On the happiness of ferroelectric surfaces and its role in water dissociation: the example of bismuth ferrite

We investigate, using density functional theory, how the interaction between the ferroelectric polarization and the chemical structure of the (001) surfaces of bismuth ferrite influences the surface properties and reactivity of this material. A precise understanding ofthe surface behavior of ferroelectrics is necessary for their use in surface science applications such as catalysis as well as for their incorporation in microelectronic devices. Using the (001) surface of bismuth ferrite as a model system we show that the most energetically favoured surface geometries are combinations of surface termination and polarization direction that lead to uncharged, stable surfaces. On the unfavorable charged surfaces, we explore the compensation mechanisms of surface charges provided by the introduction of point defects and adsorbates, such as water. Finally, we propose that the special surface properties of bismuth ferrite (001) could be used to produce an effective water splitting cycle through cyclic polarization switching.


8093, Zürich, Switzerland
(Dated: 29 October 2020) We investigate, using density functional theory, how the interaction between the ferroelectric polarization and the chemical structure of the (001) surfaces of bismuth ferrite influences the surface properties and reactivity of this material. A precise understanding of the surface behavior of ferroelectrics is necessary for their use in surface science applications such as catalysis as well as for their incorporation in microelectronic devices. Using the (001) surface of bismuth ferrite as a model system we show that the most energetically favoured surface geometries are combinations of surface termination and polarization direction that lead to uncharged, stable surfaces. On the unfavorable charged surfaces, we explore the compensation mechanisms of surface charges provided by the introduction of point defects and adsorbates, such as water. Finally, we propose that the special surface properties of bismuth ferrite (001) could be used to produce an effective water splitting cycle through cyclic polarization switching. a) Electronic mail: chiara.gattinoni@mat.ethz.ch

I. INTRODUCTION
Transition metal oxides occupy a prominent place in heterogeneous catalysis, and are nowadays the most used industrial catalyst type 1 . A variety of industrially relevant processes, for example water splitting or the degradation of pollutant molecules, however, still lack an efficient catalyst. In the search of novel catalytic materials, the Sabatier principle, which states that effective catalysis occurs when the adsorption between a molecule and a surface is of intermediate strength, is a limiting factor 2 . However, the adsorption strength between a molecule and the surface can be controlled by utilizing oxides with tunable functionalities, such as piezo-and ferroelectricity 3 , and research in this field is flourishing [4][5][6][7] . In particular, there is great potential for the use of ferroelectric thin films 8 or nanoparticles 5,6,9 in electricity generation, water remediation or drug delivery 4,7 .
Ferroelectric materials present a spontaneous switchable bulk polarization, and their surfaces, where reactions occur, are complex. In particular, the ferroelectric polarization results in surface bound charges which need to be compensated in order to avoid a polar discontinuity 10 . Thus, the surface structure of a ferroelectric and, as a consequence, its reactivity are largely determined by the interplay between bound charges and compensation mechanisms 11,12 .
Much progress has been made in our understanding of ferroelectricity at a material's surface.
Indeed, it is now well understood that compensation of the ferroelectric bound charges at a surface occurs preferentially through adsorbates and defect formation rather than by electronic reconstructions [12][13][14][15] . It has also been shown that switching of the surface polarity can be used to promote catalysis for molecular dissociation 3 . The precise structure of the surface has also been shown to influence the strength and direction of the ferroelectric polarization in thin films, and engineering of surface stoichiometry has been used to manipulate the polarization on ferroelectric surfaces 11,16-20 . There are still, however, many open questions regarding the surface science of ferroelectrics 8 .
In particular, how the ionic charge in the layers of ferroelectric perovskites interact with the ferroelectric polarization, and the effect of this interplay on the surface structure, is still poorly understood. Here, we investigate this question in bismuth ferrite (BFO), a material which has a robust ferroelectric polarization at room temperature and, in the (001) direction, neighboring positivelycharged Bi 3+ O 2− and negatively-charged Fe 3+ O 2− 2 layers (see Fig. 1a). It is also an especially promising catalyst for applications in water remediation 9 , water splitting 6,21 and nanoscale drug delivery 5 . In the following, we investigate the stability of the (001) surface of BFO, including the interaction of the polarization with defects and water molecule adsorbates. Our findings allow us to propose a catalytic cycle for efficient water splitting taking advantage of the special properties of BFO (001) surfaces.

