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

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.^4–7 In particular, there is great potential for the use of ferroelectric thin films⁸ 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.^12–15 It has also been shown that switching of the surface polarity can be used to promote catalysis for molecular dissociation.^3,47,48 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 interacts 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 that has a robust ferroelectric polarization at room temperature and, in the (001) direction, neighboring positively charged Bi³⁺O²⁻ and negatively charged $Fe3+O22−$ layers [see Fig. 1(a)]. 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.

Density functional theory calculations were performed within the periodic supercell approach using the VASP code.^22–25 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.^28–30 The strong Coulomb interaction between the localized d orbitals of Fe atoms was taken into account by adding a Hubbard U term in the Dudarev approach³¹ with a U–J = 4 eV. Core electrons were replaced by projector augmented wave (PAW) potentials,³² 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. We used a unit with a $2a×2a$ surface area and 2a height [shown in Fig. 1(a)], 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 in the calculated lattice parameters with respect to the experimental structure is below 0.5%.³³ A Monkhorst–Pack k-point grid of (5 × 5 × 1) was used for all calculations. 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/m² along the (111) direction;³⁴ we calculated P with the formula

where e is the charge of the electron, V is the unit cell volume, N is the number of atoms in the unit cell, u is the atomic displacements from the high symmetry positions, and Q are the Born effective charges. For the bulk structure, we obtained a value of P = 0.94 C/m² along the [111] direction, which leads to a polarization (thus a surface charge) of 0.44 C/m² along the [001] direction. The Born effective charge tensor was computed by adding an electric field of 0.01 eV/Å along the three cartesian directions shown in Fig. 1(a) and by determining the resulting change in the Hellmann–Feynman forces.³⁵ 

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

BFO (001) has interesting surface properties when we consider the interplay between layer charge and ferroelectric polarization, and they are schematically shown in Fig. 1. The formal charges of Bi³⁺, Fe³⁺, and O²⁻ result, in the (001) direction, in alternating positively charged BiO (+1 C/m²) and negatively charged FeO₂ (−1 C/m²) layers [see Fig. 1(a)]. Note that the use of the formal charges, rather than Born effective charges, to look at this polarization arising from the paraelectric lattice is formally correct.^10,36 This surface charge requires a compensating charge of opposite sign and half the magnitude^10,37 (∼±0.5 C/m², negative for BiO and positive for FeO₂) to obtain surface stability. Remarkably (also coincidentally), the (001) component of the ferroelectric polarization in BiFeO₃ has the value P ∼ ±0.5 C/m² (resulting in the surface charge density of ∼±0.5 C/m²), positive when the polarization is directed toward the surface and negative when away from the surface. Thus, the interplay of these two contributions of equal magnitude can result in either fully self-compensating surfaces with a total surface charge density σ = 0 C/m² in which the surface polarization compensates the layer charge or highly uncompensated surfaces in which both the layer charge and the surface polarization contribute to a non-zero surface charge. The self-compensating case, shown in Fig. 1(b), occurs in BiO surfaces with the polarization pointing away from them (we will refer to these surfaces as BiO^neutral) and FeO₂ surfaces with the polarization pointing toward them (Fe$O2neutral$⁠). The highly uncompensated surfaces, shown in Fig. 1(c), are, instead, the BiO (FeO₂) surfaces with the polarization pointing toward (away from) them and we will refer to these surfaces as BiO^pos and Fe$O2neg$⁠.

In this work, we study the two stoichiometric (001) systems shown in Figs. 1(b) and 1(c). In panel (b), there is a fully compensated BFO (001) slab that 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 with both 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.

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. 2(a) shows that the ferroelectric polarization is stable throughout the slab thickness. Upon geometry relaxation, the unhappy slab also relaxes into the structure of Fig. 2(a), 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 the unhappy system, we consider Bi and O adatoms and vacancies: the positively charged Bi adatom and O vacancy compensate the negatively charged Fe$O2neg$ surface, and the negatively charged Bi vacancy and O adatom compensate the positive BiO^pos surface. Bi defects, rather than Fe ones, are considered here as they are seen to occur more often in experiments.³⁸ 

Figure 2(b) shows the geometry-optimized structure and the unit cell by unit cell polarization in the unhappy slabs compensated with point defects at both surfaces. We note that, indeed, compensation of the surface charges by vacancies and adatoms is effective in stabilizing the downward-pointing polarization direction in the unhappy slab. We also observe surface enhancements of the polarization above the bulk value of 0.9 C/m², especially at the surfaces where O and Bi adatoms are present, which are driven by the surface chemistry. In particular, the bonding between a surface Bi and the O adatom [top of Fig. 2(b)] pulls the Bi atom away from the surface, enhancing the polarization at the BiO surface of the slab.

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 investigate the BiO^pos and Fe$O2neg$ surfaces. The results are shown in Fig. 2(c).

