Molecular Dynamics Characterization of Rutile-Anatase Interfaces

In order to minimize model variables (i.e., size of interfacial supercell), we chose .... with a wholesale rearrangement of the top anatase layer to f...
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9290

J. Phys. Chem. C 2007, 111, 9290-9298

Molecular Dynamics Characterization of Rutile-Anatase Interfaces N. Aaron Deskins,* Sebastien Kerisit, Kevin M. Rosso, and Michel Dupuis Chemical & Materials Sciences DiVision, Pacific Northwest National Laboratory, Battelle BouleVard, K1-83, Richland, Washington 99354 ReceiVed: February 15, 2007; In Final Form: April 11, 2007

We report molecular dynamics (MD) simulations of interfaces between rutile and anatase surfaces of TiO2. These interfaces are important for understanding mixed-phase catalysts, such as the Degussa P25 catalyst, and in particular as a first step toward characterizing electron/hole transport in these photoactive materials. Construction of these interfaces was possible with near-coincidence-site lattice (NCSL) theory. The results suggest adhesion energies for the most stable structures typically near -2 J/m2, and the interfaces appear energetically favorable due to an increase of six-coordinate Ti atoms (Ti6c). Two other notable observations emerge from this work. First, the interfaces are characterized as slightly disordered, with the disorder limited to a narrow region at the interface, in agreement with experiment. Second, formation of rutile octahedral structures was observed at the anatase side of the interface due to surface rearrangement. This appears as the beginning of an anatase-to-rutile phase transition.

1. Introduction Mixed-phase titania (TiO2) photocatalysts have been shown to often be more active than single phase catalysts alone.1-5 Titania photocatalysts are especially useful for pollutant and waste treatment6-8 and further understanding of the mixed-phase structure could lead to better catalyst design. It is now wellestablished that the degree of interconnectivity between titania crystallites and the structure of grain boundaries control transport9-11 of photogenerated holes and electrons that are responsible for catalytic activity. Grain boundaries as well as sites at the oxide surfaces are the primary loci for charge carrier trapping and recombination.9-12 A primary issue for catalyst optimization is understanding the diffusive e-/h+ transport across structurally complex metal oxide interfaces. Consequently, as a first step toward this goal, in this work, we present our modeling of the interface between rutile and anatase surfaces. In addition to catalysis applications, such structures may be relevant to phase transformations, such as anatase to rutile transformations.13,14 A well-known catalyst is the P25 formulation by Degussa, consisting of approximately 80% anatase and 20% rutile. It has been proposed that in P25 electrons selectively migrate to either rutile15 or anatase,16 leading to excess holes in the other phase. This separation slows electron/hole recombination, and the phase with excess holes is presumably more reactive, leading to greater catalyst activity. The morphology of the P25 catalyst has been examined by several authors. Early work17 used transmission electron microscopy (TEM) and described P25 as an amorphous mixture of rutile and anatase. They suggested that some anatase particles were covered with a rutile over-layer. Later highresolution TEM experiments18 however showed that individual catalyst particles are single-phase (either rutile or anatase) and that any amorphous phase is confined to at most a monolayer. Still later TEM work1 showed individual rutile and anatase particles joined together to form the active P25. Other results19 * Corresponding author. Phone: 509-372-6422. Fax: 509-375-4381. E-mail: [email protected].

Figure 1. Formation of an NCSL interface. The surface lattices of the two structures (solid and dashed lines) are shown with lattice parameters a1, b1, a2, and b2. Large supercells are created that obey the relationships in eqs 1-4. In the above case, 3a1 ≈ 2a2 and 3b1 ≈ 4a2.

