Titania single crystals with a curved surface

Abstract

Owing to its scientific and technological importance, crystallization as a ubiquitous phenomenon has been widely studied over centuries. Well-developed single crystals are generally enclosed by regular flat facets spontaneously to form polyhedral morphologies because of the well-known self-confinement principle for crystal growth. However, in nature, complex single crystalline calcitic skeleton of biological organisms generally has a curved external surface formed by specific interactions between organic moieties and biocompatible minerals. Here we show a new class of crystal surface of TiO₂ , which is enclosed by quasi continuous high-index microfacets and thus has a unique truncated biconic morphology. Such single crystals may open a new direction for crystal growth study since, in principle, crystal growth rates of all facets between two normal {101} and {011} crystal surfaces are almost identical. In other words, the facet with continuous Miller index can exist because of the continuous curvature on the crystal surface.

ARTICLE

Received 24 Jul 2014 | Accepted 23 Sep 2014 | Published 6 Nov 2014

Shuang Yang1,*, Bing Xing Yang2,*, Long Wu1,*, Yu Hang Li1, Porun Liu3, Huijun Zhao3, Yan Yan Yu2, Xue Qing Gong2 & Hua Gui Yang1,3

Owing to its scientic and technological importance, crystallization as a ubiquitous phenomenon has been widely studied over centuries. Well-developed single crystals are generally enclosed by regular at facets spontaneously to form polyhedral morphologies because of the well-known self-connement principle for crystal growth. However, in nature, complex single crystalline calcitic skeleton of biological organisms generally has a curved external surface formed by specic interactions between organic moieties and biocompatible minerals. Here we show a new class of crystal surface of TiO2, which is enclosed by quasi continuous high-index microfacets and thus has a unique truncated biconic morphology. Such single crystals may open a new direction for crystal growth study since, in principle, crystal growth rates of all facets between two normal {101} and {011} crystal surfaces are almost identical. In other words, the facet with continuous Miller index can exist because of the continuous curvature on the crystal surface.

DOI: 10.1038/ncomms6355

Titania single crystals with a curved surface

1 Key Laboratory for Ultrane Materials of Ministry of Education, School of Materials Science and Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China. 2 Key Laboratory for Advanced Materials, Centre for Computational Chemistry and Research Institute of Industrial Catalysis, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China. 3 Centre for Clean Environment and Energy, Gold Coast Campus, Grifth University, Gold Coast, Queensland 4222, Australia. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to X.Q.G. (email: mailto:[email protected]

Web End [email protected] ) or to H.G.Y. (email: mailto:[email protected]

Web End [email protected] ).

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Understanding the principles that determine crystal shape is a major challenge in many elds18. Theoretical studies of crystal morphology including Wulff construction and

current models of crystal growth mechanisms are all underpinned by a consensus that crystals are convex polyhedrons and the interface between crystals and surrounding media is at1. Such Wulff equilibrium crystal morphology has been extensively explored theoretically and experimentally for numerous atomic, molecular or even nanoparticle crystallization processes912. However, in nature, crystals with curved external surface, such as calcitic skeleton of biological organisms, usually exhibit unique mechanical property, light-management capacity and biological compatibility1316. Unfortunately, continuous curved surface has been scarcely discovered in articial single crystals. As an important semiconductor, TiO2 crystals have attracted intense research interests owing to its potential applications in a wide range of elds such as catalysis, photovoltaic cells, photochromic devices and gas sensors1728. For TiO2 crystals in the anatase phase, the equilibrium shape built through Wulff construction is a slightly truncated tetragonal bipyramid enclosed by eight thermodynamically stable {101} facets and two {001} facets2931.

