Article pubs.acs.org/JPCC
Theoretical Insights into the Mechanism of Water Oxidation on Nonstoichiometric and Titanium-Doped Fe2O3(0001) Maytal Caspary Toroker*,∥ ∥
Department of Materials Science and Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel ABSTRACT: Fe2O3 is widely considered a promising material for converting solar energy through oxidizing water. We model the mechanism of water oxidation on Fe2O3(0001) surface in the presence of defects that have been recently modulated experimentally. We use a density functional theory type method (DFT + U) on several surface models that include oxygen vacancies, iron vacancies, and Ti−dopants. Our calculations reveal that these multiple defects do not change the cumulative free energy of the reaction, but do change the overpotential. Moreover, the mechanism details are different. The excess holes generated by iron vacancies suppress the first hydrogen cleavage reaction, and reduce the free energy for the final reaction step of oxygen release. This work sheds light into the origin of the thermodynamic limitations, paving the way toward possible control over surface reactivity.
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INTRODUCTION The quest for efficiently converting solar energy into hydrogen fuel has attracted major interest worldwide.1,2 Generating hydrogen fuel along with oxygen gas from water (a process called “water splitting”) can be fulfilled in a photoelectrochemical cell device.3 In a photoelectrochemical cell, absorbing solar energy at the cathode and/or anode electrodes enables creation of an electron−hole pair. The electron facilitates reducing water to hydrogen fuel at the cathode while the hole participates in oxidizing water at the anode. Oxidizing water is therefore a central step in this device operation. A promising anode material for oxidizing water is Fe2O3 (iron(III) oxide),4 which has several advantages, including abundance, nontoxicity, stability, having a band gap that allows absorbing light, and having a valence band edge position suitable for water oxidation. A major disadvantage is the need for a high external bias (overpotential) to overcome the inefficient surface chemistry. Although several advances have been made in the development of Fe2O3 anodes, including nanostructuring,5,6 coating with a cocatalyst,7,8 doping,9−11 and light trapping,12 the efficiency is still too low for commercialization.13,14 A breakthrough could take place if we continue to make efforts in understanding the optical transitions,15−17 charge transfer dynamics18−20 and the surface reaction mechanism of Fe2O3.21−24 One of the most pressing problems is how defects affect performance. The profound influences of defects, such as cation and oxygen vacancies, particularly on surface reactivity was recently suggested for TiO2.25 Oxygen vacancies have been identified experimentally as the dominant defect in Fe2O3,26 but iron vacancies could also exist under oxygen-rich conditions.27 Furthermore, iron vacancies could compensate either oxygen vacancies or titanium (electron donating) dopants.28 A very recent experiment demonstrated ability to modulate iron © XXXX American Chemical Society
vacancy concentration in Ti-doped Fe2O3 by varying processing conditions.29 In this paper, we use a theoretical scheme developed by the Nørskov group30 to follow the water oxidation reaction mechanism proposed recently for pure and doped Fe2O3(0001)31 while taking into account in addition to surface oxygen vacancies and Ti−dopants also the presence of iron vacancies. The reaction mechanism includes the following steps,31−34 H 2O + * → *OH 2
(A)
*OH 2 → *OH + H+ + e−
(B)
*OH → *O + H+ + e−
(C)
H 2O + *O → *OOH + H+ + e−
(D)
*OOH → O2 + * + H+ + e−
(E)
where “*” represents a surface and “*OH2”, for example, represents a surface with an adsorbed OH2 specie. We use density functional theory + U (DFT + U),35 which was found to be appropriate for describing the properties of the bulk and surface of Fe2O3,36,37 and use several models for capturing the surface environment. Finally, we explain how these defects affect the free energy of each intermediate reaction step and discuss implications for solar energy conversion through water splitting. Received: July 23, 2014 Revised: September 15, 2014
A
dx.doi.org/10.1021/jp5073654 | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