II. METHODS
Density functional theory calculations were performed within the periodic supercell approach using the VASP code [22][23][24][25] . The optB86b-vdW functional 26 , a revised version of the van der Waals (vdW) density functional of Dion et al. 27 , was used throughout, as it has been shown to describe well molecular adsorption on transition metal oxides [28][29][30] . Core electrons were replaced by projector augmented wave (PAW) potentials 31 , while the valence states (5e − for Bi, 8e − for Fe and 6e − for O) were expanded in plane waves with a cut-off energy of 500 eV. In all calculations we used slabs with a √ 2a × √ 2a surface area and 4a height (shown in Fig. 1a), where a is the lattice parameter of the pseudocubic unit cell. Using the optB86b-vdW functional the pseudocubic lattice parameter was calculated to be a = 3.95 Å, with the γ angle in the rhombohedral structure being γ= 90.23 • . The difference of the calculated lattice parameters with respect to the experimental structure is below 0.5% 32 . A Monkhorst-Pack k-point grid of (5 × 5 × 1) was used for all calcula- tions. An antiferromagnetic G-type ordering was imposed, which gave a magnetic moment of 4.2 µ B per Fe ion in the bulk. The BFO (001) slabs had a thickness of four cubic unit cells and were separated from their periodic repetitions in the direction perpendicular to the surface by ∼ 20 Å of vacuum. Upon testing we found that this thickness was sufficient to converge the adsorption energies of the water molecules (see Table S1). A dipole correction along the direction perpendicular to the surface was applied, and geometry optimizations were performed with a residual force threshold of 0.01 eV/Å. BFO has a large intrinsic polarization, P, whose experimental value is ∼ 0.9 C/m 2 along the (111) direction 33 ; we calculated P with the formula: where e is the charge of the electron, V the unit cell volume, N the number of atoms in the unit cell and u the atomic displacements from the high symmetry positions. We obtained a value of P=0.86 C/m 2 when using the formal charges for Q and of P=1.19 C/m 2 when using the Born effective charges.
Adsorption energies for the water molecules, E ads , were calculated as: where E BFO , E water and E water/BFO are the total energies of the relaxed bare slab, an isolated gas phase water molecule and a system containing n water molecules adsorbed on the slab, respectively. Negative values of the adsorption energy indicate favorable (exothermic) adsorption. Water coverages varying between 1/2 and 1 monolayer (ML) -where 1 monolayer is one water molecule per surface metal atom -were considered.
To calculate the charge density differences of Fig. 4 we first obtained the real-space charge for the slab/water system (ρ all ) and for the isolated slab (ρ slab ) and water molecules (ρ water ). The difference was then obtained as:

III. RESULTS AND DISCUSSION
BFO (001) has interesting surface properties when we consider the interplay between layer charge and ferroelectric polarization, and they are schematically shown in Fig  in BiO surfaces with the polarization pointing away from them (we will refer to these surfaces as BiO neutral ) and FeO 2 surfaces with the polarization pointing towards them (FeO neutral 2 ). The highly uncompensated surfaces, shown in Fig. 1c, are, instead, the BiO (FeO 2 ) surfaces with the polarization pointing towards (away from) them and we will refer to these surfaces as BiO pos and FeO neg 2 .
In this work we study the two stoichiometric (001) systems shown in Fig. 1b and c. In panel b there is a fully compensated BFO (001) slab which we we will refer to as the "happy" system, since the full surface charge compensation means that there is no polar discontinuity at the surface and the polarization is stable. The uncompensated slab of panel c will be referred to as the "unhappy" system, because the non-zero surface charge density results in an unphysical polar discontinuity, and the surface charge needs to be compensated to render the surface stable 10 .
In the following we explore ways to stabilize the polarization in the unhappy system both with defect engineering and molecular adsorption. In particular, we investigate how the different surface electronic properties of the two slabs-their "happiness", if you will-affect the geometry and adsorption strength of water. We show that the resulting polarization-dependent dissociation behavior has great potential for catalytic applications.
A. Achieving surface stability through point defect engineering It is known that point defects and adsorbates can provide charge compensation to ferroelectric surfaces 3,11,12 . As already remarked, the self-compensating surfaces of the happy system have no polar discontinuity and do not require any further compensation. Indeed, our calculated unit cell by unit cell polarization plotted in Fig. 2a shows that the ferroelectric polarization is stable throughout the slab thickness. Upon geometry relaxation, the unhappy slab also relaxes into the structure of Fig. 2a, meaning that in order to avoid the polar discontinuity at the surface, the polarization direction reverses, resulting in a happy system. This indicates that the polarization direction in the unhappy system cannot exist without a means to compensate the surface charges.
To stabilize  We also investigated partial compensation of the slab, by including point defects on only one surface, rather than both. This allows us to understand whether compensation from one surface only is sufficient to ensure stable polarization throughout the slab thickness, and also to separately Charge compensation in the bulk forces a metallic layer at the site of the polar discontinuity, which requires band bending. The energy cost of the band bending is however offset by the favorable -happy -surface configuration. However, also the local surface chemistry drives this surface structure. On BiO pos the cation has a lone pair of electrons which orients towards the vacuum, pushing the ion towards the subsurface (here, FeO 2 ) layer and creating a ferroelectric polarization pointing away from the surface, and, as a consequence a BiO neutral surface. A similar behavior is observed for the PbO surface of lead titanate 11 which also has a lone pair of electrons. On FeO neg 2 the bond labelled b in Fig. 2c is shorter than in the bulk, as it is generally the case for atomic bonds between the two topmost layers of a slab 37 . This shorter bond b forces the Bi lone pair downwards and the ion upwards, thus imposing a polarization which points towards the surface, which persists, to a lesser degree, in the unit cell below. Note that in the previous example of lead titanate, no polarization inversion is observed for the TiO 2 termination with the polarization pointing away from it 11 . The difference in behavior between these two ferroelectric perovskites is probably due to the higher relative polarizability of Ti 4+ compared to Fe 3+ .
Having shown how intrinsic point defects can stabilize the ferroelectric polarization in the unhappy systems, we now investigate how stability can be obtained through adsorbates, by examining the behavior of water on BFO (001).

B. Achieving stability through adsorbates: the example of water
As well as intrinsic surface defects, adsorbates can play an important role in shaping the surface structure of a ferroelectric 12 . The interaction of a surface with water is especially important because of water's ubiquity in air and in solutions, and also because of the potential for applications which arise from the interaction between water and functional materials. In the following, we analyse the behavior of water adsorbed on the surfaces of the systems in Fig. 1b and c, and reveal how water can stabilize the unhappy system and, in turn, how surface charges affects the water adsorption energy and propensity for dissociation.

Water adsorption on a happy surface
We identified the most stable sites for water adsorption on the surfaces of the happy system, and they are shown in Fig. 3 Fig. 3a). For the BiO neutral termination, the water O atom sits at the bridging site between two Bi atoms, aligned perpendicularly to the surface. This configuration permits only one hydrogen bond of length 1.54 Å (Fig. 3b). Indeed, charge density difference calculations, presented in Fig. 4b, show that minimal charge transfer between the water O and the Bi surface atom occurs. The water-surface binding is stronger on the FeO neutral 2 termination than on the BiO neutral by ∼ 0.13 eV, since in the former molecular adsorption is established by a strong ionic bond and a hydrogen bond (Fig. 4a).
For a dissociated water molecule, the favored binding sites for the hydroxyl groups are a surface Fe for the FeO neutral 2 termination (see Fig. 3c) and the Bi-Bi bridging site for the BiO neutral termination (see Fig. 3d), similar configurations to the molecularly adsorbed water. Also, the rotation of the hydroxyl with respect to the surface is similar to that of the intact water molecule: to an O surf (Fig. 3c-d).
The adsorption energies in Fig. 3 and Table I  It is worth noting that in all systems the polarization throughout the film is bulk-like and minimally affected by the adsorption of either molecular or dissociated H 2 O.