Here we demonstrate a facile synthetic strategy to prepare unconventional TiO2 single crystals with a curved surface, in which organic citric acid (CA) and inorganic hydrouoric acid (HF) were used as synergistic capping agents. Such curved surfaces of TiO2 in anatase and rutile phase are composed of quasi continuous high-index microfacets. Moreover, we investigate the formation mechanism of curved crystal surface by density functional theory (DFT) calculations, which suggest the

key role of synergistic effects of chemisorbed HF and CA and, particularly, the concentration of CA and its competitive adsorption on the high-index surfaces (such as (112)) that provide unique stabilization effect on the formation of bicone-like curved anatase TiO2. The synthetic strategy in this work may be applied to other functional crystals, with practical applications in catalysis, photonics and bio-inspired materials.

Results

Synthesis and characterizations of round anatase TiO2. The

synthetic approach used in this work was on the basis of the method of Yang et al.19 via a hydrothermal reaction of titanium tetrauoride (TiF4), HF and CA as the precursor and co-capping agents, respectively. The inorganic capping agent of HF shows strong bonding to titanium species that could provide effective means for regulating the rate of hydrolysis and stabilizing specic high-reactive surfaces, such as (001) (refs 19,32). In the inset of Fig. 1a, we present the molecular structure of CA, which contains three carboxyl groups and one hydroxyl group; these molecular characteristics may provide various chemisorbed congurations on specic crystal surfaces, including monodentate, bidentate and/or other congurations3.

In contrast to the prior examples of faceted microcrystals4,19, the typical scanning electron microscope (SEM) images of the products reveal truncated biconic-shaped crystals with curved surface as shown in Fig. 1ac. All diffraction peaks in the X-ray diffraction (XRD) pattern can be well indexed to the crystal structure of anatase TiO2 phase (space group I41/amd, JCPDS No.

68.3 020 200

(001)

(001)

(001)

z

i

[010]

r1

(101)

(011)

(011)

(101)

iii

[afii9850]=0

[afii9850]=90

[afii9850]=90

h

[100]

ii

[afii9850]=45

r2

68.3

[afii9850]

(cos[afii9850], sin[afii9850], 1)

(011)

y

(101)

[afii9850]=0

[afii9850]=90

x

[afii9850]=45

[afii9850]=0

(112)

[afii9850]=45

Figure 1 | Structural determination and geometric analysis of round anatase TiO2 single crystals. (ac) High-magnication SEM images of the as-prepared anatase TiO2 single crystals viewed from various orientations. The inset in a shows three-dimensional (3D) molecular structure of the organic capping agent (CA). (d) Typical TEM images of a round anatase TiO2 single crystal indexed with [001] incidence. Single-crystal characteristic of anatase TiO2 phase can be conrmed by the SAED pattern in the inset. (e) High-resolution TEM image taken from c with [001] orientation. (f) Schematic illustration of the geometric model of the round anatase TiO2 single crystals. j, Azimuthal angle in spherical coordinate system. (g) Unfolded views of the facets (presented by different colours) of crystals synthesized with CA concentrations of (i) 0, (ii) 0.127 M and (iii) 0.476 M. Scale bars are 1 mm in ad and 1 nm in e.

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21-1,272)33, in good consistence with Raman data (Supplementary Fig. 1). The single crystal characteristic of the products was further conrmed using transmission electron microscopy (TEM) and corresponding selected area electron diffraction (SAED) pattern, as shown in Fig. 1d. According to the crystallographic symmetries of anatase TiO2, the at surfaces at both truncated ends must be {001} facets (further evidence is given in Fig. 1d). The round crystal prole of curved surface (Fig. 1d) reveals that the crystals may be enclosed by quasi continuous microfacets, rather than at surfaces, implying the equal growth rates of any facets other than {001}. High-resolution TEM image in Fig. 1e allows a direct view of the surface features of the curved microfacets. Evidently, the atomic arrangements of crystal surfaces change gradually resulting in quasi continuous vicinal microfacets, illustrating that our synthetic method favours a non-connement growth by forming numerous high-index microfacets. We then statistically analysed the geometric characteristics with a schematic model (Fig. 1f) of an ideally round anatase TiO2 single crystal. For the sample shown in

Fig. 1a, the average radius of the fringe circle (r1), the middle circle (r2) and the height (h) are 1.14, 1.94 and 1.97 mm, respectively (Supplementary Fig. 2). Further analysis based on these statistical results reveals that the interfacial angle between the frustum base plane and slant edge is 67.87 on average, being consistent with the interfacial angle between {001} and {101} facets of classical well-developed anatase TiO2 single crystals34.