TABLE 1: Potential Parameters for TiO2 interaction

Aij (eV)

Fij (Å)

Cij (eV‚Å6)

Ti-Ti Ti-O O-O qTi ) +2.196 e

16957.53 31120.2 11782.76 qO ) -1.098 e

0.194 0.154 0.234

12.59 5.25 30.22

showed a distinct interface when rutile inclusions were grown in anatase films. Therefore, we chose to consider the direct interaction of rutile and anatase surfaces from different particle faces. A review by Diebold20 gives many details about the rutile and anatase surfaces of TiO2. The most stable rutile surface is the (110) surface. This surface has been extensively studied by many authors and Diebold has prepared another review21 of this surface. Besides the (110) surface, other surfaces are common and computational work22 indicates a surface stability order of (110) > (100) > (011) > (001). A variety of surface reconstructions are known to occur23-30 under specific conditions.

10.1021/jp0713211 CCC: $37.00 © 2007 American Chemical Society Published on Web 05/27/2007

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Figure 2. Interface formation between rutile (110) and anatase (101) before and after the cooling steps of the protocol described in the text.

TABLE 2: Results for Interfaces between Rutile (110) and Anatase

TABLE 4: Results for Interfaces between Rutile (100) and Anatase

anatase surface (101)

(100)

(001)

interface

config.

ΣR/ΣA

Mx (%)

My (%)

Wadhesion (J/m2)

anatase surface

[11h0]/[1h01] [11h0]/[1h01] [11h0]/[010] [11h0]/[010] [11h0]/[001] [11h0]/[001] [11h0]/[010] [11h0]/[010] [11h0]/[010] [11h0]/[010] [11h0]/[100] [11h0]/[100]

A B A B A B A B A B A B

99/49 99/49 21/10 21/10 27/14 27/14 48/25 48/25 27/35 27/35 27/35 27/35

0.40 0.40 -1.17 -1.17 -2.37 -2.37 0.40 0.40 -2.74 -2.74 -2.74 -2.74

-0.41 -0.41 -2.74 -2.74 -0.68 -0.68 -3.02 -3.02 -0.41 -0.41 -0.41 -0.41

-1.71 -1.71 -0.57 -1.13 -1.44 -1.51 -1.33 -1.40 -1.07 -1.01 -1.45 -1.45

(101)

TABLE 3: Coordination of Ti Atoms at the Interface interface

phase

fraction Ti5c

fraction Ti6c

(110)r/vacuum (101)a/vacuum (100)a/vacuum (001)a/vacuum (110)r/(101)a

rutile anatase anatase anatase rutile anatasea rutile anataseb rutile anatase

0.50 0.50 1.00 1.00 0.22 0.09 0.15 0.58 0.11 0.66

0.50 0.50 0.00 0.00 0.78 0.90 0.85 0.39 0.89 0.34

(110)r/(100)a (110)r/(001)a a

Ti7c: 0.01. b Ti4c: 0.03.

Computational work however has focused mainly on the unreconstructed surfaces. In another review, Diebold et al.31 give an overview of the lesser studied anatase surfaces. Typical surfaces of anatase expressed are the (101), (100), and (001) faces.32-34 Theoretical work35 indicates a surface stability order of (101) > (100) > (001) with the (101) surface being the most prominent on an equilibrium crystal derived from a Wulff construction. TEM work36 also predominantly shows (101), (100), and (001) faces. Surface reconstructions are also observed37-40 for the anatase surfaces, and although different models have been proposed for the reconstructed surfaces, there is still some debate over their actual structure. For this work, we focused our attention on the

(100)

(001)

interface

config.

ΣR/ΣA

Mx (%)

My (%)

Wadhesion (J/m2)

[010]/[1h01] [010]/[1h01] [010]/[010] [010]/[010] [010]/[001] [010]/[001] [010]/[010] [010]/[010] [010]/[010] [010]/[010] [010]/[100] [010]/[100]

A B A B A B A B A B A B

81/28 81/28 35/12 35/12 36/14 36/14 80/30 80/30 45/42 45/42 45/42 45/42

-0.85 -0.85 -1.17 -1.17 3.47 3.47 0.40 0.40 -0.92 -0.92 -0.92 -0.92

-0.41 -0.41 -0.92 -0.92 -0.68 -0.68 -1.19 -1.19 -0.41 -0.41 -0.41 -0.41

-1.73 -1.64 -1.39 -1.36 -2.82 -1.56 -2.37 -2.22 -1.25 -1.36 -1.30 -1.33

TABLE 5: Results for Interfaces between Rutile (001) and Anatase anatase surface (101) (100) (001)

interface

config.

