The effect of γ-Al₂O₃ surface hydroxylation on the stability and nucleation of Ni in Ni/γ-Al₂O₃ catalyst: a theoretical study

Abstract

Using recent well-defined models of γ-Al₂O₃ surfaces, the interactions of Ni_n(n = 1–7) clusters with different γ-Al₂O₃ surfaces have been investigated in order to illustrate, by density functional theory periodic calculations, the effect of γ-Al₂O₃ surface hydroxylation on the stability and nucleation of Ni in Ni/γ-Al₂O₃ catalyst. Three types of γ-Al₂O₃ surfaces, dehydrated γ-Al₂O₃(100), dehydrated γ-Al₂O₃(110) and hydrated γ-Al₂O₃(110) were considered. Our results show that for the adsorption of Ni_n(n = 3–7) clusters, the γ-Al₂O₃(110) surface is more favorable than the γ-Al₂O₃(100) surface, however, for single Ni atoms and Ni₂ clusters, the reverse becomes true. Meanwhile, for the adsorption of Ni_n(n = 2–7) clusters, the hydrated (110) surface is not favorable compared to the dehydrated (110) surface, due to the presence of surface hydroxyls on the former. The reverse is true for single Ni atoms due to weaker surface deformation. Further, the support stabilizes Ni_n(n = 2–7) clusters well in the supported state, in which the presence of surface hydroxyls reduces the stability of the supported Ni_n clusters. On the other hand, the nucleation ability of Ni_n clusters on different γ-Al₂O₃ surfaces, is more favorable on the γ-Al₂O₃(110) surface than on the γ-Al₂O₃(100) surface, and the dehydrated (110) surface is more favorable than the hydrated (110) surface due to the presence of surface hydroxyls, namely, surface hydroxylation reduces the nucleation ability of Ni_n clusters on the γ-Al₂O₃ surface. More importantly, the exothermicity of supported Ni_n(n = 2–7) clusters on different γ-Al₂O₃ surfaces is lower than that of isolated Ni_n clusters, indicating that the support is not favorable for the nucleation of Ni_n(n = 2–7) clusters, as a result, the support can inhibit the aggregation of clusters, and favors the formation of small clusters.

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1. Introduction

Oxide-supported metal catalysts play a pivotal role in a lot of technologically important applications, including sensors, solid oxide fuel cells, and heterogeneous catalysts.¹ Among the oxide-supported metal catalysts, Ni-based catalysts are often used in industrial processes such as the hydrogenation, hydrotreatment and hydrogenolysis of hydrocarbons, steam reforming of hydrocarbons, and methanation.^2–5 Different supports are widely used to disperse Ni particles, such as γ-Al₂O₃,^6,7 TiO₂,⁸ CeO₂,⁹ SiO₂ ^10,11 or La₂O₃,⁷ among them, γ-Al₂O₃ is one of the most common supports as its large surface area and high degree of porosity favors the good dispersion of active species.¹²

Hydroxylation is a common process that occurs in many processes.^13–18 For the oxide-supported metal catalysts, the hydroxylation of the oxide support has an effect on the metal–support interaction, and further on the reactions taking place on the catalyst.^19–24 For example, Cu(111) and Cu/TiO₂(110) are both active towards the water–gas shift (WGS) reaction, however, due to the surface hydroxylation of the TiO₂ support, the Cu/TiO₂(110) catalyst has a much higher catalytic activity in the WGS reaction than the Cu(111) catalyst.¹⁹ For γ-Al₂O₃-supported metal catalysts, under normal reaction conditions, the surface of the γ-Al₂O₃ support inevitably becomes hydrated/hydroxylated; subsequently, the surface nature of the support changes,^22–29 this change affects both the metal–support interaction and the reactions taking place over the catalyst. For example, Valero et al.³⁰ have investigated the effect of γ-Al₂O₃ surface hydroxylation on the stability and diffusion of a single Pd atom, and found that the binding energy of the Pd atom decreases as the OH coverage of the γ-Al₂O₃ surface increases. In addition, previous studies have shown the effect of γ-Al₂O₃ surface hydroxylation on the selectivity of CO₂ hydrogenation over different Ni/γ-Al₂O₃,²⁷ Pd/γ-Al₂O₃ ³¹ and Cu/γ-Al₂O₃ ³² catalysts, suggesting that the hydroxylation of the γ-Al₂O₃ surface can alter the reaction pathway and the selectivity of CO₂ hydrogenation.

On the other hand, the activity and selectivity of metal-supported catalysts are strongly influenced by the size of the dispersed metal particles, and the metal–support interaction.^33–38 Small metal clusters or particles have interesting properties for catalytic processes due to the presence of low-coordination atoms and electron confinement effects,³⁹ which is different from those of bulk metals. For example, Zhang et al.³¹ have suggested that the presence and number of low-coordinated Pd particles on a Pd/γ-Al₂O₃ catalyst is of great importance to improve the overall activity and selectivity of CO₂ hydrogenation. The quasi in situ X-ray photoelectron studies of Loviat et al.⁶ have shown that the reactivity and the observed reaction mechanisms for methane production from syngas using a Ni/γ-Al₂O₃ catalyst are directly influenced by both the size and the composition of the Ni particle on the γ-Al₂O₃ support. Moreover, on the basis of EXAFS and IR spectra studies using an Ir/γ-Al₂O₃ catalyst, Argo et al.³⁵ have pointed out that the rate of ethene hydrogenation on Ir₄ clusters is typically several times greater than that on Ir₆ clusters. Further, Prasad and co-authors^37,38 and Meier et al.⁴⁰ also pointed out that the metal cluster size, the support material, or both, are critical in determining the catalytic activity.

