Point Defect Model Research Articles

Early stages of iron anodic oxidation: Defective growth and density increase of oxide layer

The early stages of anodic oxidation in the potentiostatic condition at the interface between a borate buffer solution at pH 8.4 and Fe(100), (110), and (111) surfaces are investigated by sub-second resolution real-time x-ray reflectometry. The growth process is composed of three stages. The electron density of the inner-oxide layer for Fe(111) after a potential step from $\ensuremath{-}0.8$ to $+0.7$ V versus Ag/AgCl in the steady-state growth, stage III (1.65 s $lt$, where $t$ denotes the time after the potential step), is 1.52 electrons/${\AA{}}^{3}$, which is close to the density of magnetite. The growth rate is proportional to ${t}^{\ensuremath{-}1}$, which follows the direct logarithmic law or point-defect model. In an earlier stage of the oxide film growth, stage II $(0.4lt\ensuremath{\le}1.65$ s), the growth rate is proportional to ${t}^{\ensuremath{-}1.5}$, while the electron density maintains the same value as that in stage III. At the first stage that can be discriminated by our time resolution, stage I $(t\ensuremath{\le}0.4$ s), the growth rate is the same as that for stage II, i.e., proportional to ${t}^{\ensuremath{-}1.5}$, while the electron density significantly decreases. The suggested structure is a highly defective spinel oxide, and defects are filled by the end of stage I; there is no signature of the growth of other phases, such as hydroxide, as the inner layer. This behavior indicates that the early stage of the oxide film growth is faster than the formation of a complete spinel layer at the iron-oxide interface. The deviation of the growth rate from the point-defect model in stages I and II is caused by the strong electric field at the iron-oxide interface.

Effect of Heat Treatment of Martensitic Stainless Steel on Passive Layer Growth Kinetics Studied by Electrochemical Impedance Spectroscopy in Conjunction with the Point Defect Model

Martensitic stainless steels are widely used materials. Their mechanical and corrosion properties are strongly influenced by their microstructure and thereby can be affected by heat treatment. In the present study, the effect of different austenitizing temperatures on the passive film growth kinetics of martensitic stainless steel is studied by electrochemical impedance spectroscopy. The data was further fitted by the point defect model to determine kinetic parameters. We show that an increasing austenitizing temperature leads to a more protective passive film and slows down passive film dissolution in sulfuric acid.

Density Functional Theory Study of the Initial Stages of Cl-Induced Degradation of α-Cr2O3 Passive Film

The ion exchange and point defect models are two prominent models describing the role of anions, such as chlorides, in the degradation of passive oxide films. Here the thermodynamic feasibility of critical steps of Cl-induced degradation of a hydroxylated α-Cr2O3 (0001) surface, as proposed by these two models, are studied. Both models begin with Cl substitution of surface OH and H2O, which becomes less favorable with increasing Cl coverage. The initial stages of Cl-induced breakdown of the α-Cr2O3 depend on Cl coverage and the presence of O vacancy near the surface as follows: (1) neither Cl insertion (supporting the ion exchange model) nor Cr vacancy formation (supporting the point defect model) is feasible at low Cl coverages except in the presence of O vacancies near the surface, where Cl insertion is thermodynamically feasible even at low coverages, (2) in the absence of O vacancies, Cr vacancy formation becomes feasible from 10/12 ML onwards whereas Cl insertion by exchange with subsurface OH only becomes feasible at full coverage. This implies that at higher coverages Cl-induced degradation first initiatesthrough a vacancy formation mechanism, but both insertion and vacancy formation would be feasible at full coverage.

Microstructural evolution and corrosion properties of Ni-based alloy coatings fabricated by multi-layer laser cladding on cast iron

To solve the problem of brittleness at the bonding interface, the multi-layer laser cladding method was carried out to fabricate Ni-based alloy coating on the compacted graphite cast iron. The effect of dilution rate on the microstructure and corrosion behavior of the coatings were investigated. The results showed that the volume fraction and the secondary dendrite arm spacing of the dendrite increase significantly with the increasing number of the deposited layers. The dendritic phase in the coatings changed from γ-Fe phase to γ-(Fe, Ni) phase, and the interdendritic phase transformed from martensite phase to M7C3 (M = Fe, Cr) phase with the decrease of the dilution rate. The lattice parameter of the dendritic phase decreased gradually, as the increase of Ni content. The corrosion tests show that the coating with six deposited layers exhibited the best corrosion resistance at room temperature in 3.5% NaCl solution. The corrosion mechanism changed from severe intragranular corrosion to pitting corrosion and intergranular corrosion. According to the analysis results of electrochemical impedance spectroscopy curves, Mott-Schottky curves, and point defect model, the improvement of the corrosion resistance was attributed to the high compactness and resistance of the passive film, which provided fewer oxygen vacancies in the corrosion process due to the increase of Ni and Cr concentration of the coating.