Compared with the sample in Fig. 2, the anatase crystals obtained in shorter reaction times are also enclosed by curved surfaces with a smaller size (Supplementary Fig. 3).

Regarding the important role of CA in the formation of curved anatase TiO2 single crystal surfaces, we rst investigated its

concentration effect when the amount of uorine was kept constant in these experiments. Without CA, only truncated bipyramidal-shaped TiO2 single crystals (Fig. 2a) can be prepared through the anisotropic growth along {101} and {001} facets19.

Interestingly, when 0.127 M CA H2O was added into the

reaction media, additional {112} facets rst evolved along the crystal edges between the two {101} facets (see Fig. 2b). For anatase TiO2 single crystals synthesized with 0.238 M CA H2O,

more microfacets are exposed along the crystal edges and these quasi continuous microfacets clearly show some curvature at this stage (Fig. 2c). At 0.476 M CA H2O (Fig. 2d), round anatase

TiO2 single crystal surfaces can be observed, suggesting the surface transformation from at ones to quasi continuous high-index facets. Furthermore, by using 0.952 M CA H2O, the

obtained anatase TiO2 crystals exhibit uniform bicone-like morphology without any at surface as in the nonconnement growth (Fig. 2e). It has been illustrated in Fig. 2d,e that the interfacial angles between quasi continuous microfacets and {001} are always kept at 68.30. Thus, the relative proportion of at surfaces versus curved microfacets is largely dependent on the concentration of CA H2O in the reaction mixture, which

emphasized its unique effect of CA as an organic capping agent.

To better describe this crystal-formation behaviour, we present the unfolded views of the crystal surfaces (Fig. 1g) in which all vicinal facets are shown in different colours. The varying varieties and size of the coloured surfaces reect the continuous change of the external crystal facets that can be fullled by the addition of organic capping agents. As the concentrations of CA H2O

changed from 0 to a certain value, the facets of the unfolded parts for each individual crystals only correspond to two {101} facets at the beginning, and then give two {101} facets together with some

68.3

(001)

(101)

(112)

(001) (001)

(001)

(101)

(101)

[010]

[001] [001]

[001] [001]

[001]

[010]

[010]

[100] [100] [010]

[100]

[010] [100]

[100]

Figure 2 | SEM images and corresponding geometric models of anatase TiO2 single crystals synthesized with different amounts of CA. (a) Truncated octahedral bipyramidal anatase TiO2 single crystals with exposed {001} and {101} facets. (b) Polyhedral anatase TiO2 single crystals exposed with {001}, {101} and {112} facets. (c) Polyhedral anatase TiO2 single crystals enclosed with {001}, {101} and quasi continuous microfacets. (d) Round anatase TiO2 single crystals exposed with {001} and quasi continuous microfacets. (e) Round anatase TiO2 single crystals only exposed with quasi continuous microfacets. Scale bars are 1 mm. All crystals were synthesized in 5.33 mM TiF4 aqueous solution with 0 g (a), 0.8 g (b), 1.5 g (c), 3 g (d) and 6 g (e) of CA at 180 C for 20 h. Panels fj are corresponding geometric models shown in ae.

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minor {112} facets. The unfolded crystal facets nally evolve into countless small vicinal microfacets with continuously changing index. Combining the SEM and TEM results, we therefore refer to this synthetic method by using synergistic inorganicorganic capping agents as a non-connement growth.