ΣR/ΣA

Mx (%)

My (%)

Wadhesion (J/m2)

[010]/[1h01] [010]/[1h01] [010]/[001] [010]/[001] [010]/[010] [010]/[010]

A B A B A B

45/24 45/24 20/12 20/12 25/36 25/36

-0.85 -0.85 3.47 3.47 -0.92 -0.92

-0.92 -0.92 -0.92 -0.92 -0.92 -0.92

-2.05 -1.93 -2.14 -2.14 -1.93 -1.80

unreconstructed rutile and anatase surfaces since they present the least ambiguity. The general morphology of P25 seems fairly understood, but the atomic-level details of such materials are incomplete. Therefore, in this work, we examine the interface between rutile and anatase surfaces. Near-coincidence-site lattice (NCSL) theory41,42 gives a method to examine the formation of an interface between two surfaces. We combine this theory with empirical potential models within the context of molecular dynamics (MD) simulations. In this manner, we can obtain interface adhesion energies and structural information. This paper is organized as follows: in section II, we describe the methodology followed in this work; in section III, we describe the results, and we give the conclusions in section IV.

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Figure 4. Anatase surfaces employed in this work. Surface lattice vectors are shown with indicated crystallographic directions. The lengths of surface vectors from experimental lattice parameters are also shown.

interface structure is obtained by satisfying the following relationships: Figure 3. Rutile surfaces employed in this work. Surface lattice vectors are shown with indicated crystallographic directions. The lengths of surface vectors from experimental lattice parameters are also shown.

2. Computational Details NCSL theory provides a framework to create surface interfaces for structures with incommensurate lattice parameters. Sayle et al.41 described the basic principles of NCSL theory as applied to cubic and hexagonal systems (BaO-MgO and CeO2Al2O3). Fisher and Matsubara42 later extended the theory to rectangular systems (NiO-ZrO2). In brief the method involves aligning near-coincidence lattice points to obtain commensurate surface interfaces. A large surface supercell is created by matching surface lattice parameters and the supercell is used in molecular dynamics simulations. Figure 1 illustrates how the supercell is constructed. The surface lattice parameters are given as a1, a2, b1, and b2. The

A1a1 ≈ A2a2

(1)

B1b1 ≈ B2b2

(2)

where A1, A2, B1, and B2 are adjustable parameters. Rectangular lattices are limited to 90° rotations relative to each other to obtain interfaces that obey the following relationships:

A1a1 ≈ B2b2

(3)

B1b1 ≈ A2a2

(4)

Because the lattice parameters do not match perfectly, a near fit is obtained and some strain is introduced into the system. Careful choice of the supercell is necessary to minimize this strain. To define the degree of fit between the two surfaces, the misfit percentage values, can be useful.

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( (

) )

My ) 1 -

a1A1 100 a2A2

(5)

Mx ) 1 -

b1B1 100 b2B2

(6)

For the case when the surfaces are rotated 90° relative to each other, a2 and b2 are switched, and new A and B values are used. We note that the misfit can be decreased by using larger surface interfaces (larger A1, B1, etc.), albeit at increased simulation time. Another relevant variable is the planar coincidence density, Σ, which gives the number of lattice points that lie within the supercell under consideration and is an indicator of the supercell size.

∑1 ) A1B1 ∑2 ) A2B2

(7) (8)

The strength of the interface can be described by the adhesion energy (Wadh).

Wadh )

(Einterface - Eslab-1 - Eslab-2) A

(9)

Figure 5. Most stable interfaces between (110) rutile and anatase (a) (101), (b) (100), and (c) (001). Red spheres represent O atoms from anatase, and green spheres represent O atoms from rutile. Grey spheres represent Ti atoms from anatase, and blue spheres represent Ti atoms from rutile. The solid circled portions show the lifting of anatase surface O atoms to form six-coordinated rutile Ti, whereas dashed circled portions show Ob bonding to anatase Ti atoms (see the text for discussion of this).

