Density Functional Theory Investigation into the B and Ga Doped Clean and Water Covered γ-Alumina Surfaces

The structures and energies of the B andGa incorporated γ-alumina surface as well as the adsorption of water are investigated using dispersion corrected density functional theory.The results show that the substitution of surface Al atom by B atom is not so favored as Ga atom.The substitution reaction prefers to occur at the tricoordinated A(4) sites. However, the substitution reaction becomes less thermodynamically favoredwhenmoreAl atoms are substituted by B andGa atoms on the surface.Moreover, the substitution of bulk Al atoms is not so favored as the Al atoms by B and Ga on the surface.The γ-alumina surface is found to have stronger adsorption ability for water than the B and Ga incorporated surface. The total adsorption energy increases as water coverage increases, while the stepwise adsorption energy decreases. The studies show the coverage of water at 7.5 H2O/nm 2 (five H2O molecules per unit cell) can fully cover the active sites and the further water molecule could only be physically adsorbed on the surface.


Introduction
The -alumina is an important material in chemistry and materials science due to its widespread applications in chemical industry [1][2][3], ceramics, and semiconductors [4][5][6][7].In order to improve the performance of the material, some heteroatoms were usually chosen to be incorporated into the -alumina bulk and surfaces [8,9].For example, the Fe atom was usually used to improve the catalytic performance of -alumina [10].Wan et al. investigated the Fe 2 O 3 /Al 2 O 3 catalyst from coprecipitated and spray-dried method with Mösbauer spectroscopy [11] and found the reduction of Fe 2 O 3 to FeO.The substitution of surface Al 3+ by Fe 3+ in alumina with mixed (Al 1−x Fe x ) 2 O 3 surface formation is also confirmed by transmission Mösbauer spectroscopy.Integral low-energy electron Mösbauer spectroscopy and Fe K-edge X-ray absorption near-edge structure characterization observed the formation of iron nanoclusters from the transformation of -(Al 1−x Fe x ) 2 O 3 to -(Al 1−x Fe x ) 2 O 3 and the iron distribution on the surface layers and in the cores of grains [12][13][14].This field also attracts the interests of theoretical researches.Feng et al. calculated the structures and energies of the Fe promoted -alumina surface [10] and found that the incorporation of Fe atom into the -alumina surface is possible, while it is thermodynamically not so favored for the Fe substitution for the bulk Al atoms.The adsorption of water on the -alumina surface is stronger than that on the Fe 2 O 3 covered surface.In addition, the electronic structures also change after the substitution of the Al atoms by the Fe atoms on the surface.Except for the incorporation of Fe into the alumina surface, the B and Ga atoms, which are often used as the trivalent substitution ions for the zeolites [15,16], are also used in experiments for the preparation of high performance catalysis and semiconductors [8,9,[17][18][19].Kibar et al. prepared nanostructured boron doped alumina catalyst support [20] and found that the morphology of the supports can be modified from cracked surface to nanosphere formation by the introduction of boron.Jansons et al. introduced Ga into the alumina crystal and prepared a new complex luminescence band at about 5 eV [19].The Garelated luminescence can be observed under the excitation of X-rays up to 600 K.In order to know the energies as well as the structures of the B and Ga incorporated -alumina surface at molecular level, the present work investigated the thermodynamic and structure properties of the B and Ga incorporated -alumina surface using dispersion corrected periodic density functional theory.Since -alumina is usually prepared and used in atmospheres containing water, the adsorption of water on the B and Ga incorporated -alumina is also investigated and compared with the water adsorption on pure -alumina surface.

Computational Details
The dispersion-corrected periodic density functional as implemented in the Vienna ab initio Simulation Package (VASP) was used for the calculations [21][22][23].The DFT-D3 method of Grimme was used to take into account the dispersive interactions as previous work reported that the dispersion correction seriously influences the relative stability order and adsorption energies [24][25][26][27][28].The exchange and correlation energies were calculated by the generalized gradient approximation (GGA) formulation with the PBE functional [21].The Kohn-Sham one-electron states were extended in accordance with plane-wave basis sets with a kinetic energy of 400 eV.The projector augmented wave (PAW) method was applied to describe the electron-ion interactions [29][30][31].
The -alumina surface was described using the Digne's model [32], and (110) surface was taken into account.As shown in Figure 1, -alumina surface was modeled using a (1 × 1) supercell with an eight-layer slab, which contains sixteen Al 2 O 3 units.A vacuum with thickness of 15 Å was employed to separate each slab from interactions.The top four layers and the adsorbates were fully relaxed, and the bottom four layers were fixed in their bulk position during the structure optimization.In order to facilitate the discussions, the surface layer Al and O atoms are indexed with number.The coordination number of each Al atom was expressed by subscript.As has been described in many previous works [33,34], the Al atoms in bulk -alumina are in tetrahedral and octahedron sites.After cleavage, the tetrahedral and octahedron Al atoms expose as the tricoordinated and tetracoordinated Al, respectively, in the (110) surface.As shown in Figure 1, the Al(4) 3c was in tetrahedral site in the bulk, and Al(1) 4c , Al(2) 4c , and Al(3) 4c were in octahedral sites in the bulk.It could be observed from the top view that Al(1) and Al (2) atoms are in the same chemical environment.
For the substitution of surface Al 3+ by X 3+ (X = B and Ga) in reaction (1) the substitution energy is defined as 1 shows the substitution energies for the substitution of Al by B and Ga on the surface.As indicated by the calculated substitution energies, the substitution of surface Al by B atoms is not thermodynamically favored, since the calculated substitution energies are positive.The tricoordinated Al(4) is the most favored site for one B incorporation with the substitution energy of 1.31 eV.The tetracoordinated Al(1) and Al(3) sites are slightly difficult with the substitution energies of 1.81 and 2.29 eV, respectively.

