Ni cluster nucleation and growth on the anatase TiO₂(101) surface: a density functional theory study

Abstract

Density functional theory (DFT) calculations are carried out to study the nucleation and growth rule of Ni clusters on both a perfect and defective anatase TiO₂(101) surface using supported Ni_n (n = 1–6) cluster models. Our results show that a single Ni atom prefers to adsorb at the bridge site formed by two-coordinated oxygen (2cO) atoms on the perfect TiO₂(101) surface and at the 3cO-bridge site on the defective TiO₂(101) surface. The active site for Ni cluster growth on the perfect TiO₂(101) surface shifts from the bridge site of two 2cO atoms or the 2cO–6cTi–3cO bridge site for Ni₁, Ni₂, and Ni₃ clusters to the 2cO–5cTi bridge site for Ni₄, Ni₅, and Ni₆. The Ni cluster cohesive energy remains constant with cluster size variation on both the perfect and defective surface. The Ni–TiO₂ interaction is the main driving force of the initial Ni nucleation stage, and the Ni–Ni interaction begins to control the Ni_n cluster growth process with increased cluster size.

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1. Introduction

Transition metal clusters supported on metal-oxide substrates are attracting considerable attention because of their importance in heterogeneous catalysis.¹ A number of studies have indicated that the interaction between metal and support significantly affects the activity and selectivity of catalytic reactions.^2–5 Therefore, understanding metal cluster nucleation and growth on oxide support mechanisms is important to further explore the metal–support interaction and improve the catalytic activity of the systems.

Among the metal-oxide supports, TiO₂ is the most widely used in many processes such as hydrogenation,^6–8 CO oxidization,^9–11 and water splitting.^12–14 The two most common TiO₂ polymorphs are rutile and anatase. Rutile TiO₂ is the most widely studied form both experimentally and theoretically, whereas, anatase TiO₂ has been found to be dominant in the nanocrystalline phase.¹⁵ Extensive experimental and theoretical investigations have been performed on metal cluster nucleation and growth patterns, including Au,^16–22 Pt,^23–27 and Pd,^28–33 on both rutile and anatase TiO₂ surfaces.

Recently, some experiment and theoretical studies concerning Ni cluster deposition on rutile TiO₂(110) surfaces have been reported. Chen et al.³⁴ studied Ni and Cu growth on TiO₂(110) using scanning tunneling microscope (STM). They reported that Ni islands grew three dimensionally at room temperature, and although the Ni–TiO₂ interfacial energy should be greater than that of Cu–TiO₂, the Ni islands did not grow flatter on the surface compared to Cu, indicating that Ni islands were located preferably at step edges with high step edge density. This was further confirmed by the Tanner group's STM study.³⁵ Asakura and co-workers³⁶ investigated Ni cluster growth mode and morphology on a TiO₂(110) surface with a wide terrace using low coverage STM. They observed that many flat and small Ni islands were located on the terrace, not at step edges with low step density. The initial stage bonding structure and binding character of Ni thin-film growth on a rutile (110) surface using first-principle density functional theory were studied by Ellis et al.³⁷ Their results showed that Ni atoms in the first monolayer were preferentially adsorbed on top of bridging oxygen atoms and upon secondary surface oxygen. The bond strength between Ni adatom and substrate was much stronger than that between Ni adatoms. However, for Ni deposition on anatase TiO₂(101), almost no report was found until J. Chen and co-workers³⁸ found that nickel catalysts supported on ZrO₂ (monoclinic phase), SiO₂, TiO₂ (anatase phase), and γ-Al₂O₃, Ni/TiO₂ (anatase phase) showed the best catalytic hydrogenation performance of o-chloronitrobenzene to o-chloroaniline. The good Ni/TiO₂ performance was attributed to the strong N=O band polarization induced by TiO_x oxygen vacancies which was produced by high temperature reduction. Therefore, to explore Ni cluster deposition nucleation and growth mechanism deposition on anatase TiO₂(101) surface is essential. Meanwhile, the role of oxygen vacancies on the TiO₂ surface in dispersing and nucleating Ni clusters should be understood.

