THE oxides of iron have great technological significance as the

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1 journal J. Am. Ceram. Soc., 85 [1] (2002) Defects and Charge Transport near the Hematite (0001) Surface: An Atomistic Study of Oxygen Vacancies Oliver Warschkow* and Donald E. Ellis* Department of Physics and Astronomy and Institute of Environmental Catalysis, Northwestern University, Evanston, Illinois Jinha Hwang,* Negar Mansourian-Hadavi,* and Thomas O. Mason* Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois Atomistic calculations were performed on a slab model of the (0001) surface of hematite as well as the bulk structure. In particular, the energetics of oxygen vacancies near the surface was studied. Atomistic modeling was used to establish the defect energies in the bulk versus distance from the surface. Transition state calculations were performed to compute barriers for several pathways of migration of oxygen vacancies in the bulk and at varying depths relative to the surface. We find energy barriers of several transitions considerably lowered closer to the surface. Considerations of literature data for electrical conductivity and Seebeck coefficient on bulk versus thin-film hematite suggest high populations of point defects near surfaces, in agreement with our predictions. I. Introduction THE oxides of iron have great technological significance as the ores from which iron and steel are produced, as pigments in ceramic stains and colors, and as magnetic recording materials. Hematite, in particular, is important as the final product of iron oxidation. It also finds application in catalysis and in photoelectrochemistry, where the surface properties are of particular interest. Although the (0001) surface of hematite has received considerable attention recently, a thorough understanding of its surface structure and chemistry is only now emerging. In the present study we focus on surface and near-surface phenomena. It is useful to review the state of the field with regard to the prevailing point defects and transport mechanisms in bulk hematite. A thorough review has recently been provided by Dieckmann. 1 At elevated temperatures, hematite is an intrinsic semiconductor with a band gap of 2.4 ev (or 2.6 ev if small polaron conduction is assumed). 1 5 This is apparent in the p O2 independence of the electrical properties measured at high temperature on high-purity materials. Although nonstoichiometry, ε,in -Fe 2 O 3 ε is small, it is measurable and consistently positive, i.e., hematite is oxygen-deficient (oxygen vacancies), cation-excess (iron interstitials), or a combination of the two. Precise in situ high-temperature thermogravimetric measurements show a p O2 dependence for ε of 1 2, which is consistent with oxygen vacancy formation under the condition of prevailing electronic disorder. 1 There is only one study reporting a p O2 dependence for oxygen tracer diffusion. 6 Although the magnitude of the oxygen exponent is substantially less than 1 2, its sign is consistent with a prevailing vacancy mechanism. At high temperature, the magnitude of iron tracer diffusion is similar to that of oxygen tracer diffusion, suggesting that both cation interstitials and anion vacancies play important roles in the defect structure. The p O2 dependence of iron tracer diffusivity is close to 3 4, 3,7 consistent with iron interstitials. Line broadening in high-temperature Mössbauer studies is also consistent with the presence of cation interstitial defects in hematite. 8 By studying the isotope effect in iron tracer diffusion, Hoshino and Peterson 9 found the diffusion mechanism to be a non-collinear interstitialcy process. Catlow et al. 10 conducted an extensive theoretical study of point defects and transport in bulk hematite. They found thermal electronic disorder to be much larger than any thermal ionic disorder, i.e., electrons and holes are the prevailing species in undoped hematite. Their value of oxygen vacancy formation enthalpy under prevailing electronic disorder is virtually identical to that measured by thermogravimetry. 1 Under the same conditions, their value of iron interstitial formation enthalpy is quite similar to that for oxygen vacancies, suggesting that both species play important roles in the defect structure. Catlow et al. 10 also considered various transition states and calculated migration enthalpies for both oxygen and iron ions, including two-ion (interstitialcy) processes for iron. There are few studies of surface or near-surface defect structure and defect-mediated transport of ions and/or charge in hematite. Hayes 11 studied the sintering of hematite at low temperature and was able to deduce surface diffusivities for iron (given the unlimited supply of atmospheric oxygen), which were orders of magnitude larger than extrapolated bulk diffusivities, with substantially smaller activation energies. Gleitzer et al. 12 studied the electrical properties (conductivity, Seebeck coefficient, work function) of thin films, which proved to differ markedly from those of bulk hematite. They concluded that near-surface layers exhibit much higher deviations from stoichiometry than the bulk. To gain insights into the complex properties of this material as they relate to surface defect structure and conductivity, the present study uses atomistic modeling techniques to look at oxygen vacancies in the bulk hematite (for benchmarking) and in the vicinity of the iron-terminated (0001) surface of hematite, for which defect energies as well as barriers to migration as a function of depth from the surface are calculated. W.