Atomistic Insights into Early Stage Oxidation and Nanoscale Oxide

Article pubs.acs.org/JPCC

Atomistic Insights into Early Stage Oxidation and Nanoscale Oxide Growth on Fe(100), Fe(111) and Fe(110) Surfaces Ram Subbaraman,† Sanket A. Deshmukh,‡ and Subramanian K.R.S. Sankaranarayanan‡,* †

Materials Science Division, ‡Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, United States ABSTRACT: Reactive molecular dynamics (MD) simulations with dynamic charge transfer between atoms is used to investigate the oxidation kinetics during the early stages of nanoscale oxide growth on Fe(100), Fe(111), and Fe(110) surfaces. The growth rate of the oxide layer was found to follow logarithmic time dependence, with limiting thicknesses ranging from 1 to 2 nm depending on the crystal orientation. Temperature and pressure effects were studied for the three surface geometries, with the (110) surface exhibiting a stronger dependence compared to the (100) and (111) counterpart. Structure and dynamical correlations in the metal/oxide/gas environments are used to gain insights into the evolution and morphology of the growing oxide film. The surface structure is found to strongly influence not only the morphology of the oxide but also the stoichiometry of the oxide layer formed. Stoichiometry of the oxide layer formed at room temperature shows evidence for the presence of a nonstoichoimetric oxide layer consisting of two phases: a surface layer dominant with mixed oxide (FexOy with y/x ≈ 1.3−1.5) oxides and a bulk layer of FexOy with y/x ≈ 0.7−0.8. This is found to be directly related to the propagation of the oxide growth through the thin film. The relative fractions and near surface distribution of the mixed oxides are dictated by the differences in cationic/anionic diffusivities which are strongly dependent on the crystal surfaces, consistent with previously established experimental observations. At any given oxidation condition, the activation energy barrier for oxidation was found to be lowest for Fe(110) (7.44 KJ/mol) compared to the other two surfaces (23.69 KJ/mol for Fe(100) and 19.88 KJ/mol for Fe(111)). The differences in oxide formation in the early stages of oxidation are explained in terms of the transport characteristics of the anion/cation for the various crystal orientations. The simulation findings agree well with previously reported experimental observations of oxidation on Fe surfaces.

1. INTRODUCTION Oxidation of metal surfaces is of considerable technological interest and is important for numerous applications ranging from heterogeneous catalysis, microelectronics, and for protection against wear and corrosion.1,2 In particular, oxides of metals such as Fe offer unique physical and chemical properties and have found a niche as functional materials for various technological applications such as information storage, catalysis, hydrogen storage, permanent magnet, optoelectronics, and ferrofluid.3−5 Even subtle variations in the stoichiometry, composition, defect density, and structure of such oxides can provide significant alteration of properties and thus offer a wide range of functionalities.6−9 In particular, the synthesis conditions as well as the surface condition of metal undergoing oxidation have a significant bearing on the ability to tune the stoichiometry, density, and the morphology of the grown nanoscale oxides.10,11 Insights into the initial stages of nanoscale oxidation and oxide growth are critical to understand the oxidation mechanism and to exercise control over the structure/morphology of the grown oxides.12 Toward this end, crystal orientation is an important factor, which has been shown to strongly influence the oxidation characteristics of metals.13−15 Experimentally, most of the materials are polycrystalline and contain myriads of orientations that contribute to the oxidation process, which makes it difficult to decipher the © 2013 American Chemical Society

crystallographic dependence of the oxidation process. Moreover, the atomistic mechanism of the dependence of the oxidation rate on the crystal orientation is also not completely understood and in particular is significantly dependent on the native crystal structure of the material.16 In this work, using molecular dynamics simulations, we demonstrate the effect of crystal orientation and oxidation conditions (temperature, pressure, etc.) on the structure and dynamics of nanoscale oxide growth on Fe surfaces. There have been several previous experimental studies that have attempted to characterize the formation mechanism and microstructure of the oxide films on Fe surfaces.10−13,17,18 For example, studies on oxygen adsorption and oxide growth on metal surfaces such as Fe(110) and Fe(100) have been reported using scanning tunneling microscopy (STM),10,19,20 low-energy electron diffraction (LEED),21 Auger electron spectroscopy (AES),22 and X-ray photoelectron spectroscopy (XPS).23 While these studies suggest that the oxide formation follows oxygen chemisorption onto the metal surface, the details regarding the oxidation kinetics, the mechanisms and the structures that evolve during the initial stages of oxidation are Received: December 19, 2012 Revised: February 13, 2013 Published: February 15, 2013 5195