Corrosion resistance mechanism of the passive films formed on as-cast FeCoCrNiMn high-entropy alloy

The present work investigates the corrosion resistance of as-cast FeCoCrNiMn high-entropy alloy in borate buffer solution. Compared with 304 and 316L stainless steels steel, as-cast FeCoCrNiMn high-entropy alloy exhibited excellent passivation ability. This should be attributed to homogenization of alloying elements. Highly corrosion-resistant elements in as-cast FeCoCrNiMn alloys, for example, Cr, Co and Ni, could promote the formation of protective passive film in borate buffer solution. Moreover, combined effect of high mixing entropy and sluggish diffusion also could improve the corrosion resistance. The formation mechanism of the passive films on the surface of as-cast FeCoCrNiMn alloys satisfied the point defect model.

XPS and EIS studies to account for the passive behavior of the alloy Ti-6Al-4V in Hank’s solution

The passivation mechanism of the film formed on the alloy Ti-6Al-4V was evaluated in Hank’s solution to infer the properties of this alloy as an implant material. Alloy passivation was found from electrochemical measurements and X-ray photoelectron spectroscopy (XPS) to strongly depend on the oxidation of Ti and Al, microstructural changes associated with the Al and V, and the formation of metallic hydroxides and oxyhydroxides that disrupt the TiO2 matrix. Experimental impedance diagrams were fitted using the point defect model (PDM, transfer function) to describe the passive character of the alloy. According to this analysis, the transport of oxygen and hydroxide defects across the film on the alloy surface determines the adsorption of oxygen from water dissociation and/or phosphate and the precipitation of calcium phosphate. Therefore, osseointegration of the alloy Ti-6Al-4V occurs across the entire surface and strongly depends on the defects present in the film, Al incorporation, the penetration of hydroxide ions (hydration), and oxygen adsorption.

Point defect model for the corrosion of steels in supercritical water: Part I, film growth kinetics

A Point Defect Model has been developed to describe theoretically the corrosion of metals and alloys in supercritical aqueous systems. The model, SCW_PDM, accounts for the kinetics of growth of the barrier layer and the total scale thickness and for the oft-reported growth of the barrier layer with the barrier/outer layer interface remaining at the location of the original metal surface. The barrier layer grows into the metal via the production of oxygen vacancies at the metal/barrier layer interface and their annihilation at the barrier layer/outer layer interface. The proposed atomic-level rate laws for the scale growth and oxidation weight gains, not only can act as deterministic equations for extracting values of some fundamental parameters in SCW_PDM, but also can be employed to describe the oxidation kinetics of steels directly and successfully.

Effect of the chloride on passivity breakdown of Al-Zn-Mg alloy

The influence of chloride on the corrosion behavior of Al-Zn-Mg alloy was explored, and the results are explained using the Point Defect Model (PDM). Cyclic potentiodynamic polarization was utilized to study the breakdown behavior, and the corrosion morphologies for different chloride concentrations were observed using scanning electron microscopy, and the depth of the corrosion pit was measured using laser confocal microscopy. Furthermore, SPM and XPS were used to further analyze the behavior of pitting corrosion of Al-Zn-Mg alloy. The findings provide strong evidence that the PDM correctly simulates passivity breakdown of aluminum alloys in chloride-bearing coastal environments.

Passivity of titanium, part IV: reversible oxygen vacancy generation/annihilation

A simplified Point Defect Model incorporating reversible oxygen vacancy generation/annihilation at the metal/film interface has been used to investigate the impedance of anodized titanium in 0.5 M H2SO4, the oxygen vacancy profile in the anodic titanium oxide film, and the surface oxygen vacancy concentration. This simplified Point Defect Model (PDM), which considers the oxygen vacancy as the only point defect in the film, successfully accounts for the impedance of anodized titanium over the potential range explored. The results indicate that there is a thin region of the non-uniform oxygen vacancy concentration adjacent to the film/solution interface, which has an exponentially decreasing dopant ( $$ {V}_O^{\cdot \cdot } $$ ) concentration. The results of the investigation show that the surface oxygen vacancy concentration normalized to the bulk oxygen vacancy concentration is in the range of 0.05–0.15 and is essentially independent of potential.