Nowadays, Ni/γ-Al₂O₃ catalyst is widely used in many chemical processes such as hydrogenation,²⁷ dehydrogenation, reformation,⁴¹ methanation, desulfurization, methane oxidation, and in the production of many bulk and fine chemicals.^42–47 Unfortunately, it is often difficult to obtain pertinent information from experiments on the metal–support interaction in Ni/γ-Al₂O₃ catalyst, as well as the stability and nucleation of metals on supports with different properties. Theoretical calculations are a valuable tool to complement experimental results, and a detailed investigation of metal–support interactions, as well as the study of the stability and nucleation of metals on the support at the molecular level not only help to increase the understanding of the underlying interaction mechanisms, but also serve as the basis for the selective design of Ni-based catalysts to improve the catalytic performance towards the desired reaction. A number of theoretical studies have examined the stability and nucleation of metals on an Al₂O₃ support, including Pd on γ-Al₂O₃,⁴⁸ Rh on γ-Al₂O₃,⁴⁹ Cu on α-Al₂O₃⁵⁰ and γ-Al₂O₃,⁵¹ as well as Ag on α-Al₂O₃(0001).⁵² For example, Valero et al.⁴⁸ have shown that with a very low metal coverage, the surface hydroxylation of hydrated γ-Al₂O₃(110) surfaces is favorable for the nucleation of Pd, whereas, with a higher metal coverage, the reverse is true for dehydrated γ-Al₂O₃(100) . Further, Shi et al.⁴⁹ have shown that the nucleation of Rh is better on hydrated γ-Al₂O₃ surfaces than on dehydrated surfaces. Hu et al.⁵³ have found that Pd₁₃ and Pt₁₃ clusters are more stable on a dehydrated γ-Al₂O₃(100) surface than on a hydrated γ-Al₂O₃(110) surface. However, to our knowledge, little attention has been paid to the effect of γ-Al₂O₃ surface hydroxylation on the stability and nucleation of Ni in a Ni/γ-Al₂O₃ catalyst.

In this study, by using density functional theory (DFT) method, we present a detailed and systematic theoretical investigation of the stability and nucleation of small Ni_n(n = 1–7) clusters on three different γ-Al₂O₃ surfaces including the dehydrated (100), dehydrated and hydrated (110) surfaces. The objective was twofold: (i) to identify the preferred adsorption site, and how the isolated Ni_n clusters were modified after adsorption on the three different γ-Al₂O₃ surfaces, and (ii) to explore the effect of γ-Al₂O₃ surface hydroxylation on the stability and nucleation of Ni in Ni/γ-Al₂O₃ catalyst.

2. Models and methods

2.1 Computational models

Both spinel and non-spinel structure models have been proposed for γ-Al₂O₃.^54–63 The non-spinel model has been well characterized both experimentally and computationally.^54–63 Moreover, the non-spinel model can produce diffraction patterns that are close to the characteristic diffraction patterns of γ-Al₂O₃.^58–60 Further, the non-spinel γ-Al₂O₃ model has been widely used to construct surfaces in previous studies,^62,64,65 thus, we employed the non-spinel-γ-Al₂O₃ as presented in previous studies to model the γ-Al₂O₃ surface in this study. The corresponding bulk model of the non-spinel-γ-Al₂O₃ used was taken from a previous theoretical investigation⁶² of the calcination of boehmite, the hydrated precursor of γ-Al₂O₃, in which a wide range of aluminum atom distributions in this oxygen atom matrix was simulated, and the most stable structure with 25% of tetrahedral aluminum was retained as the best model for γ-Al₂O₃, as shown in ref. 55.

On the other hand, it has been reported in ref. 55 and 63 that by using the neutron diffraction analysis method of Beaufils and Barbaux,⁶⁶ the (110) surface was estimated to be 83% of the total surface area, whereas the (100) surface was 17% of the total surface area. In addition, the electron microscopy study carried out by Nortier et al.,⁶⁷ confirmed that the (110) surface is the predominant facet, covering about 70% of the total surface area, the remaining 30% corresponding to the (100) and (111) surfaces. Further, the (100) surface was found to be poorly hydrated under a broad range of experimental conditions.⁶⁸ Thus, in this study, we chose the (110) and (100) surfaces to study the stability and nucleation of Ni using DFT slab calculations. The (100) surface was modeled by a (2 × 1) supercell with a dimension of 11.17 × 8.41 × 20.44 Å, and included ten atomic layers, as shown in Fig. 1(a). The vacuum region was set to 12 Å in order to separate the slabs in the direction perpendicular to the surface. During geometry optimization, the bottom four layers were frozen in their bulk position, whereas, the remaining six layers together with the adsorbed Ni_n(n = 1–7) clusters were allowed to relax. For the γ-Al₂O₃(110) surface, the dehydrated and hydrated surfaces were considered. The supercell for the (110) surface included six layers with a vacuum region of 12 Å, resulting in a supercell size of 8.41 × 8.07 × 19.17 Å. In this case, the adsorbed Ni_n(n = 1–7) clusters and/or hydroxyls together with the Al and O atoms in the top four layers were allowed to relax.

Fig. 1 The top and side views of (a) the dehydrated γ-Al₂O₃(100) surface, (b) the dehydrated γ-Al₂O₃(110) surface, and (c) the hydrated γ-Al₂O₃(110) surface. Pink, red and white balls stand for Al, O and H atoms, respectively.

In the dehydrated γ-Al₂O₃(100) surface presented in Fig. 1(a), 5-fold-coordinated aluminum Al(1), Al(2) and Al(3), and 3-fold-coordinated oxygen O(A), O(B), O(C) and O(D) are exposed. For the dehydrated γ-Al₂O₃(110) surface, as shown in Fig. 1(b), the 3-fold-coordinated aluminum (Al_3c), 4-fold-coordinated aluminum (Al_4c), 6-fold-coordinated aluminum (Al_6c), 2-fold-coordinated oxygen (O_2c), and 3-fold-coordinated oxygen (O_3c) atoms are exposed, of which Al_3c, Al_4c, O₂ are coordinately unsaturated.

For the hydrated γ-Al₂O₃(110) surface, under normal reaction conditions as demonstrated by Digne et al.,⁵⁵ the (110) surface inevitably becomes hydrated/hydroxylated, thus, a partially hydrated γ-Al₂O₃(110) surface was employed to characterize the effect of surface hydroxylation on the stability and nucleation of Ni in the Ni/γ-Al₂O₃ catalyst. The hydroxylated surfaces are formed by dissociative adsorption of water on the dry surface. The thermodynamics of hydroxylation with various OH coverages were studied by Digne et al.⁵⁵ However, our aim in this work was to study the qualitative effect of γ-Al₂O₃ surface hydroxylation on the stability and nucleation of Ni in the Ni/γ-Al₂O₃ catalyst, not to describe the specific hydroxyl coverage, which can vary under the given experimental conditions. As a result, only one H₂O molecule was considered for the hydrated γ-Al₂O₃(110) surface in this study. The previous DFT studies carried out by Pan et al.²⁹ investigated the hydroxylation process by the dissociation of one H₂O molecule on the dry γ-Al₂O₃(110) surface, which is the same as our model of the dry γ-Al₂O₃(110) surface, as shown in Fig. 1(b), their results showed that water dissociation across the O_2c–Al_3c bridge site is favorable both thermodynamically and kinetically, and the hydroxylation of the dry γ-Al₂O₃(110) surface is an activated process with only a very small barrier of 40.5 kJ mol⁻¹. Fig. 1(c) presents the side and top views of the partially hydroxylated γ-Al₂O₃(110) surface, in which one H₂O molecule dissociates into an hydroxyl (O_wH_a) with a bond length of 0.967 Å, which occupies the Al_3c site through an O_w–Al_3c bond (1.726 Å). Meanwhile, a proton (H_b) binds with a neighboring O_2c–3 site through the H_b–O_2c–3 bond (1.027 Å). Thus, two hydroxyls are formed in each surface unit cell.

