Dimension of the Gibbs function topological manifold: 2. Thermodynamically stable binary quasicrystals: Reality or artefact?

Abstract

In complex systems with at least three independent components, one-phase normal states may transform into exotic states. The former are represented by a non-branching tree, while the latter are represented by a branching tree. The transformation takes place through a non-congruent two-phase equilibrium. Until recently, researchers using this process were able to obtain stable quasicrystals with three, four, or more components. It therefore seemed justified to suppose that exotic states constituted quasicrystals. In 2000, however, Tsai’s team discovered two stable binary quasicrystals formed through a congruent process. Virtually no reports on other stable binary quasicrystals have been obtained since that discovery despite considerable effort on the part of researchers. The graph-based representation of equilibrium states rules out the existence of exotic one-phase equilibria (i.e., stable quasicrystals) in binary systems. A question arises: What types of systems did Tsai discover?.