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Electronic structure of alumina surface

1998, International Journal of Quantum Chemistry

Abstract

The electronic structure of the 001 and 110 ␣-alumina surfaces was Ž. determined by periodic Hartree᎐Fock method in statically relaxed geometries. Both 001 Ž. and 110 surfaces generate specific surface states into the energy gap. Significant influence of charge-transfer effect on the surface᎐adsorbate potential is possible in both cases studied. The inclusion of the exponential part to the standard potential forms was suggested for the description of the interaction potential in such cases.

Introduction n extraordinary interest in understanding of

At he surface electron structure of alumina is motivated by the wide application of Al O , rang- 2 3 ing from catalysis to microelectronics including materials science.

The strategic, long-term goals of our project are Ž . specifically i to find physically justified model Ž potential between the adsorbed particle molecule, . ion and the alumina surface. The potential should include all types of particle᎐surface interactions and should provide an estimate of the possibility Ž . of chemisorption. ii To find physically well-justified types of cluster models for description of localized chemisorption.

To reach a reasonable description of the surface Ž . potential acting on an adsorbate molecule ion , the atomar and electron structure of both objects should be known. Concerning the ␣-alumina surface, we will take its atomar structure from known w x experimental data 1 modified by inclusion of the effect of relaxation of the surface layers of atoms. The electron structure of alumina surface must be described by means of quantum chemistry. The quality and the occurrence or nonoccurrence of the specific, localized surface states, which could be a source of chemisorption or noncovalent strong in-Ž teractions e.g., hydrogen bonding, charge-transfer . complexes between the surface and the adsorbate, will then serve as a guide for construction of a potential function, specific for the surface considered.

Method

Two surfaces of ␣-alumina were used for the Ž . Ž . present study: the 001 surface and 110 surface. These surfaces belong to the most stable surfaces with the most frequent occurrence at the crys-Ž talline corundum. Theoretical studies both quanw x w tum chemical 2᎐5 and atomistic simulations 6,

x. 7 are in accordance with these facts, and they predict large relaxation effects on these surfaces. Both methods, quantum chemical calculations and Ž . atomistic potential simulations, predict the 001 Ž . surface terminated with Al atoms and the 110 surface terminated with O atoms.

For modeling of the surfaces two-dimensional slab models were used. To construct the slab, the Ž proper primitive cell having the thickness of the . slab was periodically replicated in two dimen-Ž . sions. The 001 surface was modeled using six atomic layers, with the layer ordering Al ᎐O ᎐ 1 3 Al ᎐Al ᎐O ᎐Al , thus making a total of 10 atoms

per primitive cell. In this notation the atomic symbol labeling the layer is followed by the number of atoms contributing from the respective layer to the Ž . primitive cell. The 110 surface was modeled using a ten-layer slab O ᎐O ᎐Al ᎐O ᎐O ᎐O ᎐O ᎐ Al ᎐O ᎐O with 20 atoms per cell.

2 1

Because of the importance of the relaxation of w x the surface atom layers 2, 3, 6, 7 and the possible influence of the relaxation on the specific surface w x states 8 , the static relaxation of the studied surfaces was also taken into account. In the case of Ž . 001 surface, only relaxation of the top surface Al Ž . atoms was considered. For the 110 surface, both the first and the second surface layer of oxygen Ž . atoms were allowed to relax. Both the 001 and Ž . 110 surfaces were relaxed using two different potentials. The Coulomb terms were not taken into account in this case. The parameters of the Lennard-Jones potential were optimized to reproduce the enthalpy of formation and the experimental geomew x w x try of the ␣-alumina. GULP 9 and WMIN 10 programs were used for this study. The relaxation Ž . of 001 slab was also studied using quantum chemical calculation at Hartree᎐Fock level with STO-3G basis set.

The calculations of electron structure for the bulk ␣-Al O , and for both, unrelaxed and relaxed 2 3 Ž .

Ž . 001 and 110 slabs were performed by the periodic Hartree᎐Fock method, using the CRYSTAL95 w x program 11 . The computations for bulk and re-Ž . laxed 001 surfaces were performed using two w x basis sets: basis set according to Catti et al. 12 and STO-3G basis set extended by adding polar-Ž . ization d-functions at Al with exponent 0.6 . The results obtained using both basis sets were mutually compared and for the study of influence of Ž . relaxation on the density of states DOS and for Ž . the slab 110 was used only the STO-3G basis set.