In the present work, we use anatase TiO₂(101) surface as the oxide support for depositing Ni_n (n = 1–6) clusters. DFT calculations on Ni cluster nucleation and growth mechanism on perfect and defective support surfaces were carried out. This work provides a fundamental understanding to further disclose the metal–support interaction and gives helpful design and synthesis instructions of supported Ni-based catalysts in heterogeneous catalysis.

2. Model catalysts and computational details

The calculated bulk anatase TiO₂ structure lattice constants: a = 3.776 Å, c = 9.486 Å were comparable with experimental data (ICSD #24276). The (101) surface was modeled with 11.33 × 10.21 × 17.84 Å dimensions, which included 1 × 3 sized supercell slab with 12 atomic layers. The vacuum region separating the slabs in the direction perpendicular to the surface was set to 12 Å. The atomic positions of the six uppermost layers were always fully relaxed. In addition, the oxygen vacancy was obtained by removing one surface 2cO atom (marked with green circle in Fig. 1b) from the 1 × 3 surface unit cell, corresponding to 1/6 oxygen vacancy density. The properties of isolated Ni_n clusters were calculated using a 15 × 15 × 15 Å cubic unit cell. Side (left panel) and top (right panel) view of the anatase TiO₂(101) surface are shown in Fig. 1.

Fig. 1 Side (a) and top (b) views of anatase TiO₂(101) supercell. The red is an O atom and the argent is an Ti atom.

The fully periodic plane-wave DFT calculations implemented in the Vienna Ab initio Simulation Program (VASP)^39,40 were employed. DFT calculations were performed with the generalized gradient approximation PW91 function⁴¹ implemented with projector augmented wave function (PAW)^42,43 for representing the non-valence core electrons. For better calculation accuracy, a 2 × 2 × 1 k-point grid determined by the Monkhorst–Pack method was used. The plane-wave cutoff energy was optimized at 400 eV. The convergence criteria for electronic self-consistent iteration were set to 1.0 × 10⁻⁴ eV, and the atomic positions were optimized by means of a conjugate-gradient algorithm until atomic forces were smaller than 0.02 eV Å⁻¹. Spin-polarized calculations were performed to account for the magnetic properties of nickel. Charge distributions were estimated using Bader's atoms in molecules (AIM) theory of using the algorithm developed by Henkelman.^44,45

To describe the interaction between Ni cluster and titania surface, adsorption energy is defined as follows:³³

E_ads = −[E(Ni_n/TiO₂) − E(TiO₂) − E(Ni_n)] (1)

where n is the total number of absorbed Ni atoms; E(Ni_n/TiO₂), E(TiO₂), and E(Ni_n) are the total energies of the TiO₂ substrate with Ni_n cluster, the bare TiO₂ substrate, and the free Ni_n cluster in the gas phase, respectively.

3. Results and discussion

3.1 Perfect and defective TiO₂(101) surface

Anatase TiO₂(101) surface presents a stepped structure, as shown in Fig. 1. 3-Fold-coordinational oxygen atoms (3cO) and 6-fold-coordinational titanium atoms (6cTi) were fully saturated whereas the 2cO and 5cTi atoms were coordinately unsaturated (these atoms are marked with black arrows in the side and top views of the surface in Fig. 1). After optimization, atomic positions of the six uppermost layers changed. The 3cO and 6cTi atoms rose by 0.41 and 0.21 Å, respectively, and the 2cO and 5cTi by 0.12 and 0.03 Å, respectively, relative to their bulk position. However, the 2cO–6cTi and 2cO–5cTi bond lengths shortened by 0.05 and 0.13 Å, respectively.

The oxygen vacancy was obtained by removing a bridging 2cO atom from a (1 × 3) surface supercell (vacancy coverage = 1/6 ML). Oxygen vacancy produced gave rise to significant structure relaxations and important changes of the electronic properties (changes of the electronic properties will be shown in 3.2.3 section). The original 6cTi and 5cTi atoms bound to the 2cO atom at the vacancy site become five- and four-coordinational, denoted as Ti_v-5c and Ti_v-4c, respectively. The 3cO atom under the oxygen vacancy relaxed upward by 0.29 Å. Ti_v-5c and Ti_v-4c relaxed inward by 0.06 and 0.09 Å, respectively. Both relaxed away from each other, which led to Ti_v-5c–3cO–Ti_v-4c angle change from 101.92° to 126.51° on the perfect surface.

