diffusion, particularly in the 0?5-0?9 TM band, and the agreement grows better the more refined the measurements become In the last ten years this result has guided most theories, and has encouraged attempts to be made with partial success to calculate the absolute rates from first principles Calculations have been founded on both the two basic theoretical models One assumes that the factor controlling creep rate lies in the deformation process, or glide movement of dislocations, itself The other assumes that the rate-controlling factor lies in the continuous annealing that takes place at the high temperatures involved The two models are really two sides of the one penny, since both slip and recovery take place simultaneously and are unavoidably interconnected When the two models are properly joined they explain the influence of composition, which may affect creep rate by well over a millionfold, and the great influence of stress as well as the temperature effect The physics of creep deformation in the middle temperature ranges is therefore quite well understood Indeed, the important parameters like diffusion rate, stress and stacking fault energy combined in a single equation give the creep rates of many simple metals with fair accuracy A consequence of the growing success in producing alloys that deform very slowly even at high stress and temperature is that the problem of creep fracture has loomed larger There is a fracture mechanism quite distinctive to creep, in which tiny holes nucleate and grow by some means until they are so large, or sufficiently linked together, that the metal breaks The speed of this fracture process increases with temperature and stress, and evidently also depends on composition in a complicated way, which has made possible a certain degree of manufacturing control if not of understanding In essence, the formation and growth of the holes is a phase change in which stress provides the driving free energy since the holes enlarge the overall dimensions Both the nucleation and growth rates help to determine the time to fracture, which is what really matters There are several obscure points such as the nature of many of the nucleating sites and the strong influence of deformation rate during nucleation and growth Both theoretically and practically, understanding of the youthful problem of creep fracture is less mature than that of the older problem of creep deformation

The dynamics of a crystal lattice with defects

Abstract: The dynamic phenomena connected with isolated defects in a lattice and the dynamics of a crystal with various types of defects are examined. Simplified models are used in the interpretation of the results and to assess orders of magnitude of the phenomena.

Isotope shifts and nuclear charge distributions

Abstract: This report is concerned with the measurement and interpretation of the field-dependent isotope shifts in atomic spectra, ie shifts due to variations in the nuclear charge distribution Mass effects are considered only in order to extract the field-dependent shifts from the measured shifts After a review of experimental techniques and a summary of the basic theory, the isotope shift results are discussed in terms of the results of other experimental investigations of nuclear charge distributions There are two striking features of isotope shift results for even-even nuclei, their overall smallness and their irregular variation with neutron number over the range of isotopes of an element The first of these has not yet been satisfactorily accounted for The irregularities are associated with neutron shell structure, but they cannot be attributed entirely to deformation effects Experimental isotope shifts and nuclear deformations are tabulated Recent work on the odd-even staggering effect is reviewed

Type II superconductors

Abstract: A review is given of recent work which has led to the discovery of type II superconductors and to an understanding of many of their properties. A brief historical introduction, which summarizes the early ideas concerning the magnetic behaviour of superconductors, is followed by a presentation of the Ginzburg-Landau equations. Some of the more general consequences of these equations, including the existence of quantized vortex lines, are examined. Abrikosov's solutions of the Ginzburg-Landau equations in homogeneous, extended defect-free, bulk specimens of type II superconductors are then presented, and the more recent work which generalizes the theory to all temperatures is mentioned. These predictions are then compared with measurements of the bulk thermodynamic properties and with various experiments which confirm the existence of vortex lines. Two special effects, the superconducting surface sheath and the influence of the paramagnetism of the normal state, are then discussed. The article concludes with a section devoted to irreversible phenomena. Particular attention is paid (i) to vortex line pinning, the static irreversible magnetic behaviour and bulk transport currents, and (ii) to the various types of vortex line motion: flux creep, flux flow, vortex line vibrations and flux jumps.

Resonant scattering of electrons by atomic systems

Abstract: The resonant scattering of electrons by atomic systems and its inter-relationship with the phenomenon of autoionization is reviewed both theoretically and experimentally. The Siegert definition of a resonance has been used to illustrate the connection underlying the various theoretical models. Particular attention has been given to the close-coupling approximation and the related effective-range theories, as well as to the formalism of Feshbach projection operators and Fano's theory of configuration interaction.

Two-beam interferometric spectroscopy

Abstract: Spectroscopy by two-beam interferometry is compared with conventional techniques and it is shown that considerable advantages may be expected in some measurements from the use of interferometers. The important advance in the last decade which allows this to be realized is the use of digital computers. Their use has also allowed the development of refractive index spectroscopy over wide spectral ranges using Michelson's interferometer. The duality of spectral and angular measurement is stressed and the potential of the spectroscopic analogue of the stellar intensity interferometer, which so far has not been developed, is analysed here.

