Graph theory and binary alloys passivated by nickel

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.