The formation energy of an oxygen vacancy was defined with respect to the energy of an oxygen molecule and calculated according to: E = −[E_perfect − E_defective − 1/2E_O2]. Our calculated oxygen vacancy formation energy was 4.80 eV. The slab was kept neutral after 2cO was removed, causing some unpaired electrons. Bader charge analysis showed that the excess electrons were mainly localized at the Ti_v-5c and Ti_v-4c atoms.

3.1.1 Single Ni atom adsorption on the perfect and defective surface. Several possible initial adsorption sites for a single Ni adatom on anatase TiO₂(101) surface were tried. After optimization, three stable adsorption structures denoted as Ni_1,a, Ni_1,b, Ni_1,c as well as their adsorption energies are presented in Fig. 2. The description of the structures (Ni_1,b, Ni_1,c) are shown in ESI.† In the most stable structure Ni_1,a, the Ni atom adsorbed at a bridge site of two edge 2cO atoms (2cO-bridge site) along the [010] direction, with the Ni–2cO bond lengths of ∼1.88 Å, respectively. The Ni–2cO bond length was much shorter compared to Pt–2cO (2.06 Å),²⁶ Pd–2cO (2.06 Å),³³ and Ru–2cO (2.05 Å),⁴⁶ which led to stronger interaction between Ni and the TiO₂(101) surface. The Ni adsorption energy on TiO₂ surface was 3.03 eV which is much larger than the reported noble metal atom (0.39 eV for Au,²² 2.84 eV for Pt,²⁶ and 2.67 eV for Pd³³) and smaller compared to the Ru atom (3.59 eV)⁴⁶ on the TiO₂(101) surface. The isolated Ni, Au, Pd, Pt and Ru electronic configurations can explain the differences in adsorption mechanisms and energies. They possess different electronic structures with different electron distribution at the d and s levels. Gas phase Ni has a 3d⁸4s² electronic configuration whereas Au, Pd, Pt and Ru have a 5d¹⁰6s¹, 4d¹⁰, 5d⁹6s¹ and 4d⁷5s¹ electronic configuration, respectively. Ni has an emptier d band compared to Au, Pd, Pt and thus has more flexibility to create electronic interactions with the ions of the surface. Therefore, Ni has a stronger binding energy with the surface. Due to the emptiest d band of Ru, it has the strongest binding energy with the surface.

Fig. 2 Optimized structures of a single Ni adatom and their corresponding adsorption energy on a perfect anatase TiO₂(101) surface: (a) Ni_1,a; (b) Ni_1,b; (c) Ni_1,c. Their corresponding adsorption energy on the surface are also shown in the figure.

Six possible single Ni adatom adsorption sites on the defective TiO₂(101) surface have been searched. The relaxed structures (Ni_1,A and Ni_1,B) and their adsorption energies are shown in Fig. 3. The description of Ni_1,B is shown in ESI.† Completely different from Au, Pt and Pd,^22,26,33 the preferable adsorption site for the Ni adatom on the defective surface was not the oxygen vacancy, but the bridge site of two 3cO atoms, with the Ni–3cO bond lengths of 1.87 (left) and 1.89 Å (right), respectively. Ni insertion in the middle of two 3cO atoms pulled these two 3cO atoms close to each other by 0.13 Å, and the right 3cO moved to left by 0.14 Å compared to the clean surface. The 3cO atom movement weakened the 3cO bond strength with its left and right side Ti atoms (Ti^a and Ti^b, respectively), and especially the interaction force of 3cO–Ti^b was nearly zero. The interaction between the Ni adatom and the remaining 2cO atom was much weaker than that in the perfect surface with the Ni–2cO bond length of 2.02 Å. The adsorption energy of Ni_1A was 3.10 eV, which is a little higher than the 3.03 eV of Ni_1a in the perfect surface.

Fig. 3 Optimized structures of a single Ni adatom and their corresponding adsorption energy on a defective anatase TiO₂(101) surface: (a) Ni_1,A; (b) Ni_1,B. Their corresponding adsorption energy on the surface are also shown in the figure.