The energies in eq 9 are the interface energy Einterface (rutile and anatase slabs together), Eslab-1 energy (rutile slab), and Eslab-2 energy (anatase slab). A is the surface area of the interface. More negative adhesion energies indicate more stable interfaces. The interatomic interactions are represented by a combination of Coloumbic long-range interactions and short-range forces described using a Buckingham potential:

( )

Uij ) Aij exp -

rij Cij qiqj - 6+ Fij rij rij

(10)

The first two terms describe electron-cloud repulsion and van der Waals attraction, respectively. The parameters used in the current work are those from the work of Matsui and Akaogi43 and are given in Table 1. These parameters were optimized for rutile, anatase, brookite, and TiO2 II structures and have been used by many authors to successfully model both rutile and anatase.44-49 All calculations were performed with the DL_POLY50 code. DL_POLY uses the Verlet leapfrog method to update the atomic positions and velocities, and we specified a time step of 1 fs. The electrostatic interactions were calculated using the threedimensional Ewald sum.51 A cutoff distance of 9.0 Å was used for the short-range interactions. Temperature was controlled by a Nose´-Hoover thermostat,52 and the pressure was controlled by a Hoover barostat.53 We performed all calculations in the NPT ensemble (constant number of particles, constant pressure, and constant temperature). By allowing the volume to relax, strain between the interfaces due to lattice parameter mismatch could be reduced. In their work on NCSL theory, Fisher and Matsubara42 provided an effective way to obtain optimized surface interfaces, and a similar approach was used in this work. Within our supercell, we constructed two slabs, one anatase and one rutile, approximately 30 Å thick each, separated from each other by 5 Å. The thickness of 30 Å was chosen so that the interfaces would not experience any vacuum, while keeping the computational expense reasonable. In order to minimize model

Figure 6. RDF for the (110) rutile/(101) anatase interface. (a) Anatase slab. Slices are taken in 2 Å intervals. (b) Rutile slab. Slices are taken in 3.2 Å intervals.

variables (i.e., size of interfacial supercell), we chose to only use the smallest interfacial supercells that gave commensurate structures. We then carried out a MD simulation for 400 ps at 1300 K. This step allowed the slabs to approach each other and overcome energy barriers that might prevent structure optimization. Next we performed a series of cooling steps for 100 ps each at 1200, 1100, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 50, and 10 K. Finally, we optimized the structures at 0 K for 200 ps. We verified that 200 ps was sufficient to reach energy minimization. An illustration of initial and final structures is shown in Figure 2. As shown, a vacuum spacing of approximately 25 Å is present to minimize interactions between the noninterfacial surfaces. For each interface, we modeled two initial configurations. In the first (designated configuration A), the origins of two

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Figure 7. Interface O structures formed between rutile (110) and anatase. The slices are parallel to the interfaces. Open circles represent O atoms from rutile and closed circles represent O atoms from anatase. (a) Anatase (101). (b) Anatase (100). (c) Anatase (001). In all cases, the x axis is parallel to the rutile [11h0] direction, and the y axis is parallel to the rutile [001] direction. Solid lines show ideal anatase O positions, while dashed lines show positions of ideal rutile Ob atoms.

surface cells of the slabs are aligned directly on top of each other. In the second configuration (B), the top slab was translated one-half the lattice parameter a1 and one-half the lattice parameter b1 relative to the positions in configuration A. These two initial configurations do not represent all the possible translational arrangements between the rutile and anatase slabs, but a full exploration of the effect of initial arrangement of the titania slabs is computationally prohibitive due to the large number of ways of arranging the slabs relative to each other. We therefore focused our efforts on interfaces formed using these two initial geometries. A method of notation to describe different interfaces is needed. The two rutile (110) surface unit cell vectors are oriented along two crystallographic directions, [11h0] and [001], as shown in Figure 3. The two anatase (101) surface cell vectors, [1h01] and [010], are shown in Figure 4. One interface can be constructed by orienting the rutile (110) [11h0] and anatase (101) [1h01] vectors parallel to each other, which would be designated as the [11h0]/[1h01] interface. The surfaces could be rotated 90° relative to each other to form a [11h0]/[010] interface. As already mentioned, we considered two different initial spatial arrangements, designated configurations A and B. Thus, we have the [11h0]/[1h01]-A, [11h0]/[1h01]-B, [11h0]/[010]-A, and [11h0]/[010]-

