Nonequilibrium Solute Capture in Passivating Oxide Films

Xiao Xiang Yu; Ahmet Gulec; Quentin Sherman; Katie Lutton Cwalina; John R. Scully; John H. Perepezko; Peter W. Voorhees; Laurence D. Marks

doi:10.1103/PhysRevLett.121.145701

Nonequilibrium Solute Capture in Passivating Oxide Films

Xiao Xiang Yu, Ahmet Gulec, Quentin Sherman, Katie Lutton Cwalina, John R. Scully, John H. Perepezko, Peter W. Voorhees, Laurence D. Marks^*

^*Corresponding author for this work

Materials Science and Engineering

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Abstract

We report experimental results on the composition and crystallography of oxides formed on NiCrMo alloys during both high-temperature oxidation and aqueous corrosion experiments. Detailed characterization using transmission electron microscopy and diffraction, aberration-corrected chemical analysis, and atom probe tomography shows unexpected combinations of composition and crystallography, far outside thermodynamic solubility limits. The results are explained using a theory for nonequilibrium solute capture that combines thermodynamic, kinetic, and density functional theory analyses. In this predictive nonequilibrium framework, the composition and crystallography are controlled by the rapidly moving interface. The theoretical framework explains the unusual combinations of composition and crystallography, which we predict will be common for many other systems in oxidation and corrosion, and other solid-state processes involving nonequilibrium moving interfaces.

Original language	English (US)
Article number	145701
Journal	Physical review letters
Volume	121
Issue number	14
DOIs	https://doi.org/10.1103/PhysRevLett.121.145701
State	Published - Oct 4 2018

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1103/PhysRevLett.121.145701

Cite this

@article{030d9282cc4d407c9a2d430ab62ecdc4,

title = "Nonequilibrium Solute Capture in Passivating Oxide Films",

abstract = "We report experimental results on the composition and crystallography of oxides formed on NiCrMo alloys during both high-temperature oxidation and aqueous corrosion experiments. Detailed characterization using transmission electron microscopy and diffraction, aberration-corrected chemical analysis, and atom probe tomography shows unexpected combinations of composition and crystallography, far outside thermodynamic solubility limits. The results are explained using a theory for nonequilibrium solute capture that combines thermodynamic, kinetic, and density functional theory analyses. In this predictive nonequilibrium framework, the composition and crystallography are controlled by the rapidly moving interface. The theoretical framework explains the unusual combinations of composition and crystallography, which we predict will be common for many other systems in oxidation and corrosion, and other solid-state processes involving nonequilibrium moving interfaces.",

author = "Yu, {Xiao Xiang} and Ahmet Gulec and Quentin Sherman and Cwalina, {Katie Lutton} and Scully, {John R.} and Perepezko, {John H.} and Voorhees, {Peter W.} and Marks, {Laurence D.}",