2.2 Computational methods

All the calculations were carried out in the framework of DFT using the Dmol³ program in the Materials Studio 4.4 package.^69,70 The generalized gradient approximation (GGA) corrected exchange-correlation functional proposed by the Perdew–Burke–Ernzerhof (PBE) functional⁷¹ was employed with a double numerical basis set with polarization (DNP).⁷² The inner electrons of Ni and Al atoms were kept frozen and replaced by an effective core potential (ECP),^73,74 and other atoms were treated with an all electron basis set. For optimization of the geometry, the forces imposed on each atom were converged to be less than 0.0004 Ha Å⁻¹ (1 Ha = 2625.5 kJ mol⁻¹), the total energy was converged to be less than 2.0 × 10⁻⁵ Ha and the displacement convergence was less than 5 × 10⁻³ Å. A Fermi smearing of 0.005 Ha for orbital occupancy was used to improve the computational performance. In addition, the properties of isolated Ni_n clusters were calculated using a 15 × 15 × 15 Å cubic unit cell, the charge transfer was calculated using Mulliken charge, and the dipolar correction was not considered in this study.

Different k-point grid samplings ranging from (1 × 1 × 1) to (4 × 4 × 1) were tested for both the bare (100) and (110) surface slabs, as well as the surfaces containing adsorbed Ni₄ clusters. The differences between the surface energies and Ni₄ cluster adsorption energies were found to be negligible using the (2 × 2 × 1), (3 × 3 × 1), and (4 × 4 × 1) k-point grids for both surfaces. As a result, for a reasonable CPU cost, the (2 × 2 × 1) k-point sampling scheme was employed in this work, and gave good converged results.

3. Results and discussion

In this section, we firstly investigate the stable configuration of isolated Ni_n(n = 2–7) clusters in section 3.1, then, the adsorption of the most stable Ni_n clusters on three different γ-Al₂O₃ surfaces, and the stability of the Ni_n clusters are discussed in section 3.2, Further, the nucleation of Ni_n clusters on the three different γ-Al₂O₃ surfaces are studied in section 3.3. Finally, a comparison of the stability and nucleation between Ni and other metals is provided in section 3.4.

3.1 Structures of isolated Ni_n(n = 2–7) clusters

Isolated Ni clusters have been widely studied previously.^6,75 In this section, details are given of the investigation of the geometries of isolated Ni_n clusters. To study the configuration of Ni_n(n = 2–7) clusters, one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) structures were considered. And only the most stable geometries and key parameters of the Ni_n(n = 2–7) clusters were considered, as listed in Table 1.

Table 1 The most stable geometry, the average Ni–Ni bond length, and the binding energy of the isolated Ni_n(n = 2–7) clusters, E_bind(Ni_n)

n	Geometry	d̄(Ni–Ni)/Å	Ebind(Nin)/kJ mol^−1/atom
2		2.163	−98.6
3		2.277	−144.5
4		2.354	−171.1
5		2.361	−198.9
6		2.413	−211.9
7		2.411	−227.7

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In order to evaluate the stability of isolated Ni_n(n = 2–7) clusters, the average binding energy of isolated Ni_n(n = 2–7) clusters, E_bind(Ni_n), was calculated as follows:^51–53

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

where E(Ni) is the total energy of the single Ni atom, n is the number of Ni atoms in the Ni_n clusters, herein, n = 2–7. With this definition, the smaller the E_bind(Ni_n) the more stable the isolated Ni_n(n = 2–7) cluster.

For Ni₂ clusters, the Ni–Ni bond length and the average binding energy were 2.163 Å and −98.6 kJ mol⁻¹, respectively, which is in accordance with the experimental results.^76,77 For Ni₃ clusters, the most stable configuration is a 2D planar one, the average Ni–Ni bond length and the average binding energy were 2.277 Å and −144.5 kJ mol⁻¹, respectively. For Ni₄ clusters, the isolated 3D tetrahedral configuration is more stable than the isolated 2D planar one, which is in accordance with the corresponding Pd₄ clusters,⁷⁸ the average Ni–Ni bond length and the binding energy of Ni₄ clusters were 2.354 Å and −171.1 kJ mol⁻¹, respectively. For Ni₅ clusters, the most stable configuration is a trigonal bipyramid with an average Ni–Ni bond length of 2.361 Å, which is in agreement with the previous results of Reuse et al.,⁷⁵ the average binding energy of the Ni₅ clusters was −198.9 kJ mol⁻¹. For Ni₆ clusters, the average Ni–Ni bond length and the binding energy were 2.413 Å and −211.9 kJ mol⁻¹, respectively. Finally, the most stable configuration of Ni₇ clusters is a pentagonal bipyramid, which is similar to that of Pd₇ ⁷⁹ and Ag₇ ⁵² clusters, the average bond length and the binding energy for Ni₇ clusters were 2.411 Å and −227.7 kJ mol⁻¹, respectively.

On the basis of the above results, we can see from Table 1 that the average Ni–Ni bond length in Ni_n(n = 2–7) clusters was shorter than that in the bulk structure (d(Ni–Ni) = 2.492 Å), and the average Ni–Ni bond length increases with an increase of the cluster size, however, it cannot reach the corresponding bulk value. Meanwhile, with an increase of atomic coordination in the Ni_n(n = 2–7) clusters, the value of the E_bind(Ni_n) decreases.

3.2 Ni_n clusters adsorbed on different γ-Al₂O₃ surfaces

Ni_n(n = 1–7) clusters were adsorbed on all possible positions of the γ-Al₂O₃ surfaces, here, only the most stable adsorption configurations are reported according to the adsorption energy, which is calculated as follows:^25,51

E_ads = E(Ni_n/γ-Al₂O₃) − E(γ-Al₂O₃) − E(Ni_n)

where E(γ-Al₂O₃) is the total energy of the bare γ-Al₂O₃ surface, E(Ni_n) is the total energy of the isolated Ni_n clusters, and E(Ni_n/γ-Al₂O₃) represents the total energy of Ni_n supported on the γ-Al₂O₃ surface. The adsorption energy can be broken down into the contributions of deformation energy and metal–support interaction energy to analyze the chemisorption process. During this process, the two partners (the γ-Al₂O₃ surface plus Ni_n(n = 1–7) clusters) are deformed with respect to their isolated geometries.

