Thermo-chemical environment-dependent vacancy formation in Fe₂WO₆: A DFT study

Abstract

Fe₂WO₆, known for its potential in photocatalytic and electrocatalytic applications due to its chemical stability and band structure, can exhibit various defects that influence its performance. Density functional theory (DFT) calculations were employed to determine the formation energies of iron, tungsten, and oxygen vacancies under different thermo-chemical environments within the Fe-W-O ternary system. The study reveals that oxygen vacancies are more likely to form in reducing environments rich in FeO and Fe₃O₄ and it can offer practicality through facilitating the formation of reactive oxygen species (ROS), which contribute to photocatalytic performance. Meanwhile, the formation of iron vacancies is more readily achieved in oxygen-rich conditions, particularly when Fe-W-O compounds can be constructed. Similarly, tungsten vacancies form more often in oxygen-rich environments but less in iron oxide-rich conditions. In conclusion, this study provides a more comprehensive understanding of the nature of vacancy defects in Fe₂WO₆ and elucidates the environmental conditions that can be exploited to maximize or minimize vacancy formation for the control of catalytic activity.

Graphical abstract

Highlights

• •Fe₂WO₆ is notable for photocatalytic and electrocatalytic applications due to its chemical stability and band structure.
• •Formation energies of iron, tungsten, and oxygen vacancies in different thermochemical environments were calculated.
• •Oxygen vacancies readily form in reducing FeO and Fe₃O₄, aiding reactive oxygen species generation for improved photocatalysis.
• •Iron and tungsten vacancies tend to form more frequently in oxygen-rich environments.
• •This study gives a detailed understanding of vacancy in Fe₂WO₆ and identifies environmental conditions to catalytic activity.

1. Introduction

Fe₂WO₆, or iron tungstate, as a member of the transition metal tungstate group, is widely recognized as a potential electrode in photo-catalytic processes due to its chemical stability and band structure [[1], [2], [3]]. At its tri-α-PbO₂ form, in which the FeO₆ and WO₆ octahedra intercept each other in a regular manner, iron tungstate's redox couples, including Fe^3+/2+, W^6+/5+, and W^5+/4+, provide the materials' characteristics pertaining to its photo-catalytic potential [1]. Considered both as a p-type and n-type semiconductor, Fe₂WO₆ reportedly possesses a band energy gap of 1.68 eV. For applications pertaining to photo-catalytic water splitting employing solar energy, this value falls near the lower end of the band gap range between 1.23 eV and 3.0 eV within which enough energy is provided for electrons and sufficient solar absorption occurs, approximately creating a solar-to-hydrogen (STH) efficiency of greater than 20 % [[2], [3], [4], [5], [6]].

Beyond photo-catalytic applications, Fe₂WO₆ is regarded as an effective electro-catalyst; Schuler et al. reported that iron tungstate retains its stability due to its low thermal conductivity at greater temperatures and oxidizing environments [3]. Such capabilities were experimentally displayed through the substance's proficiency as an anode in lithium batteries, with an exceptional volumetric specific capacity high due to the greater compact density with tungsten [7].

Almost every solid, including Fe₂WO₆, appears in nature or in synthetic process possessing potential defects under various circumstances. In Fe₂WO₆, various type of defects affect photo- and electro-catalytic performance and among such defects, point defects affect the movements of the surrounding electrons [8]. It is important to understand the basic properties of these defects to improve photo- and electro-catalytic performance. Formation energy is one of the basic properties of the defects so in this study we calculated formation energy of the point defects, particularly vacancy.

To precisely determine the formation energies, external environment which interacts with the host material should be considered along with structural characteristics. In this study, we employed density functional theory (DFT) to calculate formation energy of the iron, tungsten, and oxygen vacancy of the Fe₂WO₆ at the various thermo-chemical environments of the Fe-W-O ternary system. Adding to the previous investigations of the photo- and electro-catalytic applications of Fe₂WO₆, this study provides basic understanding on the formation energies for each vacancy and the environments at which the vacancies can be tuned to maximize photo- and electro-catalytic performance.