-Y. Ching contributing editor II. Background Manuscript No Received January 5, 2001; approved August 14, Supported by the U.S. Department of Energy, under Grant No. FG02 84ER Supported in part by the EMSI program of the National Science Foundation and the U.S. Department of Energy Office of Science, under Grant No. CHE , at the Institute for Environmental Catalysis, Northwestern University. *Member, American Ceramic Society. The atomic structure of the hematite (0001) surface has been fairly well characterized by both experimental and theoretical means as being essentially iron-terminated with comparatively little reorganization of surface atoms. A recent theoretical study by Wang et al. 13 determined the surface atomic structure of hematite 213

2 214 Journal of the American Ceramic Society Warschkow et al. Vol. 85, No. 1 Fig. 1. Profile view of iron-terminated (0001) surface of hematite. Oxygen and iron sites are colored in dark and light gray, respectively. through geometric optimization at a first-principles density functional (DF) level of theory, giving a structural model of surface relaxation that is consistent with the experimentally deduced surface relaxations of Chambers and Yi. 14 The DF work also predicts an alternative oxygen-terminated (0001) surface for highly oxidizing conditions; however, experimental evidence for the existence of this surface appears to be controversial at present. 14,15 The iron-terminated surface is characterized by a stacking of Fe O 3 Fe Fe O 3 Fe... layers, as illustrated in Fig. 1. (1) Oxygen Vacancy Migration in Hematite Geometric Considerations For oxygen vacancies in bulk hematite, five migration pathways (A1 to A5) have been identified by Catlow et al. 10 For convenience, we have reproduced a schematic representation of these pathways in Figs. 2 and 3. A1 and A2 pathways involve oxygen vacancy migration within the (0001) oxygen plane (referred to in the following as in-plane transitions). In A3, A4, and A5 pathways, the migration is from one (0001) oxygen plane to the next (cross-plane transitions). The in-plane pathways A1 and A2 are geometrically very similar, differing only in the relative positioning of cations to the path. In both, an anion migrates to a neighboring oxygen vacancy site. The A1 path brings the migrating anion into close proximity to two occupied cation sites (above and below in [0001] direction), whereas for the A2 path, one of these two cation sites is structurally vacant (Fig. 2). Similar to A1 and A2, cross-plane mechanisms A3 and A4 differ only in the relative positioning of cation sites to the path. The A3 path takes the migrating oxygen atom from one oxygen (0001) plane through the iron (0001) planes to another oxygen (0001) plane. Doing this, the migrating anion also comes into close proximity with two occupied cation sites. The A4 path differs from A3 in that, again, one of these cation sites is structurally vacant (Fig. 3). Finally, the A5 pathway involves an oxide ion migrating from one (0001) plane to another; however, its path differs from A3 and A4 in that it ends at a non-nearest-neighbor oxygen, and its path proceeds directly through a structurally vacant cation site (Fig. 3). Near the (0001) surface, three-dimensional periodic lattice symmetry (along the [0001] axis) is broken. This means that the A2 and A4 paths each split into two subtypes, which, in the following, we denote using ( ) or( ) qualifiers, e.g., A4( ), A2( ), depending on whether a nearby characteristic cation is, in relation to the path, located closer or farther away from the surface. In addition, A3, A4, and A5 transitions are further qualified by 1 and 2 to denote transitions to the neighboring (0001) plane toward and away from the surface, respectively. It is instructive to look at the multitude of options by which a given oxygen vacancy can migrate in bulk hematite using these five pathways (Fig. 4): Each oxygen site has twelve nearest oxygen neighbors; six in the same (0001) plane, and three each in the (0001) planes above and below. Two of the six in-plane neighbors Fig. 2. In-plane migration pathways A1 and A2 for oxygen vacancies in hematite.