dx.doi.org/10.1021/jp312514m | J. Phys. Chem. C 2013, 117, 5195−5207

The Journal of Physical Chemistry C

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on the ions is a function of the oxygen/iron ratio. During the oxidation of metals, significant positive charges are induced on the metal atoms and significant negative charges are induced on the oxygen atoms. Thus, the charges induced on these ions and atoms are environment dependent and their valency is determined by the stoichiometry of the resulting oxide. Additionally, the fixed charge models cannot be used to study the structure of the interface between a metal and its oxide. Hence, to model oxidation and oxide growth on metal surfaces, a potential model which can switch between one dominated by ionic interactions in the oxide regions and metallic interactions in the metal region is required.31,32 Recently, a reactive force field (ReaxFF) developed for Fe oxides by Adri et al. can deal with the complexities of the changing nature of interatomic bonding in the oxide and metallic region by taking into account the dynamic charge transfer between the various species.36,37 Here, we demonstrate, using a variable charge (ReaxFF) molecular dynamics simulation study, the influence of crystallographic orientation on the oxidation behavior of Fe surfaces. We specifically report on the early stages of oxidation and dynamics of oxide growth on a technologically important substrate such as Fe, with focus on temperature, and pressure effects. The oxidation kinetics and oxide growth are shown to be strongly dependent on the crystal orientation of the metal substrate. Structure and dynamics of the formation of the oxide scale on various Fe surfaces is investigated in detail. Structure and dynamical correlations in the metal/oxide/gas environments are used to gain insights into the evolution and morphology of the growing oxide film. The temporal evolution of oxide composition, oxide density as well as the resulting morphologies is evaluated using dynamical correlation functions. Stoichiometry variations across the oxide film and valence state of the oxide constituents are characterized using the simulated trajectories. The activation energy barriers for oxidation on the metal surfaces are derived from the simulated oxidation kinetic curves. Finally, the atomic trajectories generated using MD simulations are also used to identify the diffusion mechanisms associated with the oxide growth. The atomistically simulated evolution of charges and atomic diffusivities for various surface orientations are used to clearly explain the observed differences in oxide composition and the stoichiometry of the grown oxide layer.

still elusive. Similarly, Qin et al. have used AES, LEED, and STM to study Fe(111) oxidation at room temperature and 500 K.19 Their study suggests that there is formation of mixed oxide at the two temperatures. Both Fe3O4 and Fe2O3 were found in the oxidized samples at 300 K, whereas oxidation at 500 K resulted in the formation of primarily Fe3O4. Low temperature oxidation of Fe(111) resulted in a more uniform oxidation whereas oxidation at 500 K resulted in a discontinuous island like growth. Grosvenor et al. suggested that oxidation on Fe(111) follows a mechanism in which oxygen adsorption is followed by thin layer oxide formation via place exchange which terminates after a few monolayers.7,9 Some have suggested that the electric field driven ionic diffusion is the rate-determining step since the oxidation reaction between the metal and oxygen occurs at the oxide/oxygen interface and therefore the metal cations must diffuse through the oxide layer for the oxidation to continue and result in growth of oxide layer.24−26 On the basis of these studies, it can be said that there are still many open questions regarding the atomistic details of the oxidation process.26,27 In particular, not much is known about the initial oxidation growth kinetics as well as atomistic details of the temporal evolution of composition, microstructure, and the limiting thickness of oxide films at the nanoscale. Given the great practical importance of such oxide materials, obtaining insights on a molecular level into the processes occurring during the oxide growth on the Fe surfaces is the main focus of the work presented here. Most of the previous theoretical approaches on modeling the interaction of iron and oxygen were mostly based on ab initio approaches and density-functional theory (DFT). Blonski et al. have studied the dissociative adsorption of O2 molecules on clean and oxygen-precovered Fe(110) and Fe(100) surfaces.28 Their studies reveal interesting differences in the reactivities of these surfaces. Oxygen adsorption on the Fe(100) surface at high temperatures leads to the formation of a p(1 × 1) monolayer, which was identified as a two-dimensional FeO(100) oxide film. However, oxidation of Fe(110) surface, at high temperatures suggests that saturation occurs at ∼0.4 ML, which is preceded by the formation of c(2 × 2) and c(3 × 1) superstructures.29 Most of these calculations, however, only consider the energetics and the structural, electronic, and magnetic properties of adsorbed O up to a complete monolayer coverage.30 However, these approaches are confined to very small system sizes and do not include the effect of thermal vibrations. Hence the dynamics associated with the oxide growth on metal surfaces may not be adequately modeled by these approaches. Therefore, oxidation of Fe surfaces leading to the formation of thin-film oxides in the nanometer length scales has not yet been reported. Molecular dynamics (MD) simulations on metal oxidation can provide a valuable complementary tool for the investigation of both the oxide structure and the atomic-level details of the growth mechanism at nanometer length scales.1,31,32 Additionally, MD simulations also make it possible to simulate much larger systems containing several thousands or even millions of atoms. Most of the MD simulations till date on modeling oxides of metals, however, employ a fixed charge model.33−35 Although the fixed charge potential model allows for an easy implementation in efficient MD algorithms, it has several shortcomings. The principal shortcoming in these fixed charge models is that it does not allow the introduction of multiple oxidation states.35 Iron, however, can form different oxide compounds such as FeO, Fe2O3, and Fe3O4 where the charge

2. COMPUTATIONAL DETAILS 2.1. Potential Model. To simulate the oxidation and oxide growth on surfaces of Fe(100), Fe(110), and Fe(111), we utilize molecular dynamic (MD) simulations employing a reactive force-field (ReaxFF) potential model that allows for variable and dynamic charge transfer between atoms.31,32 In particular, reactive force-field (ReaxFF) implements the feature of quantum chemistry calculations, including molecular association/dissociation and charge transfer between cations and anions, and therefore ensure a more accurate description of the oxidation simulation. By calculating many-body interactions of a single particle, characteristics of quantum chemistry effect are employed in multiple-components of particle interactions as shown in eq 1, such as bond energy, over/under coordination, lone-pair energy, valence angle, torsion, hydrogen bond, van der Waals, and Coulomb.38 Etotal = E bond + Eover + Eunder + E lp + Eval + Etors + E H + Evdw + ECoul 5196

(1)