Distortion of the surface or the metal cluster alone towards the geometry needed to overcome some energy is defined as the surface or metal cluster deformation energy. The surface deformation energy is calculated as follows:^25,51

E_def,surface = E(γ-Al₂O₃′) − E(γ-Al₂O₃)

where E(γ-Al₂O₃′) is the total energy of the surface with deformed geometry obtained after Ni_n cluster adsorption. With this definition, lower the E_def,surface results in weaker surfaces.

The deformation energy of the Ni_n(n = 1–7) clusters is calculated in a similar way:^25,51

E_def,Nin = E(Ni_n′) − E(Ni_n)

where E(Ni_n′) is the total energy of the Ni_n clusters supported on the γ-Al₂O₃ surface. With this definition, the lower the E_def,Nin the weaker the cluster deformation is.

The interaction between the Ni_n clusters and the support is another key parameter. The metal–support interaction energy, E_MSI, is calculated as follows:^25,51

E_MSI = E(Ni_n/γ-Al₂O₃) − E(Ni_n′) − E(γ-Al₂O₃′)

E_MSI is simply the adsorption energy between the already deformed partners, i.e., without the energy contributions of geometry deformation in either fragment of the Ni/γ-Al₂O₃ system.

Therefore, the adsorption energy can be decomposed according to the following equation:^25,51

E_ads = E_MSI + E_def,Nin + E_def,surface

This energy decomposition scheme clearly shows that adsorption energy is a trade-off between two antagonistic effects: metal–support interaction energy and deformation energy.

3.2.1 Dehydrated γ-Al₂O₃(100) surface. Ni_n(n = 1–7) clusters were placed on the large number of well-defined adsorption sites that are available on the dehydrated γ-Al₂O₃(100) surface, Fig. 2 presents the most stable adsorption configurations, Table 2 lists the corresponding key parameters of these configurations.

Fig. 2 The most stable adsorption configuration of Ni_n(n = 1–7) clusters on the dehydrated γ-Al₂O₃(100) surface. Bond lengths are in Å. The blue balls represent Ni atoms, and the others are the same as in Fig. 1.

Table 2 The adsorption energy, E_ads, Ni_n metal–support interaction energy, E_MSI, Ni_n cluster deformation energy, E_def,Nin, surface deformation energy, E_def,surface, and the average Ni–Ni bond distance d̄(Ni–Ni) for the most stable adsorption configuration of Ni_n(n = 1–7) clusters on three different γ-Al₂O₃ surfaces

n	Eads/kJ mol^−1	EMSI/kJ mol^−1	Edef,Nin/kJ mol^−1	Edef,surface/kJ mol^−1	d̄(Ni–Ni)/Å
Dehydrated γ-Al2O3(100) surface
1	−352.2	−476.2	—	124.0	—
2	−480.3	−750.4	50.9	219.2	2.603
3	−374.4	−569.1	41.6	153.1	2.501
4	−442.8	−567.3	3.9	120.6	2.377
5	−431.7	−600.1	40.2	128.2	2.362
6	−464.7	−706.0	36.4	204.9	2.434
7	−493.5	−658.0	42.6	121.9	2.427
Dehydrated γ-Al2O3(110) surface
1	−269.9	−359.4	—	89.5	—
2	−408.8	−540.7	3.5	128.4	2.251
3	−483.6	−623.2	6.7	132.9	2.366
4	−578.9	−730.3	6.0	145.4	2.377
5	−571.2	−859.6	95.4	193.0	2.434
6	−602.9	−870.1	64.5	202.7	2.477
7	−563.1	−813.8	52.6	198.1	2.463
Hydrated γ-Al2O3(110) surface
1	−277.6	−331.6	—	54.0	—
2	−349.9	−449.6	0.8	98.9	2.204
3	−470.3	−572.0	1.4	100.3	2.281
4	−524.2	−625.5	9.3	92.0	2.387
5	−504.1	−656.9	29.4	123.4	2.426
6	−524.0	−702.0	41.8	136.2	2.452
7	−500.5	−652.0	40.1	111.4	2.404

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For single Ni atoms, it is preferrable to occupy the bridge site along O(C)–O(D) with an adsorption energy of −352.2 kJ mol⁻¹, as shown in Fig. 2(a), and 0.027e was transferred to support the surface from single Ni atoms. The adsorption of a single Ni atom can lead to strong surface deformation of the dehydrated γ-Al₂O₃(100) surface with a surface deformation energy of 124.0 kJ mol⁻¹, this has also been observed in previous studies of the adsorption of single Rh atoms,⁴⁹ Pd atom^s48 and Cu atoms.⁵¹ The bond lengths of Ni–O(C) and Ni–O(D) were 1.866 and 1.905 Å, respectively. The Ni₁–support interaction energy was −476.2 kJ mol⁻¹, which makes a major contribution to the adsorption energy.

For Ni₂ clusters, the most stable configuration is shown in Fig. 2(b), which is different from that of Cu₂ clusters.⁵¹ In this configuration, two Ni atoms interact directly with the surface sites: the Ni₁ atom occupies the O(C)–O(D) bridge site with Ni₁–O(C), Ni₁–O(D) and Ni₁–Al(2) bond lengths of 1.895, 1.905 and 2.267 Å, respectively, while the Ni₂ atom is located at the O(A)–O(B) bridge site with Ni₂–O(A) and Ni₂–O(B) bond lengths of 1.925 and 1.858 Å, respectively. The adsorption of Ni₂ clusters introduces strong surface deformation (219.2 kJ mol⁻¹). The Ni₁–Ni₂ bond length of the adsorbed Ni₂ clusters was stretched to 2.603 Å from 2.163 Å in the isolated Ni₂ clusters with a cluster deformation energy of 50.9 kJ mol⁻¹. The adsorption energy and the Ni₂–support interaction energy were −480.3 and −750.4 kJ mol⁻¹, respectively, which are lower than the corresponding energies for single Ni atoms (−352.2 and −476.2 kJ mol⁻¹). Meanwhile, 0.038e was transferred to the Ni₂ clusters from the support surface. Thus, the decrease of adsorption energy is mainly due to the decrease of the Ni₂–support interaction.