3 January 2002 Defects and Charge Transport near Hematite (0001) Surface Atomistic Study of Oxygen Vacancies 215 Fig. 3. Cross-plane migration pathways A3, A4, and A5 for oxygen vacancies in hematite. are reached through an A1 transition, the other four through A2 transitions. Two of the three paths to a neighboring plane are of the A4 type, the other is an A3 type transition. A5 paths connect an oxygen site with a non-nearest oxygen site in a neighboring (0001) plane. From any given oxygen site, there is one such path to the neighboring (0001) planes on either side. A3 and A4 pathways separately form three-dimensionally connected networks in the lattice, by which we mean here that (purely geometrically, leaving all energetic arguments aside) continuous migration of oxygen vacancies in all three directions is possible by any one of these two pathways alone. The A2 pathway forms a two-dimensionally connected network, allowing continuous migration only within a (0001) plane (and, for obvious reasons, not across). The A5 pathway network is one-dimensional, where continuous migration is possible only in the [0001] direction. Lastly, the set of A1 pathways in the lattice does not form a connected network at all: Three A1 transitions form a circular (triangular) closed path (see Fig. 5), but a transition from one triangle to another requires a path other than A1; thus, continuous migration of an anion vacancy in any direction is not possible by A1 transitions alone. (2) Computational Methodology For the calculation of structural, lattice, and defect energies, the atomistic Born model of polar solids as implemented by the GULP package 16,17 has been used in this work. The atomistic model is an empirical one, in that it is parameterized to reproduce a set of known experimental properties of the material, such as bulk lattice structure, elastic constants, dielectric properties, etc. Thus, the model effectively serves as a carrier to extrapolate from available experimental data to yet unknown material properties. For main group and transition metal oxides, this is reliable regarding its ability to predict defect and surface properties based on bulk-parameterized potentials. (References may serve as illustrative examples.) Technically, the Born atomistic model assumes the interaction of lattice ions, represented by point charges, to be pair-wise, Fig. 4. Possible pathways by which oxygen vacancy can migrate from given oxygen site to other nearby oxygen sites in hematite lattice. In this diagram, positions of nearby iron atoms are not included for simplicity.

4 216 Journal of the American Ceramic Society Warschkow et al. Vol. 85, No. 1 Fig. 5. Network of in-plane migration paths for oxygen vacancies in hematite: A1 and A2 paths are colored in black and light gray, respectively. Diagram at top shows six possible in-plane migration paths open to vacancy (square) located at center. Symbols and are used to denote location of iron atoms above and below oxygen layer. Diagram below shows resulting network of A1 and A2 paths between oxygen sites in (0001) plane. The set of A2 paths forms a connected network by which conduction within plane is possible. This is unlike the set of A1 paths (black) that only form separated circular (triangular) paths, i.e., conduction by A1 transitions alone is not possible. consisting of Coulombic, Pauli-repulsion, and dispersion forces. The latter two are modeled using the well-known Buckinghampotential form ij r A ij exp r ij C ij r 6 (1) where A ij, ij,, and C ij are parameters particular to each pair of atom types. Ionic polarization is modeled using the shell model, which describes each lattice ion by a pair of point charges (core and shell) attached to each other by a spring potential. 24 The interaction parameters for iron oxides used in the present work are those given by Minervini and Grimes. 25 Defect energies are calculated using the Mott Littleton procedure as implemented in the GULP package, which yields defect energies in the limit of infinite dilution. 