note = "Funding Information: Yu Xiao-xiang 1 Gulec Ahmet 1 Sherman Quentin 1 Cwalina Katie Lutton 2 Scully John R. 2 Perepezko John H. 3 Voorhees Peter W. 1 Marks Laurence D. 1 ,* Department of Materials Science and Engineering, 1 Northwestern University , Evanston, Illinois 60208, USA Department of Materials Science and Engineering, 2 University of Virginia , P.O. Box 400745, 395 McCormick Road, Charlottesville, Virginia 22904, USA Department of Materials Science and Engineering, 3 University of Wisconsin-Madison , 1509 University Avenue, Madison, Wisconsin 53706, USA * Author to whom correspondence should be addressed. L-marks@northwestern.edu . 4 October 2018 5 October 2018 121 14 145701 25 July 2018 {\textcopyright} 2018 American Physical Society 2018 American Physical Society We report experimental results on the composition and crystallography of oxides formed on NiCrMo alloys during both high-temperature oxidation and aqueous corrosion experiments. Detailed characterization using transmission electron microscopy and diffraction, aberration-corrected chemical analysis, and atom probe tomography shows unexpected combinations of composition and crystallography, far outside thermodynamic solubility limits. The results are explained using a theory for nonequilibrium solute capture that combines thermodynamic, kinetic, and density functional theory analyses. In this predictive nonequilibrium framework, the composition and crystallography are controlled by the rapidly moving interface. The theoretical framework explains the unusual combinations of composition and crystallography, which we predict will be common for many other systems in oxidation and corrosion, and other solid-state processes involving nonequilibrium moving interfaces. Office of Naval Research 10.13039/100000006 N00014-16-1-2280 Every metal, with the sole exception of gold, is unstable in air relative to its oxide at room temperature. The only reason they can be used in many applications is because protective oxide films form that limit further oxidation; many metals in aerospace, medical, nuclear, solar, geothermal, and spent nuclear fuel disposal rely on a protective, nanoscale oxide film. Although much of the general science of how the oxides form is known, there are still gaps. Much of our current knowledge is from the mesoscale down to several nanometers, but multiple processes over wide spatial and temporal scales control their nucleation, composition, stability, and structure. Understanding and predicting oxide growth is critically important if we are to move beyond remedial treatment and coating of metallic surfaces or empirical alloy composition selection towards science-guided alloy design. This is becoming increasingly urgent with aging infrastructure in the developed world, the use of metallic alloys in increasingly harsh environments, as well as the ever-increasing costs of failure of corroded components. We demonstrate here that unusual combinations of structure and chemical composition are a general phenomenon in these oxide films and provide a predictive explanation building upon the well-established science of nonequilibrium interfaces [1] , extended to moving oxide-substrate interfaces. The experimental evidence indicates that rather than analyzing the development of these oxides using crystallography, chemical composition, or concepts based upon equilibrium thermodynamics, one has to analyze both the crystallography and chemistry, combining these with a nonequilibrium approach. We use “nonequilibrium” deliberately to denotes a phase, reaction, or process that departs from full equilibrium. At the first level of departure, equilibrium phases are present, but their compositions are not in equilibrium except at the interfaces where there is more rapid diffusion than in the bulk; the interface is in local equilibrium. At the next level of departure, metastable phases are present and the interface is in local equilibrium. The metastable phases can be equilibrium phases with a nonequilibrium composition, or ones absent from the equilibrium phase diagram. In nonequilibrium there is a full breakdown of the local equilibrium approximation in the phases and at the interface, and the oxide composition is a function of the interface velocity. One has to use approaches such as extended irreversible thermodynamics [2] or the nonequilibrium thermodynamics of interfaces [3] . We show here that during corrosion, whether high-temperature oxygen, steam, aqueous, or other, frequently the interfaces move fast compared to the timescale for establishing local equilibrium, and a nonequilibrium approach is needed. As general background on how these oxide films develop, starting from a clean alloy a thin oxide film develops with a potential gradient across it, as first described by Cabrera and Mott [4] . As the film thickness increases, point defects diffuse across the oxide driven by the chemical potential gradients and electric fields [4–15] , until the film thickness becomes large enough that diffusion controls, as first described by Wagner [16] , and expanded upon by others [7,16–22] . In an aqueous environment, the film may never reach this limit due to dissolution at the oxide-electrolyte interface [23,24] . Throughout the existing literature, thermodynamically favored oxide phases are commonly assumed to form [25–28] , or phases which are stable in Pourbaix diagrams [29] , for instance, pure nickel oxide and chromia for nickel-chromium-based alloys [30–34] , often enriched with alloying elements [35–38] . One explanation is that during oxidation the more energetically favored (lowest free-energy) oxides form first [25,39] . As noted by Wagner [18,40] and further developed by Chattopadhyay and Wood [41] , free energies do not explain the development of the oxide. Experimentally the initial oxide is sometimes a metastable variant that converts to the thermodynamically stable form with slower kinetics [42–45] , suggesting Ostwald{\textquoteright}s step rule [46–50] where faster growing phases form first. For aqueous films there is extensive x-ray photoelectron spectroscopy (XPS) data [25,51] , typically interpreted in terms of the thermodynamically stable oxides. For oxidation, x-ray or electron diffraction [43,52–54] has been widely used to identify the lattice parameters of the phases which are then compared to known oxides. There are two critical issues with the current literature. The first is interpretation of crystal structures from XPS measurements of local valence states or diffraction experiments. XPS is sensitive to the valence and local coordination, not the crystallographic arrangement of atoms. Hence a spectroscopic signature similar to that of a standard only proves that the local chemical environment is similar. Similarly, a lattice parameter and/or spacings close to a known standard only proves that the atomic arrangement is similar. To rigorously identify a phase one has to simultaneously determine both the crystallographic arrangement of the atoms and the chemical composition. The second issue involves approaches to solving the transport equations for oxidation. These have chemical rate equations or some other boundary condition for how atoms cross the interface between the metal and oxide. Such formulations will lead to solute atoms being injected into the oxide; however, there is a physical inconsistency. In both oxidation and aqueous corrosion there is a moving oxidation front that combines point defect migration across the interface and physical motion of the interface. The interface therefore has an effective velocity proportional to the rate of incorporation of alloy atoms as cations in the oxide. As this velocity tends to infinity, a necessary constraint is that the chemical composition of cations in the oxide has to be that of the alloy, A second constraint is that as the interface velocity tends to zero, thermodynamics stable or metastable phases with compositions bounded by thermodynamic solubility limits have to be formed. Valid models have to obey these constraints, which requires a term for exchange of cations across the interface that is missing in conventional formulations. A nonequilibrium formulation for the moving oxide interfaces correctly includes a velocity dependence. As we will show, the compositions formed can be predicted and calculated using a “nonequilibrium solute capture” framework based solely upon the ratio of the velocity of the interface and an effective velocity for equilibration. Independent of whether the phases formed follow Ostwald{\textquoteright}s step rule [46–50] , or are those of lowest free energy, the composition is controlled by the metal-oxide interface velocity. The systems herein are Ni-Cr-Mo alloys oxidized in air at intermediate temperatures in the range 500 – 800 ° C , as well as the same alloys passivated electrochemically in aqueous environments. While specific details varied with the particular alloys and treatment conditions, we will demonstrate that solute capture during oxide film growth is a general phenomenon. The main experimental tools used are transmission electron microscopy and atom-probe tomography (APT). We have examined bulk samples which were oxidized and then appropriate regions extracted using conventional sample preparation methods, as well as samples first prepared in the appropriate geometry for examination and then oxidized or corroded. More details are provided in Supplemental Material, Sec. I [55] . Independent of whether the oxide formed by dry oxidation or in aqueous conditions, the first product is an oxide with a rocksalt structure ( F m 3 ¯ m ). (We describe the oxides by both the crystallographic space group and chemical composition; both need to be specified.) Similar oxides have been reported in the literature, typically interpreted as nickel oxide since they have similar lattice parameters, with perhaps additional solute metal atoms at low concentrations. From electron diffraction data as well as high-resolution imaging (see Fig. S1 of Supplemental Material [55] ) the crystallographic structure is rocksalt ( F m 3 ¯ m ), but examination using both APT and chemical analysis inside electron microscopes (Fig. 1 for an aqueous sample) shows that there is very significant chromium and traces of molybdenum in the F m 3 ¯ m oxide. Ignoring the low molybdenum concentration, the composition of this rocksalt ( F m 3 ¯ m ) structure is Cr 1 − x Ni x O y , with x ∼ 0.5 . The oxygen content is approximately y = 1.25 at the outer surface and closer to y = 1 adjacent to the metal or for very thin oxides. This implies Cr 3 + at the external surface and Cr 2 + at the metal-oxide interface. This chromium content is significantly larger than the thermodynamic solubility limit of chromium doping in NiO [56] . According to equilibrium thermodynamics this oxide should phase separate into nearly pure rocksalt NiO ( F m 3 ¯ m ) and corundum Cr 2 O 3 ( R 3 ¯ c ). It has not, neither during high-temperature oxidation, the aqueous corrosion, nor the days to weeks after sample preparation before examination by electron microscopy or APT. 1 10.1103/PhysRevLett.121.145701.f1 FIG. 1. Chemical data for the oxide on a Ni-22%Cr-6%Mo (wt %) alloy oxidized in K 2 S 2 O 8 and Na 2 SO 4 . (a) High-angle annular dark field image (left) and annular bright field image (right), with (b) the composition from an electron energy loss line scan. The metal-oxide interface is marked in red, the oxide-vacuum in white. The oxide next to the metal is rocksalt ( F m 3 ¯ m ) of composition ∼ Cr 0.5 Ni 0.5 O . Shown in (c) and (d) are atom-probe tomography results for a tip treated under the same conditions with a 12 at. % isosurface in (c) and a proxigram (compositional line scan) in (d), corrected for oxygen detection efficiency, cross-validating the electron microscopy results. The rocksalt phase is not the only structure with a composition far from conventional thermodynamic expectations. For nickel-chromium-iron alloys and nickel-chromium-molybdenum alloys, an oxide with the corundum ( R 3 ¯ c ) structure has been reported [25,51,57–60] , and assumed to be chromia with perhaps some nickel solute. We can verify the existence of an oxide with a corundum ( R 3 ¯ c ) structure; in some cases it is chromia Cr 2 O 3 ( R 3 ¯ c ), but in others the composition is Cr 2 − x Ni x O 3 − y , with x ∼ 1 (Fig. 2 ). Here a sample was oxidized in situ at 700 ° C in 1 × 10 − 4 torr of oxygen. A metastable R 3 ¯ c Ni 2 O 3 phase with the corundum ( R 3 ¯ c ) crystallography is well established [61] , so a metastable corundum Cr 2 − x Ni x O 3 − y ( R 3 ¯ c ) is feasible, but far from expectations based upon the published thermodynamic data. [Figure 2(a) is from an in situ experiment where F m 3 ¯ m Cr 1 − x Ni x O y was also observed [62] .] 