The aim of this successful book is to describe and analyse peculiarities of classical and quantum dynamics of a crystal as a spatially periodic structure. In the second revised and updated edition, the author focuses on low-dimensional models of crystals and on superlattices. Both traditional questions like the spectrum of vibrations, the idea of phonon gas, dislocations etc. and new aspects like the theory of quantum crystals, solitons in 1D crystals, dislocation theory of melting of 2D crystals etc. are discussed. The author gives an explanation of a set of phenomena which entered into solid state physics during the last decades. It is shown that the crystal properties are sensitive to the dimension of the crystal and its defect structure, and depend slightly on whether the periodic structure consists of atoms, or electrical dipoles, or magnetic moments (spins). Considerable attention is devoted to the dislocation mechanisms as a basis of the theory of plasticity and numerous technological applications of crystalline materials.
Arnold M. Kosevich studied at Kharkov University (PhD 1954 and Dr.Sci. 1964). Between 1954 and 1957 he worked at Chernovtsy University and 1957-1974 at the Kharkov Institute of Physics and Technology. He was appointed professsor at Kharkov University in 1966. Since 1974 he has been Head of the theoretical department at the B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine. Now he works also at the Kharkov Institute of Physics and Technology. His main scientific works concern the theoretical physics of condensed matter, namely, the electron theory of metals, the dynamics of crystal lattice, the theory of dislocations and point defects in solids, and the nonlinear dynamics of magnetization in magnetically ordered crystals. A.M. Kosevich jointly with Prof. I.M. Lifshits determined a quantitative relation between the de Haas-van Alphen oscillations and the shape of the Fermi surface for electron gas in metals (Lifshitz-Kosevich formula). He is the author of more than 200 scientific papers and of several book publications.
Prefaces. PART I: INTRODUCTION. Geometry of crystal lattice. PART II: CLASSICAL DYNAMICS OF A CRYSTAL LATTICE. Mechanics of a one-dimensional crystal. General analysis of vibrations of monoatomic lattices. Vibrations of polyatomic lattices. Frequency spectrum and its connection with the Green's function. Acoustics of elastic ssuperlattices: Phonon crystals. PART III: QUANTUM MECHANICS OF CRYSTALS. Quantization of crystal vibrations. Interaction of excitations in a crystal. Quantum crystals. PART IV: DEFECTS. Point defects. Dislocations and disclinations. Linear crystal defects. Localization of vibrations. Localization of vibrations near extended defects. Elastic field of dislocations in a crystal. Dislocation dynamics. Bibliography. Index.