Stability of Excess Electrons Introduced by Ti Interstitial in Rutile TiO2

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Stability of Excess Electrons Introduced by Ti Interstitial in Rutile TiO(110) Surface 2

Kazuki Morita, Taizo Shibuya, and Kenji Yasuoka J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09669 • Publication Date (Web): 27 Dec 2016 Downloaded from http://pubs.acs.org on January 1, 2017

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The Journal of Physical Chemistry

Stability of Excess Electrons Introduced by Ti Interstitial in Rutile TiO2(110) Surface Kazuki Morita,† Taizo Shibuya,‡ and Kenji Yasuoka∗,† †Department of Mechanical Engineering, Keio University, Yokohama 223-8522, Japan ‡IoT Devices Research Laboratories, NEC Corporation, Tsukuba, Ibaraki 305-8501, Japan E-mail: [email protected]

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Abstract The surface chemistry of rutile TiO2 (110) has long been ascribed to surface bridging oxygen vacancies (VO ) and accompanying excess electrons. However, recently there has been debate whether titanium interstitials (Tiint ), a subsurface defect, participates in the surface reactions of TiO2 (110). We used a combination of ab initio molecular dynamics and static density functional theory calculations to systematically investigate the spatial distribution of excess electrons introduced by Tiint . We found that these excess electrons form polarons and that the most stable structure had one polaron located at the Tiint site, and the other three at second-layer Ti sites below five-coordinate Ti sites. This behavior of Tiint providing excess electrons to the near-surface region is similar to that of VO , which suggests that Tiint may contribute to the surface chemical reactions of TiO2 (110).

INTRODUCTION The surfaces of transition metal oxides have attracted much attention because of their suitability for use in a wide variety of applications. 1 In particular, rutile TiO2 (110) has been studied intensively as a model surface. 2 Rutile TiO2 , which is used in photocatalysis, dyesensitized solar cells, and biocompatible materials, 3–5 is an insulator with a band gap of 3 eV. The (110) surface of rutile TiO2 consists of alternating rows of bridging oxygen atoms and five-coordinate titanium atoms. 2 The Ti sites are not equivalent because of the broken symmetry on the rutile TiO2 (110) surface, so we have labeled each site, as shown in Figure 1. A successful model used to describe the chemistry of surfaces is the bridging oxygen vacancy (VO ) model established by Henrich and co-workers. 6 In the VO model, the chemistry of a reduced surface is explained by VO and accompanying excess electrons attributed to the band gap states observed 0.7 eV below the conduction band edge in photoelectron spectroscopy (PES). Despite the simplicity of this model, it has been successfully used to explain many surface chemical reactions. 7–10 2 ACS Paragon Plus Environment

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Recent advances in experiment and theory have provided new evidence that the excess electrons introduced by VO form a polaron in the second layer below the Ti5c row (Ti5c-2nd ), 10–15 and that other defects such as the Ti interstitial (Tiint ) and the surface OH can also introduce excess electrons. 11,16–27 Wendt et al. 16 used PES with scanning tunneling microscopy to observe a band gap state on a rutile TiO2 (110) surface without VO . However, if all excess electrons are introduced by the VO , this result cannot be explained. They suggested that excess electrons are mainly withdrawn from Tiint in the near-surface region. More recently, Lira and co-workers used temperature-programmed desorption to measure the change in the amount of adsorbed O2 as they reduced the surface to increase the amount of VO . 22,23 The surface properties were explained by excess electrons introduced by these donors. However, the contribution of Tiint is under debate. 28 The existence of Tiint that diffuse on the rutile TiO2 (110) surface was confirmed more than a decade ago. 29 Recently, it was reported that one Tiint introduces four excess electrons. 20,21,30–34 Thus, both VO and Tiint can provide excess electrons. It is known that the former provides excess electrons to Ti5c-2nd and those excess electrons contribute to the surface chemistry of rutile TiO2 (110). In contrast, the behavior of excess electrons on the rutile TiO2 (110) surface introduced by the latter is yet unclear. Because TiO2 is largely ionic, a growing consensus is that its characteristics can often be explained using electrostatics. 13,35 The question here is: will excess electrons introduced by Tiint overcome the against attraction force and be provided to the surface? In this paper, we use density functional theory (DFT) to calculate the stability of excess electrons at different Ti sites and compare our results with the known behavior of excess electrons introduced by VO . First, we use ab initio molecular dynamics (AIMD) to generate possible polaron configurations and their probability at a finite temperature, and identify Ti sites that excess electrons are more likely to localize on. Next, we focus on these Ti sites and perform structure relaxation using static DFT to closely compare stability at low temperature by removing the effect of thermal fluctuations. We show that, with the exception