2 10.1103/PhysRevLett.121.145701.f2 FIG. 2. A Ni-22%Cr-6%Mo (wt %) sample oxidized in situ at 700 ° C in 1 × 10 − 4 torr of oxygen, and later analyzed by electron energy loss spectroscopy. (a) A bright field image during in situ growth showing fringes characteristic of the corundum ( R 3 ¯ c ) structure. (b) A high-angle annular dark field image with the corresponding electron energy loss line scan in (c). The corundum structure adjacent to the metal has a composition of approximately CrNiO 3 . Figures 1 and 2 are for relatively thin films, so they could be artifacts of very thin oxide layers or short times. Figure 3 shows results for a sample annealed in oxygen for 24 h at 800 ° C , where similar results are found in oxide films more than 300 nm thick. Adjacent to the metal is an approximately 100 nm thick Cr 1 − x Ni x O 1.5 − x / 2 rocksalt structure ( F m 3 ¯ m ), then over this is nearly pure rocksalt NiO ( F m 3 ¯ m ), with nearly pure corundum Cr 2 O 3 ( R 3 ¯ c ) at the outer surface. The same sample was examined after being stored for a year in air at room temperature, and had the same overall structure with indications that a small amount of corundum had started to form but rocksalt still dominated for the 100 nm thick region adjacent to the metal-oxide interface; see Fig. S2 in Supplemental Material [55] . 3 10.1103/PhysRevLett.121.145701.f3 FIG. 3. Results for a Ni-22%Cr-6%Mo (wt %) oxidized at 800 ° C for 24 h in air. Shown in (a) is an overview high-angle annular dark field image of a focused ion-beam region cut from the sample. The different layers in (b)–(e) are shown as bright field and diffraction pattern pairs, in (b) of the metal, (c) rocksalt ( F m 3 ¯ m ) Cr 1 − x Ni x O y , (d) nickel oxide ( F m 3 ¯ m ), and (e) chromia ( R 3 ¯ c ). Shown in (f) is an APT tomogram taken from the interface layer which shows a Cr 1 − x Ni x O 1.5 − x / 2 rocksalt ( F m 3 ¯ m ) phase, with a one-dimensional composition plot with the metal on the right in (g) of the local chromium fraction on the y axis as a function of position along the x axis. While the most definitive evidence is local structural and chemical analysis, in situ atomic emission spectroelectrochemistry experiments support the chemical compositions observed in the electron microscopy and APT. These track the metal ions leaving the oxide at the oxide-solution interface versus those oxidized [63] (see Supplemental Material Sec. S3 and Figs. S3 and S4 [55] ). The concentrations are quantitatively consistent with those predicted by the solute capture model described later and the results in Fig. 1 , namely, rocksalt Cr 1 − x Ni x O 1.5 − x / 2 ( Cr 3 + and Ni 2 + ) with x = 0.7 . The experimental evidence demonstrates the presence of nonequilibrium rocksalt ( F m 3 ¯ m ) and corundum ( R 3 ¯ c ) phases with either Ni 2 + or Ni 3 + with dominantly Cr 3 + , possibly Cr 2 + very close to the metal-oxide interface, and chemical composition far from equilibrium. These are a result of what we call nonequilibrium solute capture at moving oxidation fronts as illustrated in Fig. S5 [55] , analogous but different from well-known solute trapping during solidification [1] . Differentiating the two is important. First, in solute trapping atoms add to a moving solidification front; hence, the velocity of the front is coupled to the rate of addition of atoms. In nonequilibrium solute capture, in addition to moving interfaces, either or both vacancies and interstitials are moving. Defining the interface by the location of the oxygen atoms, with the nickel-nickel oxide system the interface can be stationary but still have a net flux of nickel vacancies crossing it. Secondly, in solute trapping the free energy of the solvent drops whereas that of the solute increases. For instance, with rapid freezing of salt water, the free energy of the water (solvent) drops but that of the retained solute (salt) increases. In contrast, in nonequilibrium solute capture the free energy of both drop. Two conditions are required for nonequilibrium solute capture. The first is that the free-energy change during formation of the oxide is negative [1] . (See also Supplemental Material Sec. S4 [55] .) As shown in Figs. S6 and S7 [55] , which combines literature thermodynamic data as well as specific density functional theory results, all oxides based upon combinations of Cr 2 + , Cr 3 + and Ni 2 + , Ni 3 + in both rocksalt ( F m 3 ¯ m ) and corundum ( R 3 ¯ c ) crystallographies satisfy this first condition. Metastable solid solutions are possible across the whole compositional range. Considering just the rocksalt crystallography of Figs. 1 and 3 , the lowest free-energy oxide (per oxygen or metal atom) has the composition Cr 2 O 3 ; i.e., 2 / 3 of the cation sites in the cubic unit cell are occupied by chromium atoms. This composition was not observed experimentally because nickel atoms were captured in the rocksalt oxide. As also shown in Fig. S6 [55] , there is the possibility of having Cr 2 + captured in an F m 3 ¯ m oxide which, rigorously, would be denoted as Ni 1 − x Cr x O —nickel oxide is the solvent. The microscopy data in Fig. 1 suggest that this occurs at the metal-oxide interface. One can also have Ni 3 + captured in corundum R 3 ¯ c , which is Cr 1 − x Ni x O 3 ; see Fig. 2 . The second condition is that the interface is moving too fast for equilibrium to be achieved. (See Supplemental Material Sec. S5 [55] .) The extent of capture is parametrized by β = v a / v D , where v a is the velocity of the cations moving into the oxide combining both the physical interface motion and the flux of atoms, which for a planar interface with no adsorption at the interface is v a = − c o v I + j o Ω , with v I the physical velocity of the metal-oxide interface, j o the number of cations crossing the interface per unit area and time (combining vacancy and interstitial contributions), c o the mole fraction of cations in the oxide, and Ω the atomic volume. The diffusive velocity is v D = D i / a , where D i is an interface diffusion coefficient for a Zener exchange of cations and a the hopping distance for exchange between the oxide and metal to equilibrate the composition of the oxide. Nonequilibrium phase compositions form when β ≫ 1 so long as the total free-energy change (condition 1 above) is negative [1] . Turning to the values of β , for planar growth of NiO and using standard values for diffusion constants in the oxide ( [64,65] and see Supplemental Material [55] ), Fig. 4(a) shows that capture of Ni is expected for a wide range of conditions during high-temperature oxidation (see also Supplemental Material Sec. S5 [55] ). It is also probable that β > 1 , during electrochemical passivation, as shown in Fig. 4(b) ; except for very slow passive aqueous dissolution at < 10 − 7 A / cm 2 , the effective velocity of the corroding interface using a Faraday{\textquoteright}s law derived electrochemical interface velocity is faster than the rate of equilibration. This is consistent with our experimental observations. 4 10.1103/PhysRevLett.121.145701.f4 FIG. 4. Kinetic conditions for solute capture, in (a) for oxidation based upon literature diffusion constants and reaction rates as a function of exposure temperature and oxygen partial pressure in atmospheres for an oxide thickness of 5 nm and a hopping distance of 1 nm. The horizontal green plane is v a a / D i = 1 , the blue surface the ratio for different temperatures and oxygen pressures. For a wide range of conditions, oxidation is expected to lead to solute capture, consistent with the experimental results. In (b) a plot of the local electrochemical corrosion current density along x and the velocity of the oxidation front along y for a range of different processes in aqueous corrosion with the approximate diffusion velocity D i / a marked on the right for a = 1.0 nm , assuming a field-affected diffusivity of 10 − 20 cm 2 / sec ; again solute capture will be common. Our experimental observations and the model for solute capture predict that for many cases of oxidation and almost all aqueous conditions, solute capture for NiCr alloys is the norm, not the exception. The possibility of capture can be predicted using the free energies of the phases and values for the interface diffusion constant and hopping distance. Where there are competing solute capture phases, which of these will form for different conditions can in principle be predicted, as briefly outlined in Supplemental Material Sec. S6 [55] , which includes Refs. [1,3,62–64,66–108] . Expanded thermodynamic databases along with the model for solute capture open the door to deliberately forming oxides of novel compositions, and thus properties for a given application, for instance, better protection and thus significantly longer lifetimes in service. To illustrate this, and the distinction of this model from the standard idea of cation injection during oxide growth, we will advance some predictions, with caveats that experimental validation is important. Almost all elements in the first transition metal row can form rocksalt oxides, so we tested using density functional theory calculations the thermodynamics of the comparable rocksalt oxides in the Sc 2 x / 3 Mg 1 − x O and Al 2 x / 3 Mg 1 − x O systems. As shown in Supplemental Material Fig. S8 [55] , both lead to metastable solid solutions, so are strong candidates for nonequilibrium solute capture. The free-energy change of a nonequilibrium solute captured rocksalt A 1 − x B x O y can be written as Δ G NSC = Δ G Oxide A + Δ G Oxide B + E ( Δ r Ion , T , … ) , where the first two terms on the right-hand side are the free energies of formation of the single cation rocksalt oxides and the third is the mixing energy, which will depend strongly upon the difference in the ionic radii Δ r Ion . The ionic radii across the first transition row are not that different. Since the free energies of formation of the single cation oxides are all significantly negative, Δ G NSC will almost certainly be negative; solute capture is likely to occur across the whole first transition row. It can also occur with elements below the first transition metal row. To minimize the strain energy we expect higher valences so the valence and coordination specific ionic radii should be similar. For instance, molybdenum is a known beneficial dopant and has ionic radii of 0.83, 0.79 and 0.75 {\AA} for sixfold 3 + , 4 + , and 5 + states, respectively, which can be compared to 0.83 for sixfold Ni 2 + and 0.755 for sixfold Cr 3 + . Hence, we predict the presence of Mo 3 + solute captured in rocksalt Cr 1 − x Ni x O 1.5 − x / 2 and Mo 4 + or Mo 5 + in corundum Cr 2 − x Ni x O 3 ; higher oxidation states are consistent with the available XPS data. We suspect solute capture occurs in other solid-fluid or solid-solid chemical reactions, not just the formation of protective oxide films or rapid solidification. If the product is lower in free energy, and the reaction front is moving fast enough, the same science holds independent of whether one is dealing with ceramics, metals, semiconductors, or polymers. The authors acknowledge support from ONR MURI “Understanding Atomic Scale Structure in Four Dimensions to Design and Control Corrosion Resistant Alloys “through Grant No. N00014-16-1-2280. X.-x. Y. and A. G. performed the oxidation and aqueous treatments of the samples and TEM observations, supervised by L. D. M., with electrochemistry input from K. L. C. and J. R. S. X.-x. Y. performed the APT experiments, supervised by L. D. M. Q. S. performed the solute trapping thermodynamics analysis supervised by P. W. V. with discussions with J. H. P. K. L. C. performed the electrochemical tests supervised by J. R. S. L. D. M. performed the density functional theory calculations. All authors contributed to the writing of the Letter. [1] 1 J. C. Baker and J. W. Cahn , Acta Metall. Mater. 17 , 575 ( 1969 ). AMATEB 0956-7151 10.1016/0001-6160(69)90116-3 [2] 2 D. Jou and G. Lebon , Extended Irreversible Thermodynamics ( Springer , Amsterdam, 2010 ), p. 483 . [3] 3 J. C. Baker and J. W. Cahn , Solidification ( American Society for Metals , Metals Park, OH, 1971 ), p. 23 . [4] 4 N. Cabrera and N. F. Mott , Rep. Prog. Phys. 12 , 163 ( 1948 ). RPPHAG 0034-4885 10.1088/0034-4885/12/1/308 [5] 5 C. Y. Chao , L. F. Lin , and D. D. Macdonald , J. Electrochem. Soc. 128 , 1187 ( 1981 ). JESOAN 0013-4651 10.1149/1.2127591 [6] 6 L. F. Lin , C. Y. Chao , and D. D. Macdonald , J. Electrochem. Soc. 128 , 1194 ( 1981 ). JESOAN 0013-4651 10.1149/1.2127592 [7] 7 A. Atkinson , Rev. Mod. Phys. 57 , 437 ( 1985 ). RMPHAT 0034-6861 10.1103/RevModPhys.57.437 [8] 8 D. D. Macdonald , J. Electrochem. Soc. 139 , 3434 ( 1992 ). JESOAN 0013-4651 10.1149/1.2069096 [9] 9 C. Chainais-Hillairet and C. Bataillon , Numer. Math. 110 , 1 ( 2008 ). 