Extending curved surface into rutile TiO2 crystals. The preferable adsorption of capping agents at specic facets is believed to determine the shape of the prepared nanoparticles3537. Therefore, further insight into the functionality of the molecular structures of organic capping agents was obtained by systematically testing ve other hydroxyl acids (Fig. 3ae). The crystal characteristics were conrmed using XRD spectra, TEM images and the SAED patterns (see details in Supplementary Figs 4 and 5). Lactic acid (CH3CH(OH)COOH) and glycolic acid (CH2(OH)COOH) have similar structures as they both have one carboxyl and one hydroxyl group, although the former contains one more methyl group. Both these capping agents give rise to curved convex disk-shaped rutile crystals with four {111} facets, as illustrated in Fig. 3f,g. The difference in thickness of the rutile crystals might be attributed to the additional methyl group in lactic acid. When using malic acid (HOOCCH2CH(OH)COOH)

with two carboxyl groups, octahedral rutile crystals were obtained with curved crystal edges (Fig. 3h). Interestingly, if we use tartaric acid (HOOCCH(OH)CH(OH)COOH) with even more hydroxyl groups, well-curved convex disk-shaped rutile crystals were prepared as shown in Fig. 3i. For the capping agents with more than two functional groups, new chemisorbed congurations may occur that favour the capping agents adsorption and further produce well-curved crystals without any at surface. By contrast, the capping agent containing rigid benzene ring structures such as salicylic acid (C6H4(OH)COOH) can only lead to the formation of truncated bipyramidal TiO2 anatase single crystals that can be rationalized by the reduced molecular exibility and large steric hindrance of the benzene in backbone (Fig. 3j). Hence, the number of functional groups, molecular exibility and steric hindrance may play a decisive role in the interaction of carboxyl and hydroxyl groups in the organic capping agents with crystal surfaces, which then results in substantial difference in morphologies and crystallographic polymorphs of TiO2.

Synergistic effect of organicinorganic capping agents. Moreover, no well-faceted anatase TiO2 single crystals can be synthesized in the absence of HF and CA as reported previously19, and

[110] [001]

[110] [110] [110]

[110]

[001] [110]

[010]

[110]

[001] [110]

[001]

[100]

[001]

Figure 3 | Controlling morphology and polymorph of round TiO2 single crystals via molecular structures of organic acids. (ae) 3D molecular structures of glycolic acid, lactic acid, malic acid, tartaric acid and salicylic acid as the organic capping agents. (fj) SEM images and (ko), corresponding geometric models of rutile TiO2 single crystals synthesized with the organic acids as shown in ae. Scale bars of the images in rst line and others are 5 and 1 mm, respectively. Note: anatase TiO2 single crystals were obtained by using salicylic acid.

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the surfaces of these crystals are at with small square shape that is likely to be (001) facets of anatase TiO2 (Supplementary Figs 2 and 6). Without hydrouoric acid, only spherical polycrystalline anatase TiO2 particles were prepared with irregular surfaces and, more importantly, no {112} facets and well-curved crystals can be observed even at high CA concentration. We therefore further believe that the essential factor for the nonconnement growth is the synergistic effect of hydrouoric and hydroxyl acids.

In order to better understand these experimental observations, we then performed systematic DFT calculations to illuminate the energetic origins of the synergistic effects of the different capping agents. Anatase TiO2 surfaces were modelled by periodic slabs, and 1 2 and 2 2 surface cells were used for (101) and (112)

surfaces, respectively. For the anatase TiO2 (112) surface, two different termination structures were considered in this work. The bulk-truncated (112) surface exhibits small dentate conformation, with unsaturated O2c and Ti5c being exposed (Supplementary

Fig. 7). Interestingly, we also found that by removing half of the dentate structural units from each surface cell we can actually obtain the 2 1 reconstructed (112) surface (see Supplementary