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of some excess electrons attracted by Tiint , most excess electrons introduced by Tiint behave in a similar manner to those introduced by VO , which suggests that Tiint contributes to the surface chemical reactions of TiO2 (110).

METHODOLOGY Calculations were performed with a plane-wave basis set using the Vienna Ab initio Simulation Package (VASP). 36 The Perdew–Burke–Ernzerhof functional was employed as an exchange and correlation functional. 37 An on-site coulomb correction, Hubbard U , was applied with the widely used U value of 4.2 eV. 38 Core-valence interaction was described using projector-augmented waves. The Brillouin zone was sampled at the gamma point with a plane-wave expansion cutoff of 450 eV. We adopted double-sided surface slab model to eliminate the effect from broken symmetry on the bulk terminated side. The slab thickness chosen was nine layers to account for the convergence of surface energy and bond length in the deepest layer. 39,40 A (6 × 2) slab model with a 15 Å vacuum between the surfaces was prepared with a Tiint at an octahedral site between the fourth and fifth layers (217 Ti and 432 O atoms in total). All atoms were allowed to move throughout all of the calculations. The AIMD simulation was performed using Born–Oppenheimer molecular dynamics, which strictly followed the Born–Oppenheimer approximation by minimizing the electronic energy for every ionic step. We raised the simulation temperature to 1000 K and enhanced thermal fluctuation to sample enough electron configurations, as conducted by Kowalski et al. 12 An AIMD simulation with a 3 fs time step was performed with a canonical ensemble for 6 ps with temperature control using a Nos´ e–Hoover thermostat. When an electron occupies an empty Ti 3d orbital, it induces a magnetic moment of 1.0 µB . Using this property, we determined the location of excess electrons from the difference between the spin up and spin down components of the projected charge density associated with each Ti site. When this difference exceeds 0.5 µB , at a particular Ti site, an excess electron is considered to be there. The


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lifetime of excess electrons at a certain Ti site can be associated with the qualitative stability of excess electrons at that site. With the grouping shown in Figure 1, the localization times of excess electrons were summed over time and normalized to give a distribution function. Because our interest was the effect of the surface on the excess electrons, we grouped Ti sites according to their depth from the surface and coordinate of Ti the site was under (Ti5c or Ti6c ). The four rows in the [001] direction closest to Tiint were grouped as “Near Tiint .” Using the calculated distribution function, configurations were chosen and calculated with the static DFT. We prepared different initial structures and compared the final structures obtained following the structure relaxation. To create different terminal structures, we lengthened the bonds around the target Ti sites in the initial structures. It should be noted that changing the initial structures was only to trigger relaxed structures into certain electron structures, and ions were not constrained during the relaxation procedure.

RESULTS AND DISCUSSION We first describe the results of the AIMD simulation, emphasizing similarities and differences between VO studies and our results. Figure 3 depicts the change in location of excess electrons over time. The excess electrons stayed at the initial position near Tiint for first ps (Figure 2(a)), and after reaching equilibrium, they started to localize on various Ti sites. Each excess electron occupied a Ti3d orbital, formally creating Ti3+ . This behavior of excess electrons is in agreement with a previous Car–Parrinello molecular dynamics study performed for the VO . 12 The average lifetime of an excess electron at a Ti site was around 0.1 ps. Together with the results of an additional calculation at 700 K that gave an average lifetime of 0.2 ps, we used the Arrhenius equation to estimate that the activation energy for excess electron hopping was 0.18 eV. This is consistent with the previously calculated activation energy in rutile TiO2 of ∼ 0.3 eV. 41,42 A difference between our results and those of VO studies is the distribution function