10.1007/s00211-008-0154-x [10] 10 C. Bataillon , F. Bouchon , C. Chainais-Hillairet , C. Desgranges , E. Hoarau , F. Martin , S. Perrin , M. Tupin , and J. Talandier , Electrochim. Acta 55 , 4451 ( 2010 ). ELCAAV 0013-4686 10.1016/j.electacta.2010.02.087 [11] 11 D. D. Macdonald , Electrochim. Acta 56 , 1761 ( 2011 ). ELCAAV 0013-4686 10.1016/j.electacta.2010.11.005 [12] 12 A. Seyeux , V. Maurice , and P. Marcus , J. Electrochem. Soc. 160 , C189 ( 2013 ). JESOAN 0013-4651 10.1149/2.036306jes [13] 13 K. Leistner , C. Toulemonde , B. Diawara , A. Seyeux , and P. Marcus , J. Electrochem. Soc. 160 , C197 ( 2013 ). JESOAN 0013-4651 10.1149/2.037306jes [14] 14 A. Couet , A. T. Motta , and A. Ambard , Corros. Sci. 100 , 73 ( 2015 ). CRRSAA 0010-938X 10.1016/j.corsci.2015.07.003 [15] 15 A. Couet , A. T. Motta , A. Ambard , and R. J. Comstock , in Proceedings of the 18th International Symposium on Zirconium in the Nuclear Industry , edited by R. J. Comstock and A. T. Motta ( ASTM International , Hilton Head Island, SC, 2016 ), p. 312 . [16] 16 C. Wagner , Z. Phys. Chem., Abt. B 21 , 25 ( 1933 ). ZPCBAL 0372-9664 [17] 17 C. Wagner , Z. Phys. Chem., Abt. B 32 , 447 ( 1936 ). ZPCBAL 0372-9664 [18] 18 C. Wagner , J. Electrochem. Soc. 99 , 369 ( 1952 ). JESOAN 0013-4651 10.1149/1.2779605 [19] 19 L. Himmel , R. F. Mehl , and C. E. Birchenall , Trans. Am. Inst. Min. Metall. Eng. 197 , 827 ( 1953 ). [20] 20 K. R. Lawless , Rep. Prog. Phys. 37 , 231 ( 1974 ). RPPHAG 0034-4885 10.1088/0034-4885/37/2/002 [21] 21 G. R. Wallwork , Rep. Prog. Phys. 39 , 401 ( 1976 ). RPPHAG 0034-4885 10.1088/0034-4885/39/5/001 [22] 22 H. Hindam and D. P. Whittle , Oxid Met. 18 , 245 ( 1982 ). 10.1007/BF00656571 [23] 23 I. Olefjord and B. O. Elfstrom , Corrosion 38 , 46 ( 1982 ). 10.5006/1.3577318 [24] 24 I. Olefjord , B. Brox , and U. Jelvestam , J. Electrochem. Soc. 131 , C299 ( 1984 ). JESOAN 0013-4651 [25] 25 N. Winograd , W. E. Baitinger , J. W. Amy , and J. A. Munarin , Science 184 , 565 ( 1974 ). SCIEAS 0036-8075 10.1126/science.184.4136.565 [26] 26 R. D. Willenbruch , C. R. Clayton , M. Oversluizen , D. Kim , and Y. Lu , Corros. Sci. 31 , 179 ( 1990 ). CRRSAA 0010-938X 10.1016/0010-938X(90)90106-F [27] 27 P. Saltykov , O. Fabrichnaya , J. Golczewski , and F. Aldinger , J. Alloys Compd. 381 , 99 ( 2004 ). JALCEU 0925-8388 10.1016/j.jallcom.2004.02.053 [28] 28 B. Ingham , S. C. Hendy , N. J. Laycock , and M. P. Ryan , Electrochem. Solid State Lett. 10 , C57 ( 2007 ). ESLEF6 1099-0062 10.1149/1.2757472 [29] 29 B. Beverskog and I. Puigdomenech , Corrosion 55 , 1077 ( 1999 ). 10.5006/1.3283945 [30] 30 J. E. Croll and G. R. Wallwork , Oxid Met. 4 , 121 ( 1972 ). 10.1007/BF00613088 [31] 31 A. D. Dalvi and D. E. Coates , Oxid Met. 5 , 113 ( 1972 ). 10.1007/BF00610840 [32] 32 J. J. Gilman , Science 306 , 1134 ( 2004 ). SCIEAS 0036-8075 10.1126/science.306.5699.1134 [33] 33 S. E. Ziemniak , L. M. Anovitz , R. A. Castelli , and W. D. Porter , J. Chem. Thermodyn. 39 , 1474 ( 2007 ). JCTDAF 0021-9614 10.1016/j.jct.2007.03.001 [34] 34 L. Kaufman , J. H. Perepezko , K. Hildal , J. Farmer , D. Day , N. Yang , and D. Branagan , CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 33 , 89 ( 2009 ). CCCTD6 0364-5916 10.1016/j.calphad.2008.09.019 [35] 35 R. Kirchheim , B. Heine , H. Fischmeister , S. Hofmann , H. Knote , and U. Stolz , Corros. Sci. 29 , 899 ( 1989 ). CRRSAA 0010-938X 10.1016/0010-938X(89)90060-7 [36] 36 L. Zhang and D. D. Macdonald , Electrochim. Acta 43 , 2661 ( 1998 ). ELCAAV 0013-4686 10.1016/S0013-4686(97)00268-5 [37] 37 J. E. Castle and K. Asami , Surf. Interface Anal. 36 , 220 ( 2004 ). SIANDQ 0142-2421 10.1002/sia.1676 [38] 38 D. D. Macdonald , Afinidad : organo de la Asociacion de Quimicos del Instituto Quimico de Sarria 62 , 498 ( 2005 ). AFINAE 0001-9704 [39] 39 L. Kjellqvist , M. Selleby , and B. Sundman , CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 32 , 577 ( 2008 ). CCCTD6 0364-5916 10.1016/j.calphad.2008.04.005 [40] 40 C. Wagner , J. Electrochem. Soc. 103 , 571 ( 1956 ). JESOAN 0013-4651 10.1149/1.2430159 [41] 41 B. Chattopadhyay and G. C. Wood , Oxid Met. 2 , 373 ( 1970 ). 10.1007/BF00604477 [42] 42 J. C. Yang , E. Schumann , I. Levin , and M. Ruhle , Acta Mater. 46 , 2195 ( 1998 ). ACMAFD 1359-6454 10.1016/S1359-6454(97)00378-9 [43] 43 J. Doychak , J. L. Smialek , and T. E. Mitchell , Metall. Trans. A 20 , 499 ( 1989 ). MTTABN 0360-2133 10.1007/BF02653930 [44] 44 V. K. Tolpygo and D. R. Clarke , Materials at High Temperatures 17 , 59 ( 2000 ). MHTEEM 0960-3409 10.1179/mht.2000.011 [45] 45 G. C. Rybicki and J. L. Smialek , Oxid Met. 31 , 275 ( 1989 ). 10.1007/BF00846690 [46] 46 W. Ostwald , Z. Phys. Chem. 22U , 19 ( 1897 ). [47] 47 I. N. Stranski and D. Totomanow , Z. Phys. Chem., Abt. A 163 , 399 ( 1933 ). ZPCAAI 0372-9656 [48] 48 R. A. Vansanten , J. Phys. Chem. 88 , 5768 ( 1984 ). JPCHAX 0022-3654 10.1021/j150668a002 [49] 49 J. Nyvlt , Cryst. Res. Technol. 30 , 443 ( 1995 ). CRTEDF 0232-1300 10.1002/crat.2170300402 [50] 50 N. Niekawa and M. Kitamura , Cryst. Eng. Commun. 15 , 6932 ( 2013 ). 10.1039/c3ce40582f [51] 51 A. Machet , A. Galtayries , S. Zanna , L. Klein , V. Maurice , P. Jolivet , M. Foucault , P. Combrade , P. Scott , and P. Marcus , Electrochim. Acta 49 , 3957 ( 2004 ). ELCAAV 0013-4686 10.1016/j.electacta.2004.04.032 [52] 52 J. Doychak and M. Ruhle , Oxid Met. 31 , 431 ( 1989 ). 10.1007/BF00666466 [53] 53 M. W. Brumm and H. J. Grabke , Corros. Sci. 33 , 1677 ( 1992 ). CRRSAA 0010-938X 10.1016/0010-938X(92)90002-K [54] 54 M. F. Toney , A. J. Davenport , L. J. Oblonsky , M. P. Ryan , and C. M. Vitus , Phys. Rev. Lett. 79 , 4282 ( 1997 ). PRLTAO 0031-9007 10.1103/PhysRevLett.79.4282 [55] 55 See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.121.145701 for methods, as well as additional material as described in the text. [56] 56 C.-H. Chen , M. R. Notis , and D. B. Williams , J. Am. Ceram. Soc. 66 , 566 ( 1983 ). JACTAW 0002-7820 10.1111/j.1151-2916.1983.tb10092.x [57] 57 P. Marcus and J. M. Grimal , Corros. Sci. 33 , 805 ( 1992 ). CRRSAA 0010-938X 10.1016/0010-938X(92)90113-H [58] 58 S. E. Ziemniak and M. Hanson , Corros. Sci. 45 , 1595 ( 2003 ). CRRSAA 0010-938X 10.1016/S0010-938X(02)00230-5 [59] 59 S. E. Ziemniak and M. Hanson , Corros. Sci. 48 , 498 ( 2006 ). CRRSAA 0010-938X 10.1016/j.corsci.2005.01.006 [60] 60 J. E. Maslar , W. S. Hurst , W. J. Bowers , J. H. Hendricks , and E. S. Windsor , J. Electrochem. Soc. 156 , C103 ( 2009 ). JESOAN 0013-4651 10.1149/1.3056038 [61] 61 W. Pies and A. Weiss , in b1468, II.1.1 Simple Oxides , edited by K.-H. Hellwege and A. M. Hellwege , Landolt-B{\"o}rnstein, Group III, Vol. 7B1, Key Element: O. Pt 1 ( Springer-Verlag , Berlin, 1975 ), https://materials.springer.com/lb/docs/sm_lbs_978-3-540-37856-3_31 . [62] 62 X.-x. Yu , A. Gulec , C. M. Andolina , E. J. Zeitchick , K. Gusieva , J. C. Yang , J. R. Scully , J. H. Perepezko , and L. D. Marks , Corrosion 74 , 939 ( 2018 ). 10.5006/2807 [63] 63 K. Lutton , K. Gusieva , N. Ott , N. Birbilis , and J. R. Scully , Electrochem. Comm. 80 , 44 ( 2017 ). ECCMF9 1388-2481 10.1016/j.elecom.2017.05.015 [64] 64 W. K. Chen , N. L. Peterson , and L. C. Robinson , J. Phys. Chem. Solids 34 , 705 ( 1973 ). JPCSAW 0022-3697 10.1016/S0022-3697(73)80177-5 [65] 65 D. L. Douglass , Corros. Sci. 8 , 665 ( 1968 ). CRRSAA 0010-938X 10.1016/S0010-938X(68)80101-5 [66] 66 M. Pourbaix , Atlas of Electrochemical Equilibria in Aqueous Solutions ( Pergamon , New York, 1966 ), Vol. 1 . [67] 67 B. L. Chamberland and W. H. Cloud , J. Appl. Phys. 40 , 434 ( 1969 ). JAPIAU 0021-8979 10.1063/1.1657087 [68] 68 D. S. Walters and G. P. Wirtz , J. Am. Ceram. Soc. 54 , 563 ( 1971 ). JACTAW 0002-7820 10.1111/j.1151-2916.1971.tb12208.x [69] 69 M. J. Aziz , J. Appl. Phys. 53 , 1158 ( 1982 ). JAPIAU 0021-8979 10.1063/1.329867 [70] 70 M. J. Aziz , Appl. Phys. Lett. 43 , 552 ( 1983 ). APPLAB 0003-6951 10.1063/1.94416 [71] 71 W. J. Boettinger , S. R. Coriell , and R. F. Sekerka , Mater. Sci. Eng. 65 , 27 ( 1984 ). MSCEAA 0025-5416 10.1016/0025-5416(84)90196-4 [72] 72 K. D. Becker and F. Rau , Phys. Chem. Chem. Phys. 91 , 1279 ( 1987 ). 10.1002/bbpc.19870911139 [73] 73 M. J. Aziz and T. Kaplan , Acta Metall. Mater. 36 , 2335 ( 1988 ). AMATEB 0956-7151 10.1016/0001-6160(88)90333-1 [74] 74 J. R. Taylor and A. T. Dinsdale , Z. Metall. 81 , 354 ( 1990 ). [75] 75 K. Sujata and T. O. Mason , J. Am. Ceram. Soc. 75 , 557 ( 1992 ). JACTAW 0002-7820 10.1111/j.1151-2916.1992.tb07842.x [76] 76 J. P. Hirth , B. Pieraggi , and R. A. Rapp , Acta Metall. Mater. 43 , 1065 ( 1995 ). AMATEB 0956-7151 10.1016/0956-7151(94)00296-T [77] 77 B. Pieraggi , R. A. Rapp , and J. P. Hirth , Oxid Met. 44 , 63 ( 1995 ). 10.1007/BF01046723 [78] 78 M. E. Gurtin and P. W. Voorhees , Acta Mater. 44 , 235 ( 1996 ). ACMAFD 1359-6454 10.1016/1359-6454(95)00139-X [79] 79 J. P. Perdew , K. Burke , and M. Ernzerhof , Phys. Rev. Lett. 77 , 3865 ( 1996 ). PRLTAO 0031-9007 10.1103/PhysRevLett.77.3865 [80] 80 S. L. Sobolev , Phys. Rev. E 55 , 6845 ( 1997 ). PLEEE8 1063-651X 10.1103/PhysRevE.55.6845 [81] 81 N. Kashii , H. Maekawa , and Y. Hinatsu , J. Am. Ceram. Soc. 82 , 1844 ( 1999 ). JACTAW 0002-7820 10.1111/j.1151-2916.1999.tb02007.x [82] 82 S. A. T. Redfern , R. J. Harrison , H. S. C. O{\textquoteright}Neill , and D. R. R. Wood , Am. Mineral. 84 , 299 ( 1999 ). AMMIAY 0003-004X 10.2138/am-1999-0313 [83] 83 K. Ogle and S. Weber , J. Electrochem. Soc. 147 , 1770 ( 2000 ). JESOAN 0013-4651 10.1149/1.1393433 [84] 84 D. Hamm , K. Ogle , C. O. A. Olsson , S. Weber , and D. Landolt , Corros. Sci. 44 , 1443 ( 2002 ). CRRSAA 0010-938X 10.1016/S0010-938X(01)00147-0 [85] 85 V. A. Kurepin , D. A. Kulik , A. Hiltpold , and M. Nicolet , Paul Scherrer Institute Report No. 02-04 , 2002 . [86] 86 P. Novak , J. Kunes , L. Chaput , and W. E. Pickett , Phys. Status Solidi B 243 , 563 ( 2006 ). PSSBBD 0370-1972 10.1002/pssb.200541371 [87] 87 F. Tran , P. Blaha , K. Schwarz , and P. Novak , Phys. Rev. B 74 , 155108 ( 2006 ). PRBMDO 1098-0121 10.1103/PhysRevB.74.155108 [88] 88 X. Y. Han and B. J. Spencer , J. Appl. Phys. 101 , 084302 ( 2007 ). JAPIAU 0021-8979 10.1063/1.2709554 [89] 89 J. P. Hirth and T. E. Mitchell , Acta Mater. 56 , 5701 ( 2008 ). ACMAFD 1359-6454 10.1016/j.actamat.2008.07.058 [90] 90 F. Tran , J. Kunes , P. Novak , P. Blaha , L. D. Marks , and K. Schwarz , Comput. Phys. Commun. 179 , 784 ( 2008 ). CPHCBZ 0010-4655 10.1016/j.cpc.2008.06.015 [91] 91 M. Asta , C. Beckermann , A. Karma , W. Kurz , R. Napolitano , M. Plapp , G. Purdy , M. Rappaz , and R. Trivedi , Acta Mater. 57 , 941 ( 2009 ). ACMAFD 1359-6454 10.1016/j.actamat.2008.10.020 [92] 92 Y. Mishin , M. Asta , and J. Li , Acta Mater. 58 , 1117 ( 2010 ). ACMAFD 1359-6454 10.1016/j.actamat.2009.10.049 [93] 93 J. M. Shi and K. D. Becker , Solid State Ionics 181 , 473 ( 2010 ). SSIOD3 0167-2738 10.1016/j.ssi.2010.02.003 [94] 94 K. W. Lee and W. E. Pickett , Phys. Rev. B 83 , 180406 ( 2011 ). PRBMDO 1098-0121 10.1103/PhysRevB.83.180406 [95] 95 Y. Yang , H. Humadi , D. Buta , B. B. Laird , D. Sun , J. J. Hoyt , and M. Asta , Phys. Rev. Lett. 107 , 025505 ( 2011 ). PRLTAO 0031-9007 10.1103/PhysRevLett.107.025505 [96] 96 M. J. Duarte , J. Klemm , S. O. Klemm , K. J. Mayrhofer , M. Stratmann , S. Borodin , A. H. Romero , M. Madinehei , D. Crespo , J. Serrano , S. S. Gerstl , P. P. Choi , D. Raabe , and F. U. Renner , Science 341 , 372 ( 2013 ). SCIEAS 0036-8075 10.1126/science.1230081 [97] 97 H. Humadi , J. J. Hoyt , and N. Provatas , Phys. Rev. E 87 , 022404 ( 2013 ). PRESCM 1539-3755 10.1103/PhysRevE.87.022404 [98] 98 P. Kuhn and J. Horbach , Phys. Rev. B 87 , 014105 ( 2013 ). PRBMDO 1098-0121 10.1103/PhysRevB.87.014105 [99] 99 L. D. Marks , J. Chem. Theory Comput. 9 , 2786 ( 2013 ). JCTCCE 1549-9618 10.1021/ct4001685 [100] 100 Y. Qian , H. P. Wu , Y. Z. Liu , J. Lu , R. F. Lu , W. S. Tan , K. M. Deng , C. Y. Xiao , and G. Lu , Solid State Commun. 170 , 24 ( 2013 ). SSCOA4 0038-1098 10.1016/j.ssc.2013.07.013 [101] 101 S. L. Sobolev , Mater. Sci. Technol. 31 , 1607 ( 2015 ). MSCTEP 0267-0836 10.1179/1743284715Y.0000000051 [102] 102 S. L. Sobolev , Acta Mater. 93 , 256 ( 2015 ). ACMAFD 1359-6454 10.1016/j.actamat.2015.04.028 [103] 103 J. Sun , A. Ruzsinszky , and J. P. Perdew , Phys. Rev. Lett. 115 , 036402 ( 2015 ). PRLTAO 0031-9007 10.1103/PhysRevLett.115.036402 [104] 104 S. L. Sobolev , Acta Mater. 116 , 212 ( 2016 ). ACMAFD 1359-6454 10.1016/j.actamat.2016.06.057 [105] 105 A. F. Kusmartseva , A. M. Arevalo-Lopez , M. Halder , and J. P. Attfield , J. Magn. Magn. Mater. 443 , 293 ( 2017 ). JMMMDC 0304-8853 10.1016/j.jmmm.2017.07.045 [106] 106 C. Xu , X. L. Gan , X. C. Meng , S. F. Xiao , H. Q. Deng , X. F. Li , and W. Y. Hu , J. Cryst. Growth 470 , 113 ( 2017 ). JCRGAE 0022-0248 10.1016/j.jcrysgro.2017.04.024 [107] 107 T. K. Andersen , S. Cook , G. Wan , H. Hong , L. D. Marks , and D. D. Fong , ACS Appl. Mater. Interfaces 10 , 5949 ( 2018 ). AAMICK 1944-8244 10.1021/acsami.7b16970 [108] 108 P. Blaha , K. Schwarz , G. K. H. Madsen , D. Kvasnicka , J. Luitz , R. Laskowsji , F. Tran , and L. D. Marks , An augmented plane wave + local orbitals program for calculating crystal properties ( Technische Universitat Wien , Austria, 2018 ). Publisher Copyright: {\textcopyright} 2018 American Physical Society.",

