Modeling Selective Intergranular Oxidation of Binary Alloys

TL;DR

This paper develops a mathematical model to predict intergranular oxidation in binary alloys, explaining differences in oxidation rates and minor element depletion distances based on element transport kinetics and diffusion properties.

Contribution

The paper introduces a novel adaptation of Wagner's thick film growth model to intergranular oxidation, incorporating element-specific transport coefficients and predicting experimental observations.

Findings

Model accurately predicts oxidation velocities and depletion distances.

Cr depletes over larger distances than Al due to diffusion differences.

Transport kinetics explain variations in oxidation behavior among alloys.

Abstract

Intergranular attack of alloys under hydrothermal conditions is a complex problem that depends on metal and oxygen transport kinetics via solid-state and channel-like pathways to an advancing oxidation front. Experiments reveal very different rates of intergranular attack and minor element depletion distances ahead of the oxidation front for nickel-based binary alloys depending on the minor element. For example, a significant Cr depletion up to 9 microns ahead of grain boundary crack tips were documented for Ni-5Cr binary alloy, in contrast to relatively moderate Al depletion for Ni-5Al (~100s of nm). We present a mathematical kinetics model that adapts Wagner's model for thick film growth to intergranular attack of binary alloys. The transport coefficients of elements O, Ni, Cr, and Al in bulk alloys and along grain boundaries were estimated from the literature. For planar surface oxidation, a critical concentration of the minor element can be determined from the model where the oxide of minor element becomes dominant over the major element. This generic model for simple grain boundary oxidation can predict oxidation penetration velocities and minor element depletion distances ahead of the advancing front that are comparable to experimental data. The significant distance of depletion of Cr in Ni-5Cr in contrast to the localized Al depletion in Ni-5Al can be explained by the model due to the combination of the relatively faster diffusion of Cr along the grain boundary and slower diffusion in bulk grains, relative to Al.