As shown in Fig. 2(c), the most stable adsorption configuration of Ni₃ clusters resembles that of the Cu₃ clusters obtained in our previous work.⁵¹ In this configuration, the plane of the Ni₃ clusters lies aslant relative to the (100) surface forming Ni₁–Al(2) (2.373 Å), Ni₁–O(C) (1.993 Å), Ni₁–O(D) (1.995 Å), Ni₂–O(A) (1.915 Å), Ni₂–O(B) (1.868 Å) and Ni₃–Al(1) (2.414 Å) bonds. The adsorption energy of the Ni₃ clusters was −374.4 kJ mol⁻¹, which is higher than that of the Ni₂ clusters (−480.3 kJ mol⁻¹). 0.145e was transferred to the Ni₃ clusters from the support surface. Meanwhile, the Ni₃–support interaction energy obviously increased to −569.1 kJ mol⁻¹ from −750.4 kJ mol⁻¹ for the Ni₂ clusters, which is mainly due to the increase of the adsorption energy of the Ni₃ clusters. Compared to the Ni₂ clusters (50.9 and 219.2 kJ mol⁻¹), the adsorption of Ni₃ clusters is accompanied by relatively weak cluster and surface deformations with corresponding energies of 41.6 and 153.1 kJ mol⁻¹.

As shown in Fig. 2(d), Ni₄ clusters interact with the surface via three Ni atoms, the Ni₄–support interaction energy was −567.3 kJ mol⁻¹, which is close to that of the Ni₃ clusters (−569.1 kJ mol⁻¹). The lengths of Ni₁–Al(2), Ni₁–O(D), Ni₂–O(A), Ni₂–O(B), Ni₃–O(C) and Ni₃–Al(1) bonds were 2.449, 1.879, 2.029, 2.023, 1.916 and 2.463 Å, respectively. The adsorption energy of the Ni₄ clusters (−442.8 kJ mol⁻¹) was lower than that of the Ni₃ clusters (−374.4 kJ mol⁻¹), meanwhile, the adsorption of Ni₄ clusters can lead to weaker cluster and surface deformations (3.9 and 120.6 kJ mol⁻¹) relative to those for Ni₃ clusters (41.6 and 153.1 kJ mol⁻¹), which is the main reason for the decrease of adsorption energy, and leads to 0.102e being transferred to the Ni₄ clusters from the support surface.

For the Ni₅ clusters, as shown in Fig. 2(e), the most stable configuration is a trigonal bipyramid with one Ni–Ni bond cleavage, and Ni₅ clusters interact with the surface via four Ni atoms. The adsorption energy (−431.7 kJ mol⁻¹) was slightly higher than that for Ni₄ clusters (−442.8 kJ mol⁻¹), and 0.204e was transferred to the Ni₅ clusters from the support surface. The Ni₅–support interaction energy (−600.1 kJ mol⁻¹) was lower than that of the Ni₄ clusters (−567.3 kJ mol⁻¹), which makes a major contribution to the adsorption energy for Ni₅ clusters. The cluster and surface deformation energies were 40.2 and 128.2 kJ mol⁻¹, respectively, which are higher than those for Ni₄ clusters (3.9 and 120.6 kJ mol⁻¹). The stronger cluster deformation of Ni₅ clusters is mainly due to the increase of adsorption energy. In the adsorption configuration, the bond lengths of Ni₁–Al(2), Ni₂–O(D), Ni₂–Al(1), Ni₃–O(B), Ni₃–O(A), Ni₄–O(C) and Ni₄–Al(1) were 2.411, 1.939, 2.598, 2.001, 2.014, 1.930 and 2.611 Å, respectively.

As shown in Fig. 2(f), five Ni atoms in the most stable adsorption configuration of Ni₆ clusters prefer to interact with the surface, and form two Ni–Al(2) bonds (2.545 and 2.630 Å), one Ni₁–O(D) bond (1.900 Å), three Ni–Al(1) bonds (2.519, 2.607 and 2.614 Å), one Ni₂–O(B) bond (1.881 Å), one Ni₃–O(A) bond (1.971 Å) and one Ni5–O(C) bond (1.897 Å). The adsorption energy and the Ni₆–support interaction energy (−464.7 and −706.0 kJ mol⁻¹) were lower than those for the Ni₅ cluster (−431.7 and −600.1 kJ mol⁻¹), and 0.289e was transferred to the Ni₆ cluster from the support surface. The decrease of Ni₆–support interaction energy has a major effect on the adsorption energy. The adsorption of Ni₆ clusters on the surface leads to a stronger surface deformation (204.9 kJ mol⁻¹) than that of Ni₅ clusters (128.2 kJ mol⁻¹). The adsorption also leads to Ni₆ cluster deformation (36.4 kJ mol⁻¹), whereas, it is slightly weaker than that of the Ni₅ clusters (40.2 kJ mol⁻¹).

The most stable adsorption configuration of Ni₇ clusters is presented in Fig. 2(g), and is characterized by a strong adsorption (−493.5 kJ mol⁻¹) and a weak Ni₇–support interaction (−658.0 kJ mol⁻¹) in comparison with the adsorption of Ni₆ cluster (−464.7 and −706.0 kJ mol⁻¹). Upon adsorption to the dehydrated (100) surface, the pentagonal bipyramid structure of the Ni₇ clusters is distorted. The adsorption of Ni₇ clusters introduces both cluster and surface deformations with deformation energies of 42.6 and 121.9 kJ mol⁻¹, respectively, 0.232e was transferred from the support surface to the Ni₇ clusters. The decrease of the adsorption energy for the Ni₇ clusters was mainly due to the weaker surface deformation compared to that for the Ni₆ clusters (204.9 kJ mol⁻¹). In this stable configuration, four Ni atoms directly interact with the surface, and form two Ni–Al(2) bonds (2.468 and 2.655 Å), Ni₂–O(D) bond (1.929 Å), Ni₃–O(B) bond (1.938 Å), Ni₃–O(A) bond (2.008 Å) and Ni₄–O(C) bond (1.940 Å).

From the obtained energy values listed in Table 2, we can obtain that on dehydrated (100) surface, for the adsorption of Ni_n cluster, Ni_n cluster deformation, surface deformation and Ni_n–support interaction, these four parameters have the strong correlation. The adsorption of Ni_n clusters on the support is not only affected by the Ni_n–support interaction, but is also affected by the Ni_n cluster and surface deformations, moreover, the Ni_n cluster deformation cannot be neglected except for the Ni₄ cluster due to the high stability of the tetrahedron. The results we obtained in the study of Ni_n clusters are different from the results obtained in previous studies of Cu_n clusters,⁵¹ which show that the deformation of Cu_n(n = 1–4) clusters is negligible.