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METHODS We performed spin-polarized periodic DFT calculations within the VASP program version 5.3.3.38,39 We used the DFT+U formalism of Dudarev et al.40 to correct the DFT selfinteraction errors for strongly correlated electrons in first-row transition metal ions.36,41 We used similar U values for the transition-metals: the ab initio value of U = 4.3 eV for iron36 and the frequently used value of U = 5 eV for titanium.42,43 We validated using this U value for titanium against U = 2 eV, which was found useful for predicting the band gap of TiO2,44 and against U = 4.3 eV, as was done previously on Ti-doped Fe2O331 in order to not bias electron occupation on one of the transition metals. Calculations were done under the correct antiferromagnetic spin ordering that Fe2O3 exhibits in the ground state. The Perdew, Burke, and Ernzerhof (PBE)45 exchange-correlation functional was chosen according to its accuracy in calculating Fe2O3 bulk and surface ground state properties.36,37 Projector-augmented wave (PAW) potentials representing the core electrons and nuclei of each atom replaced the Fe 1s2s2p3s, Ti 1s2s2p3s, and O 1s electrons.46,47 Slabs were initially constructed from the optimized bulk rhombohedral unit cell of Fe2O3 containing ten atoms (please see details on optimizing the bulk in refs 36 and 48). We chose to focus on constructing the (0001) surface which has less reconstruction than the second neutral growth face, the (011̅2) surface, and at one of the possible dominant terminations found in aqueous solutions.49,50 The initial locations of surface terminating hydrogen atoms and water molecules were set according to the optimized geometries reported in ref 31. For comparison, we recalculated the process of water oxidation with no defects according to the information given in ref 31. We built four slabs as shown in Figure 1: (a) a nine atomic-layer
relative to the center of the slab. Hence, the two surfaces of slab (d) are identical. Reactive species and defects were introduced on both sides of the slab so that there is no dipole moment across the slab. The iron vacancy is located at a position that gives the lowest energy for slab (a) (as seen in Figure 1, the absence of Fe4). We chose the position of Ti−dopant to be nearest to the surface (as seen in Figure 1a, substituting Fe1) where the dopant may be most influential and also to have a fair comparison to previous investigations that placed the Ti− dopant at this location.31 All slabs had at least 10 Å vacuum (measured after the adsorbant), which converges the total energy relative to a thicker vacuum layer.31,48 The plane wave basis was truncated at kinetic energy of 700 eV. Gamma-point-centered k-meshes were used with a k-point grid size of 3 × 3 × 1 and 2 × 2 × 1 for the narrow and wide slabs, respectively (Figure 1, parts a and c). The kinetic energy cutoff for the planewave basis and k-point grid converged the total energy to within 1 meV.36,48 Symmetry was not imposed. The Brillouin zone was integrated with the efficient Gaussian smearing method, using a smearing width of 0.05 eV for the slab. The conjugate-gradient method was used to relax the ions until forces on all atoms were smaller than 0.03 eV/Å. Bader charges were calculated by integrating the electron densities within zero flux surfaces around nuclei and were converged to within 0.1 electrons compared to a grid 1.5 times denser along each lattice vector.52 We used the reaction mechanism scheme that was previously suggested for pure and doped hematite31−34 to calculate the free energy ΔG for each intermediate reaction step. In calculating the free energy, the total energy of the slab was divided by two because the slab has two surfaces. We used values of −6.774, −9.871, and −14.225 eV for the total energy for molecules H2, O2 and H2O, which were obtained in previous literature.31 The effective binding energy ΔG* of an adsorbed species at an intermediate reaction is calculated from the cumulative reaction free energy of that reaction step.34 We assumed that zero point energies (ZPE) and entropic contributions do not depend significantly on surface defects and use those of the pure Fe2O3(0001) slab model.31
