Phonons in nontransition metals

The article reviews the present status of the microscopic theory of non-transition-metal lattice vibrations. A regular scheme is described, which makes it possible to analyze in detail the role of the electrons in the formation of the phonon spectrum of metals. It is based on a consistent utilization of a small parameter $V_\mathbf{K}/\varepsilon F$, corresponding to the effective weakness of the interaction between the conduction electron and the ion core ($V_\mathbf{K}$ is the Fourier component of this interaction with a momentum transfer equal to one of the reciprocal-lattice vectors). Expansion of the electron-ion energy of the system in terms of this parameter yields, besides the pair interactions that are traditional for metals, also automatically the effective three-particle etc. unpaired inter-ion forces. It is shown that the unpaired forces play an important and sometimes decisive role in a number of questions, such as lattice stability, compressibility, the Cauchy relations for the elastic moduli, and singularities in the phonon spectrum. The theoretical analysis is illustrated by calculations of the static and dynamic properties of metals, and by comparison with experiment, using Na, Mg, Al, and $\beta$-Sn as examples.