3.2.2 Dehydrated γ-Al₂O₃(110) surface. Detailed information on the adsorption of Ni_n(n = 1–7) clusters on the dehydrated γ-Al₂O₃(110) surface is given in the ESI† and the corresponding key geometrical parameters of the most stable adsorption configurations are also listed in Table 2.

We found that the Ni–Ni bond length of adsorbed Ni_n(n = 2–7) clusters is longer than that of the isolated clusters, and increases with an increase of Ni_n cluster size, as a result, the Ni–Ni bond length gradually approaches the value in the bulk structure (2.492 Å). For adsorbed Ni_n(n = 2–4) clusters, the corresponding cluster deformation is very weak, and makes a negligible contribution to the adsorption energy. However, beginning with Ni₅ clusters, the cluster deformation increases sharply, and cannot be neglected. On the other hand, for Ni_n(n ≥ 5) clusters, the surface deformation changes slightly. The results presented above indicate that when the number of Ni atoms in Ni_n(n = 1–7) clusters is 5 or more, the adsorption can lead to a strong Ni_n cluster deformation, however, the adsorption cannot lead to a large change of surface deformation.

3.2.3 Hydrated γ-Al₂O₃(110) surface. Similar to the dehydrated γ-Al₂O₃(110) surface, the corresponding key geometrical parameters of the most stable adsorption configurations are also listed in Table 2. We found that for Ni_n(n = 2–4) clusters, the cluster deformation has little effect on the adsorption energy, however, for Ni_n(n ≥ 5) clusters, the effect of cluster deformation cannot be neglected. Meanwhile, the Ni_n–support interaction contributes considerably to the adsorption ability. For Ni_n(n = 1–7) clusters, the adsorption energy and the Ni_n–support interaction energy have the same varying tendency with an increase of Ni_n(n = 1–7) cluster size, which is consistent with those on the dehydrated (110) surface.

On the other hand, compared to the dehydrated (110) surface, both the adsorption energy of Ni_n(n = 2–7) clusters and the Ni_n–support interaction energy increase due to the presence of surface hydroxyls, whereas, for single Ni atoms, the adsorption energy decreases because of the weaker surface deformation. For Ni_n(n = 1–7) clusters, the surface deformation of the hydrated (110) surface is weaker than that of the dehydrated (110) surface, namely, the presence of surface hydroxyls can make the (110) surface more stable. Similarly, the adsorption of Rh_n(n = 1–5) on both dehydrated and hydrated γ-Al₂O₃(100) surfaces also shows that the presence of surface hydroxyls is favorable for the stability of the γ-Al₂O₃ surface.⁴⁹ Meanwhile, for Ni_n(n ≥ 5) clusters, due to the presence of surface hydroxyls, cluster deformation on the hydrated γ-Al₂O₃(110) surface is weaker than that on the dehydrated γ-Al₂O₃(110) surface, which means that the surface hydroxyls can reduce the effect of the support on the adsorbed cluster.

3.2.4 Brief summary about stability. On the basis of the above studies of the adsorption of Ni_n(n = 1–7) clusters on three different γ-Al₂O₃ surfaces, we firstly deduced that there is a strong correlation between the adsorption energy of Ni_n clusters, cluster deformation energy, surface deformation energy, and Ni_n–support interaction energy, suggesting that the adsorption stability of Ni_n(n = 1–7) clusters on the γ-Al₂O₃ surface is not only affected by the Ni_n–support interaction, but is also affected by the cluster and surface deformations, in which the deformation of the Ni_n(n = 2–7) clusters on the dehydrated γ-Al₂O₃(100) surface cannot be neglected except for Ni₄ clusters due to the high stability of the tetrahedron, however, for the γ-Al₂O₃(110) surface, the deformation of the Ni_n(n = 2–4) clusters is negligible. Meanwhile, due to the stronger Ni_n–support interaction, Ni_n(n = 3–7) clusters are much more stably adsorbed on the γ-Al₂O₃(110) surface than the corresponding cluster on the γ-Al₂O₃(100) surface, however, for single Ni atoms and Ni₂ clusters, the reverse becomes true.

Secondly, for the γ-Al₂O₃(110) surface, due to the weaker surface deformation, the adsorption stability of single Ni atoms on the hydrated surface is stronger than that on the dehydrated surface. Whereas, for Ni_n(n = 2–7) clusters, both the adsorption energy and the Ni_n–support interaction energy for the hydrated surface are higher than those for the dehydrated surface, indicating that surface hydroxyls have a negative effect on the adsorption stability of Ni_n(n = 2–7) clusters, and reduce the interaction between the Ni_n clusters and the γ-Al₂O₃ surface, which is in accordance with the previous studies.^32,49 Meanwhile, the surface deformation of the hydrated surface is weaker than that of the dehydrated surface, namely, the presence of surface hydroxyls can improve the stability of the (110) surface. Moreover, for Ni_n(n ≥ 5) clusters, the cluster deformation is much larger than that of the Ni_n(n = 2–4) clusters, and the cluster deformation of Ni_n(n ≥ 5) clusters on the hydrated surface is weaker than that on the dehydrated surface, which means that the surface hydroxyls can reduce the effect of the support on the adsorbed cluster.

On the other hand, to probe into the effect of the support and surface hydroxyls on the stability of Ni_n(n = 2–7) clusters, the average binding energy of supported Ni_n(n = 2–7) clusters on three different γ-Al₂O₃ surfaces, E_bind(Ni_n/γ-Al₂O₃), was calculated, as listed in Table 3.

Table 3 The binding energy of Ni_n(n = 2–7) clusters supported on the different γ-Al₂O₃ surfaces per metallic atoms for the most stable adsorption configuration, E_bind(Ni_n/γ-Al₂O₃), and the binding energy of isolated Ni_n(n = 2–7) clusters, E_bind(Ni_n)

n	Ebind(Nin)/kJ per mol per atom	Ebind(Nin/γ-Al2O3)/kJ per mol per atom
	Isolated	Dehydrated (100)	Dehydrated (110)	Hydrated (110)
2	−98.6	−338.8	−303.0	−273.5
3	−144.5	−269.3	−305.7	−301.2
4	−171.1	−281.8	−315.8	−302.1
5	−198.9	−285.2	−313.1	−297.1
6	−211.9	−289.4	−312.4	−295.6
7	−227.7	−298.2	−308.1	−299.2

---

E_bind(Ni_n/γ-Al₂O₃) is given by the following equation:^51,53

E_bind(Ni_n/γ-Al₂O₃) = [E(Ni_n/γ-Al₂O₃) − n × E(Ni) −E(γ-Al₂O₃)]/n

herein, n = 2–7. E_bind(Ni_n/γ-Al₂O₃) reflects the stability of Ni_n clusters supported on the γ-Al₂O₃ support surface, the small value of E_bind(Ni_n/γ-Al₂O₃) denotes that the Ni_n clusters supported on the γ-Al₂O₃ surface are more stable.