1.1. Computational method

To calculate DFT formation energies of each vacancy with respect to various external conditions, this study employed the Vienna ab initio simulation package (VASP) code [9]. The projector-augmented wave (PAW) method [10] with Perdew-Bruke-Ernzerhof (PBE) functional [11] was used for all calculations. An energy cutoff for the plane wave was 800 eV for lattice parameter optimization and 400 eV for ionic relaxations. The Brillouin zone integration using a 4 × 1 × 4 Monkhorst-Pack scheme [12] was carried out for primitive Fe₂WO₆ (Pbcn), and appropriate k-point densities were used for supercell structures and several Fe-W-O ternary system compounds to ensure the same level of accuracy.

The convergence of formation energy with supercell size is an important factor in the reliability of the results. Due to the limitation of computational cost, convergence tests up to 3 × 1 × 3 size only for the oxygen vacancy were performed, depicting that the calculated formation energy of the 2 × 1 × 2 supercell possessed approximately a 0.1 % error with that of the 3 × 1 × 3 supercell (Fig. S1). Therefore, the supercell of 2 × 1 × 2 size was chosen. Vacancies in orthorhombic Fe₂WO₆ can exist in six unique crystallographic positions: two iron vacancies, one tungsten vacancy, and three oxygen vacancies, respectively labelled Fe1, Fe2, W, O1, O2, and O3. Ionic relaxation was performed after removing the atom corresponding to each vacancy from the 2 × 1 × 2 pristine supercell.

DFT calculations were also performed for compounds in the Fe-W-O ternary system, including Fe (bcc), W (bcc), FeO ($Fm\overline{3}m$), Fe₂O₃ ($R\overline{3}c$), Fe₃O₄ ($Fd\overline{3}m$), WO₂ (P2₁/c), WO₃ (P2₁/n), and molecular O₂ to determine the chemical potentials of Fe, W, and O in various environments [[13], [14], [15], [16]]. The structural parameters are in good agreement with the experimental values (Table S1). The chemical potential of each compound is determined by the DFT total energy of corresponding compound per formula unit.

2. Results and discussion

As illustrated in Fig. 1(a), the primitive cell of Fe₂WO₆ is comprised of the metal atoms surrounded by six oxygen atoms in an octahedral configuration. The observed symmetry is reminiscent of the corner-sharing AB₆ octahedra that are characteristic of perovskite structures [17]. In contrast to the conventional perovskite structure, which is composed of octahedrons sharing the oxygen vertices, Fe₂WO₆ is constituted by an arrangement of tilted octahedrons that not only share the oxygen vertices but also the edges of the octahedron. Fig. 1(b) illustrates the alternating layers of oxygen and the metals. The latter form in pairs of proximity, either of a tungsten atom and an iron atom or two iron atoms. In Fig. 1(c), which is showing bc-plane, hexagonal patterns of Fe₂WO₆ are observed surrounding a central oxygen atom. The vertices of this pattern are formed by two iron atoms, one tungsten atom, and three pairs of oxygen. In Fig. 1(d), the same as in Fig. 1(b), the metal layer and oxygen layer alternate.

Fig. 1.

Atomic model for the primitive cell of the orthorhombic Fe₂WO₆. (a) Perspective view of the unit cell and it shows octahedrons centered on Fe and W. (b–d) Views of ab-, bc-, and ca-planes, respectively.

