CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201402153

Defective a-Fe2O3(0001): An ab Initio Study Manh-Thuong Nguyen,* Nicola Seriani, and Ralph Gebauer[a] By using density functional theory calculations at the PBE + U level, we investigated the properties of hematite (0001) surfaces decorated with adatoms/vacancies/substituents. For the most stable surface termination over a large range of oxygen chemical potentials (mO ), the vacancy formation and adsorption energies were determined as a function of mO . Under oxygenrich conditions, all defects are metastable with respect to the ideal surface. Under oxygen-poor conditions, O vacancies and

Fe adatoms become stable. Under ambient conditions, all defects are metastable; in the bulk, O vacancies form more easily than Fe vacancies, whereas at the surface the opposite is true. All defects, that is, O and Fe vacancies, Fe and Al adatoms, and Al substituents, induce important modifications to the geometry of the surface in their vicinity. Dissociative adsorption of molecular oxygen is likely to be exothermic on surfaces with Fe/Al adatoms or O vacancies.

1. Introduction Hematite (Fe2O3) has been shown to possess great potential as a material for photocatalytic and photovoltaic applications, owing to its band gap of about 2.2 eV, its abundance, and its thermodynamic stability in nature.[1–3] It is most promising for water splitting,[1, 4] because it is not only able to operate as an anode in the oxygen-evolution reaction, but also as a material for the hydrogen-evolution reaction in photoelectrochemical cells.[5] As the surface plays a fundamental role in photocatalytic applications, crystal surfaces of hematite have been subjected to intense studies with particular attention being devoted to the (0001) surface, a highly stable surface that is usually exposed in natural hematite crystals.[6, 7] Numerous experimental and theoretical studies have been carried out to determine its structure, morphology, chemical composition, and electronic properties under various conditions, ranging from fresh, briefly wetted surfaces to ones in dry and humid air, in water under bias, or covered with graphene.[8–14] The abundance of studies reflects the complexity of the behavior of this surface, which displays both O- and Fe-rich terminations that sometimes even coexist.[6] In an oxygen atmosphere, the thermodynamically stable defect-free termination is a single-Fe-terminated one in a wide range of chemical potentials of oxygen (mO ).[11] It is, however, known that point defects are often present in the bulk and at the surface of metal oxides, and they are crucial in modifying the physical and chemical properties of the crystal.[15, 16] It has been shown that O vacancies can dramatically change the chemical reactivity of an oxide surface.[17] Also, adatoms can improve the reactivity of host surfaces with adsorbed molecules,[18] and even steer growth[19] and self-assembly[20] at surfaces. Given that vacancies and other point defects can be generated in the crystal-growing process or created at

[a] Dr. M.-T. Nguyen, Dr. N. Seriani, Prof. R. Gebauer The Abdus Salam International Centre for Theoretical Physics Strada Costiera 11, 34151 Trieste (Italy) E-mail: [email protected]

 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

a later stage, for example by electron bombardment, it is desirable to understand their formation, stability, and properties. Experimentally, Fe vacancies and adatoms on the hematite (0001) surface have been observed by scanning tunneling microscopy.[6, 18] The presence of O vacancies on this surface has also been reported.[21] It has recently been shown that coating hematite photoanodes with a thin Al2O3 layer considerably reduces the water oxidation overpotential;[22] evidence has been presented that this is connected with the disappearance of surface electronic states that trap holes during the photocatalytic process. These findings underline the importance of a detailed understanding on how structural surface modifications affect chemical and electronic properties of the surface. In this work, by using density functional theory (DFT) calculations at the PBE + U level of theory, we investigate properties of hematite surfaces induced by O and Fe vacancies, Al substitutional impurities, and Fe and Al adatoms. We first determined the formation energy of such defective sites as a function of mO . The defect-induced geometry relaxation was then examined. The electronic properties and reactivity with oxygen of some defects were finally addressed.

