Structure determination of the rutile-TiO 2 (110)-(1×2) surface using total-reflection high-energy positron diffraction (TRHEPD)

The exact structure of the rutile-TiO 2 (110)-(1 × 2) surface, which had been under debate over the past 30 years, was investigated using the newly developed technique of total-reflection high-energy positron diffraction (TRHEPD), which is a positron counterpart of reflection high-energy electron diffraction (RHEED). The rocking-curves for the 00-spot obtained from the experimental diffraction patterns were compared to the curves for various models calculated with a full-dynamical theory. It was found that the rocking-curves matched those for a surface consisting of a Ti 2 O 3 configuration, originally suggested by Onishi and Iwasawa [H. Onishi and Y. Iwasawa, Surf. Sci., 1994, 313 , L783], but with a further modification of atomic positions close to the ones proposed by Wang et al. [Q. Wang, A. R. Oganov, Q. Zhu and X. F. Zhou, Phys. Rev. Lett., 2014, 113 , 266101]. This result demonstrates that TRHEPD can distinguish between the existence and absence of the oxygen atoms on the topmost surface, and between the Ti atoms residing in positions at the interstitial-vertical sites and those at interstitial-horizontal sites.


Introduction
Titania (TiO 2 ) is a transition metal-oxide material used in a variety of applications including photo-catalysts [1][2][3] , metalnanoparticle catalyst supports, gas sensors and corrosionprotective coating materials [4][5][6] . In these applications, knowledge of the structure of the surface is a critical factor in the understanding of the processes involved and in the appraisal of their functionality. Single-crystal TiO 2 surfaces have been studied extensively as a testing ground for molecule-and metal-nanoparticle adsorptions [7][8][9][10][11][12][13] . High-quality TiO 2 surfaces, obtained by mechanochemical polishing and insitu cleaning in ultra-high vacuum (UHV), have been used in the investigations above to elucidate the mechanisms of catalytic reactions on an atomic level. Among the reconstructed rutile-TiO 2 (110) surfaces, the (1×1) structure has been found to be the most stable 13 . Its detailed atomic geometry has been studied intensively since the 1970s 13 using a number of techniques such as low-energy electron diffraction (LEED) 14 , surface X-ray diffraction (SXRD) 15, 16 and ab initio calculations with the density functional theory (DFT) 17,18 .  The early studies interpreted the (1×2) structure to be one where alternate rows of the bridging oxygen (labelled A in Figure 1) are missing from the (1×1) structure (missing-row model) 19 , as shown in Figure 2(a). However, this model is now discounted 13 . Onishi and Iwasawa proposed a Ti 2 O 3 (iv) model 20 , depicted in Figure 2(b). In this model, the Ti atoms (labelled 1 and 2) reside in positions at the so-called interstitial-vertical (iv) sites 20,23,24 Figure 2(c), is also mentioned in [24,28], where the Ti atoms (labelled 1 and 2) reside in positions at the interstitial-horizontal (ih) sites 24 . The vertical (z) coordinates of atomic positions are identical to those in the Ti 2 O 3 (iv) model (Figure 2 The LEED analyses in the previous investigations did not identify this structural difference 28 . To determine which of these models is plausible for the structure of the rutile-TiO 2 (110)-(1×2) surface, we have performed studies using total reflection high-energy positron diffraction (TRHEPD) which is the positron counterpart of reflection high-energy electron diffraction (RHEED).
When a positron beam impinges on a material surface at a glancing angle smaller than a certain critical value, it undergoes total-reflection because of the positive electrostatic potential inside the material 30,31 . Since the positrons do not penetrate into the bulk under this condition, the diffraction intensity depends entirely on the structure of the topmost surface. When the glancing angle is slightly larger than the critical value, the diffraction intensity depends on the immediate subsurface structure as well 30 ; the positrons penetrate into the bulk, being refracted toward the surface, and those elastically scattered contribute to the diffraction pattern. There are no contributions in the observed diffraction patterns from the region deeper than the depth determined by the direction of the refracted beam and the mean free path for the inelastic scattering of the positrons. This method was proposed by Ichimiya 31