Our results show that the average binding energy of Ni_n(n = 2–7) clusters in the supported state is higher than that in the corresponding isolated state, which means that the support can stabilize the Ni_n(n = 2–7) clusters well. Meanwhile, the stability of the supported Ni_n(n = 3–7) clusters on the γ-Al₂O₃(110) surface is better than that on the γ-Al₂O₃(100) surface, however, for Ni₂ clusters, the reverse becomes true. For the γ-Al₂O₃(110) surface, the stability of the supported Ni_n(n = 2–7) clusters on the dehydrated surface is better than that on the hydrated surface, namely, surface hydroxyls reduce the stability of the supported Ni_n clusters.

3.3 Nucleation of Ni_n cluster on the different γ-Al₂O₃ surfaces

Based on the above stable adsorption configurations of Ni_n(n = 1–7) clusters on the different γ-Al₂O₃ surfaces, the nucleation of Ni_n clusters on the different γ-Al₂O₃ surfaces has been further discussed. The nucleation is defined as the chemical reaction of Ni_n−1/γ-Al₂O₃ + Ni₁/γ-Al₂O₃ = Ni_n/γ-Al₂O₃, and the corresponding nucleation energy is calculated as follows:⁵¹

E_nuc = E(Ni_n/γ-Al₂O₃) + E(γ-Al₂O₃) − E(Ni_n−1/γ-Al₂O₃) − E(Ni₁/γ-Al₂O₃)

where E(Ni_n−1/γ-Al₂O₃) is the total energy of the γ-Al₂O₃ slab together with the Ni_n−1 clusters, and E(Ni₁/γ-Al₂O₃) is the total energy of the γ-Al₂O₃ slab together with a single Ni atom. The nucleation energy indicates the energy gained (or lost) when an adsorbed atom is combined with a Ni_n−1 cluster to form a Ni_n cluster, and the negative value denotes that the nucleation of the Ni_n cluster is exothermic, and is thermodynamically favorable, whereas, the positive value denotes that the nucleation of the Ni_n cluster is endothermic, and thermodynamically unfavorable.

Table 4 lists the calculated nucleation energies on different surfaces together with the corresponding isolated Ni_n cluster. We can see that on the dehydrated (100) surface, the nucleation of Ni_n(n = 2–7) clusters is not thermodynamically favored, namely, the dehydrated (100) surface is unfavorable for the nucleation of Ni clusters. On the dehydrated (110) surface, the nucleation of all the Ni clusters is exothermic, whereas, on the hydrated (110) surface, the nucleation of Ni₂ clusters is thermodynamically unfavorable; however, for the Ni_n clusters with 3 or more Ni atoms, the nucleation becomes favorable, which means that the critical cluster size for Ni cluster nucleation on the hydrated (110) surface is 3. More importantly, the exothermicity of supported Ni_n(n = 2–7) clusters on different γ-Al₂O₃ surfaces is lower than that of isolated Ni_n clusters, which means that the support can reduce the nucleation ability of Ni_n(n = 2–7) clusters, therefore, the support can inhibit the aggregation of clusters, and favors the formation of highly dispersed Ni particles to prevent their sintering into supranano ones. This result is in agreement with previous studies on the nucleation of Pd,⁴⁸ Rh,⁴⁹ Cu ⁵¹ and Pt ⁸⁰ on γ-Al₂O₃ surfaces.

Table 4 The nucleation energy E_nuc of Ni_n(n = 2–7) clusters supported on three different γ-Al₂O₃ surfaces, and the isolated Ni_n(n = 2–7) clusters

n	Enuc/kJ mol^−1
	Dehydrated (100)	Dehydrated (110)	Hydrated (110)	Isolated
2	26.8	−66.2	8.1	−197.2
3	221.8	−41.1	−79.1	−236.3
4	32.8	−76.3	−27.2	−250.9
5	53.4	−32.3	−12.2	−309.9
6	41.9	−39.1	−10.3	−277.2
7	1.0	−12.6	−21.2	−322.4

---

On the other hand, for the nucleation energy of Ni_n(n = 2–7) clusters, the γ-Al₂O₃(110) surface is weaker than the γ-Al₂O₃(100) surface, namely, the nucleation of Ni_n(n = 2–7) clusters is preferred on the γ-Al₂O₃(110) surface compared to the γ-Al₂O₃(100) surface. For the γ-Al₂O₃(110) surface, the nucleation energy of Ni_n(n = 2–7) clusters on the dehydrated surface is lower than that on the hydrated surface except for Ni₃ clusters, suggesting that the nucleation of Ni_n(n = 2–7) clusters is preferred on the dehydrated (110) surface, namely, the presence of surface hydroxyls reduces the nucleation ability of Ni_n(n = 2–7) clusters.

Further, although the Ni/γ-Al₂O₃ catalyst has been widely studied both experimentally and theoretically,^27,81–89 these studies have all focussed on the effect of Ni particle size on the target reaction or products, for example, the studies by Chen et al.⁸³ have reported CH₄ decomposition over supported Ni catalysts with different Ni particle sizes, suggesting that the smaller sizes of Ni particles give lower carbon yield. Meanwhile, the support plays a key role in the particle size, metal–support interactions, as well as Ni particle crystallographic orientations. Thus, the support has a significant effect on the structure of the target product nanofibers and carbon yield. The effect of various supports has been investigated.^86–89 Up to now, to our knowledge, little attention has been paid to the effect of γ-Al₂O₃ surface hydroxylation on the stability and nucleation of Ni in a for Ni/γ-Al₂O₃ catalyst, meanwhile, the effect of the support surface properties on Ni particle sizes, Ni-support interactions, and Ni morphology has not been systematically well-studied. Recently, only Briquet et al.^90–92 have investigated the adsorption of the single Ni atom on the clean and hydrated (0001) surface of α-Al₂O₃, as well as the adsorption of Ni₆ cluster on the clean (0001) surface, suggesting that the adsorption on hydrated surfaces is different from that on the clean surface, strong stabilization of the single Ni atom by the hydroxyl group was observed, which agrees with our calculated result. The studies by Li et al.⁹³ have investigated the adsorption of the tetrahedrally configured Ni₄ cluster on a γ-Al₂O₃(100) surface, the optimized stable configuration was different, the corresponding adsorption energy in our study was much higher than that obtained by Li et al., thus, the optimized Ni₄/γ-Al₂O₃(100) configuration in our study is thought to be the most stable.

