Article pubs.acs.org/JPCC
Mixed Termination of Hematite (α-Fe2O3)(0001) Surface Adam Kiejna* and Tomasz Pabisiak Institute of Experimental Physics, University of Wrocław, plac M. Borna 9, PL-50-204 Wrocław, Poland ABSTRACT: The detailed structure of hematite (0001) surfaces is both of fundamental interest and of crucial meaning in understanding the reactivity of the surfaces with respect to different adsorbates. The structure and electronic properties of mixed terminations of the α-Fe2O3(0001) surface were studied with the spin-polarized density functional theory (DFT) and the DFT+U methods in order to explore possibilities of their stable coexistence. The DFT+U results show that the mixed terminated slabs consisting of Fe- and O-terminated domains of large periodicity are energetically more stable than those resulting from the combination of pure Fe- and O-terminated fragments.
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INTRODUCTION Iron oxides are considered an efficient support for catalytic applications. To understand the reactivity of iron oxide surfaces and structures resulting from adsorption thereon1−4 more complete information about the structural and electronic properties of different terminations is needed. A hematite (αFe2O3) crystal of corundum structure may expose five different surface terminations when cleaved perpendicular to the [0001] direction.5 Two of them are Fe-rich while the others are terminated with oxygen atoms. Our recent first principles study3 has demonstrated that the Fe−O3−Fe− termination is most stable. Under higher oxygen pressure the oxygenterminated O3−Fe−Fe− surface may also be stable. However, the structure of the α-Fe2O3(0001) surface is not fully understood.5 The ideal surfaces reconstruct and at the resulting surface both Fe- and O-terminated domains can coexist. Scanning tunneling microscopy (STM) studies of Condon et al.6,7 have revealed stable α-Fe2O3(0001) surface reconstructions, which they attributed to a superlattice of coexisting islands of O-terminated α-Fe2O3(0001) and FeO(111). The islands form a hexagonal superlattice with a periodicity of 40 ± 5 Å rotated by 30° relative to the α-Fe2O3 (1 × 1) structure, which they called biphase ordering.6 More recently Lanier et al.8 have proposed a new model for the biphase termination consisting of an unrotated misfitting Fe3O4(111) overlayer on top of α-Fe2O3(0001), producing a supercell with periodicity of 43.6 Å rotated by 30° relative to the α-Fe2O3 (1 × 1) structure. Liu et al.9 have reported a coexisting phase of Fe−Fe2O3(0001) and Fe3O4(111) upon annealing Fe−FeO(0001) films, different from previous reported biphase surfaces.6,7 Bauer has suggested that the biphase is a superlattice of Fe- and Oterminated domains stabilized by long-range interactions (E. Bauer, private communication, 2012). On the other hand, some other STM studies10 have reported evidence for coexisting periodic domains of Fe- and O-terminations distributed with a smaller periodicity of 22 ± 2 Å. All this calls for more experimental and theoretical studies to explore the structure of this surface. © 2013 American Chemical Society
To contribute to elucidation of this problem, in this work we demonstrate the possibility of the coexistence of Fe- and Oterminated domains on the hematite (0001) surface by applying first-principles total energy calculations of the mixed Fe−O3−Fe− and O3−Fe−Fe− terminations. Hematite is a strongly correlated material, and plain DFT with standard (local or semilocal) exchange-correlation functionals fails to correctly describe its electronic structure. To account for the strong Coulomb interaction between the Fe-3d electrons we have applied the DFT+U method. In this approach the on-site Coulomb repulsion is described by an additional (Hubbard) term U acting on the Fe-3d orbitals. Usually, a semiempirical variant of the method is applied where the (effective) parameter U is varied until measured bulk properties are reproduced as good as possible. In general, there is no single value of U that is optimal for all material properties. Its value may vary from the bulk to the surface or from one termination to the other. It has been even suggested11 that phase stability of the different hematite terminations is better described by DFT than by the DFT+U approach. Therefore, though our previous work3 has given arguments in favor of the DFT+U method in the description of the hematite surface, in this work the energies of the surface structures obtained with DFT+U as a primary method are also compared to the corresponding plain DFT results in order to assess to what extent they are influenced by different approaches.