The densities of states and projected densities of Ž . states PDOS were calculated and used as a main tool for the identification of the occurrence of specific surface states. Because of our interest on the states near bandgap, only the highest valence band was considered.

Results and Discussion

The relaxations of surface atomic layers obtained using the Buckingham plus electrostatic pow x tential with the parametrization according to 9 were 60% for the surface layer of aluminum atoms Ž . of the slab 001 and 100% for the two oxygen Ž . layers of the slab 110 . The surface density of the Ž . aluminum containing layers of the 110 slab is so low that the inclusion of the oxygens from the two surface layers does not produce unrealistic interatomic distances.

Almost the same results were obtained using the Lennard-Jones potential. The potential constants were optimized to reproduce the energy of formation of the ␣-alumina and simultaneously to minimize the norm of gradient of energy with respect to lattice parameters and coordinates of atoms. The formation energy with respect to isolated Al and O atoms was determined using ther- . kcalrmol, O, O s 2.902 A. Because it was not possible to reach exactly the zero norm of the energy gradient, the obtained potential functions were examined to reproduce the experimental geometry of ␣-alumina. The primitive cell volume was contracted to 70% of its original value. Despite this fact, the relaxations obtained were in very good agreement with the results provided by the Buckingham plus electrostatic potential: relax-Ž . ation 65% for the Al layer of the 001 slab and Ž . 100% for two oxygen layers of the 110 slab.

w x The atomistic potential simulations 7 provided Ž . the relaxation of the Al layer of the 001 surface 59%, which is in good accordance with our results obtained using classical mechanics potential relaxations. However, these methods underestimate the Ž . relaxation of the 001 surface in comparison with quantum mechanical computations. The maximum Ž . value of relaxation of the top Al layer of the 001 surface was obtained using density-functional the-Ž . ory DFT periodic quantum chemical calculation w x Ž . 2 . This value 86% is in relatively good agreement with the 80% obtained in the present study using quantum chemical computation of much lower quality. Because of the well-known fact that the STO-3G basis set reproduces relatively well the geometries, this agreement is not surprising.

Concerning the very high, 100% relaxation of Ž . two oxygen layers of the 110 surface, one should notice that the shift of the atomar positions is not very high-the interplane distances are 0.19 and 0.8 A, respectively. For the consecutive quantum Ž . chemical computations the slab 110 with 100% relaxed first and second oxygen layer was taken as input.

The study of relaxation of the surface Al-con-Ž . taining layer of the 001 slab by means of periodic Hartree᎐Fock calculation using STO-3G basis set provided the value of relaxation of 80%. portant for our purposes, is well reproduced also in the STO-3G basis set despite the differences in the value of Fermi energy and in the width of the bandgap. The presence of the surface states and the trends of energy shifts of individual bands are clearly expressed using STO-3G basis set. The evo-Ž . lution of the DOS with relaxation of the 001 Ž . surface and the DOS of the 110 slab were then studied using STO-3G basis set. Figure 5 shows the evolution of the total DOS of Ž . the 001 slab with relaxation. With growing relaxation, the Fermi energy shifts to more negative values, the bottom of the conduction band slightly shifts to the lower energy and the energy of the surface states increases. The principal result, demonstrated in Figure 5 is that not only the unrelaxed but also the relaxed surface produces surface states into energy gap. One can clearly see that these states have their origin in the surface states of the unrelaxed surface and that these states are not only a broadening of the conduction band. This result is in contradiction with the result obtained using semiempirical tight-binding Hamiltow x nian 8 , where surface states are shifted by the relaxation above the conduction band. Ž .

Figure 5

2.

In the case of the 001 relaxed surface, the width of bandgap grows in comparison to the bulk, Fermi energy is lower than in the bulk, and the surface excited states are close to the upper border of the bandgap. As a Ž . consequence of these facts, the 001 relaxed surface is a worse electron donor and a slightly better electron acceptor than the bulk.

Ž . In the case of interaction of the 001 surface of ␣-alumina with a very strong electron donor, the effect of charge-transfer interaction should be taken into account.

Ž .