Fig. 7). Such termination with bigger dentate and much less compact conformation can undergo drastic relaxation during optimization. Accordingly, these two surfaces, donated as (112)-s and (112)-b, give the calculated surface energies of 0.73 and0.65 J m 2, respectively. To study the interaction between capping agents and crystal surfaces, we considered various possible congurations for the adsorption of HF and CA at (101), (112)-s and (112)-b surfaces. For their single adsorption, at most 8 (1), 16 (4) and 16 (1) HF (CA) molecules can adsorb at slab surfaces (top and bottom) of the (101), (112)-s and (112)-b slabs, respectively. The dissociative adsorption of HF gives rise to the formation of surface hydroxyls as well as TiF species and, for CA, each molecule forms two OTi bonds at the (112)-s and (112)-b surfaces but only one OTi bond at (101) (Supplementary Fig. 8). However, it should be noted that the dissociated CA at anatase TiO2 (112)-s forms the two OTi bonds at one carboxyl group in bidentate conguration, while that at (112)-b forms the

two OTi bonds at two carboxyl groups each and the CA adsorbs molecularly intact at (101).

The adsorption energies of HF and CA molecules were calculated by taking into consideration the solvation effect, and the results are listed in Supplementary Table 1, 2 and Table 1 (see equation 2). As we can see from the calculated average adsorption energies (Table 1), the bonding strengths of HF at the various (101) and (112) surfaces are very similar. However, for CA, it gives much higher adsorption energy (3.07 eV) at (112)-b than that at (101) (1.02 eV) or the other (112) surface (0.51 eV). This could be simply because that the adsorption congurations for dissociated HF at all the surfaces are very similar, while those for CA are quite different and only the dissociated CA at the (112)-b surface can form two strong OTi bonds and multiple H bonds between the three carboxyl groups and surface O. These results clearly indicate that the coexistence of CA in capping agents would have strong tendency to favour the occurrence of (112)-b surfaces. Moreover, considering that the extraordinarily strong interaction between CA and (112)-b occurs at the characteristic V-type ditch structure, one may also expect that, with the increasing amount of CA in the synergistic capping agents, (112)-b facets would occur rst since it has the highest concentration of such ditch structure and other high-index vicinal surfaces containing both (101) terrace and (112)-b would then gradually form. In addition, the preferential adsorption at surface ditch structures may largely explain why other polyacid or exible

Table 1 | Calculated average adsorption energies of HF and CA at TiO2 (101), (112)-s and (112)-b surfaces in solution.

Acid Adsorption energy (eV)

(101) (112)-s (112)-b HF 1.10 1.22 1.17

CA 1.02 0.51 3.07

CA, citric acid; HF, hydrouoric acid.

(001) O

O

(001)

(101)

O OH

HO OH

OH

(101)

(112)

Figure 4 | HF and CA molecules chemisorbed on TiO2 crystal surfaces. The polyhedrons are 3D Wulff construction diagrams of the anatase TiO2 crystals using the surface energies of HF-covered (001)/(101) (left), and CA/HF-covered (101) and (112)-b facets (right) in solution. The insets show the atomic model of capping agents (co-)chemisorbed on different crystal surfaces of anatase TiO2. Ti, O, H, F and C atoms are represented by balls in light grey, red, white, light blue and dark grey, respectively.

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Table 2 | Calculated surface energies (in J m 2) of the clean (g) and HF/CA co-covered anatase TiO2 (101) and (112)-b surfaces in solution (g0).

(101) (112)-b

g 0.44 0.65Ead 0.84 (HF CA) 1.05 (HF CA)

E0ad 0 0.21

g0 0.44 0.44

CA, citric acid; HF, hydrouoric acid.

Original (E ) and modied (E0 ) co-adsorption energies are also listed. These values were calculated with the same strategy as in ref. 42.

hydroxyl acid agents can have similar synergistic capping effect as CA as we have determined in our experimental studies. In fact, by carefully analysing the SEM images of the rutile crystals prepared in this work, we can nd that the curved surfaces are initiated at the 1 11

f g facets, which also gives clear ditch structure (see

Supplementary Fig. 9).