year = "2018",

month = oct,

day = "4",

doi = "10.1103/PhysRevLett.121.145701",

language = "English (US)",

volume = "121",

journal = "Physical Review Letters",

issn = "0031-9007",

publisher = "American Physical Society",

number = "14",

}

TY - JOUR

T1 - Nonequilibrium Solute Capture in Passivating Oxide Films

AU - Yu, Xiao Xiang

AU - Gulec, Ahmet

AU - Sherman, Quentin

AU - Cwalina, Katie Lutton

AU - Scully, John R.

AU - Perepezko, John H.

AU - Voorhees, Peter W.

AU - Marks, Laurence D.

N1 - Funding Information: Yu Xiao-xiang 1 Gulec Ahmet 1 Sherman Quentin 1 Cwalina Katie Lutton 2 Scully John R. 2 Perepezko John H. 3 Voorhees Peter W. 1 Marks Laurence D. 1 ,* Department of Materials Science and Engineering, 1 Northwestern University , Evanston, Illinois 60208, USA Department of Materials Science and Engineering, 2 University of Virginia , P.O. Box 400745, 395 McCormick Road, Charlottesville, Virginia 22904, USA Department of Materials Science and Engineering, 3 University of Wisconsin-Madison , 1509 University Avenue, Madison, Wisconsin 53706, USA * Author to whom correspondence should be addressed. L-marks@northwestern.edu . 4 October 2018 5 October 2018 121 14 145701 25 July 2018 © 2018 American Physical Society 2018 American Physical Society We report experimental results on the composition and crystallography of oxides formed on NiCrMo alloys during both high-temperature oxidation and aqueous corrosion experiments. Detailed characterization using transmission electron microscopy and diffraction, aberration-corrected chemical analysis, and atom probe tomography shows unexpected combinations of composition and crystallography, far outside thermodynamic solubility limits. The results are explained using a theory for nonequilibrium solute capture that combines thermodynamic, kinetic, and density functional theory analyses. In this predictive nonequilibrium framework, the composition and crystallography are controlled by the rapidly moving interface. The theoretical framework explains the unusual combinations of composition and crystallography, which we predict will be common for many other systems in oxidation and corrosion, and other solid-state processes involving nonequilibrium moving interfaces. Office of Naval Research 10.13039/100000006 N00014-16-1-2280 Every metal, with the sole exception of gold, is unstable in air relative to its oxide at room temperature. The only reason they can be used in many applications is because protective oxide films form that limit further oxidation; many metals in aerospace, medical, nuclear, solar, geothermal, and spent nuclear fuel disposal rely on a protective, nanoscale oxide film. Although much of the general science of how the oxides form is known, there are still gaps. Much of our current knowledge is from the mesoscale down to several nanometers, but multiple processes over wide spatial and temporal scales control their nucleation, composition, stability, and structure. Understanding and predicting oxide growth is critically important if we are to move beyond remedial treatment and coating of metallic surfaces or empirical alloy composition selection towards science-guided alloy design. This is becoming increasingly urgent with aging infrastructure in the developed world, the use of metallic alloys in increasingly harsh environments, as well as the ever-increasing costs of failure of corroded components. We demonstrate here that unusual combinations of structure and chemical composition are a general phenomenon in these oxide films and provide a predictive explanation building upon the well-established science of nonequilibrium interfaces [1] , extended to moving oxide-substrate interfaces. The experimental evidence indicates that rather than analyzing the development of these oxides using crystallography, chemical composition, or concepts based upon equilibrium thermodynamics, one has to analyze both the crystallography and chemistry, combining these with a nonequilibrium approach. We use “nonequilibrium” deliberately to denotes a phase, reaction, or process that departs from full equilibrium. At the first level of departure, equilibrium phases are present, but their compositions are not in equilibrium except at the interfaces where there is more rapid diffusion than in the bulk; the interface is in local equilibrium. At the next level of departure, metastable phases are present and the interface is in local equilibrium. The metastable phases can be equilibrium phases with a nonequilibrium composition, or ones absent from the equilibrium phase diagram. In nonequilibrium there is a full breakdown of the local equilibrium approximation in the phases and at the interface, and the oxide composition is a function of the interface velocity. One has to use approaches such as extended irreversible thermodynamics [2] or the nonequilibrium thermodynamics of interfaces [3] . We show here that during corrosion, whether high-temperature oxygen, steam, aqueous, or other, frequently the interfaces move fast compared to the timescale for establishing local equilibrium, and a nonequilibrium approach is needed. As general background on how these oxide films develop, starting from a clean alloy a thin oxide film develops with a potential gradient across it, as first described by Cabrera and Mott [4] . As the film thickness increases, point defects diffuse across the oxide driven by the chemical potential gradients and electric fields [4–15] , until the film thickness becomes large enough that diffusion controls, as first described by Wagner [16] , and expanded upon by others [7,16–22] . In an aqueous environment, the film may never reach this limit due to dissolution at the oxide-electrolyte interface [23,24] . Throughout the existing literature, thermodynamically favored oxide phases are commonly assumed to form [25–28] , or phases which are stable in Pourbaix diagrams [29] , for instance, pure nickel oxide and chromia for nickel-chromium-based alloys [30–34] , often enriched with alloying elements [35–38] . One explanation is that during oxidation the more energetically favored (lowest free-energy) oxides form first [25,39] . As noted by Wagner [18,40] and further developed by Chattopadhyay and Wood [41] , free energies do not explain the development of the oxide. Experimentally the initial oxide is sometimes a metastable variant that converts to the thermodynamically stable form with slower kinetics [42–45] , suggesting Ostwald’s step rule [46–50] where faster growing phases form first. For aqueous films there is extensive x-ray photoelectron spectroscopy (XPS) data [25,51] , typically interpreted in terms of the thermodynamically stable oxides. For oxidation, x-ray or electron diffraction [43,52–54] has been widely used to identify the lattice parameters of the phases which are then compared to known oxides. There are two critical issues with the current literature. The first is interpretation of crystal structures from XPS measurements of local valence states or diffraction experiments. XPS is sensitive to the valence and local coordination, not the crystallographic arrangement of atoms. Hence a spectroscopic signature similar to that of a standard only proves that the local chemical environment is similar. Similarly, a lattice parameter and/or spacings close to a known standard only proves that the atomic arrangement is similar. To rigorously identify a phase one has to simultaneously determine both the crystallographic arrangement of the atoms and the chemical composition. The second issue involves approaches to solving the transport equations for oxidation. These have chemical rate equations or some other boundary condition for how atoms cross the interface between the metal and oxide. Such formulations will lead to solute atoms being injected into the oxide; however, there is a physical inconsistency. In both oxidation and aqueous corrosion there is a moving oxidation front that combines point defect migration across the interface and physical motion of the interface. The interface therefore has an effective velocity proportional to the rate of incorporation of alloy atoms as cations in the oxide. As this velocity tends to infinity, a necessary constraint is that the chemical composition of cations in the oxide has to be that of the alloy, A second constraint is that as the interface velocity tends to zero, thermodynamics stable or metastable phases with compositions bounded by thermodynamic solubility limits have to be formed. Valid models have to obey these constraints, which requires a term for exchange of cations across the interface that is missing in conventional formulations. A nonequilibrium formulation for the moving oxide interfaces correctly includes a velocity dependence. As we will show, the compositions formed can be predicted and calculated using a “nonequilibrium solute capture” framework based solely upon the ratio of the velocity of the interface and an effective velocity for equilibration. Independent of whether the phases formed follow Ostwald’s step rule [46–50] , or are those of lowest free energy, the composition is controlled by the metal-oxide interface velocity. The systems herein are Ni-Cr-Mo alloys oxidized in air at intermediate temperatures in the range 500 – 800 ° C , as well as the same alloys passivated electrochemically in aqueous environments. While specific details varied with the particular alloys and treatment conditions, we will demonstrate that solute capture during oxide film growth is a general phenomenon. The main experimental tools used are transmission electron microscopy and atom-probe tomography (APT). We have examined bulk samples which were oxidized and then appropriate regions extracted using conventional sample preparation methods, as well as samples first prepared in the appropriate geometry for examination and then oxidized or corroded. More details are provided in Supplemental Material, Sec. I [55] . Independent of whether the oxide formed by dry oxidation or in aqueous conditions, the first product is an oxide with a rocksalt structure ( F m 3 ¯ m ). (We describe the oxides by both the crystallographic space group and chemical composition; both need to be specified.) Similar oxides have been reported in the literature, typically interpreted as nickel oxide since they have similar lattice parameters, with perhaps additional solute metal atoms at low concentrations. From electron diffraction data as well as high-resolution imaging (see Fig. S1 of Supplemental Material [55] ) the crystallographic structure is rocksalt ( F m 3 ¯ m ), but examination using both APT and chemical analysis inside electron microscopes (Fig. 1 for an aqueous sample) shows that there is very significant chromium and traces of molybdenum in the F m 3 ¯ m oxide. Ignoring the low molybdenum concentration, the composition of this rocksalt ( F m 3 ¯ m ) structure is Cr 1 − x Ni x O y , with x ∼ 0.5 . The oxygen content is approximately y = 1.25 at the outer surface and closer to y = 1 adjacent to the metal or for very thin oxides. This implies Cr 3 + at the external surface and Cr 2 + at the metal-oxide interface. This chromium content is significantly larger than the thermodynamic solubility limit of chromium doping in NiO [56] . According to equilibrium thermodynamics this oxide should phase separate into nearly pure rocksalt NiO ( F m 3 ¯ m ) and corundum Cr 2 O 3 ( R 3 ¯ c ). It has not, neither during high-temperature oxidation, the aqueous corrosion, nor the days to weeks after sample preparation before examination by electron microscopy or APT. 1 10.1103/PhysRevLett.121.145701.f1 FIG. 1. Chemical data for the oxide on a Ni-22%Cr-6%Mo (wt %) alloy oxidized in K 2 S 2 O 8 and Na 2 SO 4 . (a) High-angle annular dark field image (left) and annular bright field image (right), with (b) the composition from an electron energy loss line scan. The metal-oxide interface is marked in red, the oxide-vacuum in white. The oxide next to the metal is rocksalt ( F m 3 ¯ m ) of composition ∼ Cr 0.5 Ni 0.5 O . Shown in (c) and (d) are atom-probe tomography results for a tip treated under the same conditions with a 12 at. % isosurface in (c) and a proxigram (compositional line scan) in (d), corrected for oxygen detection efficiency, cross-validating the electron microscopy results. The rocksalt phase is not the only structure with a composition far from conventional thermodynamic expectations. For nickel-chromium-iron alloys and nickel-chromium-molybdenum alloys, an oxide with the corundum ( R 3 ¯ c ) structure has been reported [25,51,57–60] , and assumed to be chromia with perhaps some nickel solute. We can verify the existence of an oxide with a corundum ( R 3 ¯ c ) structure; in some cases it is chromia Cr 2 O 3 ( R 3 ¯ c ), but in others the composition is Cr 2 − x Ni x O 3 − y , with x ∼ 1 (Fig. 2 ). Here a sample was oxidized in situ at 700 ° C in 1 × 10 − 4 torr of oxygen. A metastable R 3 ¯ c Ni 2 O 3 phase with the corundum ( R 3 ¯ c ) crystallography is well established [61] , so a metastable corundum Cr 2 − x Ni x O 3 − y ( R 3 ¯ c ) is feasible, but far from expectations based upon the published thermodynamic data. [Figure 2(a) is from an in situ experiment where F m 3 ¯ m Cr 1 − x Ni x O y was also observed [62] .] 