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the outermost layers and ±0.01e in the bulk alloy. Similar charge fluctuation was observed in the oxidation simulations of Hasnaoui et al.1 The oxidation of the Fe surfaces is initiated by introducing O2 molecules in the vacuum with their radial positions chosen randomly (Figure 1). The pressure is adjusted based on the ratio of number of metal surface atoms and the oxygen gas phase molecules. Therefore, a ratio of 1 corresponds to the low pressure condition and a ratio of 3 corresponds to the high pressure case. The velocities of the O2 are chosen from a Maxwell−Boltzmann distribution corresponding to the required temperature. Additionally, reflecting boundary conditions are imposed to the molecules that might reach the simulation box limit. The gas pressure is maintained constant during the simulation by introducing a new O2 molecule only when the previous molecule dissociates and forms bonds with the metal atoms. The equations of motion are integrated using a leapfrog scheme with time steps of 1 fs. The charge relaxation procedure used to minimize the electrostatic energy subject to the electroneutrality principle is very time-consuming. Hence, the atomic charges were updated every 10th MD step. The influence of a more frequent charge update was found to have no influence on the observed simulation results. The simulations were carried out using the Large-scale Atomic/ Molecular Massively Parallel Simulator (LAMPPS).

Additionally, the temporal charges of cations/anions are calculated using the electronegativity equalization method as shown in eq 2. ⎡

E(q) =

∑ ⎢⎢χi qi + ηiqi2 + Tap(rij)kc i

⎣

⎤ ⎥ (rij2 + γij−3)1/3 ⎥⎦ qiqj

(2)

In the above equation, q, χ, η, Tap(r), γ, and kc are ion charge, electronegativity, atomic hardness, seventh order taper function, shielding parameter, and dielectric constant, respectively. ReaxFF potential parameters are determined from training sets and the resulting accuracy is therefore highly dependent on the employed training set. Detailed implementation and development of ReaxFF models for Fe oxidation can be found in the work by Adri et al.38 Van Duin et al. provided two kinds of parameter sets, such as full and oxide, and full version of the library is employed in this study. The Fe−Fe interaction can be found in a more recent paper by Van Duin and co-workers.39 It is capable of treating both metallic and ceramic systems as well as bond formation and bond breakage involved in oxidation processes. Additionally, it can take into account the presence of multiple oxidation states as well as partial oxides in the oxide film. The oxidation setup and computational details are similar to that discussed in ref 31 and are summarized below. 2.2. Set-up of the Oxidation Simulations. A schematic showing the actual oxidation setup is shown in Figure 1. The

3. RESULTS AND DISCUSSION 3.1. Oxidation Kinetic Curves. The kinetics of oxide growth on Fe surfaces with different crystallographic orientations is presented in this section. Dynamic properties through the oxidation process and the effect of crystal orientation as well as temperature and pressure on the oxide growth characteristics are studied and discussed. Comparisons with experimental studies on oxide growth kinetics of Fe surfaces are also carried out, where possible. 3.1.1. Function of Crystal Surface Orientation. Figure 2 shows the total oxygen uptake as a function of the simulation time up to the limiting value of oxide thickness for the three different Fe surfaces. The oxidation of all of the three Fe surfaces shows an initial fast oxidation followed by a slow oxide growth phase. For exposure times less than 75 ps, the kinetic curves obtained across different crystal orientations are more or less similar. At longer simulation times beyond 75 ps, significant differences between the various substrate surfaces begin to show up. Our simulations suggest that the oxidation kinetics follow the order Fe(110) > Fe(111) > Fe(100). The orientational dependence of the oxidation kinetics is not surprising, although one would have expected a more open surface such as Fe(100) to be more reactive than Fe(110),15 which is consistent with what is observed at time t < 20 ps. However, interestingly, this observation is in accordance with previous experimental investigations of oxidation on Cr surfaces, which also have a bcc structure.41 They find that the oxidation rate increased in going from (001) to (011). In the case of Cr, the rate of oxidation increased as the surface normal deviated from (001). The differences in the oxidation kinetics for the various crystals were attributed to the anisotropy in the ionic diffusion through the growing oxide layer. The anisotropic nature of the diffusion in mixed oxide layers is indeed true in oxidation of Fe surfaces as well and is discussed in more detail in later sections. Our simulation results thus imply that the oxidation kinetics are dependent on the crystallographic

Figure 1. Simulation cell of metal surfaces and the vacuum surrounding it.

simulation cell comprised of metal slabs: ∼44 × 44 × 44 Å for the three surfaces and vacuum space surrounding it for oxygen molecule insertion. Prior to the actual oxidation simulations, the Fe(100), Fe(111), and Fe(110) metal surfaces are subjected to an equilibration procedure, which starts by increasing the temperature, in steps of 20 K from 0 to 300 K. For each temperature, a run of 1000 MD steps using isokinetic MD was performed. The temperature was maintained constant at each temperature using a Nose-Hoover thermostat.40 The surfaces are allowed to relax during these equilibration runs. The equilibrated samples are then simulated in a NVT ensemble for 1 ps with dynamic charge transfer using the ReaxFF potential model to generate the final 300 K relaxed configuration. The atomic charges in the metal samples were found to fluctuate around zero with a magnitude of ±0.05e at 5197



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Figure 2. Effect of oxygen partial pressure on the oxidation kinetics of Fe surfaces. Pressures are based on the ratio of surface metal atoms to oxygen gas atoms, low (ratio of 1) and high (ratio of 3).

Figure 3. Effect of temperature on the oxidation kinetics of Fe surfaces at (a)−(c)−(e) low pressure and (b)−(d)−(f) high pressure.

