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

TL;DR

This paper develops a Riemann geometry-based formalism to analyze atomic packing and structural peculiarities in inhomogeneous media, providing insights into stability criteria of phases in metallic systems.

Contribution

It introduces a novel geometric formalism to describe atomic arrangements and stability in complex crystalline and inhomogeneous materials.

Findings

Criterion for stability of Frank-Kasper precipitates

Explanation of the 'rhenium effect' in W-Re alloys

Application of Riemann geometry to crystal structures

Abstract

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.