Lattice Dynamics of Metals

Abstract

Publisher Summary This chapter discusses the lattice dynamics of metals. The essential approximations in the general theory of the lattice dynamics of crystals developed within the framework of the Born-von Karman approach are that the atoms vibrate harmonically about their equilibrium positions and that the electrons in the lattice follow the nuclear motion adiabatically—that is, they are always in equilibrium with their surroundings. The adiabatic approximation for metals is developed and description of the elements of the classical theory of lattice dynamics is presented to introduce the notation and terminology, and also to establish a framework for the detailed discussion of various models. The x-ray and neutron scattering techniques of obtaining valuable information about lattice vibrations in solids are also discussed. These techniques have aided much in setting up more general and more realistic models for crystals. The method of neutron inelastic scattering has proved to be a versatile and powerful tool in the study of lattice dynamics of metals. Recent developments in the method of calculating the frequency distribution function are reviewed. The lattice dynamical models are enumerated possessing extreme simplicity, which are useful in calculating a number of physical properties involving lattice vibrations in a complicated manner. Force constant models for crystals and various specific force model calculations for metals are also given. The methods of analysis of experimental data on frequency–phonon wave vector dispersion curves in terms of Born-von Karman force models are also discussed.