To further verify the synergistic effect of capping agents on the TiO2 morphologies, we also made Wulff construction plots (Fig. 4) by using the surface energies (Table 2) estimated by taking into consideration the adsorption and solvation effect of capping agents. It should be noted that, as one can see from Supplementary Fig. 8d,f, the favourable adsorption of the CA molecule at (101) and (112)-b surfaces still leaves free Ti5c and O2c sites because of its big size. Therefore, considering the coexistence of the two capping agents in solution, we calculated the surfaces with all the free sites occupied by dissociated HF. As shown in Fig. 4, the TiO2 crystal covered by

CA and HF gives rise to the shape in line with the experimental observation in the current work (see Fig. 2c), again conrming that such carboxylic acids can work as the co-capping agents with HF to favour the formation of the high-index surfaces and the corresponding biconic-shaped crystals with quasi continuous microfacets.

DiscussionUsing synergistic organicinorganic capping agents, we successfully prepared titania single crystals with a thermodynamically unexpected shape. The surface of TiO2 with regular curvature is composed of quasi continuous high-index microfacets and the Miller index (cosj, sinj, 1) of these microfacets also changes gradually between (101) and (011) crystal facets (see Supplementary Note 1). These ndings cannot be readily understood with the classical anisotropic crystal growth theories such as crystal self-connement and Wullf construction. Through DFT calculations, we found that the continuous bending of the external crystal surface can be attributed to the synergistic effects of chemisorbed hydrouoric acid and CA and, particularly, the unique adsorption mode of organic CA that favours its attachment to high-index facets.

We have also demonstrated the promise held by round TiO2 single crystals both in anatase and rutile phases (shown in Figs 1 and 3d) for the application as photocatalysts, with truncated bipyramidal-shaped anatase TiO2 single crystals (faceted TiO2, shown in Fig. 2a) as comparison. After removal of the capping agents, all the round TiO2 crystals show higher photocatalytic activities than faceted TiO2 crystals (see Supplementary Table 3, Supplementary Figs 10 and 11). Moreover, this synthetic strategy provides the principles for designing a new family of functional crystals with a non-at surface, which have potential applications in catalysis, photonics, bio-inspired materials and chemical mechanical planarization of advanced integrated circuits and may

also shed light on fundamental mechanisms of the organic inorganic interactions in the biomineralization process.

Methods

Synthesis of round TiO2 single crystals. Curved anatase TiO2 crystals were synthesized by a modied procedure reported in ref. 19. An aqueous TiF4 (Aldrich Chemical) solution (5.33 mM) was prepared by dissolving TiF4 in a weakly acidic solution that was adjusted to the pH of deionized water (B2.1) by the addition of hydrochloric acid (1.5 M). In a typical synthesis, 30 ml of TiF4 aqueous solution was added into a 50-ml Teon-lined reactor. Then 1.5 g CA monohydrate (C6H8O7 H2O, Aldrich Chemical) was put into the reactor subsequently and the

mixture was stirred for 5 min to form an aqueous solution by using a Teon-coated magnetic stirrer bar. After that, 0.4 ml of hydrouoric acid (10 wt%) was added to the above solution and the reactor was transferred into a stainless steel autoclave immediately. The Teon-lined autoclave was kept at 180 C for 1424 h in an electric oven. The autoclave was then cooled to room temperature under ambient environment. The solid products were collected from the bottom of the vessel. After that, the curved anatase TiO2 crystals were washed with deionized water three times and then dried in vacuum overnight.

Material characterizations. Crystallographic information of TiO2 single crystals was obtained with XRD (Bruker D8 Advanced Diffractometer with Cu Ka radiation). The morphology and structure of the samples were characterized by high-resolution TEM and SAED (JEOL JEM-2010F) and eld emission SEM (HITACHI S4800 and SEM, JOEL JSM 6380). Moreover, the crystal structure of the samples was determined with Raman spectroscopy (Renishaw, inVia Reex).

