Graph theory and binary alloys passivated by nickel

Abstract The passivity of a nickel binary alloy is considered in terms of a network of –Ni–O–Ni– bridges in the oxide film, where Ni is the component of the binary alloy which produces passivity. The structure of the oxide is represented by a mathematical graph, and graph theory is used to calculate the connectivity of the oxide, given by the product of the number of edges in the graph and the Randic index. A stochastic calculation is employed to insert ions of the second metal into the oxide film so as to disrupt the connectivity of the –Ni–O–Ni– network. This disruption occurs at a critical ionic concentration of the oxide film. Mathematical relationships are developed for the introduction of a general ion B + n into the oxide film, and critical ionic compositions are calculated for oxide films on the nickel binary alloys. The notation B refers to any metal B which produces B + n ions in the oxide film, where + n is the oxidation number of the ion. The results of this analysis for Fe–Ni and Cu–Ni binary alloys are in good agreement with experimental results.