Oxide networks, graph theory, and the passivity of Ni–Cr–Mo ternary alloys

The passivity of Ni–Cr–Mo ternary alloys is considered in terms of a continuous network of –Cr–O–Cr– bridges in the oxide film (which also contains Ni2+ and Mo4+ ions), or in terms of a continuous network of –Ni–O–Ni– bridges in the oxide film (which also contains Cr3+ and Mo4+ ions). The structure of the oxide is represented by a mathematical graph, and graph theory is used to calculate the connectivity of the oxide. This approach shows that a continuous network of –Cr–O–Cr– bridges occurs when the cation fraction of Cr3+ ions in the oxide is 0.35 or greater. A continuous network of –Ni–O–Ni– bridges occurs when the cation fraction of Ni2+ ions in the oxide is 0.55 or greater. Experimental results support the –Cr–O–Cr– model.