Монографии

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.

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.

В монографии изложены результаты экспериментального исследования и математического моделирования изменения физических свойств интерметаллического соединения Ni3Al при образовании на его основе тройного сплава с переходным легирующим элементом. В качестве легирующих элементов рассмотрены Nb, Co, Fe, Ti, Cr, W. V. Для исследований широко привлекаются монокристаллические образцы. Особое внимание уделяется процессам формирования структуры таких сплавов в процессе кристаллизации и влиянию легирования на характер фазовых превращений в тройных сплавах. На основании собственных исследований и литературных данных делаются выводы о закономерностях, определяющих тип замещения для каждого из легирующих элементов. Для широкого круга специалистов – научных работников, инженеров, работающих в области материаловедения и физики конденсированного состояния. Может быть полезна студентам и аспирантам соответствующих специальностей.

В книге дано систематическое изложение современной квантово-статистической теории магнетизма в диэлектриках, переходных и редкоземельных металлах и сплавах на основе четырёх фундаментальных моделей: модели Гейзенберга, ферми-жидкости, модели Хаббарда и s-d-модели. Анализ базовых моделей проведён с помощью единого подхода, основанного на диаграммной технике и методе производящего функционала.

Для научных работников-физиков-теоретиков и специалистов, интересующихся проблемами физики магнитных явлений в твёрдых телах, а также для студентов старших курсов и аспирантов.

В монографии систематизированно излагаются результаты экспериментальных исследований в области оптики и магнетооптики металлов и сплавов, проведённых в СССР и за рубежом в течение последних 20 лет. Предполагается, что читатель знаком с основами современной теории металлов. Возможность детального ознакомления с оригинальными теоретическими работами предусмотрена в списке литературы. Обозначен круг проблем физики металлов, решаемых с помощью металлооптики; описаны основные её экспериментальные методы. Монография охватывает практически все металлические элементы, за исключением актинидов, и написана на основе новейших данных.

Книга рассчитана на экспериментаторов-научных сотрудников, инженеров, работающих в области физики металлов и оптики, а также аспирантов и студентов старших курсов физических и физико-технических факультетов высших учебных заведений.

This monograph offers a concise overview of the theoretical description of various collective phenomena in condensed matter physics. These effects include the basic electron-hole properties of metals and semiconductors, lattice vibrations, superconductivity, light-matter interaction and more advanced topics such as analysis of dislocation systems and the soliton mechanism of anomalous acoustic emission near the martensitic transition.

This book presents a theoretical framework for magnetism in ferromagnetic metals and alloys at finite temperatures. The objective of the book is twofold. First, it gives a detailed presentation of the dynamic spin-fluctuation theory that takes into account both local and long-wave spin fluctuations with any frequency. The authors provide a detailed explanation of the fundamental role of quantum spin fluctuations in the mechanism of metallic magnetism and illustrate the theory with concrete examples. The second objective of the book is to give an accurate and self-contained presentation of many-body
techniques such as the functional integral method and Green's functions, via a number of worked examples. These computational methods are of great use to solid state physicists working in a range of specialties.

The book is intended primarily for researchers, but can also be used as textbook. The introductory chapters offer clear and complete derivations of the fundamentals, which makes the presentation self-contained. The main text is followed by a number of well-organized appendices that contain a detailed presentation of the necessary many-body techniques and computational methods. The book also includes a list of symbols and detailed index. This volume will be of interest to a wide range of physicists interested in magnetism and solid state physics in general, both theoreticians and experimentalists.

https://www.springer.com/us/book/9783319929729

В сборнике представлены научные произведения выдающегося физика, сотрудника ИФМ УрО РАН, И.Ш. Трахтенберга в виде библиографического списка, а также его литературные произведения и воспоминания его друзей и коллег.