3.1.2. Function of Oxygen Partial Pressure. To investigate the dependency of oxide growth on the gas pressure, we simulated oxidation of Fe surfaces at two different pressures.

orientation of the surface making the Fe(110) crystal surface more reactive than the (111) and (100) ones. 5198



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Figure 4. Radial distribution function obtained for various iron oxide reference structures (a) wüstite or FeO (b) magnetite or Fe3O4 (c) hematite or Fe2O3.

The temperature is kept constant at 300 K. The kinetic curves showing the effect of gas pressure on oxide growth on Fe crystal surfaces are shown in Figure 2. The oxidation kinetics are found to increase with increasing gas pressure for all three surfaces, which is in qualitative agreement with the experimental investigation of Grosvenor et al.9 As also observed at higher temperatures, the kinetic curves show an initial fast oxide-film growth followed by a slower oxide growth phase. Our simulations suggest that the early stage oxidation kinetics follows the order Fe(110) > Fe(111) > Fe(100). At lower oxygen partial pressures, the difference in the rate of oxide growth on Fe(100) and Fe(111) is smaller. Comparing Figure 2, parts (a) and (b), however, we find the differences in the growth rate kinetics between Fe(100) and Fe(111) surfaces to increase with increasing oxygen pressures, especially at higher exposure times. The lowering of the activation barrier for the oxidation with oxygen partial pressure appears to be higher in

the case of Fe(111) compared to Fe(100) surfaces. The activation barrier calculation for the three different surfaces under various oxidation conditions, based on a logarithmic growth law model is discussed in detail in a later section. 3.1.3. Oxidation Kinetics as a Function of Temperature. The effect of temperature on the oxidation kinetics was investigated by simulating the three different Fe surfaces at temperatures ranging from 300 to 800 K. The gas pressure was maintained constant across all of the temperatures considered here. The rate of oxygen atom intake for the three surfaces is shown in Figure 3. As expected, the kinetics of oxide growth increases at higher temperatures, which is consistent with the experimental studies on Fe oxidation by Vink et al. and Campo et al.11,42 The oxidation kinetics at any given temperature exhibits an initial stage of fast oxide growth followed by low growth rate. Comparing Figure 3, parts (a)−(f), it can be seen that the oxygen uptake and therefore the oxide growth kinetics 5199



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Figure 5. Radial distribution function obtained as a function of oxygen partial pressure for the three different Fe surfaces (a) high pressure (b) low pressure.

Figure 6. Pair distribution function for Fe−O pair obtained as a function of temperature for the three different Fe surfaces (a) Fe(111), (b) Fe(110), and (c) Fe(100).

on Fe surfaces follows the order Fe(110) > Fe(111) > Fe(100) for the range of simulated temperatures and pressure. As seen in Figure 3, the difference in the rate of oxide growth for all three surfaces is found to increase with increasing temperature, which is consistent with experimental observations for the various Fe surfaces.11,42 3.2. Structural Analysis. We have analyzed the structure of the oxide film during the oxidation process using various dynamical correlation functions such as radial distribution functions as well as atomic density profiles. We also discuss the spatial and temporal evolution of the charges during the oxidation and oxide growth process. 3.2.1. Radial Distribution Functions (RDF) and Coordination Number Analysis. Radial distribution functions (RDF) between various ion pairs were used to investigate the structural evolution of the three crystal surfaces during the oxidation and oxide growth process. The RDF is defined as the probability of finding an atom at a distance r from another atom compared to a homogeneous distribution and is given by the following:43−45

g (r ) =

V 1 2 NN 4 r π δr i j

∑ ∑ δ(r − rij) i

j>i

(3)

In the above equation, V is the volume, whereas Ni and Nj are the atom types of the RDF. The delta function in the RDF function must give rise to a value of one for a range of r (δr), allowing for the formation of a histogram. The pair distribution function (PDF) of the atoms in the oxide film as well as partial PDF of each type of atoms was calculated at the end of the simulation for the three surfaces at room temperature and the two simulated pressures. For all of the surfaces studied, the Fe−O PDF exhibits a peak around 1.8 Å during the whole oxidation process, except for the very early stage that corresponds to the oxide nucleation. Our simulations of standard Fe oxide structures suggest that wüstite shows Fe− O peak around 1.65 Å, whereas Fe3O4 or magnetite exhibits a characteristic Fe−O distance of 1.8 Å. Fe2O3 or hematite shows a distinct peak at 1.7 Å, while a prominent shoulder can be seen at 2.1 Å. The results are shown in Figure 4. We use the PDF 5200



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profiles of the standard oxides to fingerprint the oxide structures formed during the early stages of oxidation of Fe single crystal surfaces. Oxide radial distribution functions for the Fe oxides formed during the early stages of oxidation are shown in Figure 5. The peak distance shown in Figure 5, parts (a) and (b), is very close to the first neighbor distance found in the case of Fe2O3 or hematite structures (Figure 4). The intensity of the first peak, which gives a measure of the extent of oxide formation suggests higher oxide formation in the case of Fe(110) surface compared to the Fe(100) and Fe(111) surfaces. As expected, the peak intensities are relatively higher for all three surfaces at higher pressure compared to lower pressure. To distinguish between the natures of crystallinity of the oxide formed, one can analyze the higher order peaks in the Fe−O RDFs. A crystalline oxide is expected to have well-defined and sharp peaks corresponding to the higher order neighbors, whereas an amorphous oxide shows a more smeared out distribution. Thus, our analysis of the higher order peaks in the Fe−O RDF (Figure 5, parts (a) and (b)) suggests that the oxide formed in the case of Fe(111) and Fe(110) are amorphous in nature whereas a more crystalline oxide structure is evident in the case of Fe(100) surface. Figure 6 shows the partial pair distribution function (PDF) of Fe−O computed for different crystal surfaces and at temperatures of 300 and 600 K. In all of these cases, the oxygen gas pressure was maintained at low pressure. Figure 6 thus illustrates the thermal effect on oxide structure for the three surfaces. The peak intensity in the calculated RDF for Fe−O increases with temperature in all three Fe surfaces, which suggests an increase in the number of Fe ions bonded to O. This is expected since oxidation kinetics and oxide growth are higher at elevated temperatures. On the basis of the peak intensities, one can conclude that high temperature oxidation also follows Fe(110) > Fe(111) > Fe(100). 3.2.2. Atomic Density Profiles. To evaluate the distribution of ions in the growing oxide film, we have plotted the ionic densities as a function of the distance normal to the exposed interfacial plane. The ion density (ρx) is defined as the number of ions of a given type within a range of perpendicular positions in the simulation cell and normalized to the average density.43−45 ρ (x ) =