Substitution of Al by B and Ga on the Surface. Table
For two Al atoms substituted by B atoms on the surface, which corresponds to 50% surface, Al were replaced by B; the Al(1,2) are the most favored, with the substitution energy of 3.22 eV, versus Al(1,2,3) for 75% surface Al substitution by B, with the substitution energy of 5.32 eV.The substitution energies positively increase to 7.82 eV as all surface Al atoms were substituted by B atoms.
Figure 2 shows the structures for the B and Ga substituted -alumina surface.The corresponding bond distances of the surface layer atoms before and after the substitution are given in Table 1.It is found that the surface Al-O bond distances are in the range of 170-186 pm on the -alumina surface.After the substitution of Al by B atoms, the Al-O bond distance almost remains the same.It should be noted that the B-O bond distances (137-167 pm) are much shorter than those of the Al-O bonds, since the radius of B atom is much shorter than that of Al [35].In addition, the B atom prefers to be tricoordinated, for example, for B(1,2,3,4) in Figure 2, bond e is elongated to 255 pm and became broken.
Since the substitution energies for the substitution of Al by Ga are much less than those for B substitution, the Ga could be more easily incorporated into to the alumina surface than B. Particularly for the Ga(4) structure, the substitution energy is −0.06 eV, which indicates the substitution reaction at Al(4) site by Ga is thermodynamically favored.Similar to that of B substitution, the substitution energy increases as more Al atoms were replaced by Ga atoms, for example, the substitution energies are 0.11, 0.49, and 0.90 eV, respectively,  for Ga (3,4), Ga(1,2,4), and Ga (1,2,3,4).Since the Ga atom radius is larger than that of Al [35], the Ga-O bond distance is much longer than that of Al-O bond distance.In order to map out whether it is possible for B and Ga substitution for the bulk Al atoms of -alumina, we also calculated the substitution energies for the substitution of the sublayer hexa-and tetracoordinated Al atom by B and Ga atoms.The calculated substitution energies for B replacing the sublayer hexa-and tetracoordinated Al atoms are 4.34 and 2.89 eV, respectively, versus 0.81 and 0.57 eV for Ga, which are larger than the substitution energies for Al substitution on the surface.It indicates that the substitution reaction should favor happening on the surface, rather than in the bulk.In addition, the substitution of tetrahedral Al sites is always more thermodynamically favored than the substitution of octahedral Al sites.
As reported in the previous work [10], the substitution of -alumina surface Al by Fe atoms is thermodynamically favored, as the substitution energy for the substitution of all surfaces Al by Fe atom is −0.87 eV.It indicates that the Fe should be more easily to be incorporated into the -alumina than B and Ga.

Adsorption of Water Molecules on the 𝑋 2 O 3
* Surfaces (X = B, Al, Ga). Figure 3 shows the structures and adsorption

Conclusions
The dispersion corrected periodic density functional theory was used to investigate the structure and energies for the B and Ga incorporated -alumina surface.The results show that the substitution of Al by B is not thermodynamically favored on the surface.However, the substitution of Al by Ga is thermodynamically favored at low coverage on the surface.The substitution reaction prefers to occur at the tricoordinated A(4) sites.The substitution reaction becomes thermodynamically not favored as more and more B and Ga substitutions take place on the surface.The substitutions of Al by B and Ga are not so favored in the bulk as that for the surface.
The adsorption of water molecules on the B and Ga incorporated -alumina surface was also investigated and compared to that of the pure -alumina surface.It shows that the -alumina surface has the strongest adsorption ability for water adsorption.The total adsorption energy increases as water coverage increases from one to six water molecules in each slab, while the stepwise adsorption energy decreases.On the B 2 O 3 * , Al 2 O 3 * , and Ga 2 O 3 * surfaces, the sixth could only be physically adsorbed on the surface, since the former adsorbed five water molecules (at the coverage of 7.5 H 2 O/nm 2 ) fully covered the active sites for water adsorption.

Figure 1 :
Figure 1: Side view of unit cell of -Al 2 O 3 (a) and side (b) and top (c) views of the -Al 2 O 3 (110) surface (Al and O atoms are in rose and red, respectively.Coordination numbers of surface atoms are shown in subscript in (c)).

Figure 2 :Figure 3 :
Figure 2: Side views of the B and Ga substituted -Al 2 O 3 (110) surface (B, Al, Ga, and O atoms are in gray, rose, dark, and red, resp.).All figures are indexed corresponding to Table 1.

Table 1 :
Substitution energies ( sub ) and the M-O bonds distances (pm) of the surface layer atoms before and after substitution for B and Gain -alumina (110) surface.