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RESULTS In this section, we first describe the mechanism of water oxidation on Fe2O3(0001) with and without iron vacancies and Ti−dopants. We analyze this process in terms of charges generated from oxygen vacancies, iron vacancies, Ti−dopants, or hydrogen atom cleavages (with Bader charge analysis52). Next, we show how this charge affects the free energies and overpotential. We also show that results are independent of the slab size. We start with presenting the process of water oxidation on Fe2O3(0001). The results without an iron vacancy were obtained in ref 31, and here we state them for comparison to our iron-deficient surface. Since the catalysis of water oxidation is repetitive, we can describe the beginning of the reaction at any one of the intermediate surface structures. We choose to start with the appearance of an oxygen vacancy at the surface (the absence of O9 in Figure 1a) since this is how water oxidation is usually modeled.31−34 Alternatively, we could have started from a surface without an oxygen vacancy (the product of reaction B), and then the energy needed to form an oxygen vacancy would be the cumulative free energy of the reverse reaction from reaction B to A (−ΔG(A) − ΔG(B) = −1.3 eV is
Figure 1. Slab models for Fe2O3(0001): (a) near vacuum, (b) with H2O monolayer coverage, (c) wide slab representing a lower concentration of defected sites, and (d) thick slab. Red, brown, and white spheres represent oxygen, iron, and hydrogen atoms, respectively. The location of an iron vacancy is indicated by a black “X” mark. Some of the atoms are numbered in the upper part of slab model a: Fe1−4 and O1−9. The structures are presented after fully optimizing the ionic positions with no vacancy or Ti−dopant in order to view a more symmetric arrangement. The figure was created with the VESTA visualization program.51
(five stoichiometric units) slab, (b) a nine atomic-layer slab with one molecular-layer of water, (c) a wide (2 × 2) lateral supercell slab representing a smaller concentration of reactive and defected sites, and (d) 13 atomic-layer slab. The latter slab (d) was not used in ref 31, and we add this thicker slab to increase the distance between near-surface iron vacancies. In comparison to slab (a), which is not completely symmetric, the thicker slab carries the advantage of having inverse symmetry B
dx.doi.org/10.1021/jp5073654 | J. Phys. Chem. C XXXX, XXX, XXX−XXX
The Journal of Physical Chemistry C
Article
with blue in Figure 2b). In the second hydrogen cleavage reaction (reaction C) and the adsorption of the second water molecule along with the third hydrogen cleavage (reaction D), similar to the case when there is no iron vacancy, as a result of hydrogen cleavage the negative charge on the adsorbed oxygen atoms is small, 0.8e and 0.5−0.6e, respectively (green circles shown in Figure 2b). Therefore, the main contribution of an iron vacancy is adding hole charge carriers on oxygen atoms. The appearance of excess holes on oxygen (and electrons on iron when there is no iron vacancy) is consistent with the known electronic structure of Fe2O3,36 with mostly occupied oxygen states at the valence band edge (and unoccupied iron states at the conduction band edge). The mechanism is similar when there is a Ti−dopant in addition to an iron vacancy. Because the Ti−dopant donates an electron, the negative charge on the inner oxygen atoms is slightly higher: 0.7−0.8e (with Ti−dopant) rather than 0.5− 0.6e (without Ti−dopant). Hence, with a Ti−dopant there is still excess hole charge on oxygen atoms. The excess charge has a direct implication on the free energy. As can be seen from Figure 3, the cumulative free energy rises
largest for iron-deficient Fe2O3 due to iron and oxygen vacancy charge compensation). As can be seen in parts a and b of Figure 2, water adsorbs at the oxygen vacancy site (reaction A). Next, a
Figure 2. Water oxidation on Fe2O3(0001) surface with (a) and without (b) an iron vacancy. The case without an iron vacancy was reported in ref 31. The intermediate steps of the reaction are marked by the letters A−E. The reaction repeats itself: the first reaction step happens again after the last reaction step. Green circles show the location of excess electron charge on iron at early reaction steps and excess hole charge on oxygen at later reaction steps. Blue circles show the location of hole charge near an iron vacancy. The black “X” marks the location of the iron vacancy. The structures are presented at fully optimized ionic positions (for the slab model shown in Figure 1a). The figure was created with the VESTA visualization program.51