26 Two cut-off radii, r I and r II, divide space around the defect into three regions in which atomic relaxations are in an increasingly approximate fashion. In this work, the cut-off radii, r I and r II, were as large as computationally permissible (12 and 22 Å, respectively). With these settings, defect calculations typically involved and atoms in regions I and II, respectively. Full transition state searches were performed using the algorithms implemented in GULP. Placing the migrating oxygen atom half-way between start and end lattice site of a given pathway (plus a small displacement to break any symmetries) was, in all cases, a sufficiently good starting geometry for the transition state optimizer to rapidly converge to a stable stationary point with one negative Hessian eigenvalue, a necessary requirement characterizing the stationary point as a true transition state. For selected transitions, two-dimensional maps of the potential energy surface were generated (using small defect radii) to verify the reaction path. III. Results and Discussion (1) Bulk Hematite Table I shows our calculated point defect formation energies, which are in reasonable agreement with the values calculated by Catlow et al. 10 The Frenkel and Schottky energies are per

5 January 2002 Defects and Charge Transport near Hematite (0001) Surface Atomistic Study of Oxygen Vacancies 217 Table I. Calculated Defect Formation Energies of Simple Point Defects (Vacancies and Interstitials) in Bulk Hematite Defect Defect energy This work (ev) Ref. 10 (ev) V Fe V O O i Fe i Fe i Anion Frenkel pair Cation Frenkel pair Schottky, Anti-Schottky, 7.8 Frenkel and Schottky energies are per constituent defect. Schottky energies are computed using calculated lattice energy of ev per formula unit. constituent defect. The Schottky energies are computed using the calculated lattice energy of ev per formula unit. The energies listed in Table I serve as reference values for the calculated defect energies in the surface slab model. Calculated transition energies in bulk transitions A1 to A5 are listed in Table II and compared with Catlow s results. 10 We found the lowest transition energy (0.63 ev) for A1 in-plane migration; the A2 transition is energetically considerably more expensive at 2.66 ev. Of the cross-plane A3 and A4 transitions, the latter is strongly preferred, with energies of 1.73 and 1.11 ev, respectively. The A5 pathway requires a considerably higher transition energy of 5.44 ev. Quantitative differences between Catlow et al. 10 and our own work are not surprising, because different parameterized potentials have been used; however, qualitative differences, i.e., the relative energetical order of transitions, are deserving of some commentary, because we find the A4 transition to be more favored. Firstly, because of the more stringent computational limitations at the time, the calculations of Catlow et al. 10 were conducted using much smaller defect relaxation radii; however, we expect this to be of minor effect on the results. Of more relevance is the following methodological difference: Catlow et al., in their calculations, held the position of the migrating ion fixed at the geometrical mid-point of the transition, while all other geometrical parameters of the model were relaxed. 10 By arguments of symmetry, this procedure does indeed yield the correct transition state for three of the five bulk pathways (A1, A3, and A5); however, for the other two pathways, it is only approximate and adds a constraint to the system. We suppose that the transition energies calculated in this manner for these latter paths are overestimates of what would have been obtained using full transition state optimization, as was done in this work. This provides a possible explanation why the transition energy of the A4 pathway in our work is so much lower in qualitative comparison with Ref. 10. We tested this hypothesis by calculating the transition energy using the approximated midpoint fixed technique that was used by Catlow et al., 10 which yielded a much higher transition energy of 1.73 ev, i.e., larger than those for A1, A2, and A3, but lower than for A5 transitions. Table II. Calculated Migration Energies for Oxide Vacancies (V O )in Bulk Hematite Pathway Transition energy This work (ev) Ref. 10 (ev) A A A A A Table III. Comparison of Calculated Interlayer Relaxations for (0001) Surface of Hematite in Percent Relative to Corresponding Bulk Separations (Fe Fe 0.63 Å; Fe O 0.83 Å). Separations in Table are Ordered Top to Bottom in Increasing Distance from Surface. Relaxations in Parentheses are those Calculated Using Smaller Slab Model (see text) Interlayer separation Models Atomistic (this work) Atomistic (Ref. 23) DFT (Ref. 13) Fe(1) O(1) 53% ( 53%) 49% 57% O(1) Fe(2) 5% ( 5%) 3% 7% Fe(2) Fe(3) 45% ( 45%) 41% 33% Fe(3) O(2) 25% ( 25%) 21% 15% O(2) Fe(4) 9% ( 9%) 5% Fe(4) Fe(5) 4% ( 5%) 3% Fe(5) O(3) 1% ( 