On the non-compensated side of the slab, polarization reversal occurs, confirming that compensation on both surfaces is needed to obtain a robust polarization throughout the thickness. In the uncompensated BiO^pos termination [top of Fig. 2(c)], polarization reversal occurs only in the outermost BiO surface layer (shown in purple), the polarization pointing away from the BiO surface. For an uncompensated Fe$O2neg$ surface [bottom of Fig. 2(c)], the polarization reversal (purple shading) involves the topmost two unit cells and the polarization points toward the surface. Thus, both uncompensated surfaces become happy by this reversal of the polarization. The problem of charge compensation now occurs within the slab, where the positive [in the top of Fig. 2(c)] and the negative [in the bottom of Fig. 2(c)] ends of the polarization meet, creating a polar discontinuity. 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 orient toward the vacuum, pushing the ion toward the subsurface (here, FeO₂) 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 Fe$O2neg$⁠, the bond labeled b in Fig. 2(c) is shorter than that in the bulk, as it is generally the case for atomic bonds between the two topmost layers of a slab.³⁹ This shorter bond b forces the Bi lone pair downward and the ion upward, thus imposing a polarization that points toward 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 TiO₂ 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 Ti⁴⁺ compared to Fe³⁺.

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).

With 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 analyze the behavior of water adsorbed on the surfaces of the systems in Figs. 1(b) and 1(c) and reveal how water can stabilize the unhappy system and, in turn, how surface charges affect the water adsorption energy and propensity for dissociation.

We identified the most stable sites for water adsorption on the surfaces of the happy system, and they are shown in Fig. 3. On Fe$O2neutral$⁠, the most favorable configuration for molecular H₂O adsorption is parallel to the surface with the formation of a 2.17 Å Fe–O bond and a 1.93 Å H–O_surf (O_surf is a surface oxygen) bond [see Fig. 3(a)]. 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. 3(b)]. Indeed, charge density difference calculations, presented in Fig. 4(b), show that minimal charge transfer between the water O and the Bi surface atom occurs. The water-surface binding is stronger on the Fe$O2neutral$ termination than on the BiO^neutral by 130 meV, since in the former, molecular adsorption is established by a strong ionic bond and a hydrogen bond [Fig. 4(a)].

For a dissociated water molecule, the favored binding sites for the hydroxyl groups are a surface Fe for the Fe$O2neutral$ termination [see Fig. 3(c)] and the Bi–Bi bridging site for the BiO^neutral termination [see Fig. 3(d)], which are 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: parallel to the surface on Fe$O2neutral$ and perpendicular on BiO^neutral. In both cases, the H ion binds to an O_surf [Figs. 3(c) and 3(d)].

The adsorption energies in Fig. 3 and Table I show that dissociation of the water molecule is disfavored on both compensated terminations of a happy BFO (001) slab by ∼30 meV for BiO^neutral and ∼350 meV for Fe$O2neutral$⁠.

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 H₂O.

We next turn our attention to the adsorption of water on the unhappy slab with Fe$O2neg$ 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 in Fig. 5(a). We refer to the adsorption energies with respect to this “frozen” substrate as $Eadsfrozen$⁠.

We simulated molecularly and dissociatively adsorbed water on the Fe$O2neg$ and BiO^pos surfaces, and we observed similar adsorption geometries as on the happy slab in both the preferred adsorption sites and bond lengths (the structures are shown in Fig. S1). Indeed, on Fe$O2neg$⁠, 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 favored by 290 meV on the Fe$O2neg$ surface and by 160 meV on BiO^pos.

It is worth noting that, despite the similarities in the adsorption geometries, there are significant differences between the electronic structures of the happy and unhappy systems, as highlighted in the local density of state (lDOS) of the surface layers and adsorbates in Fig. 5(a). In the happy system (left), the lDOS of both Fe$O2neutral$ and BiO^neutral surface layers presents an insulating behavior with a ∼2 eV-wide bandgap around the Fermi level, as in bulk BFO. The conduction and valence band edges on both Fe$O2neutral$ and BiO^neutral are at the same energy, showing that the ferroelectric polarization is well screened and no band bending occurs through the slab. Conversely, the Fe$O2neg$ and BiO^pos surfaces in the unhappy system [right of Fig. 5(a)] are metallic, since the large surface charge of ±1 C/m² is compensated by electrons (BiO^pos) and holes (Fe$O2neg$⁠).¹⁰ 

When water is molecularly adsorbed on happy and unhappy surfaces alike [dashed lines in the graphs in Fig. 5(a)], the lDOS of the water molecules and the surface overlap away from the Fermi level and the position of the band edges have only a small effect on the water/surface interaction. This can explain the similar adsorption energies for intact water on the happy and unhappy system (see Table I). The increased stability in the adsorption energy of dissociated water on the unhappy system can instead be related to a partial compensation of the surface charge by the OH⁻ (on BiO^pos) and H⁺ (on Fe$O2neg$⁠), which results in the change in the lDOS at the Fermi level for the unhappy surfaces (especially on Fe$O2neg$⁠).

