Монографии

В монографии изложены результаты экспериментальных и теоретических исследований статических свойств и динамической перестройки доменных структур в железокремнистых электротехнических сталях. Приведены данные о влиянии на них материальных и геометрических факторов, внешних переменных и статических магнитных полей, внешних напряжений и температуры. Описаны процессы стабилизации доменных структур и известные способы ее дестабилизации. Прослежено влияние квазистатического и динамического поведения доменных структур на важнейшие магнитные свойства электротехнических сталей.

Монография предназначена для специалистов в области исследования магнитных материалов.

This book should fill a gap which has existed in the literature on superconductivity. There have been a number of excellent textbooks available on the phenomenon of superconductivity, which describe in detail the variety of effects connected with it and the mathematical techniques to deal with them properly. However, until now there has not been a textbook available in English which concentrates on the material aspects of superconductivity. This is a major shortcoming since most physicists working in the field of superconductivity are mainly concerned with specific materials and subsequently often need to know more about the interplay of superconductivity and material properties. On the other hand, people working in the field know that a competent and well-written book by S.V. Vonsovsky, Y.A. Izyumov, and E.Z. Kurmaev has been available in Russian. It presents a thorough discussion of superconducting transition-metal alloys and compounds.

I sincerely hope that the book will turn out to be useful to physicists working in the field of superconductivity as well as to nonspecialists and interested graduate students.

The quantum theory of solids occupies a peculiar and important place in the general structure of modern theoretical physics. There are currently no grounds for questioning the statement that all properties of solids can, in principle, be accounted for on the basis of firmly established principles of quantum and statistical mechanics. Nevertheless, these properties of real solids and the condensed state of matter in general, are so complicated and diverse that it is well nigh impossible, at least at present, to explain rigorously and fully from first principles the observed characteristics of crystals, even those which are close to perfect, - let alone explain the fact that they exist! Therefore, alongside the mathematical methods and physical concepts applied in other more fundamental areas of theoretical physics, solid state theory has developed approaches of its own to account for the most important properties of the various substances. Significantly, these approaches now have a profound reciprocal effect on not only statistical physics but also on particle physics, and even on astrophysics and cosmology. Apart from this, the tremendous and ever-increasing applied significance of solid-state theory must be noted. Suffice it to mention here the theory of semiconducting devices, the theory of strength and plasticity, the theory of magnetic properties of materials, etc. In this respect, modern solid-state theory employs with great practical success a sufficiently simple and, at the same time, adequate theoretical background, based on a purely phenomenological approach and microscopic models that are comparatively simple in terms of mathematics and very lucid physically.

As stated above, a quantum theory of solids that realizes the “first-principles” program in its entirety, i. e., a theory in which all properties of solid are derived from those of individual constituent atoms, does not exist. However it may well be assumed that, for example, the indubitable and sizable success of the pseudopotential method that now enjoys wide use in the theory of simple (normal) metals is an important step toward the construction of such a physically consistent first principles theory. Rather than choosing the deductive method of presentation, we have therefore opted, in this text, for a method based on a treatment and analysis of simple empirically established properties of solids, resorting to more соmplicated models only where necessary. In a way, such an exposition reproduces the evolution of this important province of modern theoretical physics (differing in this respect from the diverse monographs and textbooks devoted to the problem concerned) and, in our view, is most appropriate to initiate the reader into the subject. We have also assumed that a detailed treatment of a number of classical topics such as the one-dimensional Schródinger equation with a periodic potential, the metal-insulator criterion, the effect of electric and magnetic fields on electronic states, and other similar problems would be very instructive. At the same time, the book presents a number of up-to-date topics: the scattering of neutrons by the crystal lattice, plasma and Fermi liquid effects, elements of pseudopotential theory, fundamentals of the theory of disordered systems, etc.

It is assumed that the essentials of quantum and statistical mechanics are a sufficient theoretical background for reading this text. As far as possible we have tried to outline the body of mathematics in conjunction with those specific problems in which it is immediately exploited. Thus, for instance, the secondary quantization method is expounded for the first time in connection with the problem of neutron scattering on phonons, the resolvent (Green’s-function) method is outlined in connection with the problem of electron localization on impurities, etc. The presentation of a number of problems, in which allowance for correlation effects in electronic systems (superconductivity, the properties of transition metals, and the like) is essential, has turned out to be extremely concise, for we did not succeed in finding a simplified enough version of the mathematical sophistication needed for a more rigorous exposition. In those (and some other) cases we had to confine ourselves to simple model problems and often to purely qualitative lines of argument.