1%) 1% O(3) Fe(6) 3% 4% Fe(6) Fe(7) 5% Fe(7) O(4) 2% O(4) Fe(8) 0 The results of both this work and Catlow et al. 10 agree in the fact that the lowest transition energy for oxygen vacancies is for the in-plane A1 mechanism. This would, in and of itself, suggest that conduction carried by oxygen vacancy migration in the (0001) plane, i.e., perpendicular to the [0001] axis, is strongly favored over conduction parallel to the [0001]. However, as pointed out above, continuous conduction is not possible by A1 transitions alone, because A1 paths do not form a connected network in any one dimension. Thus, paths other than A1 are rate-determining for any conduction carried by oxygen vacancies. In our work, we find the A4 path the most favored, and not, as would follow from Ref. 10, the A3 path. (2) Hematite (0001) Surface (A) Relaxation: In this work, the (0001) surface of hematite was modeled using a three-dimensional periodic surface slab model. Hematite is made up of successive layers of O Fe Fe O Fe Fe O along the [0001] direction. A starting slab model of an iron-terminated surface was generated by taking the hexagonal unit cell of hematite and creating a slab super cell by shifting apart two consecutive iron layers by 10 Å. Thus Fe 2 O 3 slabs 13 Å thick were generated, separated by gaps of 10 Å vacuum. We verified that the use of wider vacuum gaps does not affect the results significantly. The majority of the results presented in this work were obtained using a larger slab model, based ona(1 1 2) supercell (c-axis, 26 Å) and inserting a 10 Å vacuum. This created Fe 2 O 3 slabs 26 Å thick separated by a 10 Å gap of vacuum. The atomic positions of these two surface models were relaxed using the atomistic potential with results shown in Table III. With the (1 1) surface unit cells used, we did not find any dramatic surface reconstruction, in agreement with the findings of other workers. 13,23 Essentially, atomic relaxation takes place largely in the vertical direction, i.e., perpendicular to the surface. A slight rotation of surface layer Fe 3 groups around oxygen atoms in the second layer, found by a recent DF study of Fe 2 O 3 surface relaxation, 13 does not occur in our models. Intuitively, it would appear that the mechanism that causes such rotation would have its origin in the magnetic or electronic structure of the material; hence, we would not expect to find it in an atomistic model with only central forces. We find, in agreement with earlier models, an inward relaxation of the iron-terminating layer. Our calculated interlayer separations given in Table III are in excellent agreement with first-principles results 13 and an earlier atomistic study, 23 which gives confidence in the quality of the potential model. We are particularly interested to know how the energies of point defects change when they are located close to the surface. The large slab model used in this work consists of a total of thirty-six

6 218 Journal of the American Ceramic Society Warschkow et al. Vol. 85, No. 1 Fig. 6. Profile of calculated defect energies (in ev) for oxygen vacancies as function of depth from surface. atomic layers twelve oxygen and twenty-four iron layers so that depth profiling of defect and transition energies is feasible. (B) Defect Energies: In Fig. 6, the calculated profile of point defect energies versus depth from the surface for oxygen vacancies is displayed. On the right-hand side of the plot, energies converge to bulk values; whereas the energy of oxygen vacancy formation drops noticeably at the surface, suggesting a somewhat increased concentration of such vacancies near the surface. Decreases in reduction enthalpy (formation of oxygen vacancies) from bulk values have been reported in other oxides when in nanocrystalline form, most notably CeO 2. 27,28 For example, reduction enthalpies of 2.28 ev 27 and 1.84 ev 28 in nanophase CeO 2 are significantly 4.2 ev reported for bulk CeO What the present results suggest is that near-surface layers in hematite can possess significantly larger oxygen vacancy populations than the bulk. We used Jonker analysis 30,31 of literature data at 900 C (the highest temperature available) for doped bulk hematite 5,32 and 980 C for undoped thin-film hematite 12 to test for the existence of enhanced defect populations near surfaces. Jonker analysis involves plotting the Seebeck coefficient versus the logarithm of conductivity in a pear-shaped plot (see Fig. 7). The left-hand side of the pear corresponds to intrinsic or lightly doped behavior. A small change in the ratio of electron and hole populations (due to acceptor doping, e.g., Mg Fe or Ni Fe or donor doping, e.g., Ti Fe, respectively) results in a large swing of Seebeck coefficient from n to p type, with only a small change in the overall conductivity. The two linear legs of the pear plot correspond to extrinsic behavior, where holes (upper leg) or electrons (lower leg) are entirely controlled by aliovalent doping. The vertical or horizontal size of the pear is determined by the band gap; in this case, a value of 2.4 ev is assumed after Dieckmann. 