3.1.2 Density of states and Bader charge analysis of the two structure kinds. The total density of state (DOS) plots for the clean perfect and defective TiO₂(101) as well as Ni_1,a and Ni_1,A are shown in Fig. 4. The Fermi level of the clean perfect anatase TiO₂(101) surface is at the top of the valence band. After Ni adsorbed at the perfect anatase (101) surface, the Fermi level moved to the bottom of the conduction band and the band gap was partly filled by the Pd states, which are almost Pd 4d-state contributions. Similarly, creation of a surface oxygen vacancy also shifted the Fermi level to the conduction band, indicating the electrons left behind by removing a neutral oxygen atom fill the antibonding orbitals. At the same time, the position of the Fermi level did not change after Ni adsorption at the oxygen vacancy. The Pd states induced not only in the band gap but also at the top of the valance band.

Fig. 4 Density of state for the (a) perfect TiO₂(101) surface (top) and Ni_1,a (bottom) and (b) defective TiO₂(101) surface (top) and Ni_1,A (bottom). The local DOS of Ni, which contributes to the total DOS in Ni_1,a and Ni_1,A, is represented in red color.

To gain further insight of the bonding nature between the supported Ni adatom and the TiO₂ support, Bader charge analysis was conducted. The Bader charges of Ni_1,a and the surface atoms which are directly associated with the Ni adatom on the perfect anatase TiO₂(101) surface, are shown in Table 1S (in the ESI†). The Ni atom was positively charged with a charge of 0.55e, suggesting charge transfer occurrence from the Ni atom to the TiO₂ surface. After Ni atom adsorption on the TiO₂ surface, 2cO¹, 2cO², 3cO¹ and 3cO² atoms that directly bonded to Ni atom became more negative owing to receiving a charge of 0.11e, 0.11e, 0.03e and 0.02e, respectively, while 5cTi and 6cTi atoms became less positive. This indicated further that all Ti and O atom types which directly interact with Ni atoms, are all electron receptors. Furthermore, the amounts of charge order transferred from Ni to 2cO, 3cO, and Ti atoms were consistent to their bond strengths. The Ni–2cO bond length was the shortest compared to Ni–Ti and Ni–3cO, which means the strongest bond strength, hence, 2cO¹ and 2cO² gained the most charge amount (both 0.11e) from Ni atom. The results indicate that the interaction between Ni atom and the surface TiO₂ atoms was formed via the electron transported among them.

The Ni_1,A and Ni_1,B atom net charge analysis and of their adjacent atoms with defective surface, is shown in Tables 2S and 3S, respectively (in the ESI†). With the same situation as Table 1S,† Ni_1,A was also an electron donor of the defective surface and the net charges were not equally distributed among all atoms bonded with Ni_1,A. Surprisingly, although Ni–3cO^a and Ni–3cO^b bond strengths are the strongest, the charge amount 3cO^a obtained was less than that of 2cO, Ti_v-5c, and Ti_v-4c atom gains, while the charge density of 3cO^b was almost constant. From the previous analysis, we know that Ni insertion pulls 3cO^a and 3cO^b atoms close together resulting to 3cO^a–Ti^a and 3cO^b–Ti^b bond strength weakening. Therefore, in addition to charge amount from Ni atom, 3cO^a and 3cO^b atoms can only accept less charge amounts from Ti^a and Ti^b, respectively, after Ni_1,A disposition on the defective TiO₂(101) surface. In spite of higher adsorption energy of Ni_1,A than Ni_1,a on the TiO₂(101) surface, Ni_1,A atom transfers less charge amount (0.35e) compared to Ni_1,a. No direct correlation between the stability of the configuration and the amount of charge that is transferred was apparent. When the Ni_1,B occupied the oxygen vacancy site, it was negatively charged with a charge of −0.29e, indicating that some charges were transferred from the TiO₂(101) surface to Ni atom. Moreover, the Ni atom deposition on the TiO₂ surface resulted in charge density increase on the Ti_v-5c and Ti_v-4c atoms and charge density decrease on the 3cO atom (marked with 3cO^v in Fig. 3b) under the oxygen vacancy and 3cO atoms (marked with 3cO¹, 3cO², 3cO³ and 3cO⁴ in Fig. 3b) directly bound to Ti_v-5c and Ti_v-4c atoms. Therefore, Ni atom interaction with the defective surface was similar to a back-donation interaction⁴⁷ where the Ni metal promotes a charge transfer from the surface oxygen to the Ti_v-5c and Ti_v-4c atoms.