(Invited) The Morphological Stability of Passive Oxide Films

Understanding the kinetics of passive oxide formation and breakdown has been an ongoing problem for corrosion scientists for several decades. A model for the formation of a passive oxide film on a metal that is an extension of the Point Defect Model (PDM) will be presented. The potential description of the PDM is replaced with a boundary value problem that ensures Gauss' law is satisfied at the oxide-solution interface by considering the presence of the Helmholtz layer in solution. Our model predicts the observed linear variation of the steady-state film thickness with anode potential, and an increasing steady-state film thickness with increasing pH. A linear stability analysis of the moving metal-oxide and oxide-solution interfaces shows that, depending on the parameters, the passive film may be unstable to morphological perturbations of the film interfaces, leading to non-planar films and potentially the formation of a pit in the oxide. This also implies that one-dimensional models of oxide growth, that assume planar interfaces, can be inapplicable in broad classes of corrosion processes. The analysis shows that a morphological instability exists if the oxide dissolution mechanism is such that an increasing Helmholtz layer potential drop leads to an increasing dissolution rate. The instability behavior is consistent with the literature on breakdown of passivity in the presence of chloride ions. The theory provides insights on the initiation of passivity breakdown leading to pitting corrosion and the role that interfacial energy plays in determining stability.

Passivity breakdown on copper: Influence of borate anion

Passivity breakdown on pure copper in borate buffer solution containing chloride has been studied and the results have been analyzed using the Point Defect Model (PDM). Boric acid acts as an inhibitor of passivity breakdown for copper in chloride-containing solution. It is postulated that the deprotonated boric acid and/or polyborate species can be absorbed into surface oxygen vacancies of the barrier layer in competition with chloride ion, as indicated from ab initio modelling. The principal inhibitive species in the boric acid/NaOH system have been studied by thermodynamic equilibrium calculation and surface enhanced Raman Spectroscopy (SERS). The critical areal vacancy concentration of condensed cation vacancies at the metal/barrier layer (Cu2O) interface that leads to the breakdown of the passive film is estimated to be ≤ 1.06 × 1014 cm−2 experimentally. The distributions of the critical breakdown potential, as measured experimentally in chloride-containing solutions having different concentrations of borate, are near normal and the cumulative probability distributions are consistent with those calculated from the PDM.

Theoretical and experimental studies of passivity breakdown of Aermet 100 ultra‐high stainless steel in chloride ion medium

AbstractPassivity breakdown and pitting behavior in the presence of aggressive Cl− on ultra‐high strength steel Aermet 100, commonly used for landing gear, has been studied, the data are explained in view of the point defect model (PDM). Cyclic potentiodynamic polarization (CPP), electrochemical impedance spectroscopy (EIS), and X‐ray photoelectron spectroscopy (XPS) were examined to observe corrosion progress and corrosion products in the salt spray tests at 4, 8, 12, 16, and 20 days intervals. The breakdown behavior was studied using CPP, whereas scanning electron microscopy (SEM) and digital confocal microscopy were used to explore the micromorphology and depth distribution of pits. The cumulative distribution basically satisfies a normal probabilistic distribution at the different concentrations of chloride and pH, which is consistent with PDM assuming a near‐normal distribution of potential breakdown sites regarding to the cation vacancy diffusivity.

Studies on Pitting Corrosion of Al-Cu-Li Alloys Part III: Passivation Kinetics of AA2098-T851 Based on the Point Defect Model.

