Close Packing of Atoms, Geometric Frustration and the Formation of Heterogeneous States in Crystals

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