hydrogen atom is cleaved and we receive a surface terminated with hydroxyl groups (reaction B). Another hydrogen atom cleavage leaves an oxygen atom at the surface edge (reaction C). The third hydrogen atom cleavage together with the entrance of another water molecule forms an oxygen−oxygen bond (reaction D). Finally, a hydrogen atom and an oxygen diatom molecule are released and we receive the original oxygen-deficient site (reaction E). This reaction can be repeated. Overall, the reaction utilizes two water molecules, involves the cleavage of four hydrogen atoms, and produces an oxygen molecule. We now analyze each reaction step in terms of atomic charges. In the beginning of the reaction there is excess electron charge from the donating surface oxygen vacancy. This is apparent from the positive charge on one of the iron atoms, 1.4e, which is lower than the bulk-like charge of 1.8e (the excess electron charge is located on the iron atom circled in green in Figure 2a). In the water adsorption reaction (reaction A) of Figure 2a, the charge on iron remains low when a neutral water molecule adsorbs. In the first hydrogen cleavage reaction (reaction B), as a result of a hydrogen atom leaving, the excess electron vanishes, and all atoms have bulk-like charges (iron atoms have 1.8e and oxygen atoms have −1.2e). In the second hydrogen cleavage reaction (reaction C) and the adsorption of the second water molecule along with the third hydrogen cleavage (reaction D), hydrogen cleavage leaves a hole on the cleaved oxygen atoms: the negative charge on the adsorbed oxygen atoms is 0.9e and 0.6e, respectively for each reaction (oxygen atoms are circled in green in Figure 2a). Hence, in the absence of an iron vacancy there is excess electron charge in the beginning of the reaction and excess hole charge in the f inal reaction steps. In contrast, an iron vacancy gives rise to excess hole charge throughout the reaction (circled in Figure 2b). This is apparent from the negative charge on oxygen, 0.5−0.6e, which is lower than the bulk-like charge of 1.2e (on the oxygen atoms circled
Figure 3. Cumulative free energy at each intermediate reaction step of water oxidation on Fe2O3(0001). The data points for cases without iron vacancies were obtained from ref 31. As indicated above the axis point “O”, this state represents Fe2O3 with an oxygen vacancy at the surface and two water molecules in the liquid state. The results correspond to the slab model in Figure 1a.
earlier when an iron vacancy is present (upper solid line with squares). The rise happens at the first hydrogen cleavage (reaction B), which generates one hole at the surface. This is most unfavorable in an iron-deficient material that already has hole charge (according to the +3 oxidation state of iron in Fe2O3, the absence of iron generates three holes at the surface). Hence, the cumulative free energy at the first hydrogen cleavage reaction (reaction B) is high when there is an iron vacancy. The cumulative free energy at the first hydrogen cleavage reaction (reaction B) gradually decreases when the number of hole carriers is reduced, by adding a Ti−dopant, by removing the iron vacancy, or both (as shown in in Figure 3 and in Table 1, the free energy for this reaction is ΔG(B) = 1.20, 0.72, −0.03, −0.38 eV in each one of these scenarios). This step becomes favorable (ΔG(B) < 0) in the case of no iron vacancy and no dopant: then the product of the first hydrogen cleavage reaction (reaction B), the hydroxylated surface, has no excess charge carriers. C
dx.doi.org/10.1021/jp5073654 | J. Phys. Chem. C XXXX, XXX, XXX−XXX
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preparation, and stoichiometry.11 A well-controlled experiment was therefore suggested in ref 29. Our results are consistent with scaling relations that were found for binding energies of *O, *OH, and *OOH on several transition metal oxides.34,53 The scaling relationship also holds for iron-deficient Fe2O3. All of our new data points on irondeficient Fe2O3 coincide with a single point of pure Fe2O3 in the volcano curve (shown in ref 31). For example, the difference in the binding energies ΔG(*OOH) − ΔG(*OH) is constant, 3.3−3.4 eV, and is close to the reported value of 3.5 eV31 for pure and doped Fe2O3 (ΔG(*O) = 3.15, 2.28 eV, ΔG(*OH) = 1.33, 0.50 eV, and ΔG(*OOH) = 4.60, 3.19 eV for iron-deficient pure Fe2O3 and iron-deficient Ti-doped Fe2O3, respectively). Finally, we note that the effect of an iron vacancy is independent of the size of the slab model (slabs are shown in Figure 1). As can be seen in Table 2, we obtained a large free
Table 1. Free Energies of Water Oxidation on Fe2O3(0001) with or without an Iron Vacancy and a Ti−Dopanta iron vacancy
no iron vacancy
model
no Ti−dopant
Ti−dopant
no Ti−dopant
Ti−dopant
ΔG(A) ΔG(B) ΔG(C) ΔG(D) ΔG(E)
0.13 1.20 1.82 1.45 −0.17
0.03 0.47 1.77 1.64 0.52
0.05 −0.03 1.82 1.69 0.90
−0.08 −0.38 0.23 3.27 1.39
a
The data points for cases without iron vacancies were obtained from ref 31. The results correspond to the slab model in Figure 1a. The energies are given in units of eV.