In this paper, the passivation kinetics of AA2098–T851 was investigated by a fundamental theoretical interpretation of experimental results based on the mixed potential model (MPM). The steady state passive layer formed on the AA2098–T851 in NaHCO3 solution in a CO2 atmosphere upon potentiostatic stepping in the anodic direction followed by stepping in the opposite direction was explored. Potentials were selected in a way that both anodic passive dissolution of the metal and hydrogen evolution reaction (HER) occur, thereby requiring the MPM for interpretation. Optimization of the MPM on the experimental electrochemical impedance spectroscopy (EIS) data measured after each potentiostatic step revealed the important role of the migration of Al interstitials in determining the kinetics of passive layer formation and dissolution. More importantly, it is shown that the inequalities of the kinetics of formation and dissolution of the passive layer as observed in opposite potential stepping directions lead to the irreversibility of the passivation process. Finally, by considering the Butler–Volmer (B–V) equation for the cathodic reaction (HER) in the MPM, and assuming the quantum mechanical tunneling of the charge carriers across the barrier layer of the passive film, it was shown that the HER was primarily controlled by the slow electrochemical discharge of protons at the barrier layer/solution (outer layer) interface.

Studies on Pitting Corrosion of Al-Cu-Li Alloys Part II: Breakdown Potential and Pit Initiation.

Prediction of the accumulated pitting corrosion damage in aluminum-lithium (Al-Li) is of great importance due to the wide application of these alloys in the aerospace industry. The Point Defect Model (PDM) is arguably one of the most well-developed techniques for evaluating the electrochemical behavior of passive metals. In this paper, the passivity breakdown and pitting corrosion performance of AA 2098-T851 was investigated using the PDM with the potentiodynamic polarization (PDP) technique in NaCl solutions at different scan rates, Cl− concentrations and pH. Both the PDM predictions and experiments reveal linear relationships between the critical breakdown potential (Ec) of the alloy and various independent variables, such as and pH. Optimization of the PDM of the near-normally distributed Ec as measured in at least 20 replicate experiments under each set of conditions, allowing for the estimation of some of the critical parameters on barrier layer generation and dissolution, such as the critical areal concentration of condensed cation vacancies (ξ) at the metal/barrier layer interface and the mean diffusivity of the cation vacancy in the barrier layer (D). With these values obtained—using PDM optimization—in one set of conditions, the Ec distribution can be predicted for any other set of conditions (combinations of , pH and T). The PDM predictions and experimental observations in this work are in close agreement.

Mechanisms of exchange and anion frenkel diffusion in uranium dioxide: Molecular dynamics study

Literature analysis reveals a significant discrepancy in the anion diffusion activation energies, calculated by the MD and the lattice statics methods using the point defects model, for a given interaction potentials set. To clarify this issue, the anion diffusion mechanisms and defect concentrations in a wide temperature range have been studied in detail.The stepped shape of the mean squared displacement (MSD) curves of anions, observed at low temperatures, is caused by the spontaneous formation and subsequent recombination of the long-living anion Frenkel defect. It is shown that correct MSD can be obtained, if at least one thermally activated defect exists (on average) in the simulation box. Otherwise the anion diffusion coefficients depend on the supercell size. Using the concentrations of defects and their mobility, calculated by the MD method, the diffusion coefficients of anions in the low-temperature region were calculated. They coincide well with the experimental data in absolute values.The mechanism of exchange diffusion has been quantitatively studied for the first time. Methods for detecting single exchange acts and calculating MSD for each type of exchange chains were developed. It is shown that exchange diffusion gives the greatest contribution at medium temperatures, before the superionic transition.

Passivity of titanium: part II, the defect structure of the anodic oxide film

The kinetic parameters of the formation of the anodic titanium oxide film on Ti in 0.5 M H2SO4 have been determined using potentiostatic polarization, electrochemical impedance spectroscopy (EIS), and the Mott-Schottky analysis (MSA). The findings are interpreted in terms of the point defect model (PDM). The oxygen vacancy is found to be the dominant point defect under all conditions studied with the metal interstitial being the minority defect. From MSA, the oxygen vacancy concentration was found to exponentially decrease from 5.03 × 1020 to 3.91 × 1019 cm−3 as the film formation voltage was increased from 2.24 to 10.24 VSHE. Using a value for the electric field strength of 1.734 × 106 V/cm, as determined by previous modeling with the PDM together with a fitted expression for the donor density and film formation potential, the oxygen vacancy diffusivity was found to be 2.6 × 10−16 cm2/s.