2 10.1103/PhysRevLett.121.145701.f2 FIG. 2. A Ni-22%Cr-6%Mo (wt %) sample oxidized in situ at 700 ° C in 1 × 10 − 4 torr of oxygen, and later analyzed by electron energy loss spectroscopy. (a) A bright field image during in situ growth showing fringes characteristic of the corundum ( R 3 ¯ c ) structure. (b) A high-angle annular dark field image with the corresponding electron energy loss line scan in (c). The corundum structure adjacent to the metal has a composition of approximately CrNiO 3 . Figures 1 and 2 are for relatively thin films, so they could be artifacts of very thin oxide layers or short times. Figure 3 shows results for a sample annealed in oxygen for 24 h at 800 ° C , where similar results are found in oxide films more than 300 nm thick. Adjacent to the metal is an approximately 100 nm thick Cr 1 − x Ni x O 1.5 − x / 2 rocksalt structure ( F m 3 ¯ m ), then over this is nearly pure rocksalt NiO ( F m 3 ¯ m ), with nearly pure corundum Cr 2 O 3 ( R 3 ¯ c ) at the outer surface. The same sample was examined after being stored for a year in air at room temperature, and had the same overall structure with indications that a small amount of corundum had started to form but rocksalt still dominated for the 100 nm thick region adjacent to the metal-oxide interface; see Fig. S2 in Supplemental Material [55] . 3 10.1103/PhysRevLett.121.145701.f3 FIG. 3. Results for a Ni-22%Cr-6%Mo (wt %) oxidized at 800 ° C for 24 h in air. Shown in (a) is an overview high-angle annular dark field image of a focused ion-beam region cut from the sample. The different layers in (b)–(e) are shown as bright field and diffraction pattern pairs, in (b) of the metal, (c) rocksalt ( F m 3 ¯ m ) Cr 1 − x Ni x O y , (d) nickel oxide ( F m 3 ¯ m ), and (e) chromia ( R 3 ¯ c ). Shown in (f) is an APT tomogram taken from the interface layer which shows a Cr 1 − x Ni x O 1.5 − x / 2 rocksalt ( F m 3 ¯ m ) phase, with a one-dimensional composition plot with the metal on the right in (g) of the local chromium fraction on the y axis as a function of position along the x axis. While the most definitive evidence is local structural and chemical analysis, in situ atomic emission spectroelectrochemistry experiments support the chemical compositions observed in the electron microscopy and APT. These track the metal ions leaving the oxide at the oxide-solution interface versus those oxidized [63] (see Supplemental Material Sec. S3 and Figs. S3 and S4 [55] ). The concentrations are quantitatively consistent with those predicted by the solute capture model described later and the results in Fig. 1 , namely, rocksalt Cr 1 − x Ni x O 1.5 − x / 2 ( Cr 3 + and Ni 2 + ) with x = 0.7 . The experimental evidence demonstrates the presence of nonequilibrium rocksalt ( F m 3 ¯ m ) and corundum ( R 3 ¯ c ) phases with either Ni 2 + or Ni 3 + with dominantly Cr 3 + , possibly Cr 2 + very close to the metal-oxide interface, and chemical composition far from equilibrium. These are a result of what we call nonequilibrium solute capture at moving oxidation fronts as illustrated in Fig. S5 [55] , analogous but different from well-known solute trapping during solidification [1] . Differentiating the two is important. First, in solute trapping atoms add to a moving solidification front; hence, the velocity of the front is coupled to the rate of addition of atoms. In nonequilibrium solute capture, in addition to moving interfaces, either or both vacancies and interstitials are moving. Defining the interface by the location of the oxygen atoms, with the nickel-nickel oxide system the interface can be stationary but still have a net flux of nickel vacancies crossing it. Secondly, in solute trapping the free energy of the solvent drops whereas that of the solute increases. For instance, with rapid freezing of salt water, the free energy of the water (solvent) drops but that of the retained solute (salt) increases. In contrast, in nonequilibrium solute capture the free energy of both drop. Two conditions are required for nonequilibrium solute capture. The first is that the free-energy change during formation of the oxide is negative [1] . (See also Supplemental Material Sec. S4 [55] .) As shown in Figs. S6 and S7 [55] , which combines literature thermodynamic data as well as specific density functional theory results, all oxides based upon combinations of Cr 2 + , Cr 3 + and Ni 2 + , Ni 3 + in both rocksalt ( F m 3 ¯ m ) and corundum ( R 3 ¯ c ) crystallographies satisfy this first condition. Metastable solid solutions are possible across the whole compositional range. Considering just the rocksalt crystallography of Figs. 1 and 3 , the lowest free-energy oxide (per oxygen or metal atom) has the composition Cr 2 O 3 ; i.e., 2 / 3 of the cation sites in the cubic unit cell are occupied by chromium atoms. This composition was not observed experimentally because nickel atoms were captured in the rocksalt oxide. As also shown in Fig. S6 [55] , there is the possibility of having Cr 2 + captured in an F m 3 ¯ m oxide which, rigorously, would be denoted as Ni 1 − x Cr x O —nickel oxide is the solvent. The microscopy data in Fig. 1 suggest that this occurs at the metal-oxide interface. One can also have Ni 3 + captured in corundum R 3 ¯ c , which is Cr 1 − x Ni x O 3 ; see Fig. 2 . The second condition is that the interface is moving too fast for equilibrium to be achieved. (See Supplemental Material Sec. S5 [55] .) The extent of capture is parametrized by β = v a / v D , where v a is the velocity of the cations moving into the oxide combining both the physical interface motion and the flux of atoms, which for a planar interface with no adsorption at the interface is v a = − c o v I + j o Ω , with v I the physical velocity of the metal-oxide interface, j o the number of cations crossing the interface per unit area and time (combining vacancy and interstitial contributions), c o the mole fraction of cations in the oxide, and Ω the atomic volume. The diffusive velocity is v D = D i / a , where D i is an interface diffusion coefficient for a Zener exchange of cations and a the hopping distance for exchange between the oxide and metal to equilibrate the composition of the oxide. Nonequilibrium phase compositions form when β ≫ 1 so long as the total free-energy change (condition 1 above) is negative [1] . Turning to the values of β , for planar growth of NiO and using standard values for diffusion constants in the oxide ( [64,65] and see Supplemental Material [55] ), Fig. 4(a) shows that capture of Ni is expected for a wide range of conditions during high-temperature oxidation (see also Supplemental Material Sec. S5 [55] ). It is also probable that β > 1 , during electrochemical passivation, as shown in Fig. 4(b) ; except for very slow passive aqueous dissolution at < 10 − 7 A / cm 2 , the effective velocity of the corroding interface using a Faraday’s law derived electrochemical interface velocity is faster than the rate of equilibration. This is consistent with our experimental observations. 4 10.1103/PhysRevLett.121.145701.f4 FIG. 4. Kinetic conditions for solute capture, in (a) for oxidation based upon literature diffusion constants and reaction rates as a function of exposure temperature and oxygen partial pressure in atmospheres for an oxide thickness of 5 nm and a hopping distance of 1 nm. The horizontal green plane is v a a / D i = 1 , the blue surface the ratio for different temperatures and oxygen pressures. For a wide range of conditions, oxidation is expected to lead to solute capture, consistent with the experimental results. In (b) a plot of the local electrochemical corrosion current density along x and the velocity of the oxidation front along y for a range of different processes in aqueous corrosion with the approximate diffusion velocity D i / a marked on the right for a = 1.0 nm , assuming a field-affected diffusivity of 10 − 20 cm 2 / sec ; again solute capture will be common. Our experimental observations and the model for solute capture predict that for many cases of oxidation and almost all aqueous conditions, solute capture for NiCr alloys is the norm, not the exception. The possibility of capture can be predicted using the free energies of the phases and values for the interface diffusion constant and hopping distance. Where there are competing solute capture phases, which of these will form for different conditions can in principle be predicted, as briefly outlined in Supplemental Material Sec. S6 [55] , which includes Refs. [1,3,62–64,66–108] . Expanded thermodynamic databases along with the model for solute capture open the door to deliberately forming oxides of novel compositions, and thus properties for a given application, for instance, better protection and thus significantly longer lifetimes in service. To illustrate this, and the distinction of this model from the standard idea of cation injection during oxide growth, we will advance some predictions, with caveats that experimental validation is important. Almost all elements in the first transition metal row can form rocksalt oxides, so we tested using density functional theory calculations the thermodynamics of the comparable rocksalt oxides in the Sc 2 x / 3 Mg 1 − x O and Al 2 x / 3 Mg 1 − x O systems. As shown in Supplemental Material Fig. S8 [55] , both lead to metastable solid solutions, so are strong candidates for nonequilibrium solute capture. The free-energy change of a nonequilibrium solute captured rocksalt A 1 − x B x O y can be written as Δ G NSC = Δ G Oxide A + Δ G Oxide B + E ( Δ r Ion , T , … ) , where the first two terms on the right-hand side are the free energies of formation of the single cation rocksalt oxides and the third is the mixing energy, which will depend strongly upon the difference in the ionic radii Δ r Ion . The ionic radii across the first transition row are not that different. Since the free energies of formation of the single cation oxides are all significantly negative, Δ G NSC will almost certainly be negative; solute capture is likely to occur across the whole first transition row. It can also occur with elements below the first transition metal row. To minimize the strain energy we expect higher valences so the valence and coordination specific ionic radii should be similar. For instance, molybdenum is a known beneficial dopant and has ionic radii of 0.83, 0.79 and 0.75 Å for sixfold 3 + , 4 + , and 5 + states, respectively, which can be compared to 0.83 for sixfold Ni 2 + and 0.755 for sixfold Cr 3 + . Hence, we predict the presence of Mo 3 + solute captured in rocksalt Cr 1 − x Ni x O 1.5 − x / 2 and Mo 4 + or Mo 5 + in corundum Cr 2 − x Ni x O 3 ; higher oxidation states are consistent with the available XPS data. We suspect solute capture occurs in other solid-fluid or solid-solid chemical reactions, not just the formation of protective oxide films or rapid solidification. If the product is lower in free energy, and the reaction front is moving fast enough, the same science holds independent of whether one is dealing with ceramics, metals, semiconductors, or polymers. The authors acknowledge support from ONR MURI “Understanding Atomic Scale Structure in Four Dimensions to Design and Control Corrosion Resistant Alloys “through Grant No. N00014-16-1-2280. X.-x. Y. and A. G. performed the oxidation and aqueous treatments of the samples and TEM observations, supervised by L. D. M., with electrochemistry input from K. L. C. and J. R. S. X.-x. Y. performed the APT experiments, supervised by L. D. M. Q. S. performed the solute trapping thermodynamics analysis supervised by P. W. V. with discussions with J. H. P. K. L. C. performed the electrochemical tests supervised by J. R. S. L. D. M. performed the density functional theory calculations. All authors contributed to the writing of the Letter. [1] 1 J. C. Baker and J. W. Cahn , Acta Metall. Mater. 17 , 575 ( 1969 ). AMATEB 0956-7151 10.1016/0001-6160(69)90116-3 [2] 2 D. Jou and G. Lebon , Extended Irreversible Thermodynamics ( Springer , Amsterdam, 2010 ), p. 483 . [3] 3 J. C. Baker and J. W. Cahn , Solidification ( American Society for Metals , Metals Park, OH, 1971 ), p. 23 . [4] 4 N. Cabrera and N. F. Mott , Rep. Prog. Phys. 12 , 163 ( 1948 ). RPPHAG 0034-4885 10.1088/0034-4885/12/1/308 [5] 5 C. Y. Chao , L. F. Lin , and D. D. Macdonald , J. Electrochem. Soc. 128 , 1187 ( 1981 ). JESOAN 0013-4651 10.1149/1.2127591 [6] 6 L. F. Lin , C. Y. Chao , and D. D. Macdonald , J. Electrochem. Soc. 128 , 1194 ( 1981 ). JESOAN 0013-4651 10.1149/1.2127592 [7] 7 A. Atkinson , Rev. Mod. Phys. 57 , 437 ( 1985 ). RMPHAT 0034-6861 10.1103/RevModPhys.57.437 [8] 8 D. D. Macdonald , J. Electrochem. Soc. 139 , 3434 ( 1992 ). JESOAN 0013-4651 10.1149/1.2069096 [9] 9 C. Chainais-Hillairet and C. Bataillon , Numer. Math. 110 , 1 ( 2008 ). 