On the other hand, as a result of accumulating excess hole charge, the final step of oxygen release becomes more favorable (ΔG(E) < 0) when there is an iron vacancy (as shown in Table 1, the free energy for reaction E increases by Ti−doping or without an iron vacancy). Hence, changes in the first hydrogen cleavage reaction (reaction B) and the final step of oxygen release (reaction E) could compensate each other and indeed we see that final cumulative free energy is similar in all cases (in Figure 3, the data points in the final step of oxygen release, reaction E, collide at 4.43 eV). The overpotential, however, is not the same in all cases. The lower limit of the overpotential is frequently approximated as the difference between the highest free energy of an intermediate reaction, denoted ϕrx, and the final cumulative free energy divided by four electron charges that participate in the reaction: 4.43 eV/4 = 1.11 eV, which is close to the known experimental free energy of 1.23 eV required for water splitting (note that if we fitted our results to this experimental value by adjusting rather than calculating the O2 free energy as was done, for example, in ref 33, then ΔG(E) would be larger by 0.5 eV, but ΔG(E) would still be negative (−0.34 eV) at lower concentrations of iron vacancies as we obtained from the wide slab shown in Figure 1c, and the trend of reducing the free energy required for oxygen release and overpotentials upon introducing an iron vacancy would remain). In the case of Tidoping without an iron vacancy, since the product of the second hydrogen cleavage reaction (reaction C) has no excess charge (holes generated from two hydrogen cleavages compensate electrons donated from a surface oxygen vacancy and a Ti− dopant), the next step (reaction D) requires a high free energy of ϕrx = 3.3 eV and therefore the overpotential is 2.2 eV.31 In the case of Ti-doping with an iron vacancy, and in cases without Ti-doping, the highest free energy is ϕrx = 1.8 eV and the overpotential is therefore 0.7 eV (see free energies in Table 1). Hence, considering iron vacancies in the model is important for determining the overpotential in the Ti-doped case. Moreover, this calculation predicts that increasing iron vacancies will not reduce the overpotential of undoped Fe2O3, but will reduce the required overpotential of Ti-doped Fe2O3. In order to validate these predictions, experiments need to test the effect of iron vacancies on the overpotential of water oxidation on Fe2O3. Without iron vacancies, the theoretical value of 0.7 eV31 is in good agreement with experiment (0.5− 0.6 eV).4 Furthermore, a very recent experiment9 on Ti-doped Fe2O3 shows that the overpotential increases upon doping with Ti and this is in agreement with theory.31 However, the experimental overpotential in Ti-doped Fe2O3 is largely dependent on conditions, including film thickness, method of
Table 2. Free Energies of Water Oxidation on Fe2O3(0001) for Different Slab Models with an Iron Vacancya model
with H2O
wide slab
thick slab
ΔG(A) ΔG(B) ΔG(C) ΔG(D) ΔG(E)
−0.31 1.49 1.68 1.70 −0.13
0.25 1.59 1.58 1.86 −0.84
0.17 1.27 1.72 1.61 −0.32
a
The slab models are shown in Figure 1b−d. The energies for the case of Figure 1a are given in the first column of Table 1. The energies are given in units of eV.
energy in the first hydrogen cleavage reaction (reaction B), and a low free energy in the final step of hydrogen release (reaction E), for each one of the slab models. We also note that the U value on titanium does not affect the free energies significantly in nonstoichiometric and Ti-doped Fe2O3: the free energies change by
