Virial theorem and some properties of the electron gas in metals

The status of the virial theorem in classical and quantum mechanics is discussed and the principal virial relationships are derived. A model of the electron Fermi gas in a metal is considered taking explicit account of the consequences of the virial theorem for a stable system of electrons and ions interacting in accordance with the Coulomb law. This model is used to obtain expressions for the total energy and the chemical potential of the conduction electrons in undeformed and deformed metals. These expressions are used to estimate the equilibrium concentrations of electrons and ions, the electron work function of a metal, and the contribution of the collective-state electrons to the bulk modulus of a metal. It is shown that an electric field appears in an inhomogeneously deformed metal and that this field is proportional to the gradient of the bulk strains. A space charge, which is compensated by a surface charge of opposite sign, also appears in such a metal.