On the basis of the above reported results, we obtained little information on the systematic investigation of the effect of γ-Al₂O₃ surface hydroxylation on the stability and nucleation of different sized Ni_n(n = 2–7) cluster in Ni/γ-Al₂O₃ catalysts, to carry out a comparison between our results and previously reported results. However, a large number of studies have focussed on the effect of γ-Al₂O₃ surface hydroxylation on the stability and nucleation of Pd,⁴⁸ Rh,⁴⁹ Cu ⁵¹ and Pt ⁸⁰ on the γ-Al₂O₃ surface, thus, a comparison of the stability and nucleation of Ni with that of other metals Pd, Rh, Cu and Pt was carried out and is presented in the following section.

3.4 Comparison of the stability and nucleation of Ni with that of other metals Pt, Rh, Pd and Cu

On the basis of the nucleation of Ni, in this section, we made a simple comparison with previous studies on the nucleation of other metals Pt, Rh, Pd and Cu. Our results show that the most stable configurations of Pd,⁴⁸ Rh,⁴⁹ Cu,⁵¹ Pt ⁸⁰ and Ni on the γ-Al₂O₃ surface are quite different, only on the γ-Al₂O₃(100) surface does the adsorption of single Pt atoms have a similar stable configuration to that of single Ni atoms, indicating that when different metals with the same size are adsorbed on the same γ-Al₂O₃ surface, they correspond to different adsorption sites and the most stable configurations. Meanwhile, the studies by Briquet et al.^90–92 have shown that the interaction of single Ni atoms on the α-Al₂O₃(0001) surface results in less exothermic values (close to 170 kJ mol⁻¹) compared to those on different γ-Al₂O₃ surfaces, this may be explained by the higher coordination of Al and O surface atoms of the α-Al₂O₃(0001) surface compared to the γ-Al₂O₃ surface, thus, the γ-Al₂O₃ surface has a higher intrinsic surface reactivity than the α-Al₂O₃ surface. Further, the nucleation of Pd,⁴⁸ Rh,⁴⁹ Cu ⁵¹ and Ni also differs, firstly, on the dehydrated (100) surface, the nucleation energy of Pd_n(n = 1–5) clusters is positive until n = 4, namely, the critical cluster size of Pd is 4; for Rh_n(n = 1–5) and Cu_n(n = 1–4) clusters, it is 3; however, for the Ni_n(n = 1–7) cluster in this study, the nucleation energy was always positive, which means that the critical cluster size for Ni is greater than 7. Secondly, on the hydrated (110) surface, the critical cluster size of Pd is 3; for Rh and Cu, it is 2; while for Ni in this study, it was 3. Thirdly, on the dehydrated (110) surface, the critical cluster size of Cu and Ni is 2.

On the other hand, the nucleation of Rh_n(n = 1–5) clusters is preferred on the hydrated γ-Al₂O₃ surface relative to that on the dehydrated γ-Al₂O₃ surface. For Pd_n(n = 1–5) clusters, nucleation at very low metal coverage on an hydrated surface is more favorable than that on a dehydrated surface, whereas, at a higher metal coverage, the reverse becomes true. For Cu and Ni clusters, compared to the γ-Al₂O₃(100) surface, the γ-Al₂O₃(110) surface is more favorable for the nucleation of Cu and Ni clusters, in which surface hydroxyls reduce the nucleation ability of Cu and Ni clusters. In addition, Mager-Maury et al.⁸⁰ carried out studies on the adsorption of Pt_n clusters (1 ≤ n ≤ 5 and n = 13) on four γ-Al₂O₃ surfaces to investigate their stability as a function of particle's size, suggesting that the migration of H and Cl on γ-Al₂O₃ surfaces induces a stronger interaction for the Pt₃ cluster, which is thus proposed to be at the origin of the formation of highly dispersed platinum particles.

4. Conclusions

The effect of γ-Al₂O₃ surface hydroxylation on the stability and nucleation of Ni_n(n = 1–7) clusters over dehydrated γ-Al₂O₃(100), dehydrated γ-Al₂O₃(110) and hydrated γ-Al₂O₃(110) surfaces has been systematically investigated by the DFT method. The results show that the Ni_n–support interaction mainly contributes to the stability of Ni_n(n = 1–7) clusters on the three different γ-Al₂O₃ surfaces, Ni_n(n = 3–7) clusters on the γ-Al₂O₃(110) surface are much more stable than the corresponding clusters on the γ-Al₂O₃(100) surface, whereas, for single Ni atoms and Ni₂ clusters, the reverse becomes true. For the γ-Al₂O₃(110) surface, surface hydroxyls do not favor the adsorption stability of Ni_n(n = 2–7) clusters, and lower the interaction between the Ni_n clusters and the γ-Al₂O₃ surface, however, surface hydroxyls increase the surface stability of γ-Al₂O₃(110).

The critical cluster size for the nucleation of Ni_n(n = 2–7) clusters on the hydrated γ-Al₂O₃(110) surface is 3, while on the dehydrated (100) surface, the critical cluster size should be greater than 7. Meanwhile, from the viewpoint of thermodynamics, the nucleation of Ni_n clusters on different γ-Al₂O₃ surfaces show different trends with an increase of the Ni_n(n = 2–7) cluster size. For the exothermicity of the nucleation, the supported Ni_n(n = 2–7) clusters are smaller than the isolated Ni_n(n = 2–7) clusters, suggesting that the support can reduce the nucleation ability of Ni_n(n = 2–7) clusters. Further, for the nucleation of Ni_n(n = 2–7) clusters on the support, the γ-Al₂O₃(110) surface is more favorable than the γ-Al₂O₃(100) surface. Finally, for the γ-Al₂O₃(110) surface, the nucleation of Ni_n(n = 2–7) clusters preferably occurs on a dehydrated surface, indicating that surface hydroxyls can lower the nucleation ability of Ni_n clusters. Therefore, the γ-Al₂O₃ support and its surface hydroxyls can inhibit the aggregation of clusters, and favor the formation of highly dispersed Ni particles preventing their sintering into supranano ones.

Acknowledgements

This works is supported by the National Natural Science Foundation of China (21276003, 20906066 and 21276171). The authors especially thank the two anonymous reviewers for their helpful suggestions on the quality improvement of our present paper.

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Footnote

† Electronic supplementary information (ESI) available: details of the adsorption of Ni_n clusters on dehydrated and hydrated γ-Al₂O₃(110) surfaces, as well as the corresponding most stable configurations of Ni_n clusters. See DOI: 10.1039/c3ra46352d

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