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COMPUTATIONAL DETAILS The calculations are based on DFT as implemented in the plane-wave-based Vienna ab initio simulation package (VASP).12,13 The generalized gradient approximation (GGA) using the Perdew and Wang14 form of the spin-polarized exchange-correlation functional with the Vosko et al. scheme for interpolating the correlation energy15 was applied. The effect of the on-site Coulomb repulsion of Fe 3d electrons, the Received: July 14, 2013 Revised: October 11, 2013 Published: October 25, 2013 24339
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fragments (respectively, for calculations of 2 × 2 and 4 × 4 surface unit cells) were arranged in a checkerboard pattern of rhombi as schematically illustrated in Figure 2. The calculated
exchange-correlation energy, was treated at the GGA+U level using the Dudarev et al. approach16 with the effective parameter of interaction between electrons Ueff = 4 eV. This value of Ueff was previously found3,17 to give the best agreement with hematite’s bulk properties. The electron ion−core interactions were described by the projector augmented-wave (PAW) generated potentials18 with iron 3d and 4s, and oxygen 2s and 2p states treated as valence states. The surfaces were modeled by supercells, built of a thick oxide slab and a vacuum region of about 16 Å, periodically repeated in space. The lattice parameters of the antiferromagnetic phase of bulk hematite, which were determined in our previous work3 in good agreement with the experimental data, were applied to construct the slabs. Symmetric slabs consisting of 18 and 16 atomic layers, with a symmetry plane in the middle of the Fe bilayer, were used to simulate the Fe−O3− Fe− and O3−Fe−Fe−surface terminations (Figure 1). For
Figure 2. Schematic illustration of the considered mixed Fe1/O3 terminations of the α-Fe2O3(0001) surface. Results for total energy differences, per 2 × 2 cell, of the different phases are given for GGA+U and GGA (in parentheses). Note that in the above formulas Fe ≡ Fe1 and O ≡ O3.
total energies for different surface unit cells are presented in Table 1. The energy difference, per 2 × 2 cell, between the mixed Fe1/O3 and pure Fe1- and O3-terminated phases of different periodicity was calculated as explained in Figure 2.
Figure 1. Side and top (lower row) view of the top layers of the Fe1 (Fe−O3−Fe−) and O3 (O3−Fe−Fe−) bulk-terminations of the αFe2O3(0001) surface. Small and large balls represent O and Fe atoms, respectively. For clarity, the Fe atoms of the top surface layers are displayed in green and the oxygen atoms in violet. The atoms of the remaining deeper layers are colored in cyan. The boundaries of the 1 × 1 supercell are marked.
Table 1. Total Energy and Work Function of Pure Fe1 and O3, and Mixed Fe1/O3 Terminations (cf. Figure 2) of the Hematite (0001) Surface. Note that the Energy of the 4 × 4 Surface Cell Is Divided by Four
brevity, in the following these two terminations will be referred to as Fe1 and O3, respectively. The largest supercell with 4 × 4 surface periodicity (20.267 × 20.267 Å) consisted of 464 atoms (176 Fe and 288 O). A plane wave basis with a kinetic energy cutoff of 450 eV was applied which gives total energy differences within 1 meV. The Brillouin zone of the 1 × 1 surface unit cell was sampled using a Γ-centered 6 × 6 × 1 Monkhorst-Pack k-point grid reduced to 3 × 3 × 1 in the 2 × 2 cell, and to a single Γ point for the 4 × 4 cell. To improve the convergence of the solutions a Gaussian broadening of the Fermi surface of 0.1 eV was applied. The positions of all atoms were optimized until the Hellman-Feynman forces were within 0.01 eV/Å.