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 Fe$O2neg$ termination, thus fully compensating the surface charges of ±1 C/m². 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 to this configuration as the “stabilized system” and it is shown in Fig. 5(b).

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 $Eadsfrozen=−3.16$ eV/mol, much larger than the values (reported in Table I) for the structures examined in Fig. 5(a).

Since the unhappy ferroelectric polarization (from FeO₂ to BiO) in the stabilized system in Fig. 5(b) 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. 5(b), despite being stable, will not occur spontaneously but will be reached by switching the polarization with an external electric field.

The results presented in this work show the complex coupling between the surface chemistry and the ferroelectric polarization at the (001) surfaces of BFO. The BiO^neutral and Fe$O2neutral$ terminations of BFO (001) surfaces are charge neutral, thanks to the interaction between the layer charge and ferroelectric bound charges. Upon reversal of the polarization, both surface terminations BiO^pos and Fe$O2neg$ present a large surface charge that can be effectively compensated by point defects or by dissociated water molecules. Upon growth of ferroelectric films and nanocrystals, it is very difficult to obtain defect-free surfaces, and these results point to which defects are likely to occur. Moreover, the surface defect engineering could be important during thin-film growth of unhappy ferroelectric surfaces, where defect formation could be engineered to stabilize or even enhance the surface polarization.^11,40

Now, we focus on water adsorption and dissociation. Our calculations reveal that the adsorption mode of water on stoichiometric BFO (001) is highly dependent on the combination of the polarization direction and surface termination. Indeed, we find that compensated surfaces favor the molecular adsorption of water, and uncompensated ones favor dissociative adsorption. The obtained adsorption structures are in good agreement with the previous theoretical work on (001) perovskites, such as strontium ruthenate,⁴¹ barium hafnate,⁴² barium zirconate,⁴² strontium titanate,⁴³ and strontium zirconate.⁴⁴ All these materials are non-ferroelectric and have charge-neutral surfaces; therefore, despite a similar adsorption structure, we do not necessarily expect the same behavior and the same energy ordering between the intact and dissociated structures. Indeed, the literature (summarized in Table II in the supplementary material) shows that water can show a range of different adsorption behavior on the surfaces of these complex materials. Together with the surface structure, the interplay of many other factors including neutrality of the crystal ionic layers, lattice parameters,⁴⁵ and dielectric/metallic characteristics of the materials should be considered to understand the interface chemistry and structure stability.

We believe that this polarization dependence of water dissociation in bismuth ferrite could have interesting ramifications for catalysis. We propose that the opposite affinity toward 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. 6. The cycle starts with a happy BFO (001) slab, which favors molecularly adsorbed water on both BiO^neutral and Fe$O2neutral$ terminations (Fig. 6, panel 1). Upon switching of the polarization, we obtain an unhappy slab with charged surfaces. The resulting system favors dissociation of the adsorbed water molecules on BiO^pos and Fe$O2neg$ surfaces (see panel 2 of Fig. 6). Our calculations then indicate that selective desorption of the H⁺ ion from the BiO^pos termination and OH⁻ group from the Fe$O2neg$ termination is favorable as it stabilizes the polarization by compensating the surface charges (see panel 3 of Fig. 6). By further switching of the polarization back into its initial happy direction, competitive adsorption would favor the further removal of dissociation products and the adsorption of molecular H₂O (see panel 4 of Fig. 6). Thus, in principle, cyclical switching of the polarization in a BFO (001) slab immersed in water could efficiently produce H and OH species, which can then be used directly in the degradation of pollutants⁹ or for H₂ 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.⁴⁶ It could thus be economically achieved with sound waves.⁹ Pyroelectricity is another way of modulating the surface charge by cyclically changing the temperature above and below the Curie temperature. In bismuth ferrite, this is a rather impractical method to provide dynamic catalysis, since the Curie temperature is around 1100 K. Regardless, the cycle would look similar to that in Fig. 6, the only difference being that the unhappy system would only need half the charge to compensate the polar discontinuity, as the only source of surface charge in the paraelectric case comes from the charged layers. We hope that this thought experiment can pave the way for the creation of an effective BFO-based water splitting device.

See the supplementary material for convergence tests and additional images of the water/BFO structures and all the coordinates of the relevant structures.

C.G. was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 744027. N.A.S. acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 810451). I.E. acknowledges the use of the Euler cluster managed by the HPC team at ETH Zurich. The work of C.G. was supported by a grant from the Swiss National Supercomputing Centre (CSCS) under Project No. s889.

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