The formation energy of vacancies $E_{\mathrm{f}}$ in Fe₂WO₆ with these structural characteristics can be calculated in different thermo-chemical environments using the following equation.

$$E_{\mathrm{f}}=E_{\text{Vac}}-E_{\text{Pri}}+\mu$$ (1)

where $E_{\text{Vac}}$ and $E_{\text{Pri}}$ are respectively the total energies of the supercell with the vacancy and the pristine supercell, and μ is the chemical potential of the removed element in the formation of the vacancy [18].

$$2{\mu }_{\text{Fe}}+{\mu }_{\mathrm{W}}+6{\mu }_{\mathrm{O}}={\mu }_{{\text{Fe}}_2\mathrm{W}{\mathrm{O}}_6(\text{bulk})}$$ (2)

The chemical potential of Fe, W, and O can be determined based on the various equilibrium conditions of the ternary system Fe-W-O. Assuming that Fe₂WO₆ is always stable, Eq. (2) is valid for any circumstance, and the chemical potentials of the Fe, W, and O can be determined from the chemical potential of the bulk Fe₂WO₆ and the relations between each of them. As shown in the schematic phase diagram for the Fe-W-O ternary system (Fig. 2), there are eight possible environments from point A to H for the vacancy formation in Fe₂WO₆, and in each case, the two neighboring compounds have dominant influence on vacancy formation. For example, at the point A, bulk FeO and molecular O₂ create an environment in which a vacancy is formed, and the chemical potential of Fe, W, and O are determined by Eq. (2) and the equation below,

$$\text{Point}A:{\mu }_{\text{Fe}}+{\mu }_{\mathrm{O}}={\mu }_{\text{FeO}(\text{bulk})}{\mu }_{\mathrm{O}}={\frac{1}{2}\mu }_{{\mathrm{O}}_2}$$ (3)

Fig. 2.

Schematic ternary phase diagram of the Fe-W-O system, with various chemical environments labelled (A–H).

Similarly, for the points B to H, the chemical potentials of Fe, W, and O can be calculated using Eq. (2) and the equations for each case below together.

$$\text{Point}B:{\mu }_{\mathrm{W}}+3{\mu }_{\mathrm{O}}={\mu }_{\mathrm{W}{\mathrm{O}}_3(\text{bulk})}{\mu }_{\mathrm{O}}={\frac{1}{2}\mu }_{{\mathrm{O}}_2}$$ (4)

$$\text{Point}C:{\mu }_{\mathrm{W}}+3{\mu }_{\mathrm{O}}={\mu }_{\mathrm{W}{\mathrm{O}}_3(\text{bulk})}{\mu }_{\mathrm{W}}+2{\mu }_{\mathrm{O}}={\mu }_{\mathrm{W}{\mathrm{O}}_2(\text{bulk})}$$ (5)

$$\text{Point}D:{\mu }_{\mathrm{W}}={\mu }_{\mathrm{W}(\text{bulk})}{\mu }_{\mathrm{W}}+2{\mu }_{\mathrm{O}}={\mu }_{\mathrm{W}{\mathrm{O}}_2(\text{bulk})}$$ (6)

$$\text{Point}E:{\mu }_{\mathrm{W}}={\mu }_{\mathrm{W}(\text{bulk})}{\mu }_{\text{Fe}}={\mu }_{\text{Fe}(\text{bulk})}$$ (7)

$$\text{Point}F:{2\mu }_{\text{Fe}}+{3\mu }_{\mathrm{O}}={\mu }_{{\text{Fe}}_2{\mathrm{O}}_3(\text{bulk})}{\mu }_{\text{Fe}}={\mu }_{\text{Fe}(\text{bulk})}$$ (8)

$$\text{Point}G:{2\mu }_{\text{Fe}}+{3\mu }_{\mathrm{O}}={\mu }_{{\text{Fe}}_2{\mathrm{O}}_3(\text{bulk})}3{\mu }_{\text{Fe}}+{4\mu }_{\mathrm{O}}={\mu }_{{\text{Fe}}_3{\mathrm{O}}_4(\text{bulk})}$$ (9)

$$\text{Point}H:{\mu }_{\text{Fe}}+{\mu }_{\mathrm{O}}={\mu }_{\text{FeO}(\text{bulk})}3{\mu }_{\text{Fe}}+{4\mu }_{\mathrm{O}}={\mu }_{{\text{Fe}}_3{\mathrm{O}}_4(\text{bulk})}$$ (10)

For all environments (A–H), the calculated chemical potentials of Fe, W, and O are summarized in Table 1. For each point (A–H), the formation energy of the various vacancies can be obtained by substituting the value of the corresponding chemical potential into Eq. (1), and the results are summarized in Fig. 3.