energy (eV)
work function (eV)
termination (cell)
GGA+U
GGA
GGA+U
GGA
O3(1 × 1) O3(2 × 2) Fe1(1 × 1) Fe1(2 × 2) M(2 × 2) N(4 × 4) M(4 × 4)
−180.581 −722.336 −202.995 −811.992 −767.234 −767.245 −767.593
−204.004 −816.003 −224.722 −898.892 −856.669 −856.693 −857.050
8.58 8.59 4.77 4.78 6.35 6.36 6.46
7.63 7.61 4.26 4.26 5.69 5.69 5.62
For GGA the mixed M(2 × 2) termination presented in Figure 2a in which the two O3- and two Fe1-terminated (1 × 1) fragments are arranged in a checkerboard pattern is strongly unfavored (i.e., its energy is higher by 0.782 eV) compared with that given by the sum of two pure O3- and Fe1 (1 × 1)terminated slabs. Similarly, the average energy of two O3- and two Fe1-terminated (2 × 2) fragments (Figure 2b) is also
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RESULTS AND DISCUSSION We have considered the possibility of formation of mixed Fe1/ O3 surface terminations by comparing the stability of slabs in which two O3- and two Fe1-terminated 1 × 1 and 2 × 2 24340
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higher (by 0.397 eV) than that of a mixed M(4 × 4) slab composed of O3- and two Fe1-terminated (2 × 2) areas. This indicates that mixing of the two terminations on this length scale is unfavorable. However, the energy of the mixed M(4 × 4) slab calculated within GGA is distinctly lower than that of a mixed N(4 × 4) checkerboard pattern of (1 × 1) domains of different terminations [cf. Figure 2c], i.e., it makes the mixed M(4 × 4) termination clearly more stable (by 0.357 eV) over the N(4 × 4) one, if the latter would ever be formed. The calculated energetics changes distinctly in the GGA+U approach. The mixed terminations considered are more stable than the respective combinations of either (1 × 1) or (2 × 2) fragments of pure phases. The M(2 × 2) phase consisting of two O3- and Fe1-terminated (1 × 1) fragments which are arranged in a checkerboard pattern (Figure 2a), is only 0.082 eV more favored than that given by the sum of two pure O3and Fe1 (1 × 1)-terminated slabs. However, for the mixed M(4 × 4) termination which is compared with the average of two pure O3- and Fe1 (2 × 2) fragments (Figure 2b) the energy gain is distinctly larger and makes the mixed termination more stable by 0.429 eV. Finally, the M(4 × 4) mixed termination slab with larger periodicity appears to be more stable (by 0.347 eV) than the N(4 × 4) one consisting of a pattern of smaller (1 × 1) periodicity units calculated in a large 4 × 4 supercell. This is nearly the same as the value resulting from GGA, and thus shows that the energy differences between mixed phases calculated within two methods (GGA and GGA+U) are nearly the same. They differ substantially, however, when one compares the energy of the mixed domains with the average energy of the pure phases. Thus both GGA and GGA+U show that the mixed termination with long periodicity is more stable. Note that the coexistence of Fe- and O-terminated domains of smaller periodicity, corresponding to that considered in this work, was concluded from the STM studies of Eggleston et al.10 On the other hand, only GGA+U calculations show that mixing of the two terminations is favored over the average of the pure phases on the considered length scale. Thus, results of this work support the view that GGA+U is a more appropriate method than semilocal GGA to describe surface properties of hematite. The apparent discrepancy between GGA+U and GGA predictions for the energetics of different terminations stems from the differences in their electronic structure, the charges on the surface layer atoms, differences in lattice relaxation, and magnetism of the Fe atoms in the surface layers, as discussed below. Before discussing them, let us comment on the comparison of the simulated structures with the experimental STM images. In Figure 3 we displayed a simulated STM image of the resulting mixed termination calculated in the Tersoff−Hamann approximation.20 The Fe- and O-terminated domains of (4 × 4) periodicity are seen in the figure, but it is clear that our images do not reproduce a hexagonal symmetry of the experimental images.6,7,10 This is because we were able to consider only a simplest possible combination of two terminations which does not possess a hexagonal symmetry. However, while the hexagonal symmetry could not be calculated, the calculations show that already the combination of two different terminations reduces the total energy in a periodic arrangement and makes the structure stable. The relaxation of surface layers, calculated as an average for atoms in a given layer of a specified domain are shown in Table 2. Most of the GGA+U relaxations are larger in both the pure Fe-terminated surface3 and the Fe-terminated domain than
Figure 3. Simulated STM image (GGA+U) of the mixed Fe1/O3 termination of the α-Fe2O3(0001) surface of (4 × 4) periodicity corresponding to the M(4 × 4) structure presented in Figure 2. The image was calculated in a constant current mode. Only the atoms of the topmost Fe and O layers are seen.
those calculated within GGA. In the cases of the O-terminated surface and domains GGA+U predicts significantly smaller relaxations, especially between the subsurface double Fe layer. However, the differences in relaxation of the Fe- and Oterminated surfaces have a distinct tendency to equalize to the same level in both domains. This is most clearly seen when the calculation is in GGA+U (Table 2). For the mixed surface terminations the contractions of the Fe(−1)−Fe(−2) distance in the double Fe layer are the same for both domains. Both for Fe1 and O3 domains of the mixed termination, the contraction of the topmost layer distance is reduced compared to the respective pure Fe1 and O3 termination. Consequently, the height difference of surface layer atoms in the Fe- and Oterminated domains is 0.43 Å (0.52 Å GGA). This agrees very well with the value of 0.4 ± 0.2 Å which was measured in an STM experiment10 which predicted the same periodicity of surface domains. The vertical displacements of individual atoms calculated within GGA+U are larger in the Fe1 domain (by 0.1−0.2 Å) whereas those calculated within GGA are larger in the O3 domain. The buckling of the topmost surface layer in the Fe1 domain is 0.06 Å (0.10 Å, GGA), whereas in the O3 domain it is 0.21 Å (0.24 Å, GGA). As reported previously,3,19 the triangles of oxygen atoms of the pure O3 termination undergo an in-plane rotation by about 9°. At the Fe1terminated surface the atoms of the subsurface O3 layer are rotated by 1−2° (3−4° GGA).3 The mixed terminations are non-uniformly strained and the angle of rotation of the oxygen atoms in the topmost surface layer of the O3 domain varies between 4 and 6° (GGA+U) and 2−10° (GGA). The largest rotation is observed for atoms at the domain boundaries. The work function (Table 1) of the mixed terminations is by ≃0.16−0.32 eV lower than the mean value of the combination of pure Fe1 and O3 terminations. The GGA+U/GGA work function increases/decreases with increased periodicity of the mixed termination with the GGA+U values consistently (≃0.7−0.8 eV) larger than those of GGA. The relatively large difference in work function obtained with GGA and GGA+U is typical for these two approaches and is related to differences in the electronic structure.3 DFT+U predicts wider eigenvalue gaps and makes the crystal more insulating which is manifested in the calculated density of states of the pure terminations and a 24341
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Table 2. Relaxation of the Fe2O3 (0001) Surface Layers (in % of the Bulk Interplanar Distance) in Fe1- and O3-Terminated 2 × 2 Domains of the M(4 × 4) Structure Resulting from GGA+U and GGA Calculations. For Comparison the Relaxations for Pure Fe1 and O3 Surface Terminations Are Given in Parentheses lattice relaxation (%) GGA+U layers
Fe1 domain
Fe−O3 O3−Fe(−1) Fe(−1)−Fe(−2) Fe(−2)−O3(−3) O3(−3)−Fe(−4) Fe(−4)−Fe(−5) Fe(−5)−O3(−6)
−56.4 (−66.6) 3.5 (7.2) −49.7 (−38.0) 20.4 (16.3) −2.6 (3.7) 9.8 (−3.7) −2.1 (0.8)
GGA O3 domain
Fe1 domain
O3 domain
−2.4 (−5.5) −49.5 (−56.1) 22.3 (25.4) 0.8 (−5.4) 0.4 (13.2) −1.8 (−4.0)
−44.5 (−51.2) −3.7 (6.3) −45.1 (−30.9) 17.8 (13.1) −3.4 (2.1) 10.6 (0.1) −4.8 (−0.6)
−1.7 (−6.1) −63.5 (−75.3) 21.4 (33.7) −5.2 (−6.2) 20.5 (13.0) −6.9 (−3.6)
Figure 4. Local density of states projected on the Fe 3d and O 2p orbitals of the atoms of top layers of the mixed Fe1 (Fe−O3−Fe−) and O3 (O3− Fe−) terminations of the α-Fe2O3(0001) surface. Red and blue lines represent the Fe 3d states of the topmost Fe, and subsurface Fe(−1) layers, respectively, whereas the green line represents the contribution of the O 2p states of the O3 layer. Majority and minority spin states are displayed as positive and negative, respectively. All plots are normalized to the number of atoms in a particular layer of the M(2 × 2) cell. For the N(4 × 4) arrangement the LDOS plots are identical to those of the M(2 × 2).
higher work function.3 This is also visible in the local density of states (LDOS) of the considered mixed structures which are displayed in Figure 4. The LDOS projected on the Fe 3d and O 2p orbitals of the atoms of top layers of the mixed Fe1 (Fe− O3−Fe−) and O3 (O3−Fe−) terminations calculated using GGA+U and GGA differ substantially. In general, the densities of the Fe 3d states calculated using the GGA+U approach are shifted down on the energy scale in comparison to GGA, and show a narrow energy gap at the Fermi level. In contrast, the
LDOS resulting from the GGA calculation predict either a semimetallic character of the bands, for a mixture of the (1 × 1) domains of Fe1 and O3, or a metallic character for the mixed (2 × 2) and (4 × 4) terminations. As can be seen, the LDOS plots for the mixed Fe1 and O3 (1 × 1) structures, considered separately for GGA+U and GGA, differ more distinctly (even qualitatively) from the M(2 × 2) structures than the LDOS of the M(4 × 4) and those of the N(4 × 4) arrangement. This may explain the relatively large difference in the stability of the 24342
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Table 3. Changes of Bader Charges (in e units) on Atoms of the Mixed (2 × 2) and (4 × 4) Cells, Calculated (GGA+U) as Difference of the Average of the Valence Charge on All Atoms of a Given Layer of the Specified Domain and in the Bulk. For Comparison the Corresponding Changes on Atoms of the Pure Fe1- and O3-Terminated Surfaces Are Also Given Fe1 domain
O3 domain
layer
M(2 × 2)
M(4 × 4)
Fe1
M(2 × 2)
M(4 × 4)
O3
Fe O3 Fe(−1) Fe(−2) O3(−3) Fe(−4) Fe(−5)
0.14 −0.35 −0.03 −0.04 −0.06 0.01 0.0
0.14 −0.21 −0.03 −0.03 −0.03 0.01 0.01
0.16 −0.06 0.01 −0.02 0.01 0.01 0.01
−0.20 −0.03 −0.04 −0.03 0.01 0.01
−0.36 −0.04 −0.04 −0.06 0.0 0.0
−0.52 −0.06 −0.05 −0.08 0.0 0.0
mixed terminations calculated with GGA and GGA+U in the case of Figure 2a, and their almost equal stability in the case of Figure 2c. The differences of the electron charge on atoms of the mixed (2 × 2) and (4 × 4) surfaces of hematite (0001) and those of the respective bulk planes, calculated using the Bader method21 are presented in Table 3. The numbers, which basically reflect the changes in the valence-electron charge, show that Fe atoms of the topmost layer of the Fe1 domain have a surplus electron charge of magnitude independent of the domain size. For the surface Fe atoms, the calculated changes are significantly smaller for GGA+U than for GGA (not shown). Because each PAW sphere around an atom is treated as a single site, the smaller changes of the electron charge on surface atoms compared to bulk atoms resulting from GGA+U are manifestation of the effect of energy U that penalizes double occupancy of the same site. In contrast, the atoms of the top Olayer in the Fe1 or O3 domain have a deficit of electron charge, both for GGA+U and GGA, which depends on the domain size. With the increase of the size of the domain this deficit becomes respectively larger/smaller for the oxygen atoms from the top O3 layer, and for those from the subsurface O-layer of the Fe1 domain. In both cases, for the increased domain size the charge deficit tends to the values observed for the pure Fe1 and O3 terminations. In agreement with the results for the pure Fe1 and O3 terminations, a magnitude of the electron charge gain on the topmost layer Fe atoms of the Fe1 domain is considerably smaller than the charge deficit on the O-atoms of the top layer of the O3 domain. The Fe atoms in the double layer of Fe(−1)−Fe(−2) and Fe(−4)−Fe(−5), show a very small or negligible deficit of electron charge (GGA+U). The magnetic moments on the atoms, calculated as average over all atoms of a given layer of a specified domain, are presented in Table 4. Compared to the pure terminations the moments on the topmost layer atoms of both the Fe1 and O3 domain are little altered. The moment on the topmost Fe layer is increased by 0.15 μB, whereas the moments on the surface O3-layer atoms are either increased or reduced by 0.05 μB. The most significant changes of the magnetic moments (up to ∼0.7 μB) occur for the subsurface Fe(−1) and Fe(−2) layer atoms. The GGA+U moments on the Fe(−1) and Fe(−2) atoms show a rather complex but small variation, depending on the specific domain and atomic layer.
Table 4. Magnetic Moments on Atoms of the Fe2O3 (0001) Surface Layers in the Fe1- and O3-Terminated 2 × 2 Domains of the M(4 × 4) Termination Resulting from GGA +U Calculations. For Comparison the Values of Moments for Pure Fe1 and O3 Terminations Are Given in Parentheses magnetic moment (μB) layer Fe O3 Fe(−1) Fe(−2) O3(−3) Fe(−4) Fe(−5)
Fe1 domain 4.14 −0.04 −3.48 −4.16 0.07 4.15 4.14
(3.99) (0.00) (−4.12) (−4.15) (0.02) (4.14) (4.14)
O3 domain −0.05 −3.09 −3.85 0.09 4.14 4.14
(0.00) (−2.82) (−3.77) (0.13) (4.15) (4.14)
+U as a more suitable method than DFT to describe the properties of the reconstructed hematite surface. Though a simplest possible combination of two terminations considered in this work does not allow a reproduction of the biphase structure of hexagonal symmetry, our results provide a helpful hint to understand structural evolution of the hematite (0001) surface. The GGA+U calculations demonstrate that a periodic pattern of the two terminations is energetically favored over the average of the pure phases and that surfaces composed of alternating domains of Fe1 and O3 terminations of large periodicity are stable. The coexisting domains appear to have substantially different heights which agree with those measured in STM images. A more clear-cut argument for stability of the bi-phase terminated hematite (0001) surface could be provided by more extended calculations for still larger surface unit cells which would allow a reproduction of the long periodicity of the pattern observed in experiment. However, such computations are at present not affordable.
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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 We are grateful to Professor Ernst Bauer for useful comments and discussions. This work was supported by the National Science Center (NCN), Poland (Grant No. 2012/07/B/ST3/ 03009). We acknowledge provision of computer time from the Interdisciplinary Centre for Mathematical and Computational
SUMMARY We have presented extensive DFT+U and DFT calculations of mixed iron and oxygen terminations of the hematite (0001) surface composed of Fe- and O-terminated domains. An analysis of results of this work allows the identification of DFT 24343
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(21) Henkelman, G.; Arnaldsson, A.; Jónsson, H. A Fast and Robust Algorithm for Bader Decomposition of Charge Density. Comput. Mater. Sci. 2006, 36, 354−360.
Modelling (ICM) of the Warsaw University (Project No. G4423).
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