Ostwaldʹs step rule and hyperthermodynamics: examples from decomposition in gold-nickel

The classical free-energy minimum and Gibbsʹ topological Phase Rule have explicit counterparts in isothermal dissipative phase space as exhibited within the kinetics of autonomous microstructure formation, in part attributable to the kT/2 of equilibrium fluctuation free energy per atom degree of freedom which is inherited by the kinetic state. The near-reversible modulated decomposition and subsequent decoherency followed by coarsening in Au-Ni alloys is examined within this and other analogues of the minimum free energy requirement. This observed sequence for T<Tc is contrary to the original conclusion that there is a unique transition to a lamellar near-equilibrium state. Furthermore, equilibrium empirical studies have indicated that Ll2 ordering of the form Ni3X with X:Ni lattice parameter ratios > 1.12 excludes the appearance of such a compound since this ratio is 1.15. On the other hand, our observations identify Ni3Au superlattice satellites in modulated alloys at 773K consistently suggesting a dynamical selection to higher free energy trajectories in accord with Ostwaldʹs Step Rule. Van Santen proved this to be corollary to the Onsager-Prigogine Principle of Minimum Dissipation (PMD) and states that where distinct isothermal patterning sequences are feasible nature selects a sequence passing near reversibly through high free energy states rather than decaying directly to the ground state. The Step Rule as a theorem in irreversible thermodynamics is also activated by the time-dependent Ginzburg-Landau equation in contrast to the extra-constrained free energy trajectories associated with the Cahn-Hilliard equation in application to double well decomposition. This article reports the multi-faceted empirical high free energy sequence of states in the decomposition of Au-Ni which strongly supports Ostwaldʹs insight as an extension of the concept of hyperthermodynamics through optimality of the dissipation.