Table 1.

Calculated chemical potentials of Fe, W, and O at eight thermo-chemistry environments (A–H).

Thermo-chemistry Environment	Chemical potential (eV)
	μFe	μW	μO
A	−9.37	−27.84	−4.37
B	−11.66	−23.26	−4.37
C	−6.68	−13.30	−7.69
D	−6.40	−13.02	−7.83
E	−7.76	−13.02	−7.38
F	−7.76	−14.46	−7.14
G	−6.41	−11.76	−8.03
H	−3.58	−4.70	−10.15

Fig. 3.

Calculated formation energies of (a) oxygen, (b) iron, and (c) tungsten under the eight thermo-chemistry environments (A–H) within the Fe-W-O ternary system.

From the results in Fig. 3(a), crystal structures with an oxygen vacancy possessed a range of formation energies of −2.17–3.79 eV. At points A and B, both O-rich with a metal oxide, the formation energies of the oxygen vacancies fell in a range of 3.62–3.79 eV, indicating that they were the least likely to form. It can be reasonably assumed that such difficulties are consequences of the saturation of oxygen in the chemical environment. The high oxygen pressure causes the formal oxidation state to stabilize, shortening the length of the bond between the oxygen atom and the transition metal. This, in turn, strengthens their attraction and limits oxygen atoms from escaping the lattice [19]. On the other hand, at point H, which consists of the two kinds of iron oxide FeO and Fe₃O₄, oxygen atoms produced the lowest oxygen vacancy formation energy of −2.17 ∼ −2.00 eV. FeO poses a reducing environment, as it becomes oxidized itself to become Fe₂O₃; furthermore, Fe₃O₄ oxidizes with a low activation energy into Fe₂O₃, demonstrating that the oxygen atoms of the nearby Fe₂WO₆ experience a reducing environment [20,21]. Consequently, the increased probability of oxygen vacancies can be attributed to the highly reducing environment. Formation of oxygen vacancies in Fe₂WO₆ will affect the photo-catalytic performance of the Fe₂WO₆ for the following reasons: When Fe₂WO₆ with oxygen vacancies is used as a photocatalyst, oxygen vacancies activate the surrounding O₂ molecules and their reaction pathways that produce reactive oxygen species (ROS), such as ^•O₂⁻, ^•OH, ¹O₂ and H₂O₂, affecting the photocatalytic performance [22].

In Fig. 3(b), iron vacancies showed opposite result to the oxygen vacancies in iron oxide rich environments G and H. In these environments, iron vacancies exhibited the greatest formation energies, with respective values of 4.03–7.29 eV. It is reported that Fe₃O₄ can easily generate iron interstitial under low oxygen pressure because it has many empty spaces between iron octahedra and tetrahedra [23]. Similar to Fe₃O₄, Fe₂O₃ also has a lot of empty space between the octahedra, making it more likely to have iron interstitials. FeO, on the other hand, has little effect on the formation of iron vacancies in Fe₂WO₆ due to the high density of the iron lattice, which makes it difficult to form for iron interstitials at low oxygen pressures. Therefore, at points G and H, the iron atoms in Fe₂WO₆ are difficult to form vacancies as they are transferred to iron oxides in the surrounding environment. As the O-rich environments, at point B, the iron vacancies have formation energies of −1.22 eV and −0.79 eV for Fe1 and Fe2, respectively. Point A is also an O-rich environment, but it is more difficult to form iron vacancies than at point B. This is likely due to the additional possibility of Fe-W-O ternary compounds being formed at point B, in contrast to point A.