1 At the point of the Jonker plot in Fig. 7, we have plotted the thin-film data of Gleitzer et al. 12 The film in question is 1 m thick, and in-plane measurements are reported versus p O2 for a slightly higher temperature (980 C) than the other data in Fig. 7. Because only conductance values are provided rather than absolute conductivities, we have arbitrarily shifted the data along the conductivity axis until the data hit the pear as shown. The placement is within an order of magnitude of the maximum conductivity calculated based on approximate film dimensions (10 mm 10 mm 1 m) supplied by Nowotny. 33 It should be stressed that defect and carrier gradients in the film combined with differences in mobility versus bulk make more precise analysis impossible. Nevertheless, the striking feature of the film data is that they exhibit an n to p transition opposite in shape from that obtained for intrinsic behavior. Gleitzer et al. 12 interpreted this in terms of small polaron behavior. At the change of sign of the Seebeck coefficient, nearly equal populations of two valence states of iron, e.g., Fe 3 and Fe 2, for donor doping (due to V O ), would be required. This would require a considerable oxygen vacancy concentration, in agreement with the reduction in vacancy formation energies calculated in the present work. (C) Transition State Energies: Table IV lists our calculated transition state energies for various migration pathways of oxide vacancies in near-surface regions. We observe that toward the right-hand side of the Table, all transition energies converge to bulk values, with the exception of the defect energies in the first row. The converged defect energy of ev calculated for the deepest oxygen layer of the slab differs quite markedly from the bulk calculated value of ev. This, we assume to be a constant shift due the finite size of our slab model. This has little Fig. 7. Jonker plot of thermopower versus logarithm of conductivity for hematite. Solid symbols are data for doped bulk material. Open symbols are data for thin films.

7 January 2002 Defects and Charge Transport near Hematite (0001) Surface Atomistic Study of Oxygen Vacancies 219 Table IV. Calculated Defect Migration Energies for Oxygen Vacancies in Vicinity of Fe 2 O 3 (0001) Surface Layer Defect energy (ev) Transition energy (ev) A1 A2 A2 A31 A32 A41 A41 A42 A42 A51 A52 O(1) O(2) O(3) O(4) O(5) O(6) Bulk effect on the calculated transition energies, because they are the difference of two defect energies whereby this shift cancels out. Furthermore, we see from Table IV that the effect of surface symmetry breaking becomes smaller for transitions farther away from the surface. The effect of the surface on migration energetics is clearly visible in Table IV. In the topmost layers, some transitions experience a dramatic energy lowering, while other transitions become more energetically expensive. A1 transition energies change very little with distance from the surface, with the exception of the oxygen layer O(1) nearest to the surface, where this transition requires a 1.66 ev activation, more than 1 ev greater than in the bulk. The A1 path in the bulk is characterized by two cations close to the path. For the A1 path in the surface-closest oxygen layer, however, only one of these two cations still remains in place (the other being cut away). Supposing that the presence of the two cations stabilizes the A1 path in the bulk (and thus makes it energetically favorable), then it is easily understandable why the A1 transition energy is so destabilized in the O(1) layer. The A2 path is stabilized by the surface (relative to the bulk A2 transition of 2.66 ev) in the O(1) and O(2) layers only. In the O(1) layer, A2( ) and A2( ) transitions require 0.99 and 2.03 ev activation; in the O(2) layer, only the A2( ) transition experiences a significant