V NAδx

to the bulk and that of the cations from the bulk to the surface of the oxide. The extent of oxygen deficiency follows Fe(100) > Fe(111) > Fe(110). Thus, in the case of Fe(110), the oxygen densities at both the oxide-gas and metal-oxide interface are significantly higher compared to the other two surfaces as shown in Figures 7 and 8. There is also a more uniformly

Figure 7. Atomic density profile of oxygen anion for oxidation of Fe(111), Fe(100), and Fe(110) at low pressure.

Figure 8. Atomic density profile of oxygen for oxidation of Fe(111), Fe(100), and Fe(110) at high pressure.

∑ δ(x − xi) i

distributed and stoichiometric oxide film that can be attributed to increased anion migration into the oxide film in the case of Fe(110) compared to Fe(111) and Fe(100). We note that there can be possible surface reorganization and reconstruction if one simulates for much longer time scales of the order of several microseconds. The kinetic Monte Carlo studies are a much more viable route for such studies on surface reconstruction and such studies would be attempted in the future. 3.3. Snapshots of Oxide Growth and Charge Distribution for the Three Surfaces. The snapshots showing the oxidized surfaces as well as charge distribution across the oxide film in the case of the three different Fe surfaces is shown in Figure 9. In our simulations, we observe that the atomic charges in the bulk metal substrates in all cases present charges, which fluctuate around a zero value. The positive charges in the oxide film are due to Fe metal atoms, whereas the negative charge is attributed to the oxygen atoms. Upon checking for the zero charge condition for the charge distributions in the three cases, we find that the fluctuations

(4)

Here, V is the simulation cell volume, N is the number of ions of a given type, A is the area of the interface, and xi is the distance of atom i perpendicular to the interface. δ is typically the bin or histogram width and is the interval over which the ion densities are time-averaged over many configurations obtained from the MD trajectories to compute the ionic densities. Our analysis of the oxygen density profiles for room temperature oxidation of the various Fe surfaces indicates significantly lower densities at the metal-oxide interface and higher densities close to the oxide-gas interface. It can be seen that there is a gradation in oxygen densities in the interior of the oxide film, with a significant drop as we approach the metaloxide interface. Thus, the oxide produced by oxidation in all the three cases appears to be substoichiometric and oxygen deficient, especially in the oxide interior and the metal-oxide interface. This can be directly correlated to the relative differences in the diffusivities of the anions from the surface 5201



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Figure 9. Snapshot showing the charge distribution for oxides grown on (a) Fe(100), (b) Fe(110), and (c) Fe(111) surfaces.

around zero value reached a maximum of 0.15−0.20e at the gas/oxide interface and 0.10−0.15e in the oxide interior. In all of the three cases, the oxygen atoms are weakly charged close to the oxide-gas interface and increase in strength of binding and hence the net charge in the oxide interior. The values reach a maximum negative value at approximately 0.5− 0.8 nm from the oxide-gas interface. The charges on oxygen atoms then decrease to lesser negative values close to the metal oxide interface. The reduction in the magnitude of the oxygen charges near the oxide gas interface is attributed to the insufficient concentrations of cations to ionize the oxygen in the oxygen rich surface region. Additionally, the oxygen charge close to the metal-oxide interface is also low since they are ionized by cations, which are weakly charged. Thus, the charge distribution in the metal oxide film is not homogeneous and is strongly correlated to the coordination number and stoichiometry (in terms of neighboring oxygen atoms) of the metal atoms in the oxide film. Details about the evolution of the oxide stoichiometry and the mechanism of nanoscale oxide growth are discussed in the following sections. 3.4. Stoichiometry Variation Based on Charges (FeO vs Fe2O3 vs Fe3O4). The average composition of the grown oxide films, expressed as the O/Fe ratio, has been plotted as a function of the oxide film thickness for the three simulated surfaces at pressures corresponding to high pressure (Figure 10(a)) and low pressure (Figure 10(b)), respectively. At all oxidation times studied, the oxide film has an overall nonstoichiometric composition. As shown in Figure 10, our simulation results indicate a gradation of oxygen stoichiometry across the oxide thickness such that the oxygen stoichiometries are lower at the metal-oxide interface and higher at the oxidegas interface. The degree of cation enrichment (and the oxygen deficiency) decreases from the metal/oxide interface toward the oxide-gas interface. This relative enrichment of the cations in regions close to the oxide-metal interface has also been observed in case of natural oxidation of several metal oxides such Zr, Al, Ni, etc.2,46−48 All of the Fe-oxide films thus have an overall nonstoichiometric composition. We note that the extent of O/Fe nonstoichiometry follows the order Fe(100) < Fe(111) < Fe(110) at both the simulated pressures. At high pressure, O/Fe stoichiometry for Fe(110) varies from ∼1.5 at the oxide gas interface to ∼1.1−1.2 in the oxide interior and ∼0.2 near the oxide-metal interface. In the