10.1007/s00211-008-0154-x [10] 10 C. Bataillon , F. Bouchon , C. Chainais-Hillairet , C. Desgranges , E. Hoarau , F. Martin , S. Perrin , M. Tupin , and J. Talandier , Electrochim. Acta 55 , 4451 ( 2010 ). ELCAAV 0013-4686 10.1016/j.electacta.2010.02.087 [11] 11 D. D. Macdonald , Electrochim. Acta 56 , 1761 ( 2011 ). ELCAAV 0013-4686 10.1016/j.electacta.2010.11.005 [12] 12 A. Seyeux , V. Maurice , and P. Marcus , J. Electrochem. Soc. 160 , C189 ( 2013 ). JESOAN 0013-4651 10.1149/2.036306jes [13] 13 K. Leistner , C. Toulemonde , B. Diawara , A. Seyeux , and P. Marcus , J. Electrochem. Soc. 160 , C197 ( 2013 ). JESOAN 0013-4651 10.1149/2.037306jes [14] 14 A. Couet , A. T. Motta , and A. Ambard , Corros. Sci. 100 , 73 ( 2015 ). CRRSAA 0010-938X 10.1016/j.corsci.2015.07.003 [15] 15 A. Couet , A. T. Motta , A. Ambard , and R. J. Comstock , in Proceedings of the 18th International Symposium on Zirconium in the Nuclear Industry , edited by R. J. Comstock and A. T. Motta ( ASTM International , Hilton Head Island, SC, 2016 ), p. 312 . [16] 16 C. Wagner , Z. Phys. Chem., Abt. B 21 , 25 ( 1933 ). ZPCBAL 0372-9664 [17] 17 C. Wagner , Z. Phys. Chem., Abt. B 32 , 447 ( 1936 ). ZPCBAL 0372-9664 [18] 18 C. Wagner , J. Electrochem. Soc. 99 , 369 ( 1952 ). JESOAN 0013-4651 10.1149/1.2779605 [19] 19 L. Himmel , R. F. Mehl , and C. E. Birchenall , Trans. Am. Inst. Min. Metall. Eng. 197 , 827 ( 1953 ). [20] 20 K. R. Lawless , Rep. Prog. Phys. 37 , 231 ( 1974 ). RPPHAG 0034-4885 10.1088/0034-4885/37/2/002 [21] 21 G. R. Wallwork , Rep. Prog. Phys. 39 , 401 ( 1976 ). RPPHAG 0034-4885 10.1088/0034-4885/39/5/001 [22] 22 H. Hindam and D. P. Whittle , Oxid Met. 18 , 245 ( 1982 ). 10.1007/BF00656571 [23] 23 I. Olefjord and B. O. Elfstrom , Corrosion 38 , 46 ( 1982 ). 10.5006/1.3577318 [24] 24 I. Olefjord , B. Brox , and U. Jelvestam , J. Electrochem. Soc. 131 , C299 ( 1984 ). JESOAN 0013-4651 [25] 25 N. Winograd , W. E. Baitinger , J. W. Amy , and J. A. Munarin , Science 184 , 565 ( 1974 ). SCIEAS 0036-8075 10.1126/science.184.4136.565 [26] 26 R. D. Willenbruch , C. R. Clayton , M. Oversluizen , D. Kim , and Y. Lu , Corros. Sci. 31 , 179 ( 1990 ). CRRSAA 0010-938X 10.1016/0010-938X(90)90106-F [27] 27 P. Saltykov , O. Fabrichnaya , J. Golczewski , and F. Aldinger , J. Alloys Compd. 381 , 99 ( 2004 ). JALCEU 0925-8388 10.1016/j.jallcom.2004.02.053 [28] 28 B. Ingham , S. C. Hendy , N. J. Laycock , and M. P. Ryan , Electrochem. Solid State Lett. 10 , C57 ( 2007 ). ESLEF6 1099-0062 10.1149/1.2757472 [29] 29 B. Beverskog and I. Puigdomenech , Corrosion 55 , 1077 ( 1999 ). 10.5006/1.3283945 [30] 30 J. E. Croll and G. R. Wallwork , Oxid Met. 4 , 121 ( 1972 ). 10.1007/BF00613088 [31] 31 A. D. Dalvi and D. E. Coates , Oxid Met. 5 , 113 ( 1972 ). 10.1007/BF00610840 [32] 32 J. J. Gilman , Science 306 , 1134 ( 2004 ). SCIEAS 0036-8075 10.1126/science.306.5699.1134 [33] 33 S. E. Ziemniak , L. M. Anovitz , R. A. Castelli , and W. D. Porter , J. Chem. Thermodyn. 39 , 1474 ( 2007 ). JCTDAF 0021-9614 10.1016/j.jct.2007.03.001 [34] 34 L. Kaufman , J. H. Perepezko , K. Hildal , J. Farmer , D. Day , N. Yang , and D. Branagan , CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 33 , 89 ( 2009 ). CCCTD6 0364-5916 10.1016/j.calphad.2008.09.019 [35] 35 R. Kirchheim , B. Heine , H. Fischmeister , S. Hofmann , H. Knote , and U. Stolz , Corros. Sci. 29 , 899 ( 1989 ). CRRSAA 0010-938X 10.1016/0010-938X(89)90060-7 [36] 36 L. Zhang and D. D. Macdonald , Electrochim. Acta 43 , 2661 ( 1998 ). ELCAAV 0013-4686 10.1016/S0013-4686(97)00268-5 [37] 37 J. E. Castle and K. Asami , Surf. Interface Anal. 36 , 220 ( 2004 ). SIANDQ 0142-2421 10.1002/sia.1676 [38] 38 D. D. Macdonald , Afinidad : organo de la Asociacion de Quimicos del Instituto Quimico de Sarria 62 , 498 ( 2005 ). AFINAE 0001-9704 [39] 39 L. Kjellqvist , M. Selleby , and B. Sundman , CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 32 , 577 ( 2008 ). CCCTD6 0364-5916 10.1016/j.calphad.2008.04.005 [40] 40 C. Wagner , J. Electrochem. Soc. 103 , 571 ( 1956 ). JESOAN 0013-4651 10.1149/1.2430159 [41] 41 B. Chattopadhyay and G. C. Wood , Oxid Met. 2 , 373 ( 1970 ). 10.1007/BF00604477 [42] 42 J. C. Yang , E. Schumann , I. Levin , and M. Ruhle , Acta Mater. 46 , 2195 ( 1998 ). ACMAFD 1359-6454 10.1016/S1359-6454(97)00378-9 [43] 43 J. Doychak , J. L. Smialek , and T. E. Mitchell , Metall. Trans. A 20 , 499 ( 1989 ). MTTABN 0360-2133 10.1007/BF02653930 [44] 44 V. K. Tolpygo and D. R. Clarke , Materials at High Temperatures 17 , 59 ( 2000 ). MHTEEM 0960-3409 10.1179/mht.2000.011 [45] 45 G. C. Rybicki and J. L. Smialek , Oxid Met. 31 , 275 ( 1989 ). 10.1007/BF00846690 [46] 46 W. Ostwald , Z. Phys. Chem. 22U , 19 ( 1897 ). [47] 47 I. N. Stranski and D. Totomanow , Z. Phys. Chem., Abt. A 163 , 399 ( 1933 ). ZPCAAI 0372-9656 [48] 48 R. A. Vansanten , J. Phys. Chem. 88 , 5768 ( 1984 ). JPCHAX 0022-3654 10.1021/j150668a002 [49] 49 J. Nyvlt , Cryst. Res. Technol. 30 , 443 ( 1995 ). CRTEDF 0232-1300 10.1002/crat.2170300402 [50] 50 N. Niekawa and M. Kitamura , Cryst. Eng. Commun. 15 , 6932 ( 2013 ). 10.1039/c3ce40582f [51] 51 A. Machet , A. Galtayries , S. Zanna , L. Klein , V. Maurice , P. Jolivet , M. Foucault , P. Combrade , P. Scott , and P. Marcus , Electrochim. Acta 49 , 3957 ( 2004 ). ELCAAV 0013-4686 10.1016/j.electacta.2004.04.032 [52] 52 J. Doychak and M. Ruhle , Oxid Met. 31 , 431 ( 1989 ). 10.1007/BF00666466 [53] 53 M. W. Brumm and H. J. Grabke , Corros. Sci. 33 , 1677 ( 1992 ). CRRSAA 0010-938X 10.1016/0010-938X(92)90002-K [54] 54 M. F. Toney , A. J. Davenport , L. J. Oblonsky , M. P. Ryan , and C. M. Vitus , Phys. Rev. Lett. 79 , 4282 ( 1997 ). PRLTAO 0031-9007 10.1103/PhysRevLett.79.4282 [55] 55 See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.121.145701 for methods, as well as additional material as described in the text. [56] 56 C.-H. Chen , M. R. Notis , and D. B. Williams , J. Am. Ceram. Soc. 66 , 566 ( 1983 ). JACTAW 0002-7820 10.1111/j.1151-2916.1983.tb10092.x [57] 57 P. Marcus and J. M. Grimal , Corros. Sci. 33 , 805 ( 1992 ). CRRSAA 0010-938X 10.1016/0010-938X(92)90113-H [58] 58 S. E. Ziemniak and M. Hanson , Corros. Sci. 45 , 1595 ( 2003 ). CRRSAA 0010-938X 10.1016/S0010-938X(02)00230-5 [59] 59 S. E. Ziemniak and M. Hanson , Corros. Sci. 48 , 498 ( 2006 ). CRRSAA 0010-938X 10.1016/j.corsci.2005.01.006 [60] 60 J. E. Maslar , W. S. Hurst , W. J. Bowers , J. H. Hendricks , and E. S. Windsor , J. Electrochem. Soc. 156 , C103 ( 2009 ). JESOAN 0013-4651 10.1149/1.3056038 [61] 61 W. Pies and A. Weiss , in b1468, II.1.1 Simple Oxides , edited by K.-H. Hellwege and A. M. Hellwege , Landolt-Börnstein, Group III, Vol. 7B1, Key Element: O. Pt 1 ( Springer-Verlag , Berlin, 1975 ), https://materials.springer.com/lb/docs/sm_lbs_978-3-540-37856-3_31 . [62] 62 X.-x. Yu , A. Gulec , C. M. Andolina , E. J. Zeitchick , K. Gusieva , J. C. Yang , J. R. Scully , J. H. Perepezko , and L. D. Marks , Corrosion 74 , 939 ( 2018 ). 10.5006/2807 [63] 63 K. Lutton , K. Gusieva , N. Ott , N. Birbilis , and J. R. Scully , Electrochem. Comm. 80 , 44 ( 2017 ). ECCMF9 1388-2481 10.1016/j.elecom.2017.05.015 [64] 64 W. K. Chen , N. L. Peterson , and L. C. Robinson , J. Phys. Chem. Solids 34 , 705 ( 1973 ). JPCSAW 0022-3697 10.1016/S0022-3697(73)80177-5 [65] 65 D. L. Douglass , Corros. Sci. 8 , 665 ( 1968 ). CRRSAA 0010-938X 10.1016/S0010-938X(68)80101-5 [66] 66 M. Pourbaix , Atlas of Electrochemical Equilibria in Aqueous Solutions ( Pergamon , New York, 1966 ), Vol. 1 . [67] 67 B. L. Chamberland and W. H. Cloud , J. Appl. Phys. 40 , 434 ( 1969 ). JAPIAU 0021-8979 10.1063/1.1657087 [68] 68 D. S. Walters and G. P. Wirtz , J. Am. Ceram. Soc. 54 , 563 ( 1971 ). JACTAW 0002-7820 10.1111/j.1151-2916.1971.tb12208.x [69] 69 M. J. Aziz , J. Appl. Phys. 53 , 1158 ( 1982 ). JAPIAU 0021-8979 10.1063/1.329867 [70] 70 M. J. Aziz , Appl. Phys. Lett. 43 , 552 ( 1983 ). APPLAB 0003-6951 10.1063/1.94416 [71] 71 W. J. Boettinger , S. R. Coriell , and R. F. Sekerka , Mater. Sci. Eng. 65 , 27 ( 1984 ). MSCEAA 0025-5416 10.1016/0025-5416(84)90196-4 [72] 72 K. D. Becker and F. Rau , Phys. Chem. Chem. Phys. 91 , 1279 ( 1987 ). 10.1002/bbpc.19870911139 [73] 73 M. J. Aziz and T. Kaplan , Acta Metall. Mater. 36 , 2335 ( 1988 ). AMATEB 0956-7151 10.1016/0001-6160(88)90333-1 [74] 74 J. R. Taylor and A. T. Dinsdale , Z. Metall. 81 , 354 ( 1990 ). [75] 75 K. Sujata and T. O. Mason , J. Am. Ceram. Soc. 75 , 557 ( 1992 ). JACTAW 0002-7820 10.1111/j.1151-2916.1992.tb07842.x [76] 76 J. P. Hirth , B. Pieraggi , and R. A. Rapp , Acta Metall. Mater. 43 , 1065 ( 1995 ). AMATEB 0956-7151 10.1016/0956-7151(94)00296-T [77] 77 B. Pieraggi , R. A. Rapp , and J. P. Hirth , Oxid Met. 44 , 63 ( 1995 ). 10.1007/BF01046723 [78] 78 M. E. Gurtin and P. W. Voorhees , Acta Mater. 44 , 235 ( 1996 ). ACMAFD 1359-6454 10.1016/1359-6454(95)00139-X [79] 79 J. P. Perdew , K. Burke , and M. Ernzerhof , Phys. Rev. Lett. 77 , 3865 ( 1996 ). PRLTAO 0031-9007 10.1103/PhysRevLett.77.3865 [80] 80 S. L. Sobolev , Phys. Rev. E 55 , 6845 ( 1997 ). PLEEE8 1063-651X 10.1103/PhysRevE.55.6845 [81] 81 N. Kashii , H. Maekawa , and Y. Hinatsu , J. Am. Ceram. Soc. 82 , 1844 ( 1999 ). JACTAW 0002-7820 10.1111/j.1151-2916.1999.tb02007.x [82] 82 S. A. T. Redfern , R. J. Harrison , H. S. C. O’Neill , and D. R. R. Wood , Am. Mineral. 84 , 299 ( 1999 ). AMMIAY 0003-004X 10.2138/am-1999-0313 [83] 83 K. Ogle and S. Weber , J. Electrochem. Soc. 147 , 1770 ( 2000 ). JESOAN 0013-4651 10.1149/1.1393433 [84] 84 D. Hamm , K. Ogle , C. O. A. Olsson , S. Weber , and D. Landolt , Corros. Sci. 44 , 1443 ( 2002 ). CRRSAA 0010-938X 10.1016/S0010-938X(01)00147-0 [85] 85 V. A. Kurepin , D. A. Kulik , A. Hiltpold , and M. Nicolet , Paul Scherrer Institute Report No. 02-04 , 2002 . [86] 86 P. Novak , J. Kunes , L. Chaput , and W. E. Pickett , Phys. Status Solidi B 243 , 563 ( 2006 ). PSSBBD 0370-1972 10.1002/pssb.200541371 [87] 87 F. Tran , P. Blaha , K. Schwarz , and P. Novak , Phys. Rev. B 74 , 155108 ( 2006 ). PRBMDO 1098-0121 10.1103/PhysRevB.74.155108 [88] 88 X. Y. Han and B. J. Spencer , J. Appl. Phys. 101 , 084302 ( 2007 ). JAPIAU 0021-8979 10.1063/1.2709554 [89] 89 J. P. Hirth and T. E. Mitchell , Acta Mater. 56 , 5701 ( 2008 ). ACMAFD 1359-6454 10.1016/j.actamat.2008.07.058 [90] 90 F. Tran , J. Kunes , P. Novak , P. Blaha , L. D. Marks , and K. Schwarz , Comput. Phys. Commun. 179 , 784 ( 2008 ). CPHCBZ 0010-4655 10.1016/j.cpc.2008.06.015 [91] 91 M. Asta , C. Beckermann , A. Karma , W. Kurz , R. Napolitano , M. Plapp , G. Purdy , M. Rappaz , and R. Trivedi , Acta Mater. 57 , 941 ( 2009 ). ACMAFD 1359-6454 10.1016/j.actamat.2008.10.020 [92] 92 Y. Mishin , M. Asta , and J. Li , Acta Mater. 58 , 1117 ( 2010 ). ACMAFD 1359-6454 10.1016/j.actamat.2009.10.049 [93] 93 J. M. Shi and K. D. Becker , Solid State Ionics 181 , 473 ( 2010 ). SSIOD3 0167-2738 10.1016/j.ssi.2010.02.003 [94] 94 K. W. Lee and W. E. Pickett , Phys. Rev. B 83 , 180406 ( 2011 ). PRBMDO 1098-0121 10.1103/PhysRevB.83.180406 [95] 95 Y. Yang , H. Humadi , D. Buta , B. B. Laird , D. Sun , J. J. Hoyt , and M. Asta , Phys. Rev. Lett. 107 , 025505 ( 2011 ). PRLTAO 0031-9007 10.1103/PhysRevLett.107.025505 [96] 96 M. J. Duarte , J. Klemm , S. O. Klemm , K. J. Mayrhofer , M. Stratmann , S. Borodin , A. H. Romero , M. Madinehei , D. Crespo , J. Serrano , S. S. Gerstl , P. P. Choi , D. Raabe , and F. U. Renner , Science 341 , 372 ( 2013 ). SCIEAS 0036-8075 10.1126/science.1230081 [97] 97 H. Humadi , J. J. Hoyt , and N. Provatas , Phys. Rev. E 87 , 022404 ( 2013 ). PRESCM 1539-3755 10.1103/PhysRevE.87.022404 [98] 98 P. Kuhn and J. Horbach , Phys. Rev. B 87 , 014105 ( 2013 ). PRBMDO 1098-0121 10.1103/PhysRevB.87.014105 [99] 99 L. D. Marks , J. Chem. Theory Comput. 9 , 2786 ( 2013 ). JCTCCE 1549-9618 10.1021/ct4001685 [100] 100 Y. Qian , H. P. Wu , Y. Z. Liu , J. Lu , R. F. Lu , W. S. Tan , K. M. Deng , C. Y. Xiao , and G. Lu , Solid State Commun. 170 , 24 ( 2013 ). SSCOA4 0038-1098 10.1016/j.ssc.2013.07.013 [101] 101 S. L. Sobolev , Mater. Sci. Technol. 31 , 1607 ( 2015 ). MSCTEP 0267-0836 10.1179/1743284715Y.0000000051 [102] 102 S. L. Sobolev , Acta Mater. 93 , 256 ( 2015 ). ACMAFD 1359-6454 10.1016/j.actamat.2015.04.028 [103] 103 J. Sun , A. Ruzsinszky , and J. P. Perdew , Phys. Rev. Lett. 115 , 036402 ( 2015 ). PRLTAO 0031-9007 10.1103/PhysRevLett.115.036402 [104] 104 S. L. Sobolev , Acta Mater. 116 , 212 ( 2016 ). ACMAFD 1359-6454 10.1016/j.actamat.2016.06.057 [105] 105 A. F. Kusmartseva , A. M. Arevalo-Lopez , M. Halder , and J. P. Attfield , J. Magn. Magn. Mater. 443 , 293 ( 2017 ). JMMMDC 0304-8853 10.1016/j.jmmm.2017.07.045 [106] 106 C. Xu , X. L. Gan , X. C. Meng , S. F. Xiao , H. Q. Deng , X. F. Li , and W. Y. Hu , J. Cryst. Growth 470 , 113 ( 2017 ). JCRGAE 0022-0248 10.1016/j.jcrysgro.2017.04.024 [107] 107 T. K. Andersen , S. Cook , G. Wan , H. Hong , L. D. Marks , and D. D. Fong , ACS Appl. Mater. Interfaces 10 , 5949 ( 2018 ). AAMICK 1944-8244 10.1021/acsami.7b16970 [108] 108 P. Blaha , K. Schwarz , G. K. H. Madsen , D. Kvasnicka , J. Luitz , R. Laskowsji , F. Tran , and L. D. Marks , An augmented plane wave + local orbitals program for calculating crystal properties ( Technische Universitat Wien , Austria, 2018 ). Publisher Copyright: © 2018 American Physical Society.