Theoretical calculations. DFT calculations have been performed with the PWScf code, which is part of the Quantum-Espresso package38. The plane-wave basis sets cutoffs for the smooth part of the wavefunctions and the augumented densities were 25 and 200 Ry, respectively. Electronion interactions were described using ultrasoft pseudopotentials39, with electrons from C, O, F 2s, 2p and Ti 3s, 3p, 3d, 4s shells were explicitly included in the calculations. For the anatase TiO2 (101) and (112) surfaces, they were modelled by slabs with 4 and 9 layers, respectively, and corresponding 1 2 1 and 1 1 1 k-point meshes were used. The adsorption

of HF and CA was modelled on both sides of the slab and, during optimization, all the slab and adsorbate atoms were allowed to move (force threshold was0.05 eV 1).

The surface energy of a clean anatase TiO2 (101) surface was taken from an

early DFT study in ref. 40, which employed nearly the same set of calculation setting and code. The surface energies of clean (112) surfaces were calculated by using the following equation:

Eslab n ETiO 2Ag 1

where Eslab is the total energy of the slab, ETiO is the energy of a bulk TiO2 unit, n is the number of TiO2 units in the slab and A is the exposed area of one side of the slab (the two sides of the slab are equivalent).

Considering the solvation effect, we calculated the adsorption energies of HF and CA at the anatase TiO2 surfaces by using the following equation:

Ead Esurf

mol

Ead sol n Emol Emol sol Esurf =n 2 in which Esurf is the total energy of the TiO2 slab, Emol is the total energy of the adsorbed molecule (HF or CA) in the gas phase, Esurfmol is the total energy of the system with adsorbed molecules at the surface, Eadsol and Emolsol are the solvation

energies of the HF (or CA)-covered slabs and a single HF or CA molecule, respectively. Specically, calculations for Emolsol were performed employing

the Gaussian 03 computational software package41. PBEPBE correlation functional in combination with the 6311 G (d,p) basis set were used42,43. The polarizable

continuum model was employed to include solvent (H2O) effects. In order to estimate Eadsol, we used the SIESTA code and the surface structures directly

obtained from PWScf calculations44. The long-range electrostatic solvationeffect for the systems in aqueous surroundings was taken into account by using a periodic continuum solvation model based on the modied PoissonBoltzmann equation4547. Moreover, in order to estimate the surface energies of surfaces covered by different capping agents in solution, the same strategy reported ina previous work was also used48.

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Acknowledgements

This work was nancially supported by the National Natural Science Foundation of China (21373083 and 21322307) and the National Basic Research Program (2011CB808505). We acknowledge Zhigang Chen for his support on TEM analysis.X.Q.G. also thanks the Shanghai Rising-Star Program (12QH1400700) and Computing time in the National Super Computing Center in Jinan.

Author contributions

H.G.Y. and X.Q.G. conceived the project and contributed to the design of the experiments and computations, analysis of the data and revising the paper. S.Y. performed the TiO2 crystal preparation and characterizations. L.W. and Y.H.L. performed measurements and data analyses of photocatalytic properties, XPS and Raman spectra. B.X.Y., Y.Y.Y. and X.Q.G. conducted DFT calculations and wrote part of the paper (calculation section). P.L. and H.Z. conducted the TEM examinations and contributed to writing the TEM sections. All the authors discussed the results and commented on the manuscript.

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How to cite this article: Yang, S. et al. Titania single crystals with a curved surface. Nat. Commun. 5:5355 doi: 10.1038/ncomms6355 (2014).

NATURE COMMUNICATIONS | 5:5355 | DOI: 10.1038/ncomms6355 | http://www.nature.com/naturecommunications

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