On the nature of the electric field within the barrier layer of a passive film

In this work, the nature of the electric field (E) in the defective oxide barrier layer on iron has been explored theoretically, within the classical regime, with the goal of ascertaining the validity of the postulates underlying the Point Defect Model (PDM). The analysis shows that if the thickness of the barrier layer under steady-state condition, L, is sufficiently small, the electric field strength and concentrations of point defects are essentially constants in the main part of this layer (with the exceptions in the very thin region near the metal/barrier layer (m/bl) and barrier layer/solution (bl/s) interfaces, depending upon the defect). A quantitative criterion was developed to decide when the barrier layer of the passive film can be considered to be sufficiently thin under these conditions. The potential drops inside the barrier layer and across the m/bl and bl/s interfaces can be represented as linear functions of applied voltage, V. This is the consequence of the change in thickness with applied voltage, with E being approximately (but with high accuracy) independent on the position inside the barrier layer and applied voltage. All conclusions stated above were derived from the solution of the system of mass transport equations for point defects and Poisson equation for the electric potential without applying any additional assumption except the small thickness of the barrier layer and without taking into account quantum (band-to-band) tunneling.

Predictions and Analyses on the Growth Behavior of Oxide Scales Formed on Ferritic–Martensitic in Supercritical Water

For 9–12Cr ferritic–martensitic steels in supercritical water, the dependencies of the thicknesses of three oxide layers (diffusion, inner, and outer layers) on each of seven principal independent variables were separately investigated using three supervised artificial neural networks (ANN) and fuzzy curve analyses. The latter were employed to evaluate the relative significances of independent variables, indicating that on the whole, temperature and exposure time are the most important variables, while the oxide dispersion strengthening (ODS) comes in the first place for the thickness of the diffusion layer. A thicker diffusion layer occurs easily at intermediate temperature approximately 600 °C and/or on ODS steels, due to higher growth rate of the barrier layer than that of the outer layer. The periodic growth of the diffusion layer, including the “shrinking”/“thickening” stages, was revealed by ANN prediction, which may be the basic cause of periodic pore-assembled layers within the inner layer. Finally, the physicochemical basis of classical point defect model was extended to describe the growth of oxide scales for explaining the ANN predictions at the atomic level. The growth of the inner layer into the metal is attributed to the inward transport of oxide ions (actually via outward transport of oxygen vacancies), while the outward transport of cations through the inner layer via a cation vacancy mechanism or as interstitials results in the thickening of the outer layer. The periodic variation in oxygen potentials at the diffusion/inner layer interface is responsible for the periodic growth of the diffusion layer. The iron caves at the inner–diffusion interface left behind by the generation reaction of cation interstitials may be the intrinsic sources of pores within the inner layer.

Investigation of chloride-induced depassivation of iron in alkaline media by reactive force field molecular dynamics

The passivity of iron in alkaline media enables the use of carbon steel as reinforcement in concrete, which makes up the majority of modern infrastructure. However, chlorides, mainly from deicing chemicals or marine salts, can break down the iron passive film and cause active corrosion. Despite recent advances in nanoscale characterization of iron passivity, significant gaps exist in our understanding of the dynamic processes that lead to the chloride-induced breakdown of passive films. In this study, chloride-induced depassivation of iron in pH 13.5 NaOH solution is studied using reactive force field molecular dynamics. The depassivation process initiates by local acidification of the electrolyte near the film surface, followed by iron dissolution into the electrolyte, and iron vacancy formation in the passive film. Chlorides do not penetrate the passive film, but mainly act as a catalyst for the formation of iron vacancies, which diffuse toward the metal/oxide interface, suggesting a depassivation mechanism consistent with the point-defect model.

Determining the electric-field strength in a passive film via photo-induced electric fields

The nature of the electric-field strength in the passive film on tungsten is explored using photo-electrochemical techniques. A theoretical expression for the photo-stimulated growth of the film has been derived. Rotating ring-disk electrode (RRDE) experiments indicate that photo-corrosion of a tungsten electrode is negligible under super-band gap light illumination. XPS results show that tungsten is in the maximum possible oxidation state (VI) in the film and hence no higher oxidation state is available. The photo-stimulated transient film growth of tungsten in pH 8.5 ± 0.1 boric-borax buffer was recorded as a function of film formation potential (1 VSCE, 2 VSCE, 3 VSCE, 4 VSCE, 5 VSCE, 6 VSCE) and light intensities (50, 200, 1000 mW/cm2). Steady state passive film thickness measurements of the passive film on tungsten indicate that super band gap, UV light suppresses the electric field in the barrier layer, and hence stimulates anodic oxide film growth. The data obtained in this study demonstrate that the electric field strength in the steady state is independent of the applied potential and film thickness, as postulated in the Point Defect Model.