The formation energies of the tungsten vacancies showed the widest range as shown in Fig. 3(c). At point H, in the presence by FeO and Fe₃O₄, the formation energy of the tungsten vacancy is 15.55 eV, indicating that tungsten vacancies are hard to form. As shown in Fig. 2, tungsten and iron do not form stable compounds; therefore, for a tungsten vacancy to form, tungsten should make bond with oxygen in FeO or Fe₃O₄. However, as mentioned above for iron vacancies, low oxygen pressure induces iron interstitials in Fe₃O₄, making it more difficult for excess oxygen to exist that could be used to form tungsten oxide. In contrast, tungsten vacancies are most likely to form in the O-rich environments A and B. The formation energy of the tungsten vacancy at point A are −7.60 eV, which is almost twice as low as the formation energy of −3.02 eV at point B. This phenomenon can be attributed to the potential formation of Fe-W-O ternary compounds, which is analogous to the formation of iron vacancies at point B.

To more accurately evaluate the importance of the vacancies in Fe₂WO₆, it is also necessary to consider the role of secondary vacancies. The negative formation energy of oxygen vacancies, including those at the H point, suggests that the initial lattice structure of the crystal is prone to degradation, and it also implies that additional secondary vacancies may be created. To calculate the formation energy of secondary vacancies, it is necessary to consider a more extensive range of combinations and their relative positions in respect to the primary vacancies. In addition, the use of larger supercells is essential to ensure the accuracy of the calculation. In the present study, however, due to the limitations of the computational resources, it was not possible to perform the calculation of secondary vacancies. Nevertheless, in a future study, it may be possible to construct a comprehensive list of potential secondary vacancies, thus providing insight into the potential vacancy formation chain reaction.

Another avenue for exploration is the investigation of charged vacancies. While computational limitations have bound this study to neutral vacancies, charged vacancies in photocatalytic reactions can provide insights into charge carrier lifetimes, adsorption, and the ratio of solar energy converted to chemical energy [24]. Additionally, they can facilitate the identification of recombination channels and reduce quantum yields [25]. Consequently, a future study on charged vacancies is likely to be highly beneficial for the practical application of Fe₂WO₆.

3. Conclusion

We calculated the formation energies of oxygen and metal atoms in Fe₂WO₆ for different thermo-chemical environments using DFT method. The study shows that oxygen vacancies are difficult to form in O-rich environments, where the formal oxidation state is stabilized, and oxygen-metal bonds are strengthened. Conversely, in reducing environments with FeO and Fe₃O₄, oxygen vacancies are more likely to be formed due to their low formation energy. Oxygen vacancies enhance photocatalytic activity by activating reaction with O₂ molecules, which produce ROS. Iron vacancies behave differently from oxygen vacancies in iron oxide-rich environments, showing the highest formation energies. In O-rich environments, iron vacancies can be easily formed, and this tendency is reinforced when the formation of Fe-W-O ternary compounds is involved. In iron oxide-rich conditions, tungsten vacancies are unlikely due to high formation energies. Conversely, the formation of tungsten vacancies is most likely to occur in environments that are O-rich and where Fe-W-O compounds can form at the same time. This study helps to understand the fundamental nature of the vacancy defect that affects the performance of Fe₂WO₆ as a photo- and electro-catalyst, which can provide guidelines for future applications. Furthermore, it has been reported that catalytic performance is enhanced when the bulk-to-surface defect ratio is low [8]. Consequently, future studies may focus on surface vacancy or other defects, as well as secondary and charged vacancies, with the objective of deepening our comprehension of their formation and applications.

CRediT authorship contribution statement

Kyuwan Seo: Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis, Data curation. Dongkyu Lee: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Investigation, Formal analysis, Conceptualization. Sungwoo Lee: Writing – review & editing, Writing – original draft, Validation, Supervision, Resources, Project administration, Conceptualization.

Data availability

The raw and processed data required to reproduce these findings are available from the corresponding author upon request.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following is/are the supplementary data to this article: