Interface-confined intermediate phase in TiO₂ enables efficient photocatalysis

Significance

In his Nobel Lecture, Herbert Kroemer coined the famous phrase, “the interface is the device.” In this work, we show a practical example for this concept in P25, a mixture of two different phases of TiO₂: anatase and rutile. It has been well established in experiments that P25 outperforms the individual phases, but the underlying mechanism has been a long-standing puzzle. Employing first-principles calculations, we uncover a metastable intermediate structure (MIS) at the anatase/rutile junction. We demonstrate that the existence of the MIS could improve the photocatalytic efficiency of TiO₂ in various ways and may rationalize the superior performance of P25. Generally speaking, we unveil an effective approach to enhance the device performance by engineering interfaces between polymorphs.

Abstract

As a prototypical photocatalyst, TiO₂ has been extensively studied. An interesting yet puzzling experimental fact was that P25—a mixture of anatase and rutile TiO₂—outperforms the individual phases; the origin of this mysterious fact, however, remains elusive. Employing rigorous first-principles calculations, here we uncover a metastable intermediate structure (MIS), which is formed due to confinement at the anatase/rutile interface. The MIS has a high conduction-band minimum level and thus substantially enhances the overpotential of the hydrogen evolution reaction. Also, the corresponding band alignment at the interface leads to efficient separation of electrons and holes. The interfacial confinement additionally creates a wide distribution of the band gap in the vicinity of the interface, which in turn improves optical absorption. These factors all contribute to the enhanced photocatalytic efficiency in P25. Our insights provide a rationale to the puzzling superior photocatalytic performance of P25 and enable a strategy to achieve highly efficient photocatalysis via interface engineering.

Titanium dioxide is one of the most promising photocatalysts for water splitting due to its high photocatalytic efficiency, good stability in water, as well as low fabrication cost (1, 2). There are two primary phases of TiO₂: anatase and rutile; they differ in lattice constants, symmetries, and electronic structures. The band gaps of anatase and rutile TiO₂ are similar: 3.2 eV (anatase) vs. 3.0 eV (rutile) (3). Interestingly, high photocatalytic efficiency is achieved in neither of the pure phases, but in a mixture of the two, which is commonly referred to as P25 (4–6).

Extensive studies have been performed to unveil the microscopic mechanisms underlying the mysterious enhancement of the photocatalytic performance by mixing the two phases. It is commonly believed that the improved photocatalytic efficiency of these two mixed phases is due to separation of electrons and holes (1, 3–8) as a result of the band alignment at the interface between anatase and rutile (9–12). However, the band alignment between anatase and rutile is still under debate: Some groups believe that electrons tend to flow from rutile to anatase (9, 10, 13, 14), while other groups argue the opposite and suggest that it is hole migrating from rutile to anatase (3, 8, 11, 12). It has also been proposed that the electron–hole migration at the interface between anatase and rutile is not dominated by band alignment but is controlled by experimentally enforced external conditions, such as light illumination (2, 14–16) and hydrogen incorporation at the interface. In addition to the phase effects, the exposing surfaces and surface defects also matter (17–19). Recently, Song et al. (20) investigated the interface between anatase and rutile and suggested that the phase transition between anatase and rutile near the interface may play a critical role in separating electrons and holes, thereby improving the efficiency of photocatalysis (9–14, 16, 20–22). However, the exact interface structure and the atomistic mechanism of how it impacts the photocatalytic performance remain elusive.

In this work, we systematically investigate the phase transition from anatase to rutile by first-principles calculations, which yields a metastable intermediate structure (MIS) between anatase and rutile. The MIS serves as an intermediate step along the phase transition pathway from anatase to rutile. It is not an energetically favorable bulk phase but is stabilized due to interface confinement, or it can be considered as an interface reconstruction with finite thickness, similar to the concept of complexion (23–26). The MIS has unique band alignments with anatase and rutile: On the one hand, the MIS induces a continuous gradient structure in the vicinity of the interface with a wide band gap distribution within 2.7 to 4.2 eV, which makes mixture of anatase and rutile more efficiently absorbs light than the pure constituent phases. The unique band alignments also result in efficient separation of electrons and holes. On the other hand, the conduction-band minimum (CBM) of the MIS is increased by about 1 eV compared to anatase, which greatly improves the hydrogen reduction during photocatalysis for water splitting.

To correctly capture the interface structure between anatase and rutile, we first examine the phase transition pathway from anatase to rutile, which requires a clear lattice correspondence between the two structures. By performing matrix transformation on the conventional unit cells of anatase and rutile based on the experimentally observed orientation relationship (22), we find that both structures can indeed be transformed into supercells with identical number of atoms, similar cell shapes, and atomic arrangements (Fig. 1). Specifically, we apply a {[2,0,0], [0,2,0], [0,0,1]} transformation to anatase, and a {[1,$\overline{1}$,1], [1,$\overline{1}$,$\overline{1}$], [1,0,3]} transformation to rutile, respectively. Thus, we obtain similar supercells of anatase and rutile (16 Ti atoms and 32 O atoms). We further develop an algorithm to automatically map the one-to-one atomic correspondence between the two structures based on the least-nearest-neighbor-distance principle (i.e., in the context of lattice matching, we identify the arrangement that minimizes the sum of squared atomic distances), with which we can interpret the two structures as follows.

Fig. 1.

(A) Conventional unit cell of anatase TiO₂. (B) Supercell of anatase after matrix transformation. (C) Conventional unit cell of rutile TiO₂. (D) Supercell of rutile after matrix transformation. Both cells have the same number of atoms and similar shapes. The distinct layers are labeled A, B, A’, and B’, and the correspondence between the two structures is indicated in the figure.

There are four layers of Ti atoms (labeled A, B, A’, B’) in the supercells of both anatase and rutile TiO₂. Oxygen atoms are octahedrally coordinated to the four layers of Ti atoms (Fig. 1 B and D). As shown in Fig. 1, anatase and rutile have an obvious delamination along the $z$-axis; the corresponding lattice constants of anatase and rutile are also comparable ($a=b=7.62$ Å, $c=9.55$ Å $[\alpha ={90}^{°},\beta ={90}^{°},\gamma ={90}^{°}]$ for anatase, and $a=b=7.19$ Å, $c=9.97$ Å $[\alpha ={86}^{°},\beta ={86}^{°},\gamma ={81}^{°}]$ for rutile). The atomic arrangements of Ti in each layer are alike. In this way, one can easily map an atomic correspondence between anatase and rutile TiO₂.

Fig. 2A presents the minimum-energy path (MEP) for the anatase-to-rutile transition without any constraints (i.e., pressure free). Anatase needs to overcome a single energy barrier of 0.153 eV/atom to transform into rutile through a smooth atomic pathway. However, anatase and rutile do not exist as isolated phases in P25; instead, they are connected with interfaces. The fraction of anatase in P25 is greater than 70%, and rutile is actually attached to the surface of anatase, as recently observed in experiments (20, 22). Hence, we reassess the phase transition from anatase to rutile with habit-plane constraints in Fig. 2B, i.e., we constrain the interface lattice constants of the rutile phase to match those of anatase. After applying the interfacial constraints, rutile [labeled “rutile_c” in Fig. 2B] becomes actually unstable. Toward the left side, rutile_c may relax to an intermediate local energy minimum along the MEP for the transition to anatase; it is also barrier-free for rutile_c to transition to bulk rutile phase when the interface strain is released. Thus, we identify a MIS along the anatase-to-rutile transition pathway.

Fig. 2.

Minimum energy path of the anatase-to-rutile transition obtained from the solid-state nudged elastic band (SSNEB) simulations: (A) without any constraints, and (B) with the constraints by anatase on the habit plane (red line) and for the transition from rutile_c (rutile under constraints) to rutile without strain (blue line), the constraints gradually disappear, and the lattice tilts to rutile. $Q$ is defined by $Q=\sqrt{{\mathrm{\Sigma }}_{\alpha }{m}_{\alpha }{\left({\mathbf{R}}_{i;\alpha }-{\mathbf{R}}_{f;\alpha }\right)}^2}$ (27), where $m_{\alpha }$ represents the mass of atom $\alpha$, and ${\mathbf{R}}_{\alpha }$ denotes the Cartesian coordinates of atom $\alpha$. The subscripts $i$ and $f$ refer to the initial and final configurations associated with the phase transition. (C) Collective displacements of Ti-O₆ octahedra along the phase transition path from anatase to rutile in B.

To understand the atomistic details of the interface structure, we analyze the structural evolution from anatase to rutile along the MEP. After a symmetry analysis of the structures, we find that the four layers A, B, A’, and B’ can be connected by symmetry operations. Therefore, for the sake of simplicity, we select layer A’ for detailed analyses. Throughout the path, Ti and O atoms are always octahedrally coordinated (Fig. 2C). As the transition proceeds, the Ti-O₆ octahedra collectively rotate.

We find that during the entire phase transition, the anatase phase continuously changes into rutile in a gradual rotation. Along the transformation path, due to the impact of the interface between anatase and rutile, a local minimum is formed near the interface, which is the MIS discussed above. The phase transition from anatase to rutile can be divided into two steps. The first step occurs near the interface; the anatase phase undergoes a transformation into the MIS. When this transition occurs, the octahedron in the upper-left corner begins to rotate clockwise, while the octahedron in the upper-right corner starts to rotate counterclockwise. After rotating by approximately ten degrees, the octahedron in the upper-left corner changes its rotation direction to along the diagonal, while the corresponding octahedron in the upper-right corner rotates in the opposite diagonal direction, as indicated by the orange arrows in Fig. 2C. With this simple rotation, anatase can be transformed into the MIS. In the second step, the MIS transitions to rutile. For this process, the Ti-O₆ octahedron no longer rotates. However, due to a gradual weakening of the habit-plane constraints, the lattice vectors of the MIS continuously change. During the phase transition, the system goes through a rutile_c phase, where the relative atomic positions closely resemble those found in rutile; nonetheless, due to the habit-plane constraints, the interfacial lattice constants of this rutile_c phase become identical to those of anatase, as shown in Fig. 2C. Eventually, the transformation concludes with an unconstrained rutile phase, which is far from the interface.

The atomic structure of the MIS is shown in Fig. 3A. Based on a symmetry analysis, we identify a primitive cell for the MIS (Fig. 3B), which clearly differs from that of rutile (Fig. 1C). The primitive cell of the MIS is twice that of rutile. Comparing the structure of each layer of Ti atoms in anatase, MIS, and rutile, the Ti atoms of two adjacent layers in anatase form a rectangle. The adjacent two layers of Ti atoms in rutile form a parallelogram, which is obtained by shuffling the upper and lower layers of the rectangular structure of rutile (Fig. 3A). The MIS is an intermediate metastable state along the transformation pathway from anatase to rutile. In the MIS, the Ti atoms in two adjacent layers form an irregular quadrilateral that lies between a rectangle and a parallelogram.

Fig. 3.

(A) Crystal structure of the MIS along the phase transition pathway from anatase to rutile. (B) Primitive cell of the MIS obtained after symmetry analysis. (C) Band structure and projected density of states of the MIS.

We compute the electronic band structure and projected density of states of the MIS in Fig. 3C. The MIS is an interface-confined intermediate phase with a large band gap, which is about 1.4 eV greater than that of the structurally similar rutile. The calculated electronic band structure and density of states of the MIS show that the CBM is an anti-bonding state composed of Ti-$3d$ orbitals. The valence-band maximum (VBM) is a nonbonding state mainly composed of O-$2p$ orbitals. We find that the octahedral rotation in TiO₂ leads to strong hybridization between Ti-$3d$ and O-$2p$ orbitals. Both anatase and rutile exhibit high symmetries, with space groups $I41/amd$ and $P42/mnm$, respectively. As a result, the CBM (Ti-3d orbitals) and VBM (O-2p orbitals) typically belong to different irreducible representations, leading to weak coupling. In the case of the MIS, the atomic disorder gives rise to a space group of $P1$, meaning that at any k-point in the reciprocal space, there is only one irreducible representation (e.g., only ${\mathrm{\Gamma }}_1$ at the $\mathrm{\Gamma }$ point). This enhanced disorder strengthens the $p$-$d$ coupling in the MIS compared to the situations in other phases of TiO₂, which pushes the antibonding CBM to higher energy levels compared to the situation in the undistorted structure. The VBM of distorted TiO₂ is shifted to slightly lower energies relative to the level in the undistorted structure due to increased repulsion between Ti-$4s,3d$ and O-$2p$ states.

In order to elucidate the impact of the MIS on the photocatalytic efficiency, we analyze the band alignment between the MIS, anatase, rutile_c, and rutile. The band alignment between anatase and rutile has been suggested to play a decisive role in separating photo-generated electrons and holes, and thus critically influences the photocatalytic performance. However, the reported alignments between the two phases have been controversial and actively debated (9–14, 16). This is because to accurately compute the band alignment between two phases, an interface that naturally connects the two is usually required; this is technically challenging, since anatase and rutile are structurally rather dissimilar. Now, with the continuous phase transition path and the MIS identified, a natural interface between anatase and rutile can be constructed (Fig. 4A). By carrying out rigorous first-principles calculations for the interface-containing supercell with accurate Heyd–Scuseria–Ernzerhof (HSE) hybrid functional (30), we obtain the offsets between the VBM and CBM values of the four structures. Among all of the phases, the VBM of the MIS is the lowest, and its CBM is the highest, as anticipated in our earlier analysis of the $p$-$d$ coupling model. Using our structural model, the VBM of anatase is 0.4 eV lower than that of rutile. Our independent result with a distinct approach agrees with both the theoretical calculations and experimental measurements by Scanlon et al. (9), which reported a 0.39 eV difference. This further confirms that the unique band alignments may help to efficiently separate electrons and holes, contributing to enhanced photocatalytic performance.