Figure 10. Variation in oxygen stoichiometry across the thickness of the oxide film grown on Fe(110), Fe(100), and Fe(111) surfaces at (a) high pressure (b) low pressure. The stoichiometry is evaluated on oxide films formed at the end of the oxidation simulations. Red, green and blue lines correspond to Fe(110), Fe(111), and Fe(100), respectively.

case of Fe(111), the oxygen stoichiometry varies from ∼1.4 at the oxide-gas interface to ∼0.6 in the oxide interior and ∼0.15 at the oxide metal interface (Figure 10(a)). Similarly, in the case of Fe(111), the oxygen stoichiometry varies from ∼1.4 at the oxide-gas interface to ∼0.5 in the oxide interior and ∼0.15 at the oxide metal interface (Figure 10(a)). We observe that qualitatively similar variation is observed at lower oxygen pressure of O2. Higher surface stoichiometry (∼1.3−1.5) is an indication of formation of both FeO and Fe2O3. In the oxide interior, the oxide is substoichiometric and comprises mainly of FexOy (y/x ≈ 0.7−0.8). The stoichiometry variation for room temperature grown oxide suggests that the oxide layer consists of two phases, the surface containing mixed FexOy (y/x ≈ 1.3−1.5) whereas the interior comprises primarily of FexOy (y/x ≈ 0.7− 0.8), the former being observed at the longer simulation times when the oxide thickness is sufficiently large. This is in excellent agreement with High Energy Ion Scattering studies on Fe(100) surface by Leibbrandt et al. who determined the stoichiometry of thin oxide layers formed by oxidation in O2 of Fe(100) to be FexO (with x = 0.95 in the interior) at room temperature and 473K.49 However, detailed angle dependent XPS studies by Jurgen et al. confirmed that higher Fe2O3 fraction is present at the oxide/oxygen interface during oxidation of Fe(100) and Fe(110) compared to that in the oxide interior.50 Comparison of Figure 10, parts (a) and (b), suggest that for any given crystal surface, higher oxygen pressure results in higher oxygen stoichiometry within the oxide film. For example, at high pressures, O/Fe stoichiometry for Fe(110) varies from 5202



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Figure 11. Comparison of the room temperature mobilities of Fe and O in the three growing oxide films (a) Fe(100), (b) Fe(111), and (c) Fe(110) at high pressure. Comparison of the relative mobilities of Fe and O at 600 K is also shown for the three surfaces.

∼1.5 at the oxide gas interface to ∼1.1−1.2 in the oxide interior and ∼0.2 near the oxide-metal interface whereas the same at low pressure varies from ∼1.35 at the oxide gas interface to ∼0.8 in the oxide interior and ∼0.2 near the oxide-metal interface. This is in excellent agreement with experiments of Brundle et al. who measured stoichiometry of Fe(100) thin films using XPS.51,52 They found mixed oxide formation of FexOy, with higher fraction y/x of ∼1.5 at high oxygen exposures and y/x of ∼1.0 dominant at lower exposures. The formation of a mixed oxide layer may have important consequences for the kinetics of oxide layer growth. In a previous combined electrochemical and surface analytical study, it has been concluded that Fe2O3 oxide layers may act as a barrier for ionic transport, and therefore may cause oxidation rates to diminish. Similar conclusions were drawn by Jurgen et al. who applied Fromhold-Cook Model to study the initial oxidation of Fe(100).50 Indeed, our temporal evolution of the oxide stoichiometry suggests that the initial oxide formed is highly nonstoichiometric (comprised mainly of FeO) in all three cases and the formation of Fe2O3 occurs in the later stages (exposure times >50 ps) when the oxidation kinetics appears to saturate. Further details regarding the oxide growth mechanism and cationic/anionic diffusional motion in the growing oxide film during the oxide growth process is discussed in the next subsection. 3.5. Mechanism of Oxide Growth Based on Relative Diffusion of Cation Vs Anion. To study the mechanism of the initial oxidation of Fe surfaces, it is necessary to first understand the dynamics of cation and anion movement. The

oxide growth characteristics of the metal surfaces were explored using the calculated mean square displacements and cation/ anion diffusion coefficients for the three surfaces. The MSDs (mean square displacements) and diffusion coefficients allow for comparison of early stages of oxide growth among the different Fe surfaces. Figure 11(a) shows the MSDs plotted for Fe(100) surface oxidation at two different temperatures. At room temperature, we find that the oxygen anion diffusion is much larger than that of Fe. Thus, room temperature oxide growth proceeds mainly via inward movement of oxygen anions across the metal-oxide/gas interface. As the temperature is increased to 600 K, although the oxygen anion diffusion is still higher than Fe, we observe that the outward movement of metal cations across the metal/metal-oxide interface also becomes comparable and contributes to the oxide growth. This result is in excellent agreement with the experimental studies of Juergen et al.50 and that of Leibbrandt et al. who used a combination of Auger electron spectroscopy (AES) with highenergy ion scattering (HEIS), nuclear reaction analysis (NRA), and ellipsometry to identify the mobile species during oxide growth on Fe(100) surface.53 They observed that room temperature oxidation of Fe(100) occurs mainly via diffusion of oxygen whereas mobility of iron is also significant at higher temperatures (>500 K). However, in the case of Fe(111), comparison of MSDs suggests that oxide growth proceeds mainly via oxygen diffusivity at room temperature. With an increase in temperature to 600 K, the diffusivity of Fe increases, but the oxide growth still proceeds predominantly due to oxygen diffusion. 5203



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and Fe(110) room temperature oxidation and contribute much to the oxide growth. As the temperature is increased from 300 to 600 K, the Fe diffusivity in the case of Fe(100) shows a 3-fold increase (0.98 × 10−5 cm2/s), whereas the oxygen diffusivity increases to 1.4 × 10−5 cm2/s. However, the diffusivity of Fe increases by a factor of 1.5 and 2.0 for Fe(111) and Fe(110) surfaces, respectively. Fe diffusivity data in Table 1 suggests that an increase in temperature to 600 K clearly results in increased mobility of Fe across all three surfaces. The contribution of Fe to oxide growth at 600 K follows the order Fe(100) > Fe(111) > Fe(110). 3.6. Activation Barrier Calculation for Oxide Growth on the Three Surfaces. To calculate the activation barrier, we fit our oxidation kinetics curve to known growth laws. The morphology and stoichiometry of the oxide layer is changing with time. Therefore, in the calculation of activation barrier, we utilize the oxidation kinetic data obtained at various temperatures and gas pressures. Such a method of calculation of activation barrier have been previously used in several other oxidation simulations and experiments.2,9,55 For the temperature/pressure regime studied here, the oxidation kinetic curves follow a direct-logarithmic growth. An example of such a fit of the kinetic curves where the number of oxygen uptake is fitted to a direct logarithmic function of exposure time is shown in Figure 12. In this work, we find that the oxidation kinetics on all of the simulated surfaces obeys direct-logarithmic growth kinetics (for example, see Figure 12). Such direct logarithmic relationship between the oxygen uptake vs ln(time) were developed originally by Eley and Wilkinson.56 This direct logarithmic growth mode is usually related to a mechanism where a thin layer of oxide develops via initial ion adsorption with further oxidation occurring due to an electric field mechanism. The electric field is formed by electrons tunnelling from the metal to the adsorbed oxygen and is able to support ion transport through the initially formed thin oxide layer enabling the oxide layer to increase in thickness. The kinetic model developed by them is shown in eq 1 below:

This is not surprising given the highly ordered nature of the surface, which results in a low degree of openness for the cation migration. Similarly observation is made in the case of Fe(110) oxidation at 300 and 600 K where oxide growth occurs primarily due to oxygen diffusion. Comparing the MSDs of O and Fe across the three substrates and at the two temperatures (Figure 11, parts (a) vs (b) vs (c)), we find the MSDs to be higher in the case of Fe(110) followed by Fe(111) and Fe(100). This is in agreement with the growth kinetics curves shown earlier for the two simulated temperatures. The MSDs calculated for the different surfaces were used to obtain the self- diffusion coefficient using eq 1: 1 Di = ri(t + s) − ri(s) 2 (5) 2dΔt where ri(t+s) is the vector position of the ith atom, the average is over atoms of type i and over choices of time origin s. In the case of Fe(100), the diffusivities of Fe and O were found to be 0.3 × 10−5 and 1.1 × 10−5 cm2/s, respectively at room temperature (Table 1). The higher oxygen diffusivity in Table 1. Comparison of the Cation and Anion Diffusion Coefficients for the Three Surfaces surface Fe(100) Fe(111) Fe(110)

temperature (K) 300 600 300 600 300 600

Fe (cm2/s) 0.30 0.98 0.31 1.4 0.25 2.1

× × × × × ×

−5

10 10−5 10−5 10−5 10−5 10−5

O (cm2/s) 1.1 1.4 2.3 2.9 4.3 5.2

× × × × × ×

10−5 10−5 10−5 10−5 10−5 10−5

the case of Fe oxidation is consistent with the experimental work of Wang et al.54 The ratio of the Fe/O diffusivities is ∼0.27. This is in good agreement with the tracer experiments of Jurgen et al. who found this ratio to be ∼0.18 for low temperature oxidation of Fe(100).24,27,50 Note that the Fe diffusivity at room temperature remains almost the same for all the three surfaces. In the case of Fe(111), we observe that at room temperature, the ratio of Fe/O diffusivities is ∼0.12, whereas it is ∼0.05 for Fe(110). This suggests that oxygen species are much more mobile than Fe in the case of Fe(111)

dX = ae−bX = ae−E / RT e−γx / RT dt

(1)

In the above kinetic model, X(t) is the thickness of the oxide at time t, a is the pre-exponential factor, E is the activation energy

Figure 12. Oxidation kinetic curves of Fe(100) substrate for a temperature ranging from 300 to 800 K. These curves represent the total uptake as a number of oxygen atoms versus exposure time for two different pressures. Pressures are based on the ratio of surface metal atoms to oxygen gas atoms, (a) high (ratio of 3) (b) low (ratio of 1). Also shown is the direct logarithmic fit to the oxidation kinetics data. The corresponding fitted equations similar to eq 5 are also shown for simulated curve at each temperature. 5204



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for oxidation, T is the temperature, R is the gas constant, and x refers to the thickness of the oxide film at any time t. γ corresponds to the increase in the activation free energy with an increase in the oxide film thickness.56 Note that the activation energy above represents an average kinetic barrier for oxidation. In this work, owing to the errors that may occur when computing the oxide thickness, we prefer to plot and fit the oxygen uptake N(t) or a number of atoms added to the Fe substrate rather than the oxide thickness. Note that this number N(t) is proportional to the thickness X(t) in an homogeneous oxide. Their ratio is a function of the exposed surface area of the oxidized sample (A) and the density of oxygen atoms in the growing oxide film:

N (t ) = ρA X (t )

as well. Furthermore, comparison of the activation energies between the three surfaces for any given pressure suggests that the activation barrier is highest for (100) followed by (111) and (110) surfaces. This explains the faster oxidation kinetics obtained earlier in the case of (110) compared to (111) and (100). The activation energy for (100) surface at low pressure is in good agreement with that calculated by Grosvenor et al. who fitted their experimental oxidation kinetics (300−450K) to a direct logarithmic relationship similar to that done in the present work.7,9 They find the activation energy for Fe(100) oxidation for low pressure oxidation in the 300−500 K range to be ∼32 KJ/mol which is in reasonable agreement with that found in this work.

4. CONCLUSIONS The oxidation kinetics of various single crystals of Fe has been studied using MD simulations. The effect of temperature (300−800 K) and oxygen gas pressure on the kinetics of oxidation and early stages of oxide growth was investigated. In the simulated temperature−pressure regime for the various crystal orientations, the oxide growth curves follow a direct logarithmic law. For the range of simulated temperatures and pressures, our simulations suggest that the oxidation kinetics is strongly correlated to the crystal orientation, with Fe(110) being more reactive than the Fe(111) and Fe(100) surfaces. The differences in the oxidation kinetics increase with an increase in temperature and pressure. The activation energy barriers for oxidation on various Fe surfaces were calculated by fitting the logarithmic growth laws to the simulated kinetic curves. We find that the activation energy barrier for oxidation of Fe (110) is lower compared to that for Fe(111) which in turn is slightly lower than that for Fe(100). Structural and dynamical correlation functions were also used to identify the morphological evolution and growth of the oxide scale formed on various single crystal surfaces. The differences in the oxidation kinetics manifest themselves in the form of differences in the oxide characteristics, i.e., oxide density and stoichiometry. Our analysis of charge distribution suggests that in all of the three single crystals, a gradation in the oxide stoichiometry is found with the oxygen deficiency increasing as we go from the oxide-gas interface to the oxide metal-interface. Compositional analysis based on the simulated atomic trajectories further suggests that the degree of overall oxide nonstoichiometry follows the order Fe(110) < Fe(111) < Fe(100). Our simulations of room temperature oxidation indicate the presence of a nonstoichoimetric oxide layer consisting of two phases: a surface layer dominant with mixed FeO and Fe2O3 oxides and a bulk layer of FeO. These findings are corroborated by the structural analysis based on the radial distribution functions of the grown oxides. The differences in oxidation kinetics, oxidation mechanism, and the evolving nanoscale oxide structure during the early stages of oxidation are explained in terms of the diffusion of anion and cation species. The relative fractions and near surface distribution of the mixed oxides are dictated by cationic/anionic diffusional motion which are strongly dependent on the exposed crystal surfaces. We find that the growth proceeds via inward oxygen migration and outward metal ion migration. The extent of outward Fe growth in all cases was found to be the similar. However, the inward growth resulting from oxygen migration follows the order Fe(110) > Fe(111) > Fe(100). The increased oxygen diffusion explains the observed oxide density and oxide stoichiometry variation among the various single

(2)

We find that this relationship is justified in our simulations as the growing oxide film is homogeneous and does not show any roughness features before reaching the limiting regime. Equation 1 can be rewritten as follows: dN = A′e−E / RT e−γ ′ N / RT dt

(3)

In the above equation, A′ = aAρ and γ′ = γAρ. Solving for eq 3, we obtain: ln(t ) = −ln(A′) +

E + γ ′N RT

(4)

Rearranging the above equation, we obtain: N=

RT ln(t ) + B γ′

(5)

−E ln(A′) γ′

(6)

where,

B=

Using eqs 5 and 6 and the simulation results on the oxidation kinetics at various temperatures, the activation energy (E) for oxidation of Fe(100), Fe(110), and Fe(111) surfaces can be found. One can plot the oxygen uptake (N) vs ln(t) as shown in Figure 12. The slope of the plot shown in Figure 12 gives an estimate of γ′ (slope = RT/γ′ from eq 5). The activation energy (E) can then be obtained by plotting the intercepts of the oxidation curves (B in eq 5) shown in Figure 12 versus −1/γ′; the slope of this new curve will represent the activation energy (E) (as shown in eq 6). The obtained activation energy for oxidation of Fe with O2 for the three surfaces for both the high pressure (100 O2) and low pressure (50 O2) is summarized is Table 2. The activation energy for oxidation of (110) surface at low and high pressures corresponds to 51.5 and 7.44 KJ/mol, respectively. As expected, we find that an increase in the oxygen pressure leads to a significant reduction in the activation energies. This is true for other surfaces (Fe(111) and Fe(110)) Table 2. Activation Energy (kJ/mol) for Oxidation and Oxide Growth Calculated for Various Fe Surfaces high pressure (100 O2)

low pressure (50 O2)

(110)

(111)

(100)

(110)

(111)

(100)

7.44

19.88

23.69

51.5

65.59

71.1 5205



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crystal surfaces. The findings of the current research agree well with previous experimental investigations and provide useful insights into the oxidation mechanism and nanoscale oxide growth on Fe surfaces.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Use of the Center for Nanoscale Materials (CNM) at Argonne was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. The authors also thank the computational facilities provided by CNM-ANL.

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Atomistic Insights into Early Stage Oxidation and Nanoscale Oxide

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