B interfaces that can form between rutile (110) and anatase (101). In all cases, the rutile surface is indicated first. 3. Results and Discussion The common rutile surfaces (110), (100), and (001) and anatase surfaces (101), (001), and (100) lead to a large number of possible interfaces. In this work, we considered many combinations from these surfaces, and our results are organized around the interfaces formed from the different rutile surfaces. We modeled these surfaces using typical unreconstructed models available in the literature.20 Our calculated surface energies for the rutile (110), (100), and (001) surfaces are 1.8, 2.0, and 2.3 J/m2, respectively. Also, our calculated surface energies for the anatase (101), (001), and (100) surfaces are 1.5, 1.3, and 1.8 J/m2, respectively. These results generally follow the trends in surface stability22,35 and are in reasonable agreement with other computational work.46 3.1. Rutile (110) Interfaces. The results (adhesion energies) of interfaces formed by rutile (110) and the anatase surfaces are given in Table 2. The table shows that a variety of interface sizes were used (ΣR/ΣA). The table also shows that the misfit values are relatively small. All but one of the adhesion energies

Rutile-Anatase Interfaces

Figure 8. Interface O structures formed between rutile (110) and anatase. The slices are perpendicular to the interfaces. Open circles represent O atoms from rutile, and closed circles represent O atoms from anatase. (a) Anatase (101). Lines are shown to guide the eye. (b) Anatase (100). (c) Anatase (001). In all cases, the x axis is parallel to the rutile [11h0] direction, and the y axis is parallel to the rutile [110] direction.

falls between -1 and -2 J/m2. These values are of similar magnitude to adhesion energies between NiO/ZrO2.42 It is interesting to note that the (110) surface binds most strongly to the (101) anatase surface, both the most stable titania surfaces. The rutile (110) and anatase (101) interfaces have the largest commensurate structures, and this strong binding could be related to the size of the interfaces, though this is not entirely clear. For example, in section 3.2, we discuss rutile (100) interfaces where this trend does not completely occur (see Table 4). In any case, since the rutile (110) and anatase (101) surfaces are the most abundant surfaces on titania crystals, these results would suggest that mixed-phase catalysts could preferentially form (110)r-(101)a interfaces. We show in Figure 5 the most stable interfaces formed between rutile (110) and anatase surfaces. The interface pictures suggest that there is some disorder at the interfaces, but further analysis is required to provide insight

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Figure 9. Most stable interfaces between rutile (100) and anatase. (a) Anatase (101). (b) Anatase (100). (c) Anatase (001). Red spheres represent O atoms from anatase, and green spheres represent O atoms from rutile. Grey spheres represent Ti atoms from anatase, and blue spheres represent Ti atoms from rutile. The circled portions show formation of Ti6c.

into the interface structure. We first examined the radial distribution functions (RDF) at the interfaces. The same general picture was seen in all of the interfaces. In the bulk, distinct peaks are seen, indicating high crystallinity, but at or near the interface, the peaks become less distinct and the interface layers appear more amorphous. As an example, we show RDF results from the (110) rutile/(101) anatase interface in Figure 6. We excised slices at various depths relative to the interface to evaluate the degree of disorder as a function of surface depth. The graphs show sharp peaks for the first and second nearestneighbor shells a few layers from the interface. The RDF drops to zero between the first and second nearest-neighbor peaks in the bulk, whereas at or near the interface, this is not the case; the top layers show some small short-range disorder not seen

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Figure 10. Most stable interfaces between rutile (001) and anatase. (a) Anatase (101). (b) Anatase (100). (c) Anatase (001). Red spheres represent O atoms from anatase, and green spheres represent O atoms from rutile. Grey spheres represent Ti atoms from anatase, and blue spheres represent Ti atoms from rutile. The circled portions show formation of Ti6c.

in the bulk. There also appears to be more disorder in anatase compared to rutile, as indicated by the shape of the RDF between 2 and 4 Å. The graphs also show that this disorder is limited to a few angstroms from the interface, which agrees with TEM results.18 The interfacial RDFs converge to the bulk RDF in the third or fourth layer away from the interface in anatase and second layer in rutile, indicating that the surfaces are affected by the presence of the interface down to a depth of approximately 4 Å. Projections of atom positions for the planes parallel to the interfaces are shown in Figure 7. The (110) rutile surface is characterized by its rows of bridging oxygen (BO) atoms, as seen in Figure 3a. These O (OB) atoms are only coordinated to two Ti ions, whereas in the bulk O atoms are coordinated to three Ti atoms. The surface Ti atoms are coordinated to five O atoms (Ti5C), compared to six (Ti6c) in the bulk. The graphs indicate that the BO rows remain relatively intact, though they are displaced at certain locations along the [11h0] direction, despite any short-range rearrangement on the surfaces. The anatase (101) surface also has rows of O atoms along the [010] direction that remain more or less intact (see Figure 7a). The

Deskins et al. other anatase surfaces (Figure 7b,c) also show some order in the plane of the first interfacial layer. The more profound changes are seen when the atom positions are viewed in the slice perpendicular to the interfaces. Figure 8 shows such slices. The (101) interface shows a buckled-like formation as the rutile and anatase surface O atoms expand and relax in the direction perpendicular to the interface to form a wave-like pattern. The smaller anatase (100) and (001) interfaces do not show the buckled formation, and this lack of buckling could be related to their smaller super cell sizes. The anatase (101) interface is much larger than the anatase (100) and (001) interfaces. The (100) and (001) interfaces however do show another interesting structural change. Inbetween the BO rows, O atoms from the anatase are lifted up to bond with the surface rutile Ti5c surface atoms. This is seen clearly in Figure 5b,c. By doing so, the rutile Ti atoms can obtain a fully coordinated octahedral structure. Rutile Ob atoms also bond with anatase surface Ti atoms, though the rutile surface structure seems more intact compared to anatase. Apparently, full coordination of rutile and anatase Ti5c atoms with the accompanying disorder (mostly in anatase) is more stable than the surfaces in their initial unsaturated states. We further analyzed the coordination of the interfacial Ti atoms. To do so, we counted the number of O atoms bound to the Ti atoms at the interfaces. If the Ti-O distance was less than 2.3 Å, then a Ti-O bond was deemed to be present. Typical Ti-O bond distances in titania are near 1.9-2.0 Å. Table 3 gives the results of this counting procedure. In all interfaces, the fraction of Ti6c atoms increases relative to the free surfaces. There appears little distinction between rutile and anatase surfaces at the interface; both phases see an increase in coordination. As noted earlier, O atoms from anatase rearrange to complete the octet of Ti and essentially form new Ob rows. Existing rutile Ob rows also appear to be able to complete the octet of anatase Ti atoms and, hence, the increase of Ti6c in anatase. Again, this can be seen in parts of Figure 5. This partial removal of unsaturated coordination in both phases is a likely reason for interface stability and favorable adhesion of the titania slabs. Mean-square-displacement (MSD) values were calculated in the span of 10 ps at 300 K. Analysis shows that no diffusion takes place either in the bulk or at the interface. We did however observe larger MSD values at the interfaces than in the bulk (center of slab) structures. For instance, in the (110) rutile/(101) anatase slabs, we observed MSD values of 2.2 Å2 for anatase O atoms at the interface, compared to 1.0 Å2 in the middle of the anatase slab. In rutile we obtained a value of 2.7 Å2 at the interface and 2.1 Å2 in the middle of the rutile slab. This indicates that the amplitude of vibration for the interfacial atoms is greater than those in the bulk, which is likely a result of the interfacial disorder. 3.2. Rutile (100) Interfaces. The (100) surface is slightly more unstable than the (110) surface and, similarly, has surface O atoms aligned in bridging O rows. When the rutile-anatase interfaces are formed, a variety of adhesion energies emerge (see Table 4). The results are not too dissimilar from the rutile (110) results, except for the case of the (100) rutile/(100) anatase interface. This interface has a fairly large adhesion energy of -2.82 J/m2. This interface also has the largest misfit percentage values (Mx and My) of the listed interfaces, though the misfit values are still rather small, being less than 3.5%. RDF and MSD analyses of (100) rutile interfaces are not shown, since the results are very similar to the results obtained with the (110) rutile interfaces. Essentially, there is disorder at

Rutile-Anatase Interfaces the interface surface that quickly disappears further away from the interface. We do show in Figure 9 the most stable interfaces. The pictures indicate that bonding between rutile and anatase is taking place at the interface, in a similar manner to those formed at the (110) rutile interfaces. There appears a very nice fit between the rutile (100) and anatase (100) surfaces, with a wholesale rearrangement of the top anatase layer to form a rutilelike layer (see Figure 9b). This could be the reason why the (100) rutile/(100) anatase interface has the largest adhesion energy. 3.3. Rutile (001) Interfaces. The rutile (001) surface has rows of O atoms arranged in the [11h0] direction and rotation of the surface 90° results in the O rows along the [1h1h0] direction. Any interfaces formed between anatase and the two rutile (001) configurations are symmetrically equivalent, so we did not model the rotated rutile (001) interfaces. From Table 5, we see that the adhesion energies lie near -2 J/m2. The energies are noticeably larger than for the other rutile surfaces. This could be a result of surface stability; the rutile (001) surface is the least stable of the three rutile surfaces we studied, so formation of an interface could have a more stabilizing effect on this surface compared to the other rutile surfaces. Structural analysis shows similar results to those for the rutile (110) and (100) interfaces. We show the most stable interfaces in Figure 10. 4. Conclusions We have formed interfaces between rutile and anatase surfaces using near-coincidence-site lattice theory to create commensurate structures. The results show adhesion energies typically between -1 and -2 J/m2, down to -2.8 J/m2, similar to previously calculated adhesion energies of NiO/ZrO2 interfaces. Structural analysis (RDF) shows disorder at the surface that dissipates quickly away from the interface; the disorder at the interface is limited to the surface layers (≈ 4 Å) in agreement with experiment. Another interesting feature is the formation of rutile Ti octahedral structures in the top layer of anatase at several of the interfaces. Rutile is the most thermodynamically stable TiO2 phase, and these rutile octahedral structures could be indicative of the start of an anatase-to-rutile phase transition. Overall, the formation of Ti6c atoms is clearly seen in both rutile and anatase which results in the surface adhesion, though greater disorder and rearrangement of surface atoms is seen in anatase. In summary this study elucidates the interfacial structure of mixed-phase catalysts, such as P25, and we have identified several stable interfaces. The results suggest several likely crystal orientations, such as (110)r/(101)a or (100)r/(100)a. Our interfaces also provide a foundation for future work modeling the trapping of holes/electrons at the interfaces and hole/electron transport across the interface. Structural information, such as realistic interfacial geometries, is necessary for such transport simulations. Acknowledgment. This work was supported by the Department of Energy, Office of Basic Energy Sciences. Computational resources were provided by the Molecular Science Computing Facility located at the Environmental Molecular Science Laboratory in Richland, WA. All work was performed at Pacific Northwest National Laboratory (PNNL). Battelle operates PNNL for the U.S. Department of Energy. K.M.R. acknowledges the support of the Geosciences program of the DOE Office of Basic Energy Sciences, and the Stanford Environmental Molecular Sciences Institute jointly funded by the National Science Foundation (NSF) and the DOE Office of Biological and Environmental Research.

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