Water adsorption on an unhappy surface
We next turn our attention to the adsorption of water on the unhappy slab with FeO neg 2 and BiO pos surfaces, and we find that on this system dissociative water adsorption is favored.
Since the unhappy slab is unstable, calculations of the BFO/water system in this section are performed with a "frozen" BFO slab: we kept the ionic positions of the inner layers of the slab fixed at the bulk values and allowed only the adsorbed molecules and topmost surface layer, where adsorption occurs, to relax. The "frozen" layers are shown in blue shading in Fig. 5a. We refer to the adsorption energies with respect to this "frozen" substrate as E frozen ads . We simulated molecularly and dissociatively adsorbed water on the FeO neg 2 and BiO pos surfaces, and we observed similar adsorption geometries as on the happy slab, both in the preferred adsorption sites and bond lengths (the structures are shown in Fig. S1). Indeed, on FeO neg 2 the water molecule and the hydroxyl adsorb parallel to the surface; on BiO pos they adsorb perpendicularly to the surface in the Bi-Bi bridge site. However, the energy trends are significantly different from the happy case, and dissociative adsorption is favorable on these uncompensated surface terminations. Indeed, the values in Table I show that dissociative adosrption is favoured by 290 meV on the FeO The molecular adsorption of water on an unhappy slab does not provide adequate charge transfer to stabilize the unfavorable polarization direction, and neither does the co-adsorption of hydroxyl and H on the same surface. Indeed, for these structures, when we allow the ions in the "frozen" slab to relax into their energetically favorable position, we obtain a happy system. However, stabilization of the polarization in the unhappy system can be achieved when 1 ML of OH − is adsorbed on the positively charged BiO pos termination and 1 ML of H + on the negatively charged FeO neg 2 termination, thus fully compensating the surface charges of ±1 C/m 2 . The adsorption structure is, as expected, at a Bi-Bi bridge site for the hydroxyl groups and atop an O surf atom for the H atoms. We will refer to this configuration as the "stabilized system" and it is shown in Fig. 5b.
The stabilized system is the most stable among the computed water structures on unhappy BFO. Indeed, the adsorption energy of dissociated water in the stabilized system, with respect to the frozen substrate is E frozen ads = −3.16 eV/mol, much larger than the values (reported in Table I) for the structures examined in Fig. 5a.
Since the unhappy ferroelectric polarization (from FeO 2 to BiO) in the stabilized system in Fig. 5b is now fully compensated, we can relax the ionic positions of the whole slab. We obtain an adsorption energy for the fully relaxed stabilized system (with respect to relaxed happy slab) of E ads = −0.47 eV/mol. In comparison, water adsorbed on the happy system leads to a more negative (by 0.2 eV/mol) adsorption energy, see Table I, and thus to a more energetically favorable structure. This comparison tells us that the system in Fig. 5b, despite being stable, will not occur spontaneously, but will be reached by switching the polarization with an external electric field.

C. Discussion
The results presented in this work show the complex coupling between the surface chemistry  We believe that this polarization dependence of water dissociation in bismuth ferrite could have interesting ramifications for catalysis. We propose that the opposite affinity towards water dissociation of the happy and unhappy systems could also be utilized for the creation of a water splitting catalytic cycle, by exploiting the ferro-and piezoelectric properties of BFO as illustrated in Fig which can then by used directly in, e.g. the degradation of pollutants 9 , or for H 2 production together with a metal cathode. Polarization switching in nanoscale BFO can be obtained not only with an electric field, but also through mechanical strain 44 . It could thus be economically achieved with, for example, sound waves 9 . We hope that this thought experiment can pave the way for the creation of an effective BFO-based water splitting device.

DATA AVAILABILITY
The data that supports the findings of this study are available within the article and its supplementary material.

I. CONVERGENCE TEST FOR SLAB THICKNESS
Calculations with the most favorable adsorption sites are carried out for the slab thicknesses of 2-6 unit cells (u.c.) for a water molecule on the charge-compensated slab of Fig. 1b. All atoms were allowed to relax. On the BiO surface the adsorption energy is converged for 4 u.c. On the FeO 2 surface, the absolute values of the adsorption energies are still varying for a slab thickness of 6 u.c., however relative energies between the intact and dissociated structure are already converged at 4 u.c.

II. WATER ON "UNHAPPY" SLAB
Structure of a single water molecule adsorbed on an "unhappy" frozen substrate, Fig. 1.