Experimental
The details of the TRHEPD station at the KEK-SPF are described elsewhere 33,34 , with an overview of the method given here. A linac-based brightness-enhanced positron beam with an energy of 10 keV was impinged onto the samples (detailed below). The intensity of the incident beam was measured to be ~10 6 positrons/s, or ~0.1 pA. A phosphor screen behind the micro-channel-plates detected the diffracted positrons. The TRHEPD patterns on the screen were recorded with a charge-coupled-device camera and the data obtained was stored on a personal computer. For the structural analysis, the glancing angle (θ) of incidence dependence of the 00-spot diffraction intensity, called the "rocking-curve" 37 , was extracted from a series of the TRHEPD patterns taken with an exposure time of 2.5 min each. The glancing angle was typically varied from 0.5° to ~6° with a 0.1° step by rotating the sample. In this study, rutile-TiO 2 (110) crystals (5×10×0.5 mm 3 ) with mechanochemically polished surfaces were provided by the Crystal Base Co., Ltd. The samples for the (1×1) surface were prepared in a UHV chamber (of base pressure 1×10 -8 Pa) by a few cycles of Ar+ ion spattering (2 kV, 1 min at 5×10 -4 Pa) at room temperature, followed by annealing with an O 2 exposure (~875 K, 30 min at 1×10 -6 Pa). The resulting single-domain and well-ordered (1×1) surfaces were ascertained using a RHEED apparatus installed in the chamber after the TRHEPD measurements. Samples were then treated with further annealing in UHV (~1175 K, 30 min) to obtain the (1×2) surface. The resulting well-ordered (1×2) surfaces were similarly confirmed with RHEED after the TRHEPD measurements. There were no streak features noted in the diffraction patterns, which indicate that no transformations had taken place from the well-ordered (1×2) surface into the single-linked and/or the cross-linked (1×2) surface(s) 38,39 during this heat treatment.
No appreciable effects from beam irradiation or sample charge-up were observed during the TRHEPD measurements; this is attributed to the very low intensity of the positron beam (of ~0.1 pA). It has been reported for this surface 40 that the use of a weak beam current (of nA regime) is necessary in LEED experiments to avoid damage, which has been observed when standard currents (of μA regime) were used. Since the surface sensitivity of the positron is much higher than that of the electron 41 , TRHEPD measurements benefit from being able to use a much weaker beam than LEED. For both the rutile-TiO 2 (110)-(1×1) and the -(1×2) surfaces, rocking-curves were first obtained under a "one-beam" condition 37 , where the beam azimuthal angle was set at 23° off This journal is © The Royal Society of Chemistry 20xx Please do not adjust margins Please do not adjust margins the [11 ഥ 0] direction. Since the low order in-plane diffractions are suppressed for the beam incidence from this direction, the variation of the 00-spot intensity is almost solely dependent on the z coordinates of the atomic positions. The reduced number of structural parameters allows a simplified and efficient analysis to be performed for the atomic configuration in the direction normal to the surface. The discrimination between the Ti 2 O 3 (iv) and the Ti 2 O 3 (ih) models is not possible by the one-beam analysis since their atomic configurations normal to the surface are the same (see the side views of Figure 2(b) and 2(c)). Many-beam measurements, where the beam azimuths were set at the [11 ഥ 0] and [001] directions, were also performed to determine the in-plane coordinates of the atoms. The 00-spot intensity in such a condition depends on in-plane coordinates of atomic positions 42 , as well as the z coordinates which have been determined in the one-beam analysis.