Although the present book outlines sufficiently general properties of solids, as well as some specific problems of the physics of semiconductors, ionic crystals, etc., it is still primarily the metal that we view as the model of “a solid in general.” This is partly because the metal is in essence a gigantic molecule and demonstrates most dramatically he features peculiar to the electronic properties of crystals, which are not reducibl to a mere “sum” of the properties of individual constituent atoms or molecules.

An acquaintance with this text should prepare the reader for a more detailed study of particular areas of solid-state theory, which at present are outlined fully enough at an up-to-date level in the abundant body of special literature. The text is intended to appeal to experimental physicists, chemists, engineers concerned with problems of solid-state theory and wishing to become conversant with the pertinent body of mathematics theoretical physicists in other fields, and undergraduate and graduate students.

The magnetic properties of alloys have been exploited in many technical applications for a long time. They have been the subject of numerous experimental investigations. However, deep theoretical studies of the magnetic properties of alloys commenced relatively recently because of considerable mathematical difficulties, some of which have not yet been overcome.

Two aspects of the theory of magnetic properties of alloys can be isolated. One is concerned with the origin and properties of the localized magnetic moments of the atoms in an alloy and with the interactions between them resulting in certain types of magnetic ordering. The other aspect is concerned with the magnetic ordering and the resultant magnetic properties of an alloy. The first aspect is closely related to the electron properties of an alloy and is usually considered within the band theory of metals. The second aspect involves the use of specified values of atomic magnetic moments and of the exchange interactions between them, which are frequently considered in the Heisenberg model of a magnetic crystal. The problem of the applicability of the Heisenberg model to a metal must be resolved by bearing in mind its magnetic properties. It is found that the Heisenberg model often provides a satisfactory description of magnetic structures and of the spectra of magnetic excitations.

The present monograph deals with the second aspect. The adoption of the Heisenberg model makes it possible to apply the theory associated with it not only to alloys but even to a greater extent to nonmetallic compounds. Our monograph is concerned with the magnetic properties of ferromagnetic crystals consisting of two types of magnetic atom, mixed in a random manner, i.e., it will be assumed that there is no atomic ordering in a crystal with impurities. Much of the book is concerned with dilute systems, in which the concentration of the second component is so low that its atoms can be regarded as isolated from one another. We shall begin by solving the properties of a crystal containing a single impurity atom and then we shall go over easily to the properties of a crystal with a finite but low impurity concentration.

The book offered to the reader’s attention is largely based on lectures that the authors have been delivering for many years at the Physics Department of the Urals State University and the Physical Engineering Department of the Urals State Technical University.

The main goal pursued by the authors in writing this book is to set forth systematic and consistent principles of non-equilibrium thermodynamics and physical kinetics in the form primarily available to both the students and undergraduates who begin to study theoretical physics and the postgraduates and experienced research scientists working in a new field of study.

First of all, we point out principles that have guided us in selecting appropriate material. Physical kinetics or a theory of transport phenomena is a very broad and rapidly developing subject area of physics. On this subject matter, there are a sufficient number of educational papers as well as monographic studies, which discuss various aspects of the kinetic theory. However, most publications are expected to be understood by readers who have a substantial scientific background rather than by third year students.

Therefore, there is an acute shortage of literature for “beginners” where natural balance between general postulates of the theory and simple examples of the practical implementation would be observed. Another guiding approach in writing the present book consists in authors’ attempting to avoid as far as possible such turns о speech as “obviously” and “it is easy to show”. There is no secret that cumbersome, time- consuming calculations are very often hidden behind these words.

The authors were trying to write the text in such a manner so that those phrases should acquire their original meaning. Perhaps, the authors did not always succeed in doing so. Finally, also the authors have done their best to present different techniques to describe non-equilibrium systems and construct schemes of the theory of transport phenomena but they would not like to focus on the problem of a calculation of the kinetic coefficients for various model systems. This approach allows one to illustrate contemporary directions of non-equilibrium statistical mechanics which are now developed along with “classical” sections of kinetics.

