Close packing of atoms, geometric frustrations and the formation of heterogeneous states in crystals

To describe the structural peculiarities in inhomogeneous media caused by a tendency towards close packing of atoms, a formalism based on the use of Riemann geometry methods (which, recently, were successfully applied in a description of the structures of quasicrystals and glasses) is developed. On the basis of this formalism we find, in particular, the criterion of stability for precipitates of the Frank-Kasper phases in metallic systems. The nature of the 'rhenium effect' in W-Re alloys is discussed.