lowering; its activation energy being 1.36 ev. A3 transitions are characterized by increased transition barriers near the surface, i.e., none of the A3 transitions has a significantly reduced barrier versus the bulk transition (1.73 ev). The 1.23 ev barrier posed to an A3 jump from layer O(3) to O(2) may seem initially as a reduction; however, it should also be noted that the defect energy for an oxygen vacancy in O(3) is already 0.3 ev higher than in the bulk. The transient vacancy starts out at a higher energy, thus facing a smaller barrier to overcome. A4 transitions near the surface are affected differently, with some increased and some reduced transition energies. Of principal interest is the A4( ) transition between O(1) and O(2), which creates 0.89 and 0.80 ev barriers to migration to and from the surface, respectively. In contrast, the A4( ) transition between these two layers is with 2.64/2.55 ev prohibitive. This is to be compared with the 1.11 ev barrier for A4 in the bulk. Finally, all A5 transition energies remain above 5 ev, suggesting that this type of transition does not play a significant role in either bulk or near-surface conduction. Looking at the overall picture presented by Table IV and pondering the question of how near-surface diffusion of oxygen might be different compared with the bulk, it is worthwhile to look at all those near-surface transitions that have a barrier similar to or lower than the bulk A4 barrier of 1.11 ev. These would be the A2( ) in O(1) of 0.99 ev, the A4( ) between O(1) and O(2) of 0.89/0.80 ev. Thus, we have several transitions that are more favorable under the same conditions in which A4 bulk transitions occur. With these favored transitions, a connected network of paths in the two surface nearest oxygen layers O(1) can be proposed, whereby an oxygen vacancy can continuously migrate parallel to the surface. This path would involve A4( ) hopping between O(1) and O(2), alternating with A2( ) and A1 shifts in the O(1) and O(2) planes, respectively. The highest barrier posed to this process is that of the A2( ) transition of 0.99 ev, slightly lower than that of the rate-determining A4 transition in bulk of 1.11 ev. This suggests that conduction by oxygen vacancy migration is somewhat easier in the vicinity of the surface. Simulations of the resulting kinetics, making use of the calculated barriers, should be able to give a more precise picture as to how oxygen vacancy migration differs in bulk and near-surface regimes. IV. Summary and Conclusions In this work, atomistic modeling techniques have been used to explore the defect chemistry of oxygen vacancies in the vicinity of the hematite (0001) surface. The potential model, parameterized to lattice structural and dielectric properties of bulk hematite, 25 describe (0001) surface relaxation, in good agreement with highquality density functional calculations, 13 supporting the assumption that the (essentially bulk) model remains valid near the surface. Our calculations find a small stabilization of oxygen vacancies in the two oxygen layers closest to the surface, suggesting an increased concentration of vacancies relative to the bulk. This is confirmed by Jonkers analysis of experimental literature data on bulk and thin-film hematite, which suggests considerable vacancy populations near the surface. In addition, transition barriers for vacancy migration have been calculated for bulk and near-surface regimes. We find the barriers of several types of paths lowered near the surface with respect to the rate-determining A4 transition in bulk. This, together with the fact that these transitions form a connected network that allows continuous migration parallel to the surface, suggests increased conductivity of oxygen vacancies near the (0001) surface. References 1 R. Dieckmann, Point Defects and Transport in Haematite (Fe 2 O 3 ε ), Philos. Mag. A, 68, 725 (1993). 2 (a)f. J. Morin, Electrical Properties of -Fe 2 O 3 and -Fe 2 O 3 Containing Titanium, Phys. Rev., 83, 1005 (1951). (b)f. J. Morin, Electrical Properties of -Fe 2 O 3, Phys. Rev., 93, 1195 (1954). (c)f. J. Morin, Oxides of the 3d Transition Metals, Bell Sys. Tech. J., 37, 1047 (1958). 3 R. H. Chang and J. B. Wagner Jr., Direct-Current Conductivity and Iron Tracer Diffusion in Hematite at High Temperatures, J. Am. Ceram. Soc., 55, 211 (1972). 4 D. Benjelloun, J.-P. Bonnet, J.-P. Doumerc, J.-C. Launay, M. Onillon, and P. 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