In Stoffen, die aus Atomen oder Ionen der Ubergangselemente (mit nicht abgeschlossenen inneren d- oder f-Elektronenschalen, die in Ubereinstimmung mitder Hundschen Regel [1] nichtkompensierte Spin- und Bahnmomente besitzen) aufgebaut sind, konnen unter bestimmten Bedingungen magnetisch geordnete Atomzustande vom Typ des Ferro- oder Antiferromagnetismus auftreten. Diese Zustande beobachtet man im Temperaturintervall von 0°K bis zu einer bestimmten kritischen Temperatur, der Curie-Temperatur 0C (bei Ferromagnetika) oder der Neel-Temperatur 0n (bei Antiferro- oder Ferrimagnetika). Offensichtlich wird die GróBe dieser Temperaturen durch den Betrag des Energiepara- meters der Wechselwirkung zwischen den Elektronen bestimmt, die das Auftreten geordneter Verteilungen fiir die magnetischen Momente der Elektronen im Kristallgitter ermoglicht.

Die physikalische Ursache dieser Wechselwirkung wurde im Rahmen der Quantenmechanik geklart, nachdem das Pauli-Prinzip aufgestellt wurde, d.h. nachiem die Symmetrieeigenschaften der Wellenfunktionen des Vielelektronen- systems und ihre Antisymmetric in bezug auf Vertauschungen der Koordinaten einzelner Teilchen erkannt wurden [2] bis [4].

Die Abhangigkeit der Energie eines w-Teilchensystems von der GroBe des Gesamtspins ist eine Folge der Coulombschen Wechselwirkung zwischen den Teilchen, der Antisymmetrie der Gesamtwellenfunktion hinsichtlich der Koordinatenvertauschung (sowohl hinsichtlich der Ortsals auch der Spinkoordinaten) und ier Uberlappung verschiedener Bestandteile der Gesamtwellenfunktion, die von den Ortskoordinaten abhangen und sich untereinander nur durch Koordinatenvertauschungen unterscheiden, im 3 n-dimensionalen Phasenraum. Der letztgenannte Punkt wird in der Einelektronendarstellung als Forderung nach von Null verschiedener Uberlappung der Einelektronenwellenfunktionen formuliert.

Fur isolierte Atome und Molekule wurde diese Wechselwirkung erstmalig quantitativ behandelt in den bekannten Arbeiten von HEISENBERG [2], [3] uber die Theorie des Heliumatoms, des einfachsten Vielelektronenatoms, und von НЕITLER und LONDON [5] uber die Theorie des Wasserstoffmolekiils, das einfachsten Zweiatommolekiils.

The internal conical refraction effect lies in the deviation of energy flow direction of elastic wave despite the wave propagates along the acoustic axis. The complete review is presented of the theory including the energy flow of the beams. The effect of electric and magnetic fields is discussed. The calculation methods of elastic field polarization are reduced under the conical refraction condition. The methods of the experimental investigation are shown.

The direction of the ultrasound energy flow in an anisotropic medium generally differs from the direction of the wave normal. These directions may coincide in some crystallographic directions only. This is the case, in particular, when an elastic wave propagates along the transverse acoustic axis, provided the mirror symmetry plane of the crystal is the normal to this axis. If the said symmetry plane is absent, the beam velocity vector deviates from the axis despite the velocity degeneration of the transverse modes. As a result, a special effect -the internal conical refraction of ultrasound - may set in.

The analogy between propagation of elastic and electromagnetic waves in an anisotropic medium has been well known. The phenomenon of the internal conical refraction (ICR) has long been known in optics. Analyzing propagation of light in a two-axis crystal, Hamilton predicted this phenomenon in 1833. The ICR was observed experimentally by Lloyd in the same year. The main properties of the ICR have been known since 1905. However, even to the present day the phenomenon of the internal conical refraction has been difficult to appreciate. In acoustics this phenomenon was observed for the first time by de Clerk and Musgrave in 1955. It reduces to the deviation of tne ray velocity vector from the acoustic axis, along which the ultrasound propagates. The direction of the ray velocity vector depends on polarization of the transverse wave. If the polarization changes 180 degrees, the ray velocity direction changes 360 degrees. Thus, if the polarization is varied, the ray velocity vector describe a conical surface.

This cone may be either an elliptical or circular one. In 1959 Waterman fully described the propagation of plane elastic waves in crystals, including the effect of the internal conical refraction. The theory of this effect allowing for the real structure of the wave field was advanced by A.G. Khatkevich. The analogy between elastic and light waves was frequently used to ascertain qualitative features of this phenomenon.