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of excess electrons, which is shown on the right-hand side of Figure 2(b). The highest intensity in the distribution function is found for the “Near Tiint ” group followed by Ti5c-2nd and then Ti5c-1st . Although this distribution function mostly agrees with the case for VO , differences arise in the near-field of the defects. The distribution function in the case of VO shows higher intensity near VO ; this is because VO attracts excess electrons. 15,43 In contrast, our distribution function showed substantial population of the deeper “Near Tiint ” region, suggesting that Tiint can also attract some excess electrons. To further examine the stability of excess electrons in the “Near Tiint ” region, we compared the possible configurations. The removal of thermal fluctuation allowed us to simulate the behavior of excess electrons at low temperature, where many experimental results are available. We created different structures in static DFT with excess electrons localized at “Near Tiint ”, Ti5c-2nd , and Ti5c-1st , and then performed structure relaxation. Figure 4 shows four representative relaxed structures A to D, plotted together with the charge density of the band gap states. Figure 4 reveals that all the excess electrons localized in a Ti site are accompanied with lattice distortion, forming polarons. The stability of these structures was calculated and is presented in Table 1. The same configuration of excess electrons was calculated with different values of Hubbard U that were used in previous studies. 44,45 Different U values only resulted a slight change in the relative stability of structure C; this is discussed in detail in the Supporting Information. The difference in stability between “Near Tiint ”, Ti5c-2nd , and Ti5c-1st can be determined by comparing structure A, C, and D, because in all of these structures, one polaron is localized at Tiint and the remaining polarons are at Ti5c-2nd , “Near Tiint ”, and Ti5c-1st , respectively. The energy differences indicate that Ti5c-2nd is more stable than “Near Tiint ” and Ti5c-1st . An electron having more stability at Ti5c-2nd than at “Near Tiint ” seems to contradict the distribution function calculated from the AIMD simulation; however, this can be explained by comparing structure A and B. The difference between structure A and B, which both have excess electrons at Ti5c-2nd , is that A has a polaron at Tiint and B does not. Structure A is more stable than structure B (Table 1), indicating that it is energetically


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more favorable for Tiint to trap a polaron than to release all four excess electrons. This result implies that the high population of excess electrons in the “Near Tiint ” region observed in the distribution function can be ascribed to trapping of excess electrons by Tiint . It is suggested that the other three excess electrons introduced to the surface behave similarly to the ones introduced by VO and are attracted to VO if it is present. This supports the Tiint -assisted surface chemical reaction model introduced by Lira et al. 22,23 In their model, Tiint provides excess electrons to the surface VO , because their results have shown that the excess electrons solely introduced by VO are insufficient to promote O2 adsorption. Table 1: Total Energies of Different Electronic Structures

Structure A B C D

Polaron location and number near Tiint Ti5c-1st Ti5c-2nd 1 0 3 0 0 4 4 0 0 1 3 0

Relative energy (eV) 0 0.148 0.179 0.291

Our results support those of Wendt et al. 16 They explained the dissociation rate of an O adatom by considering the diffusion of Tiint to the surface. We propose that Tiint may contribute more to surface chemistry if it is closer to the surface. Comparison of different electronic structures in our study revealed that Tiint can trap one excess electron, and provides only three excess electrons to the surface. This implies that with same reduction rate, two VO , which provide a total of four excess electrons to the surface, have more potential to contribute to surface chemical reactions than one Tiint . If the surface preparation and temperature conditions are met, Tiint will diffuse to the surface, allowing trapped excess electrons to participate in surface chemical reactions and increasing the role of Tiint . Yoon et al. 35 reported that Tiint may not exist until the third layer. Thus, it would be illuminating to study the stability of excess electrons introduced by a Tiint located deeper in the slab. Our results are also relevant to H diffusion on the surface. Li et al. proposed a model of H diffusion involving complex formation with an excess electron. 46 In their model, H diffusion