Fig. 4.

(A) An anatase-MIS-rutile_c supercell constructed based on the derived phase transition pathway. (B) Band alignment between anatase, MIS, rutile_c, and rutile (eV). The dotted lines represent the redox levels of H and O during photocatalysis (21, 28, 29). (C) Band-gap evolution along the transition path.

Compared to rutile under zero-pressure conditions, the band gap of rutile_c is 0.3 eV smaller. It is well known that the energy range of sunlight is mainly concentrated in the visible light region with a wavelength of 400 to 700 nm (i.e., 1.7 to 3.0 eV). The band gaps of pure-phase anatase and rutile both fall outside of this range. However, the band gap of rutile_c falls into this range, which improves light absorption. In addition, compared to the isolated anatase and rutile, the continuous anatase-rutile interface creates a wide distribution of the band gap (2.7 to 4.2 eV) that also enhances light absorption.

The CBMs of both anatase and rutile are close to the reduction energy level of H ions, which makes it hard to reduce H ions during photocatalysis for water splitting. However, the CBM of the MIS is much higher than that of the pure anatase or rutile, which greatly enhances the reduction ability of H ions, thus further improving the photocatalytic efficiency of P25.

Conclusions

To conclude, we have investigated the phase transition pathway from anatase to rutile, and identified an intermediate phase (termed MIS) in between stabilized by interfacial constraints. The interface reduces the band gap of rutile to the visible light range, enhancing light absorption. The unique band alignment at this interface leads to efficient separation of electrons and holes. The MIS at the interface has a higher CBM, which greatly enhances the reduction ability of H ions, thereby improving the photocatalytic effect of the mixture of anatase and rutile. It is important to point out that the phenomenon of continuous interfaces between different phases is ubiquitous in nature, and the MIS we found between anatase and rutile is not accidental; any mixture with continuous coherent interfaces may form similar interface-confined metastable states, which could have significant effects on the material properties of the mixture. Our study, therefore, reveals an avenue to understand and utilize the interface-induced phase transition between these different phases, and warrants careful studies in the future.

Materials and Methods

Identification of Transformation Matrices.

The phase transition between different phases of polymorphic materials should adhere to a fundamental principle: Their transition path should proceed along the direction of minimum energy consumption. In our approach, we utilize lattice parameters, angles, and relative atomic positions between two phases as the objective functions. By searching for possible symmetry and matrix transformation operations that minimize the objective function, we determine the matrix transformation, atomic supercells, and lattice correspondence. Identifying the optimal atomic correspondence implies finding the reaction coordinate with the lowest energy barrier for the phase transition. This method is general and our results for TiO₂ are illustrated in Fig. 1.

First-Principles Calculations.

To understand the atomistic transformation pathway, we perform first-principles calculations for different phases of TiO₂ with accurate HSE hybrid functional (30) using the Vienna Ab-initio Simulation Package (31, 32). A $5\times 5\times 4$k-point grid and a plane-wave energy cutoff of 500 eV are used for the supercell [i.e., the structures in Fig. 1 B and D] calculations. We set the nonlocal-Fock-exchange mixing parameter to 0.25. We use the SSNEB method (33) to obtain the MEP for the structural transition from anatase to rutile.

Band Alignment.

We calculate the band alignment of various phases by combining them into a supercell along the direction of the phase transition using the MIS-based interface. We perform first-principles calculations to determine the difference in the local electrostatic potential after concatenating the structures. Further, we take into account the corrections of the absolute deformation potential caused by volume changes in each phase [see more details of the method in ref. 34]. The corrected potential difference serves as a reference to establish the offset between the VBM of each phase. When computing the band alignment, we utilize a $5\times 2\times 4$k-point grid to match the supercell used for splicing, with other parameters consistent with those in the “First-Principles Calculations.”

Data, Materials, and Software Availability

All study data are included in the main text.