Methods and Models We employed first principles calculations by using spin-polarized plane-wave DFT as implemented in the Quantum ESPRESSO package,[23] within the framework of GGA(PBE) + U formalism.[24, 25] The effective Coulomb repulsion parameter for Fe 3d orbitals of hematite in our calculations was set at 4.2 eV, which indeed leads to an energy gap of about 2.0 eV in hematite. The interactions between the electrons and ions were represented with ultrasoft pseudopotentials.[26, 27] We used a kinetic-energy cutoff of 40 Ry for the wavefunction and 320 Ry for the charge density. The force convergence threshold was set at 103 eV 1 for structural optimizations. In the framework of the slab model, the surface free energy (g) was calculated as [Eq. (1)]: ChemPhysChem 2014, 15, 2930 – 2935

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CHEMPHYSCHEM ARTICLES g¼

X 1 nmÞ ðG  i i i 2A

www.chemphyschem.org ð1Þ

where A is the total surface area (here we use 2A to account for the two surfaces in the slab model), G is the Gibbs free energy ni and mi are the number of atoms and the chemical potential of the component I, respectively. In free energy G = U + p VT S, where U is the internal energy, p is the pressure, V is the volume, T is the absolute temperature, and S is the entropy, we assumed that the (p VT S) contribution is small and the same for all the surface terminations, thus, it does not affect the relative stability between them. U is approximated as the electronic energy from DFT calculations. Given, in thermodynamic equilibrium, that [Eqs. (2), and (3)]: 2mFe þ 3mO ¼ mFe2 O3

ð2Þ

2mAl þ 3mO ¼ mAl2 O3

ð3Þ

where mM2O3 (M = Fe/Al), the chemical potential of bulk hematite/ alumina, is calculated as the energy per Fe2O3 formula unit; g of hematite is given by Equation (4): g¼

    1 1 3 Eslab  nFe mFe2 O3 þ nFe  nO mO 2A 2 2

ð4Þ

Finally, we defined the substitution energy of Al for Fe (EAlFeX ; note X ) as that both Fe and Al are 3 + , the notation accordingly is AlFe [Eq. (10)]: 1 1 EAlFeX ¼ Esys=Al þ mFe  Esys=Fe  mAl ¼ Esys=Al þ mFe2 O3  Esys=Fe  mAl2 O3 2 2 ð10Þ Here, Esys/Al and Esys/Fe are the energy of the system with and without Al replacing Fe. In this work, we only dealt with mO , which is given by Equation (11):[29]    p 1 1 ~ðp0 ; TÞ þ kB T ln O02 mO ¼ mO ¼ EO2 þ m 2 2 p

ð11Þ

where kB is the Boltzmann constant and EO2 is the total energy of ~ðp0 ; TÞ is the chemical potential at presa free oxygen molecule. m sure p0 = 1 atm, excluding EO2 , and can be determined from thermodynamic tables[29] or from the calculation of vibrational and translational degrees of freedom of the oxygen molecule.[30] Along the [0001] direction, hematite has a layered structure, the (0001) surface of hematite is, thus, terminated with either O or Fe atoms, see Figure 1. For convenience, these terminations are

where Eslab is the energy of the slab. In this work, we adopted the commonly used notation proposed by Krçger and Vink for pointq , a vadefect species[28] of solids. EVf q , the formation energy of VO=Fe O=Fe cancy O or Fe (O/Fe) of charge state q (the energy needed to remove an atom in thermodynamic equilibrium), was determined by Equation (5): EVf q

O=Fe

q ¼ Ehost;VO=Fe  Ehost þ mO=Fe þ qEF

ð5Þ

where EVf q and Ehost are the energies of the host (bulk or surfaces) O=Fe with and without the vacancy, respectively, mO/Fe is the chemical potential of the removed atom, and EF is the Fermi energy. We only X , Krçger–Vink notaconsidered neutral vacancies in this work (VO=Fe tion), therefore the last term of Equation (5) is removed. The formation energy of an O vacancy (EVf X ) is, thus, given by Equation (6): O

f VOX

E

¼ Ehost;VOX  Ehost þ mO

ð6Þ

Combining Equations (2) and (5), the formation energy of a neutral Fe vacancy (EVf X ) is [Eq. (7)]: Fe

1 EVf X ¼ Ehost;VFeX  Ehost þ ðmFe2 O3  3mO Þ Fe 2

ð7Þ

In the same fashion, we calculated the adsorption energies of O a ) as [Eq. (8)]: (EOa ) and Fe/Al (EFe=Al EOa ¼ Ehost;O  Ehost  mO

ð8Þ

and [Eq. (9)]: 1 a ¼ Ehost;Fe=Al  Ehost  ðmFe2 O3 =Al2 O3  3mO Þ EFe=Al 2

ð9Þ

where Ehost;Fe=Al and Ehost are the energies of the host with and without the adatoms, respectively.  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Figure 1. Top-view defect-free unit cell of the hematite stoichiometric termination (Fe O3Fe): Fe in gray, large spheres; and O in black, small spheres (a). A, B, C indicate the outermost, second outermost, and third outermost Fe atoms of the surface, respectively (b).

named FeFeO3, OFeFe, O2FeFe, O3FeFe, and Fe O3Fe, as in our previous papers,[11, 13] corresponding to surfaces terminated with a double Fe layer, a 1/3 O layer, a 2/3 O layer, a 3/ 3 O monolayer, and a single Fe layer, respectively. Additionally, as discovered experimentally [31] under oxygen pressure, the ferryl termination, OFeO3, in which atomic O is bound on Fe sites of FeO3Fe, is also considered. Here, we use the calculated lattice constants for a 30-atom hexagonal unit cell, namely, a = b = 5.07  and c = 13.90 . The surface unit cell to host adatoms/vacancies is of the 2a  2b periodicity, containing approximately 120 atoms. The antiferromagentic ordering of the bulk was taken as the initial configuration for all calculations. All atoms were allowed to relax. A vacuum layer of 24  was added between slabs and their periodic images. A 2  2  1 k-point grid in the reciprocal space was chosen to sample the Brillouin zone in the self-consistent calculations and 4  4  1 k-point grid was used for post-processing calculations of projected density of states (PDOS). Vacancies are initialized by removing O (Fe) atoms from the defect-free hosts (see Figure 1 b). In our structural optimizations, all atoms are allowed to relax. Lçwdin analysis[32] was also employed to estimate partial atomic charges.

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CHEMPHYSCHEM ARTICLES 2. Results 2.1. Defect Formation and Adsorption Energies Figure 2 a shows the dependence of g on mO for different surface terminations. In line with various theoretical studies,[11, 12] over a large range of from 2.5–0 eV, FeO3Fe appears to be the most stable. Moving to a lower energy range, O1Fe Fe and FeFeO3 are the most stable structures. Thus, in this work, we focus on these terminations.

www.chemphyschem.org most O atoms, that is, by generating a full layer of vacancies. Figure 2 reveals that FeFeO3 becomes more stable than OFeFe at a DmO of 3.3 eV, and that EOf is zero at a DmO of 1.7 eV. The difference here is due to the density of vacancies; the unit cell in use implies that, in the system with a single vacancy, the vacancy concentration corresponds to a 1/4 monolayer, whereas the different termination corresponds to a 4/4 monolayer of vacancies. Thus, a single vacancy is stable at DmO values at which OFeFe is still more stable than FeFeO3. This means that there are pressures and temperatures at which termination with O vacancies is not the result of poor kinetics of crystal growth, but the stable surface configuration. This result underlines, once more, the peculiar properties of surfaces and the need to study them in detail. In this case, the range in which the defected termination is stable is between DmO = 3.3 and 2.8 eV. A DmO of 2.8 eV corresponds, for example, to temperatures above 2000 K at 1 atm of oxygen pressure and to temperatures of ~ 1300 K at 1010 atm, a pressure accessible under ultrahigh vacuum conditions. The FeO3Fe and O3FeFe terminations share the same picture, although the crossing points at DmO values of 0.8 and 1.0 eV are outside the allowed mO range. Now we compare the formation energies of vacancies that are on and near the surface (of FeO3Fe), and in the bulk. Moving from the on-surface to near-surface positions leads to a significant variation in the vacancy formation energy. In Table 1, we show the formation energies (calculated at DmO =

Table 1. Formation energies (in eV, at DmO = 0) of O and Fe vacancies on and near the FeO3Fe surfaces at frozen (fro) and relaxed (rel) geomeX tries. VO=Fe 1=2=bulk = O/Fe vacancies on the surface (1), near the surface(2), or in the bulk (bulk).

f fro;V f rel;V

E E Figure 2. g, for different terminations (a), vacancy formation energy (b), and adsorption energy (c) as a function of the oxygen effective chemical poten1 tial, DmO ¼ mO  2 EO2 . Vertical dotted lines, where DmO = 0 eV, indicate the 1 upper limit of mO ð2 EO2 Þ.

In Figure 2, we show the vacancy formation energies against 1 mO. At the upper limit of mO (mO  2 EO2 ¼ 0), that is, under oxygen-rich conditions, it requires 2.46 and 1.51 eV to create an outermost O vacancy on FeO3Fe and OFeFe, respectively. At the same mO, an energy of 1.53 eV is needed to generate an Fe vacancy on FeO3Fe. Moving to lower mO, the formation energy of the O vacancies decreases, whereas that of the Fe vacancy increases. When mO is low enough, the formation energy becomes negative and the O vacancies become thermodynamically stable at the surface. By using our results for the formation energy for a single vacancy (EOf ) and the g of the different phases, we can also get an insight into the dependence of the vacancy formation energy on the vacancy concentration. It must be kept in mind that FeFeO3 can be generated from FeFeFe by eliminating its outer 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

VOX1

VOX2

VOXbulk

X VFe 1

X VFe 2

X VFe bulk

2.78 2.46

3.06 2.66

3.08 2.74

2.65 1.53

3.69 2.19

3.88 2.42

0) of vacancies created by removing the outermost and the second outermost O (Fe) atoms from the slab of FeO3Fe. For both O and Fe vacancies, from the on-surface to near-surface positions, the formation energy becomes larger, quickly approaching its bulk value. This is because atoms on the surface are under-coordinated compared to atoms near the surface (or in the bulk); thus, creating a vacancy near the surface (or in the bulk) means introducing more dangling bonds and is, consequently, energetically more costly. This is more pronounced in the case of Fe. As a consequence, there is a driving force for the defects to migrate from sites in the bulk or in near-surface positions towards the surface, and the surface can be expected to display a higher concentration of defects than the bulk. Moreover, we can use the values from Table 1 (at DmO = 0 eV) to calculate formation free energies at any temperature and pressure. At a temperature of 300 K and a pressure of 1 atm (DmO = 0.27 eV[29]) the formation energy of O vacancies (2.47 eV) is lower than the formation of Fe vacancies (2.82 eV) in the bulk; this is in agreement with the notion that ChemPhysChem 2014, 15, 2930 – 2935

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pure hematite is an intrinsic n-type semiconductor. On the toms, we also considered the B and C adsorption sites: the Al contrary, under the same conditions, at the surface an Fe vaatoms energetically prefer the latter. Thus, both Fe and Al cancy forms more easily than an O vacancy (1.93 vs. 2.19 eV). prefer to sit in a C position. The adsorption energy of Al has To evaluate effects of geometry relaxation we calculated the the same mO dependence as that of Fe; however, the Al adf frozen formation energy (Efro;X sorption is less stable. , where X = O, Fe), which is deterFinally, the substitution energy of Al for Fe is calculated to mined by Equations (6) and (7), in which, however, Ehost;X is the be 0.75 eV. This positive value is consistent with the weaker energy calculated in the geometry of the defect-free slab. Our adsorption of Al compared to Fe adatoms. calculations suggest that the vacancy-induced relaxation reduces the formation energy by 0.3–0.4 eV (O) and 1.1–1.5 eV (Fe). The effect is more evident in the case of Fe vacancies, 2.2. Defect-Induced Geometry Relaxation and in near-surface positions; this might be explained with the higher coordination number of Fe in hematite. Defect-induced geometry relaxation of the surface region f a As EOf decreases and EFe increases, EOa increases and EFe dearound vacancies/adatoms/Al-substituent is explored by concreases, against mO. The mO -dependent adsorption energy of O sidering atoms numbered in Figure 3 (related structural data and Fe adatoms at FeFeO3 is plotted in Figure 2 c. At Fe are shown in Table 2). O3Fe, atomic O prefers to bind to a low-electronegativity site, for example a surface Fe atom, forming a ferryl group. At the upper limit of mO, EOa amounts to 0.36 eV and becomes negative at a DmO of about 0.4 eV. The positive range of DmO is irrelevant, however, to obtain a complete comparison, we plotted g against positive values of DmO and observed that that OFeO3 becomes more Figure 3. Defects on the FeO3Fe terminations: VOX and VFeX in the topmost layer (a, b; highlighted by the trianX stable than FeO3Fe at DmO = gle); O, Fe/Al adatom (c, d) indicated by letter a; and AlFe indicated by the letter s. Gray and black spheres indicate 0.7 eV (Figure 2 a). Given that metal and O atoms, respectively. Only neighboring surface atoms are implicitly shown. FeO3Fe covered with a full monolayer of atomic O adatoms We start with the O vacancy. Removing an O atom means recan be seen as OFeO3, the connection between the g and ducing the coordination numbers of its three Fe bonding partthe adsorption energy is thus present. Note that, as clearly ners, namely, Fe1, Fe2, and Fe3, as denoted in Figure 3 a; this shown in Figure 2 b, the formation energy of VOX is mostly X lower than that of VFe over a wide range of allowed mO values, leads to strong relaxation of these atoms. This Fe triangle X . This is thus implying that VOX will be more populous than VFe shrinks, in particular, the Fe1Fe2 and Fe1Fe3 distances in agreement with experimental work by Kurtz and Henrich on become smaller and Fe2Fe3 is almost unchanged. Fe1 moves [21] properties of Fe2O3(0001) decorated with point defects, in down inwards, whereas Fe2 moves out towards the surface. which bombarding hematite surfaces primarily leads to the forThe Fe1O4 and Fe2O5 bonds are longer, and Fe3O6 is shortmation of O vacancies. er. For Fe adatoms, as a starting point, we considered two posTaking away one of the topmost Fe atoms leads to the exsible positions, as suggested by the bulk atomic arrangement, pansion of the triangle made up by its three O bonding partthat is, the positions above the centers of O triangles that are ners: O1, O2, and O3 (Figure 3 b). Reduced in their coordination located above Fe-atoms B and C (Figure 1). Furthermore, two numbers, these atoms bind more strongly to Fe atoms in the different spin states (one the same as and one the opposite to second layer, in particular, the initial O1Fe4 and O1Fe5 bond that of the outermost surface Fe atoms) are also taken into aclengths of 1.95 and 2.07  are shortened by 0.22 and 0.07 , count. Of these structures, the one above Fe-atom C with the respectively. This is roughly in agreement with distances of same spin appears to be most stable. This adsorption position 1.75–2.06  found by DFT–PBE.[33] Three O atoms (O1, O2, and corresponds to the stacking order of layers along the [0001] diO3) move downward to the surface compared to other O rection of bulk hematite. As described by Equation (9), Fe on atoms in the same layer. Owing to strengthened O1Fe5 and the surface becomes more stable if mO is more negative. The O1Fe4 bonds, neighboring bonds O7Fe5 and O6Fe4 are adsorption energy is about zero at a DmO of 2.2 eV. Note, somewhat weakened, as they are slightly elongated. For the O however, that a full monolayer of Fe adatoms on FeO3Fe adatom, we consider the ferryl group and the three neighborresults in FeFeO3, which is more stable than FeO3Fe ing surface O atoms (Figure 3 c). The Fe1O2 bond length is apwhere DmO

Defective α-Fe2O3(0001): an ab initio study.

By using density functional theory calculations at the PBE+U level, we investigated the properties of hematite (0001) surfaces decorated with adatoms/...
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