Singularities of the electronic structure and pre-martensitic anomalies of lattice properties in β-phases of metals and alloys

Basic ideas concerning the effect of singularities in the electron energy spectrum on martensitic transitions and pre-martensitic anomalies in elastic moduli and phonon spectra of metals and alloys are reviewed. The microscopic mechanisms of the pre-martensitic anomalies in the lattice properties are thoroughly analyzed. It is shown that in some cases investigation of the singularities in the behaviour of the electron state density near the Fermi level is an efficient tool for analyzing qualitatively the stability of crystalline structures. With alkali and alkaline-earth metals taken as an example, the Hume-Rothery rule is generalized to transitions under pressure and it is shown that the loss of the structural stability can be a consequence of the Fermi level approaching a peak in the electron state density. The contribution of the singularities in the shape of the Fermi level ("nesting") to martensitic transitions and pre-martensitic anomalies in βl-phases of alloys and intermetallic compounds is considered.