Dynamic equations of the theory of elasticity of metals

In pure metals at low temperatures, when the mean free path of conduction electrons is very large, the electron contribution to elastic forces becomes nonlocal. The forces that appear in the equations of motion of the lattice are then functionals of the electron distribution. The dynamics of conduction electrons, and the influence of the external magnetic field and of the self-consistent electric fields then become important. In this review, we examine the equations of elasticity, using the general assumptions of the modern theory of metals, based on the model-independent macroscopic approach. A detailed discussion is given of the deformation potential and its symmetry properties, and of the role of directional symmetry of the magnetic field. The effective interaction between electrons and sound waves and the role of electric fields accompanying an elastic wave are discussed as examples.