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A percolation theory for designing corrosion-resistant alloys


Iron–chromium and nickel–chromium binary alloys containing sufficient quantities of chromium serve as the prototypical corrosion-resistant metals owing to the presence of a nanometre-thick protective passive oxide film1,2,3,4,5,6,7,8. Should this film be compromised by a scratch or abrasive wear, it reforms with little accompanying metal dissolution, a key criterion for good passive behaviour. This is a principal reason that stainless steels and other chromium-containing alloys are used in critical applications ranging from biomedical implants to nuclear reactor components9,10. Unravelling the compositional dependence of this electrochemical behaviour is a long-standing unanswered question in corrosion science. Herein, we develop a percolation theory of alloy passivation based on two-dimensional to three-dimensional crossover effects that accounts for selective dissolution and the quantity of metal dissolved during the initial stage of passive film formation. We validate this theory both experimentally and by kinetic Monte Carlo simulation. Our results reveal a path forward for the design of corrosion-resistant metallic alloys.

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Fig. 1: Passivation on a 2D topological surface.
Fig. 2: LSV and potential step integrated chronoamperometry results with numerical fits to the theoretical equation, \({\it{h}} = {\it{c}}\left( {{\it{p}}_{{\mathrm{c}}}\left( {\it{h}} \right) - {\it{p}}_{{\mathrm{c}}}^{\mathrm{3D}}} \right)^{ - {\it{\nu }}^{\mathrm{3D}}}\).
Fig. 3: Online ICPMS results for passivation of Fe–Cr and Ni–Cr alloys in 0.1 M H2SO4.
Fig. 4: Representative results of first-principles calculations for the dissociative adsorption of dioxygen on Fe(100), Fe(110), Cr(100), Cr(110) and Cr-doped Fe surfaces.

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Data availability

The data used in this study are available from the corresponding author upon request.

Code availability

The KMC and data analysis computer codes used in this study are available from the corresponding author upon request.


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K.S., A.A. and Y.X. acknowledge funding from the National Science Foundation under award DMR-1708459. M.L.T. and K.S. acknowledge funding in part from the Office of Naval Research, Multidisciplinary University Research Initiative programme under award N00014-20-1-2368. D.M.A. and R.C.N. were funded by NSERC (Canada) and UNENE, the University Network of Excellence in Nuclear Engineering. P.P.L. acknowledges support by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division.

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Authors and Affiliations



Y.X. and A.A. performed the electrochemical experiments. P.P.L. performed the in situ ICPMS measurement of the dissolution profile for the alloys. Y.X., D.W. and H.Z. performed the first-principles-based calculations, and J.L.H., E.A. and M.L.T. performed the supplementary scanning transmission electron microscopy (STEM) analysis. D.M.A. performed the KMC simulations and the MC-RNG analysis with input from R.C.N. and K.S.; Y.X., R.C.N., A.A. and K.S. analysed and interpreted all the results. K.S. conceived and supervised the study.

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Correspondence to Karl Sieradzki.

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Peer review information Nature Materials thanks Sannakaisa Virtanen, David Williams and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Discussion, Figs. 1–10, Tables 1–3 and refs. 1–20.

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Xie, Y., Artymowicz, D.M., Lopes, P.P. et al. A percolation theory for designing corrosion-resistant alloys. Nat. Mater. 20, 789–793 (2021).

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