3.2 Adsorption of Ni₂ on the perfect and defective surface

After searching different possible sites for Ni dimer adsorption on perfect anatase TiO₂(101) surface, four stable structures denoted as Ni_2,a, Ni_2,b, Ni_2,c and Ni_2,d as well as their adsorption energies were obtained and they are shown in Fig. 5. Ni_2,b, Ni_2,c and Ni_2,d are described in ESI.† The Ni–Ni bonds are parallel to the TiO₂(101) surface in all four structures. Ni_2,a was built by adding the second Ni atom to the most stable single Ni adsorption (Ni_1,a) and allowing the structures to relax again. It presents the most stable structure with a Ni atom located at the 2cO bridge site, another Ni adatom adsorbed at the 2cO–6cTi–3cO bridge site. The Ni1–Ni2 distance was 2.56 Å, which is significantly longer than the 2.09 Å of the calculated gas-phase Ni dimer. Combined with various single Ni atom adsorption energies on different surface sites, it can be concluded that the decreasing sequence for Ni adsorption active site is 2cO bridge site, 2cO–6cTi–3cO bridge site, and 2cO–5cTi bridge site.

Fig. 5 Adsorption structures and energies of Ni dimer on the perfect anatase TiO₂(101) surface. (a) Ni_2,a; (b) Ni_2,b; (c) Ni_2,c; and (d) Ni_2,d.

Three stable adsorbed structures of Ni dimer on defective TiO₂ surface as well as their adsorption energies were obtained, namely, Ni_2,A, Ni_2,B, Ni_2,C and they are shown in Fig. 6. The description of Ni_2,B and Ni_2,C are presented in ESI.† The preferable Ni dimer adsorption sites on defective TiO₂(101) surface are shown in Fig. 5a, wherein Ni1 adatom is located at the oxygen vacation, and Ni2 sites are in between Ni1 and one nearby 2cO site. Moreover, Ni2 atom preferred a slight displacement to the left of Ni1 atom thus Ni2 atom has no interaction with its neighboring right 3cO atom. The Ni1–Ni2 bond length was 2.27 Å, which is much shorter than that of Ni₂ on a perfect surface, but is longer than the Ni–Ni bond (2.09 Å) in the gas-phase. This indicates stronger interaction of Ni1 and Ni2 in defective surface than in the perfect surface. The adsorption energy of Ni_2,A was 3.81 eV, which is higher by about 0.80 eV than that of the Ni dimer on a perfect surface. However, this most stable Ni dimer structure adsorbed on the defective TiO₂(101) surface is different from the adsorbed Au dimer and Pd dimer,^22,33 but similar with the Pt dimer.²⁷

Fig. 6 Adsorption structures and energies of Ni dimer on the defective anatase TiO₂(101) surface. (a) Ni_2,A; (b) Ni_2,B; (c) Ni_2,C.

3.3 Ni₃ adsorption on the perfect and defective surface

Two kinds of Ni trimer structures at the gas phase were considered (i.e., linear and triangular configurations) as the initial states absorbed on the perfect surface. The configurations of Ni_3,a, Ni_3,b, Ni_3,c, Ni_3,d as well as their adsorption energies were determined in Fig. 7. The description of Ni_3,b, Ni_3,c and Ni_3,d are shown in ESI.† Ni_3,a, the most stable adsorption configurations, was obtained by adding a third Ni adatom to the Ni_2,b structure, in which two Ni atoms symmetrically occupied 2cO–6cTi–3cO bridge sites. The third Ni atom was bound at the 2cO-bridge site and the plane formed by these three Ni atoms was almost parallel with the TiO₂ terrace. The Ni1–Ni2, Ni1–Ni3 and Ni2–Ni3 bond lengths were 2.50, 2.45 and 2.46 Å, respectively. The Ni1–Ni2 bond parallel to the 2cO–2cO bond was slightly longer than the other two Ni–Ni bonds, but shorter compared to the dimer Ni_2,d, indicating Ni3 adatom strengthens the interaction between Ni1 and Ni2 atoms. The stability order of these Ni₃ trimers on the perfect anatase TiO₂(101) surface further demonstrated that the 2cO–6cTi–3cO bridge site was much more active than the 2cO–5cTi bridge site for Ni cluster adsorption.