Spin waves in ferromagnets

Abstract: In this review a qualitative description is given of the various types of exchange interactions which might be present in metals and insulators and which might lead to co-operative interactions - particularly ferromagnetism. The theory of spin waves is then described and this is extended to include non-linear and temperature effects both in the localized and in the itinerant electron models. The experimental observation of spin-wave phenomena is discussed with particular reference to measurements of the specific heat, the magnetization, inelastic neutron scattering and spin-wave resonance. A short description of spin-wave relaxation mechanisms and of parallel pumping is also given.

Microscopic transport phenomena in liquids

Abstract: Over the past ten years there have been significant advances in the theoretical understanding of, and the experimental techniques for studying, the microscopic behaviour of liquids. This has been most marked in the field of thermal motion and in the understanding of transport phenomena. The basic treatment through correlation functions and expressions for some macroscopic constants in terms of the microscopic correlation functions are presented. General transport coefficients depending on frequency and wave number are discussed in detail. Some data obtained over the last five years in these fields are presented and used to discuss processes contributing to the diffusion and viscosity coefficients. Special attention is paid to the variation of the parameters involved with frequency and wave number. These data are used to examine relationships between the general diffusion and viscosity coefficients, and to test models of the liquid state. It is concluded that a simple `solid-like' model is the most effective for discussing microscopic behaviour.

Cosmological models and their observational validation.

Abstract: The observational data of cosmology are presented in considerable detail and their interpretation in terms of various cosmological models is described. The data survey the nature and cosmic distribution of luminous matter (galaxies), radio sources, quasars, intergalactic matter, the radio and optical background radiation, x rays, γ rays and cosmic rays. The theoretical basis of cosmological models is described in its general aspects and in particular cases. Topics discussed include the homogeneous anisotropic models, isotropic models, Mach's principle, relativistic cosmology, Newtonian cosmology and the various versions of the steady-state theory and creation of matter. Theoretical observable relations are derived or described for the isotropic models of relativistic cosmology and the steady-state theory. The theoretical relations between observables are compared with the data from various observational tests. These include the red-shift-apparent-magnitude relation, counts of radio sources, the radiation background at radio and optical frequencies and the x-ray and γ-ray background. The possibility of intergalactic cosmic rays is discussed and an account is given of recent observational tests for intergalactic hydrogen. The relevance to particular cosmologies of neutrino degeneracy, the absorber theory of radiation, the age distribution of galaxies and the origin of the chemical elements is analysed in some detail. The most important conclusion is that several tests, among them the measurements of red shift and apparent magnitude, the counts of radio sources, the radio background at high frequency and the present He/H abundance ratio, all support a universe that was denser in the past. Furthermore, recent tests suggest that the density of hydrogen in intergalactic space is below the mean density of luminous matter (galaxies) by several orders of magnitude. Thus the evidence is now extremely strong against the steady-state cosmology in its original simple form, while relativistic cosmology to the above extent finds support. On the other hand, there is the difficulty that the evolutionary ages of some star clusters are estimated to exceed the predicted ages of galaxies in both cosmologies, while the absorber theory of radiation gives consistent retarded solutions in the steady-state theory but not in relativistic cosmology. Although contrary arguments exist, there is strong theoretical evidence that a singularity in the relativistic cosmology is inevitable, and no way has yet been found in conventional physics either to prevent it or to describe it. However, the discovery of new force fields in physics at high density, on the lines of the negative energy C field of the steady-state theory, may show how a contracting universe may be reversed into expansion without singularity. This might imply a finitely oscillating universe, for which there are special difficulties. The theoretical and observational study of the recently discovered quasars may throw light on this issue. But from the point of view of present-day physics the evidence points to a fundamental singularity of the observable Universe that occurred about ten thousand million years ago. There is also considerable evidence that this was followed by a hyperbolic expansion.

The origin of the elements

Abstract: Observations of element abundances in different astronomical objects indicate that hydrogen and helium are very much more abundant than all of the other elements put together. This suggests that the light elements may have been created cosmologically while the heavier elements have been produced in subsequent astrophysical processes. A satisfactory discussion of the origin of the elements thus involves a decision about which cosmological model is valid and an understanding of how much element synthesis occurs in the various astronomical objects. This article reviews the progress that has so far been made with this problem. The article falls into four main parts. The observations of element abundances are first reviewed and a discussion is given of the uncertainties involved in converting raw observations into abundances. An account is given of several cosmological theories. The main discussion centres on whether only hydrogen or both hydrogen and helium were created cosmologically, but other factors which may cause cosmological theories to be discarded are also mentioned. Some nucleosynthesis certainly occurs in stars, but it is still not clear that ordinary stars are the main site of the synthesis of all elements other than hydrogen and helium. It is stressed that it is not only necessary for nucleosynthesis to occur in astronomical objects but that the processed material must be expelled into space so that subsequent use can be made of it. Observations of element abundances and theories of element production cannot be more accurate than the physical laws and parameters which enter into them. The physical parameters with uncertain values, which are important in a discussion of the origin of the elements, are listed.