Graph Theory and the Passivity of Binary Alloys

Abstract

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 having the oxide of the lower free energy of formation. 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, which is then related to the concentration of alloying element in the metal alloy by means of experimental surface analysis data. The results of this analysis for Fe–Cr, Ni–Cr, Cu–Ni, and Fe–Si are each in good agreement with experimental observations.