Fig. 7 Top (left) and side views (right) of the stable structures and energies for Ni trimer adsorption on the perfect anatase TiO₂(101) surface: (a) Ni_3,a; (b) Ni_3,b; (c) Ni_3,c; (d) Ni_3,d.

Various possible Ni₃ adsorptions (triangular and linear) on the defective anatase TiO₂(101) surface were investigated. Four Ni₃ stable adsorption structures (Ni_3,A, Ni_3,B, Ni_3,C and Ni_3,D) as well as their adsorption energies were determined and they are shown in Fig. 8. The description of Ni_3,C and Ni_3,D are shown in ESI.† Ni_3,A and Ni_3,B were the most stable structures with similar adsorption energies (4.79 and 4.74 eV, respectively). Ni_3,A resulted from relaxing initial structures constructed from adding a third Ni atom over the Ti_v-5c atom of Ni_2,B. In this structure, the Ni3 atom rose above the surface with Ni3–Ti_v-4c distance of 2.35 Å, which made the triangle plane almost perpendicular to the terrace of TiO₂(101) surface. The Ni1–Ni2, Ni1–Ni3, and Ni2–Ni3 bond lengths were 2.46, 2.28 and 2.26 Å, respectively. Ni_3,B was obtained based on Ni_2,B by adding a third atom on the 3cO and Ti_v-5c bridge site. The Ni₃ triangle was almost parallel to the TiO₂(101) terrace and the Ni1–Ni2, Ni1–Ni3, and Ni2–Ni3 lengths were 2.46, 2.29 and 2.29 Å, respectively. In contrast to Ni_2,A dimer, the Ni1–Ni2 length was elongated by 0.19 Å with the Ni3 atom in both Ni_3,A and Ni_3,B structure.

Fig. 8 Top (left) and side views (right) of the stable structures and energies for Ni trimer adsorption on the defective anatase TiO₂(101) surface: (a) Ni_3,A; (b) Ni_3,B; (c) Ni_3,C and (d) Ni_3,D.

3.4 Ni₄, Ni₅, and Ni₆ adsorptions on the perfect and defective surface

Both 2D and 3D structures of Ni_n (n = 4, 5, and 6) and their different possible adsorption sites on the perfect anatase TiO₂(101) surface have been searched. Three stable Ni₄ configurations and the most stable Ni₅ and Ni₆ structures, and their adsorption energies are shown in Fig. 9. The description of Ni_4,b and Ni_4,c are shown in ESI.† Ni₄ cluster most preferred a tetrahedral structure (Fig. 8a) by adding the fourth Ni atom on top of the triangle Ni plane based on the configuration of Ni_3,c. Interestingly, the Ni trimer active sites grown to Ni tetrahedron on the perfect anatase TiO₂(101) surface was shifted. Ni₃ would likely grow based on the 2cO–6cTi–3cO bridge site while Ni₄ prefered nucleation at the 2cO–5cTi bridge site. The Ni₅ and Ni₆ clusters both preferred 3D geometries (Ni_5,a and Ni_6,a) than 2D structures and their last atom was introduced based on the Ni_n−1 geometry.

Fig. 9 Top (left) and side views (right) of the stable structures and energies for Ni₄, Ni₅ and Ni₆ adsorption on the perfect anatase TiO₂(101) surface: (a) Ni_4,a; (b) Ni_4,b; (c) Ni_4,c; (d) Ni_5,a; (e) Ni_6,a.

Various possible 2D and 3D Ni_n (n = 4, 5, and 6) cluster structures adsorbed on the defective anatase TiO₂(101) surface, were considered and only the most stable geometries with their adsorption energies are shown in Fig. 10. For Ni_4,A, the geometry can be treated as a combination of Ni_3,A and Ni_3,B configurations in which Ni1 and Ni2 atoms almost symmetrically distribute two sides of the oxygen vacancy site, Ni3 atom bridges the 3cO and Ti_v-5c and Ni4 atom binds with Ti_v-4c. In Ni_5,A configuration, the fifth Ni atom was added right above the Ni1, Ni3, and Ni4 triangular plane. In Ni_6,A, Ni4 and Ni5 atoms symmetrically occupied two sides of Ti_v-4c while other atoms were nearly distributed at the same sites as those of Ni_4,A. Ni_n (n = 4, 5, and 6) clusters on the defective surface also tended to present 3D geometries. As atom number increased, the Ni_n cluster transformed from 2D (n < 4) to 3D geometry (n = 4, 5, and 6) on both perfect and defective anatase TiO₂(101) surfaces, which has similar trend to that of Pd and Ru clusters on the TiO₂(101) surface.^33,46