This review is concerned just with the effect of the ir ternal conical refraction (ICR) in cubic crystals. The findings on the crystals having other symmetries are used here as may be necessary. The ICR in tetragonal and hexagonal crystals and in orthorhombic crystals has been treated in Refs. and respectively. The phenomenon of the external conical refraction-the formation of a cone of wave normals corresponding to the given ray-has been known in crystal acoustics, too.

This review mostly is a compiled treatise. The contents of the review have been arranged in accordance with the following scheme. Our initial concern will be the theory of the ICR effect in cubic symmetry crystals, in particular the propagation of plane waves. The effect that deviation on the propagation direction from the axis of third-fold symmetry has on the energy flow will be discussed. Special situations of the ICR-reflection of the beam from the boundary surface and generation of the second wave harmonic-will be considered. Finally, the experimental refraction observation methods will be described.

The overwhelming majority of technological processes for producing metallic alloys involve the conversion of initial materials into the molten condition and the subsequent solidification of the system at various, sometimes very high, cooling rates. In an attempt to improve the structure and service properties of ingots, castings and deformed semifinished products, process engineers have paid considerable attention to the search for optimal solidification conditions. The regimes of heat and mechanical treatment of cast metal are progressively improving. Only the first stage of the process - initial melt - is traditionally of marginal interest to metallurgists. In most cases, attempts to affect the system at this stage are confined to additional alloying with the aim of optimizing the system composition, and to refining the system in an effort to remove deleterious impurities.

At the same time a great body of data has been accumulated in scientific periodicals over the past 30-40 years, which indicates that metallic melts are dynamical systems of high complexity. They can exist in different structural states and make transit ons between these states under the influence of various external actions. The role of the structural state of the initial melt in the formation of the structure and properties of ingots produced from this melt and, consequently, the structure and properties of deformed semi-finished products is also established. As applied to steels, cast iron and nickel alloys, these facts are systematized in the collective monograph under the title Liquid Steel * published in the USSR in 1984. However, information regarding aluminium alloys has not been generalized to date, although the data accumulated in this field are equally impressive.

In the authors’ opinion, this monograph may fill this gap. It owes its origin to the collaboration of three researchers who over the past 20-30 years have studied various aspects of interrelation between the structure of aluminium melts am the structure and properties of ingots formed in solidification of these melts, or have searched actively for effective ways of influencing liquid metals to improve the quality of solid metals. We consider in this monograph a few possible ways of governing the structure and properties of cast metal by applying different external actions to the initial melt.

This book had its conception when Dr. Gudkov visited me in Austin in the Fall of 1995 and urged me to join him in writing a review of the field of magnetoacoustic polarization phenomena. I protested that, although my students and I had done some early work on this topic, most of the later work was done by researchers at the Institute for Metal Physics and by other investigators in the former Soviet Union. He eventually persuaded me that my initial contribution and general experience with magnetoacoustic phenomena qualified me to serve as a co-author. When I considered the fact that the extensive exploration of magnetoacoustic phenomena in the former Soviet Union was relatively unknown to Western scientists, I agreed to work with him on this project. 

In order to make the material more accessible to nonspecialists, we have adopted consistent notation throughout the text and redrawn the figures from published papers in a consistent fashion.

Монография посвящена исследованию структуры и свойств интерметаллидов начиная с широко известного сплава Ni3Al, составляющего основу современных суперсплавов. Особое внимание обращено на деформационное поведение интерметаллида TiAl, при исследовании которого авторами получены приоритетные результаты. На основе анализа обширной экспериментальной информации сделана попытка составить исчерпывающую в настоящий момент и целостную картину явлений, связанных с деформационным поведением интерметаллидов. Постоянно растущий интерес к ним связан с решением как технологических, так и фундаментальных проблем. Благодаря уникальной природе, некоторые из интерметаллидов уже стали основой аэрокосмических материалов нескольких поколений, а другие - потенциальными кандидатами для следующих поколений. Представлены экспериментальные данные по температурным аномалиям предела текучести и коэффициента упрочнения интерметаллидов Ni3Al и TiAl и сопутствующие им изменения дислокационной структуры. Излагаются современные представления о термоактивированных процессах блокировки дислокаций различных типов и дислокационных источников. Авторами разработан общий подход к описанию процесса пластической деформации как эволюции дислокационной популяции, в которой происходят и размножение дислокаций, и их превращения. Рассмотрены модели поведения дислокационной популяции, которые объясняют наблюдаемые аномалии деформационных характеристик интерметаллидов. Обсуждается связь дислокационных превращений и хрупко-вязкого перехода в интерметаллидах.