Dimension of the Gibbs function topological manifold. I: Graph representation of the thermodynamic equilibrium state (Q2353519)

The paper analyses the conditions of the graph theory onto phase transformations. Stable quasi crystals may be formed through non-congruent processes in systems with at least three components. It is shown that quasi crystals are not binary quasi crystals. Isotope compositions were a stabilizing factor for the three quasi crystals earlier discovered by \textit{A. P. Tsai} et al. [``A stable binary quasicrystal'', Nature 408, 537--538 (2000; \url{doi:10.1038/35046202})] and \textit{A. T. Goldman} et al. [``High-energy x-ray diffraction studies of i-\(\mathrm{Sc}_{12}\mathrm{Zn}_{88}\)'', in: Proceedings of the Eleventh International Conference on Quasicrystals:13-18 June 2010, Sapporo. Philos. Mag. 91, No. 19--21, 2427--2433 (2011; \url{doi:10.1080/14786435.2010.511599})]. In phenomenological thermodynamics, branching trees represent the state of phase transitions. The graph based representation of equilibrium states rules out the existence of an exotic one-phase equilibrium in binary systems.