Results and discussion
The open circles in Figure 3 show the experimental rockingcurve obtained for the (1×1) surface in the one-beam condition. The experimental uncertainty of each point is shown by the bar on the circle, and indicates the root-meansquare deviation of the average of the intensity obtained experimentally over three separate runs. The rocking-curve was calculated using the structure determined by the SXRD analysis 16 , adjusting the values of the parameters necessary for TRHEPD analysis 37 , which were: the averaged crystal potential (V crys ); the averaged imaginary potentials for Ti and O atoms via electronic excitations (ν eTi , ν eO ); and those via phonon scattering (ν pTi , ν pO ). The solid (red) curve in Figure 3 shows the calculated result giving the best (lowest) value for the reliability factor (R) 37  The optimised values of the parameters are: V crys = 19 V; ν eTi = 1.8 V; ν eO = 1.5 V; ν pTi = 0.8 V; and ν pO = 0.1 V. Further adjustments for the z coordinates of atomic positions (together with the parameter values) did not improve the R value. Thus, it has been reconfirmed by TRHEPD that the (1×1) structure determined by SXRD 16 is valid. The critical angle for the total-reflection corresponding to the above V crys value is 2.5° for the incident beam energy of 10 keV. The angular region for total-reflection is indicated by the line with an arrowhead in Figure 3. The open circles in Figure 4(a) show the experimental data for the (1×2) surface in the one-beam condition. The  Neither the missing-row (orange single-dotted-broken curve) model nor the Ti 3 O 5 (purple double-dotted-broken curve) model reproduces the peak-shape in the total-reflection region around θ = 1.5°, giving poor R values of 7.1% and 6.9%, respectively. Therefore, these models were eliminated as possible candidates and are not shown further.
The Ti 2 O 3 (blue broken curve), the Ti 2 O (green dotted curve) and the asymmetric-Ti 2 O 3 (red solid curve) models, giving R values of 4.6%, 5.3% and 3.1%, respectively, have a peak in the total-reflection region. Taking these three as the more likely contenders, their rocking-curves were recalculated to give better (smaller) R values by adjusting the z coordinates from those proposed 23,25,27 ; the results are shown in Figure   4(b) using the same key as in Figure 4(a Thus, the z coordinates of the atomic positions predicted by the "Ti 2 O 3 " configurations, as shown in Figures 2(b), 2(c) and 2(f), are essential for a correct (1×2) structural model. It is to be noted that TRHEPD has clearly distinguished between the presence (Figures 2(b), 2(c) and 2(f)) and absence ( Figures  2(e)) of the oxygen atoms on the topmost surface. This is clear evidence for the high sensitivity of the technique to the topmost surface structure.
The adjusted z coordinates of the atomic positions for the Ti 2 O 3 and the asymmetric-Ti 2 O 3 models are listed under (z) in Table 1. The uncertainty of z for each atom is estimated as follows. First, the standard deviation of the R obtained, D R , is calculated by using the R values between the rocking-curves for the individual measurement runs and that for their average (the D R obtained was 0.6% in the present case). Then, R is calculated between the rocking-curve for the best fit structure and that for the structure where the z coordinate of the atom in question alone deviates by Δz from that of the best fit structure. The value of Δz, which makes R increase by D R (0.6%), is assigned as the uncertainty of z for the atom in question.
In order to distinguish which of the "Ti 2 O 3 " models (the Ti 2 O 3 or the asymmeric-Ti 2 O 3 with (iv) and (ih) configurations) matched the (1×2) structure, many-beam rocking-curves were analysed. The open circles in Figure 5 Coordinates of atomic positions for the Ti 2 O 3 (iv) and the asymmetric-Ti 2 O 3 (iv) models (4) Ti (5) Ti (6)  The optimised results are shown by the blue broken curve for the Ti 2 O 3 (iv) model and the red solid curves for the asymmetric-Ti 2 O 3 (iv) model, where the in-plane coordinates along the [11 ഥ 0] direction are adjusted from those reported in [23,25], to give the best R values, while keeping the z coordinates fixed to those determined in the one-beam analysis.
The in-plane coordinates in question for those models with the respective (ih) configuration are identical to those with the (iv) configuration, since the in-plane coordinates along the [11 ഥ 0] direction are the same. The corresponding R values are 2.4% for the Ti 2 O 3 (iv, ih) model and 1.9% for the asymmetric- The open circles in Figure 5 The calculated results are shown by the blue broken curve for the Ti 2 O 3 (iv) model, the red solid curve for the asymmetric-Ti 2 O 3 (iv) model, the green dotted curve for the Ti 2 O 3 (ih) model and the orange cross-pointed curve for the asymmetric-Ti 2 O 3 (ih) model. The corresponding R values are 1.7% for the Ti 2 O 3 (iv) model, 1.8% for the asymmetric-Ti 2 O 3 (iv) model, 6.4% for the Ti 2 O 3 (ih) model and 5.7% for the asymmetric-Ti 2 O 3 (ih) model.
From Figure 5(b), it is clearly confirmed that the Ti atoms reside in positions at the interstitial-vertical (iv) sites 24 , and thus the model originally proposed by Onishi and Iwasawa 20 is more plausible for the (1×2) structure than that using the (ih) sites mentioned in [24,28]. The schematic views of these optimised configurations are shown in Figure 6(a) for the Ti 2 O 3 (iv) model and in Figure 6(b) for the asymmetric-Ti 2 O 3 (iv) model. The in-plane coordinates of the atomic positions for these models optimized in the above many-beam analysis are added in Table 1: (x) along the [ 11 ഥ 0 ] direction; and (y) along the [001] direction. The uncertainties are estimated similarly to those of z coordinates.
In the case of the incident beam direction set along the [001] direction ( Figure 5(a)), the R value for the asymmetric-Ti 2 O 3 (iv) model, 1.9%, was better than that for the Ti 2 O 3 (iv), 2.4%, while the corresponding R values were almost the same in the case of the incident beam direction set along the [11 ഥ 0] direction ( Figure 5(b)). In addition, that on the one-beam analysis for the asymmetric-Ti 2 O 3 (iv) model, 1.3% was better than that for the Ti 2 O 3 (iv), 1.7% (Figure 4(b)).
Our preliminary DFT calculation in fact shows that the Ti 2 O 3 (iv) model is unstable by 1.3 eV and the asymmetric-Ti 2 O 3 (iv) model is stable by 0.23 eV per (1×2) unit cell than the original Ti 2 O 3 (iv) model 23  Thus, from the TRHEPD analysis and the theoretical results, the asymmetric-Ti 2 O 3 (iv) model is the best candidate for the (1×2) structure.
For the Ti 2 O 3 (iv) model in Figure 6 (2). The lower tetrahedron is more distorted than the higher one, but now closer to an octahedron. Such a local octahedral structure is often found in high valence transition metal oxides, like an orthorhombic MoO 3 structure 43 .

Figs. 5
The TRHEPD rocking-curves for the rutile-TiO 2 (110)-(1×2) surface under the many-beam conditions: (a) along the [001] direction; and (b) along the [11 ത 0] direction. Open circles denote the experimental data. Uncertainties determined as for the data in Figure 3 are also shown. The calculated results are shown by the blue broken curves for the Ti 2 O 3 (iv) model, the red solid curves for the asymmetric-Ti 2 O 3 (iv) model, the green dotted curve for the Ti 2 O 3 (ih) model and the orange cross-pointed curve for the asymmetric-Ti 2 O 3 (ih) model. The results for the (ih) configuration are not shown in (a), because they coincide exactly with those for the corresponding (iv) configuration.