PY - 2018/10/4

Y1 - 2018/10/4

N2 - We report experimental results on the composition and crystallography of oxides formed on NiCrMo alloys during both high-temperature oxidation and aqueous corrosion experiments. Detailed characterization using transmission electron microscopy and diffraction, aberration-corrected chemical analysis, and atom probe tomography shows unexpected combinations of composition and crystallography, far outside thermodynamic solubility limits. The results are explained using a theory for nonequilibrium solute capture that combines thermodynamic, kinetic, and density functional theory analyses. In this predictive nonequilibrium framework, the composition and crystallography are controlled by the rapidly moving interface. The theoretical framework explains the unusual combinations of composition and crystallography, which we predict will be common for many other systems in oxidation and corrosion, and other solid-state processes involving nonequilibrium moving interfaces.

AB - We report experimental results on the composition and crystallography of oxides formed on NiCrMo alloys during both high-temperature oxidation and aqueous corrosion experiments. Detailed characterization using transmission electron microscopy and diffraction, aberration-corrected chemical analysis, and atom probe tomography shows unexpected combinations of composition and crystallography, far outside thermodynamic solubility limits. The results are explained using a theory for nonequilibrium solute capture that combines thermodynamic, kinetic, and density functional theory analyses. In this predictive nonequilibrium framework, the composition and crystallography are controlled by the rapidly moving interface. The theoretical framework explains the unusual combinations of composition and crystallography, which we predict will be common for many other systems in oxidation and corrosion, and other solid-state processes involving nonequilibrium moving interfaces.

UR - http://www.scopus.com/inward/record.url?scp=85054525751&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevLett.121.145701

DO - 10.1103/PhysRevLett.121.145701

M3 - Article

C2 - 30339439

AN - SCOPUS:85054525751

SN - 0031-9007

VL - 121

JO - Physical Review Letters

JF - Physical Review Letters

IS - 14

M1 - 145701

ER -

Nonequilibrium Solute Capture in Passivating Oxide Films

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