General Relations Regarding Graph Theory and the Passivity of Binary Alloys

The passivity of a binary alloy is considered in terms of a network of -M-O-M- bridges in the oxide film, where M 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 -M-O-M- 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 oxides where passivity is due to the existence of continuous networks of -Cr-O-Cr-, -Si-O-Si-, or -Mo-O-Mo-. Thus, critical ionic compositions are calculated for oxide films on the binary alloys B-Cr, B-Si, or B-Mo where passivity is provided in turn by the presence of Cr, Si, or Mo, respectively, in the binary alloy. In each case, B refers to any metal B which produces B + n ions in the oxide film, where + n is the oxidation number of the ion.