Fig. 10 Top (left) and side views (right) of the stable structures and energies for Ni₄, Ni₅ and Ni₆ adsorption on the defective anatase TiO₂(101) surface: (a) Ni_4,A; (b) Ni_5,A; (c) Ni_6,A.

3.5 Ni cluster nucleation and growth rule on anatase TiO₂(101) surface

According to the various geometry of Ni_n (n = 1–6) stable adsorption on the perfect and defective TiO₂(101) surfaces, we made some conclusions: a single Ni atom prefers to adsorb at the 2cO-bridge site on the perfect TiO₂(101) surface, and 3cO-bridge site on the defective TiO₂(101) surface, whereas the oxygen vacancy is the most active site for Au, Pt and Pd deposition on the defective surface.^22,27,33 Furthermore, a single Ni atom prefers 2cO-bridge site rather than 2cO–5cTi bridge site, and the Ni atoms of Ni₂ and Ni₃ clusters both prefer to occupy the 2cO-bridge site or 2cO–6cTi–3cO bridge site on the perfect TiO₂(101) surface. However, when n was greater than four, the Ni_n growth was based on the 2cO–5cTi bridge site. For Ni_n (n = 1–6) clusters on the defective TiO₂(101) surface, the nucleation site was constant with Ni atoms bridging two 3cO atoms. Like Pd and Ru clusters,^33,46 the adsorbed Ni₃ clusters prefer to form planar triangles and the adsorbed Ni₄, Ni₅ and Ni₆ clusters tend to three-dimensional structures on both perfect and defective TiO₂ surfaces.

To further understand the rule and mechanism of Ni_n clusters nucleation on the TiO₂(101) surface, the cohesive energy (E_coh) is defined in this paper in addition to E_ads. The definition of the cohesive energy of adsorbed Ni clusters is as follows:⁴⁶

E_coh = −[E(Ni_n/TiO₂) − E(TiO₂) − nE(Ni)]/n (2)

where E(Ni) is the total energy of a free Ni atom in the gas phase and n is the number of Ni atoms in the Ni_n clusters. Apparently, E_ads = E_coh for a single Ni adatom on the surface. E_coh represents the ability of metal atoms to grow together on the TiO₂(101) surface. The cohesive energy for Ni_n (n = 1–6) and Au_n (n = 1–3)²² and Pt_n (n = 1–6)^26,27 as a function of cluster sizes are shown in Fig. 11. At the perfect TiO₂ surface, for Pt and Au clusters, E_coh increases gradually with the increase of cluster size indicating that the Pt and Au atoms easily form big clusters. By contrast, because their cohesive energy decreased as the size of metal cluster became bigger signifies that when the size of the cluster increased, the advantage of the oxygen vacancy as the nucleation center for Pt and Au clustering was expected to diminish eventually. Compared to Pt and Au clusters, the cohesive energy of Ni clusters was almost kept constant with variation of the cluster sizes both on the perfect and defective surface. Moreover, the clustering energy on the defective surface was greater indicating that the 3cO bridge site of defective surface has some advantages over the bridging 2cO site on the perfect surface as an anchoring site for the adsorbed Ni particle.

Fig. 11 Cohesive energy of Ni, Au and Pt on the perfect and defective anatase TiO₂(101) surfaces at different cluster sizes.