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is explained by excess electrons moving in the [110] direction, and H on bridging oxygen hopping to the neighboring site following the excess electrons. The H hopping rate was underestimated in their DFT calculation. This is probably because in real systems, more excess electrons are provided from VO or Tiint than were considered in the calculation, which enhances the hopping rate. Although the distribution function indicates that it is rare for excess electrons to visit Ti6c-1st (Ti site under bridging oxygen), the presence of positively charged H+ may attract excess electrons to its nearby sites. Meanwhile, we still consider that VO strongly influence surface chemistry. If a surface is prepared to suppress the formation of Tiint , as done by Yim et al., 9 the chemistry of the resulting surface will be explained by VO . Results for the varying dominance of different defects suggest that the ratio of Tiint to VO in a sample depends on its preparation conditions. Modification to the VO model to consider excess electron donors and excess electrons will expand our knowledge of the surface chemistry of rutile TiO2 (110) surfaces in a more unified matter. Accounting for Tiint as an electron donor will allow us to understand surface chemical reactions on TiO2 more accurately, representing a step towards the development of TiO2 surfaces for specific applications such as photocatalysis.

CONCLUSIONS Explicit calculations with AIMD and static DFT showed that excess electrons introduced by Tiint localize on Ti sites and form polarons on rutile TiO2 (110) surfaces. Out of the four polarons introduced by one Tiint , the most stable structure was when one polaron was at Tiint and other three were at Ti5c-2nd . This result indicates that three quarters of excess electrons are trapped by Ti5c-2nd rather than stabilized near the Tiint region because of the electrostatic attraction of Tiint even without VO . It suggests that the behavior of excess electrons is influenced more strongly by the location, rather than the type of defect it originates from. Excess electrons associated with Tiint could contribute to surface reactions


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such as O2 adsorption or O adatom diffusion. 16,22 Our results support the modification of the classical VO model to explain surface chemistry to also consider the excess electrons introduced by various electron donors, rather than directly relating band gap states and VO . By generalizing the VO model, a greater variety of surface chemical reactions may be explained for not only TiO2 but also other metal oxides such as ZnO, CeO2 , and SnO2 .

Supporting Information Available A comparison of calculation results obtained using different values of Hubbard U is presented in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement The authors thank the Supercomputer Center, Institute for Solid State Physics, The University of Tokyo for use of their facilities.

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Figure 1: Schematic image of the surface slab model used in simulations. Small blue spheres represent titanium and large red spheres represent oxygen. Grouping of Ti sites was performed according to the row and depth of each Ti site. The “Near Tiint ” group was defined as the four rows near Tiint . Ti sites that did not belong to any group were denoted as the “other” group.



(b)

(a) Ti5c-1st Ti6c-1st Ti5c-2nd Ti6c-2nd Ti5c-3rd Ti6c-3rd Near Tiint Other 0

1000

2000

3000

4000

5000

6000 0.0

0.5

1.0

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Time (fs)

Distribution function of population

Figure 2: (a): Location of excess electrons during the simulation. The size of the circle indicates the population of excess electrons at specific Ti sites. Red, blue, dark green, and light green circles represent four, three, two, and one electron, respectively. Population of excess electrons at specific Ti sites. Grouping was performed as described in Figure 1. (b): Distribution function of the population calculated for each group.

1.2 1 0.8 Population

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0.6 0.4 0.2 0 3000

3200

3400

3600

3800

4000

Time (fs) NearTiint Ti6c−1st Ti5c−1st

Ti5c−2nd Ti6c−2nd Ti5c−3rd

Ti6c−3rd Other

Figure 3: The change in population of excess electrons between 3000 and 4000 fs. The duration of population being around 1 represents the lifetime of excess electrons at that site. Grouping of Ti sites was conducted as defined in Figure 1.


2.0

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Figure 4: Representative electronic structures calculated from different initial structures. Electron density corresponding to the band gap state is shown in yellow. Total energies of these structures are given in Table 1. The figures are ordered from the most stable structure A to the least stable structure D.



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Graphical TOC Entry


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Stability of Excess Electrons Introduced by Ti Interstitial in Rutile TiO2

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