What then is the driving force for the growth of Ni clusters? Exploring the definition essence of the cohesive energy, Ni–Ni and Ni–TiO₂ interaction jointly dominated the nucleation behavior of Ni_n clusters. Therefore, we can divide the cohesive energy (E_coh) of adsorbed Ni cluster at the perfect and defective TiO₂(101) surface into two parts: one is E_Ni–TiO2 and the other one is E_Ni–Ni. In addition, the average binding energy of isolated Ni_n (n = 2–6) clusters, E_bind (Ni_n), was introduced. The definition of E_Ni–TiO2, E_Ni–Ni (ref. 33) and E_bind (Ni_n)⁴⁸ are as follows:

E(Ni–TiO₂) = −[E(Ni_n/TiO₂) − E(TiO₂) − E(Ni_n*)]/n (3)

E(Ni–Ni) = E_coh − E_Ni–TiO2 (4)

E_bind(Ni_n) = −[E(Ni_n) − n × E(Ni)]/n (5)

where the E(Ni_n*) represent the total energy of adsorbed Ni_n cluster (not in the gas phase). E_bind is the average Ni–Ni interaction of bare Ni clusters.

The variation of E_Ni–TiO2 and E_Ni–Ni of bare and adsorbed Ni_n clusters with the cluster sizes are shown in Fig. 12. The interaction between a single Ni atom and both the perfect and defective surface was the strongest and then upon Ni adatom addition, the interactions both gradually weakened. However, the Ni–Ni interactions began to increase from zero to one with Ni atoms in both the perfect and defective surfaces. For Ni₁ and Ni₂ clusters absorbed on the perfect and defective surface, the Ni–TiO₂ interaction was much larger than the Ni–Ni interaction, indicating that the Ni–TiO₂ interaction was the main driving force at the initial stage of Ni nucleation. With regard to Ni₄, Ni₅ and Ni₆ clusters, the Ni–Ni interactions have greatly exceeded the Ni–TiO₂ interaction, showing that the Ni–Ni interaction begins to control the growth process of Ni_n clusters as the cluster size gets larger. This is why Ni₁, Ni₂ and Ni₃ clusters preferably occupy the active sites like 2cO-bridge site or 2cO–6cTi–3cO bridge site, whereas Ni₄, Ni₅ and Ni₆ tend to aggregate at the inactive 2cO–5cTi bridge site to reduce the Ni–TiO₂ interaction. The Ni–Ni interaction for Ni₂ and Ni₃ clusters on the perfect surface was stronger than on the defective surface, while that for Ni₄, Ni₅ and Ni₆ clusters were nearly equal on these two kinds of surfaces. Compared to bare clusters, the perfect surface weakens the strength of Ni–Ni interaction to a certain degree, whereas the strength would not be affected by the defective surface.

Fig. 12 Variation of E_Ni–TiO2 and E_Ni–Ni with the cluster sizes of Ni on the perfect and defective anatase TiO₂(101) surface as well as E_Ni–Ni for bare Ni.

4. Conclusion

First principles DFT calculations were carried out to investigate the energetically stable adsorption structures of Ni_n (n = 1–6) clusters at both perfect and defective anatase TiO₂(101) surface and further disclose the nucleation and growth rule of Ni clusters on these two kinds of surfaces. Our results show that a single Ni atom prefers to adsorb at the 2cO-bridge site on the perfect TiO₂(101) surface, and 3cO-bridge site on the defective TiO₂(101) surface (not the oxygen vacancy). The active site for Ni cluster growth on the perfect TiO₂(101) surface shifted from the bridge site of two 2cO atoms or 2cO–6cTi–3cO bridge site for Ni₁, Ni₂ and Ni₃ clusters to the 2cO–5cTi bridge site for Ni₄, Ni₅ and Ni₆. The adsorbed Ni₃ clusters prefer to form planar triangles and the adsorbed Ni₄, Ni₅ and Ni₆ clusters tend to 3D structures on both perfect and defective TiO₂ surfaces.

The cohesive energy of Ni cluster was almost kept constant with variation of the cluster sizes on both the perfect and defective surface. Moreover, the clustering energy on the defective surface was larger than that on the perfect surface. The Ni–TiO₂ interaction was the main driving force at the initial stage of Ni nucleation and the Ni–Ni interaction began to control the growth process of Ni_n clusters as the cluster size gets larger.

Acknowledgements

We gratefully acknowledge the National Natural Science Foundation of China (NSFC, Grant no. 11304208), the National Natural Science Funds of China (NSFC, Grant no. U1203293) and the Ph.D. Programs Foundation of the Xinjiang Production and Construction Corps (no. 2013BB010).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra13975e

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