- Email: [email protected]
Molecular dynamics study on the stability of γ-Al2O3 surfaces
Applied Surface Science 130–132 Ž1998. 549–554
Molecular dynamics study on the stability of g-Al 2 O 3 surfaces Isao Gunji, Kazuo Teraishi, Akira Endou, Ryuji Miura, Xilin Yin, Ryo Yamauchi, Momoji Kubo, Abhijit Chatterjee, Akira Miyamoto ) Department of Materials Chemistry, Graduate School of Engineering, Tohoku UniÕersity, Aoba, Aramaki, Aoba-ku, Sendai 980-77, Japan
Abstract Molecular dynamics method was applied to investigate the structure and stability of g-Al 2 O 3 surface with reference to three plane indices, namely, Ž100., Ž110., and Ž111.. Analyses of coordination number shows that surface tetrahedral Al’s were found to have more mobility than octahedral Al’s. The largest change of the coordination number was observed in the Ž111. surface, which matches with the largest relaxation energy. The relaxation energies of Ž100. and Ž110. surfaces were found to be almost equal, and the stability of the octahedral Al’s in these surfaces were compared from the analyses of the coordination numbers. q 1998 Elsevier Science B.V. All rights reserved. Keywords: g-Al 2 O 3 ; Surface; Structure; Molecular dynamics; Hydroxyl group
1. Introduction Unique character of g-Al 2 O 3 , in terms of high surface area, acidity, and mechanical strength, has prompted its application in many catalysis processes like automobile exhaust treatment, hydrotreating, and combustion w1x. In these processes, g-Al 2 O 3 act directly as a catalyst or indirectly as a support. In case of its use as a catalyst, the catalytic reactions take place on the surface, and when in case of its use as a support, other catalytically active species like metals are impregnated on its surface. Therefore, understanding of the g-Al 2 O 3 surface is essential to rationalize its activity, or to design a new catalyst. Experimentally, however, it is difficult to characterize the )
Corresponding author. Tel.: q81-22-217-7233; fax: q81-22217-7235; e-mail: [email protected].
surface of g-Al 2 O 3 due to problem of getting a single crystal. Computational studies were also carried out to shed a light on the surface structure of g-Al 2 O 3 . Alvarez et al. w2x performed molecular dynamics simulation for bulk g-Al 2 O 3 and the layers corresponding to several plane indices were analyzed. Although they compared their results with IR spectra of hydroxyl groups adsorbed on g-Al 2 O 3 ; surface relaxation or reconstruction evidenced by the experiment w1x, was not taken into consideration in this simulation. Alvarez et al. w3,4x later simulated the reconstruction process of the Ž100. surface of gAl 2 O 3 . Porous amorphous-like structure was obtained after the simulation, which, in turn, indicated the instability of this surface. They infer that under this experimental condition of synthesis, Ž100. surface would never be exposed.
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 1 1 3 - 5
550
I. Gunji et al.r Applied Surface Science 130–132 (1998) 549–554
In this study, the structure and the stability of g-Al 2 O 3 surface corresponding to several plane indexes, namely Ž100., Ž110., and Ž111., are investigated by molecular dynamics method. Prior to this, bulk g-Al 2 O 3 was simulated to test the validity of the potential parameters used here and to compare with the results obtained from the surface simulations. The mechanism of the reconstruction was analyzed by the change of the coordination number. Larger change in the coordination number corresponds to the higher degree of reconstruction, which further indicates the instability of the surface. Also the relaxation energies were calculated by subtracting the initial energy from the final energy. Here also a large relaxation energy is expected from the unstable surface. The most stable surface which is subjected to the least relaxation is determined. The results are in company with earlier observations.
2. Computational details Molecular dynamics calculations were performed using MXDORTO program w5x, in which Coulombic interaction is calculated by Ewald method and the periodic boundary condition is applied to all directions. Potential parameters developed to simulate a-Al 2 O 3 is also used in the present g-Al 2 O 3 simulations. Therefore, at first, we tested the validity of parameters for bulk g-Al 2 O 3 . Initial structure of the bulk model was constructed by eliminating Al atoms from the perfect spinel randomly but is retained the condition that 10% of tetrahedral and 46.7% of octahedral sites are occupied. Cubic box consisting of 864 Oxygen atoms and 576 Aluminum atoms was taken as a simulation cell. During 20 ps of simulation, jumps of Al’s from one site to neighboring vacant site were observed, but the oxygen’s positions and the tetrahedral Alroctahedral Al ratio were well preserved. The potential parameters are thus proved to be valid for g-Al 2 O 3 simulations. Three kind of surfaces, namely Ž100., Ž110., and Ž111., were expressed by the slab models extracted from the bulk ŽFig. 1.. Each model consists of four tetrahedral Al layers as well as four Žin the cases of Ž100. and Ž111.. or eight Žin the case of Ž110.. octahedral Al layers and appropriate number of oxygen layers. The upper and lower surfaces of Ž110.
Fig. 1. The g-Al 2 O 3 slab models extracted from the bulk. AlŽoct. means Al’s in octahedral site in initial state. AlŽtet. means Al’s in tetrahedral site in initial state.
model correspond to C-layer and D-layer, respectively. In case of Ž111. surface, the concentration of Al in the upper surface ŽA-layer. becomes very high, and the simulation resulted in the destruction of the lattice structure, and therefore 1r3 of Al’s in the Ž111. A surface are moved to the bottom surface. These slabs are placed inside the boxes whose base plane has the same size as that of the exposed ˚ . to surface and the height is large enough Ž95 A consider the surface as being exposed to the void. For this box, periodic boundary condition was applied to all directions. The variation of the coordination number was analyzed for each layer by tracing the Al’s in each layer and monitoring their coordination numbers to oxygen. The degree of the reconstruction was then
I. Gunji et al.r Applied Surface Science 130–132 (1998) 549–554
evaluated by the change of the coordination number. Also the relaxation energy of the surface was calculated by the energy difference between initial and final configuration. Now, as the surface area of the models are different, the relaxation energies were scaled in terms of surface area for comparison. MD simulations were carried out for 25 000 steps with a time interval of 0.4 ps. The temperature and pressure are kept at a constant of 300 K and 0.1 MPa, respectively through the calculation. RYUGA package w6x was employed for the visualization of the simulated result.
3. Results and discussion 3.1. (100) surface On the upper surface of Ž100. model, uppermost octahedral Al’s, whose coordination number to oxygen is five ŽOC 1., are exposed. The lowest tetrahedral Al’s whose coordination number to oxygen is two ŽTE 4., and the octahedral Al’s above them, which are coordinated to five oxygens ŽOC 4., are exposed to the lower surface. The coordination number and number of atoms being in same layer is given in Table 1. The unsaturated coordination numbers are due to dangling bond. The coordination number of Al’s to oxygen was monitored during the simulation and their final distribution is given in Table 2. The coordination number of OC 1 is unchanged during the simulation, which indicates stability of this layer. Next tetrahedral Al’s ŽTE 1. are initially coordinated to four oxygen, same as bulk,
551
Table 2 In Ž100. surface model: the final distribution of the coordination number of Al’s in octahedral and tetrahedral site Layer
4
5
6
OC 1 OC 2 OC 3 OC 4 TE 1 TE 2 TE 3 TE 4
1.449 3.704 9.231 5.926 64.815 75.000 61.667 25.000
97.826 10.370 2.308 93.333 35.185 0.000 23.333 66.667
0.725 85.926 88.462 0.741 0.000 25.000 15.000 8.333
but about 35% of them moved to the surface which is observed from the change in the coordination number from four to five ŽTable 2.. The octahedral Al’s in the middle layers ŽOC 2, OC 3. are quite stable, and the coordination numbers were constant during the simulation. The tetrahedral Al’s in the middle layers ŽTE 2, TE 3., on the other hand, changed their coordination number significantly. This implies that tetrahedral Al’s are less stable than octahedral ones. The coordination number of OC 4 was also constant during the simulation. In case of TE 4 Al’s moved to either second lowest octahedral site, or inner octahedral or tetrahedral site. Conclusively, when the octahedral layer is exposed as a surface, the five coordinated Al’s in the surface are fairly stable, where as the tetrahedral Al’s near the surface were found to move to the surface octahedral site, which increases the density of Al near the surface. This may be responsible for the activity of g-Al 2 O 3 . 3.2. (110) surface
Table 1 In Ž100. surface model: number of Aluminum in same octahedral and tetrahedral layer and the initial coordination number of aluminum to oxygen Layer
Number
First coordination number
OC 1 OC 2 OC 3 OC 4 TE 1 TE 2 TE 3 TE 4
138 135 130 135 54 56 60 60
5 6 6 5 4 4 4 2
On the upper surface of Ž110. surface C-layer, tetrahedral Al’s ŽTE 1., whose coordination number to oxygen is three and the octahedral Al’s ŽOC 1. under them, which are coordinated to four oxygens, are exposed. On the lower surface D-layer, octahedral Al’s whose coordination number to oxygen is four ŽOC 8. are exposed. The coordination number and number of atoms being in the same layer is given in Table 3. The octahedral Al’s in the bulk ŽOC 2–7. maintained their initial coordination number of six during the simulation ŽTable 4.. The octahedral Al’s which are located on or near the
I. Gunji et al.r Applied Surface Science 130–132 (1998) 549–554
552
Table 3 In the Ž110. surface model: number of aluminum in same octahedral and tetrahedral layer and the initial coordination number of aluminum to oxygen Layer
Number
First coordination number
OC 1 OC 2, 3, 4, 5, 6, 7 OC 8 TE 1 TE 2 TE 3 TE 4
56 56 56 49 50 46 48
4 6 4 3 4 4 4
face were found to move to the bulk octahedral or tetrahedral site, which decreases the density of Al near the surface. 3.3. (111) surface
surface ŽOC 1, OC 8. remained on the surface, but about 1r5 of OC 8 Al’s move to the neighboring site whose coordination number is five. Most of the TE 1 are migrated to tetrahedral or octahedral sites in the bulk, and only a few of them remained on surface ŽTable 4.. Some of the tetrahedral Al’s in the bulk ŽTE 2, TE 3, TE 4. moved to octahedral site while others stayed at their initial site. Five coordination is observed in case of TE 4. The examination of the structure using the computer graphics revealed that these tetrahedral Al’s did not expose to surface but the lattice oxygen at the surface moved. Conclusively, when the Ž110. C-layer or D-layer is exposed to the surface, the unsaturated octahedral Al’s in the surface remains there. Tetrahedral Al’s on the sur-
On the upper surface, the octahedral Al’s, whose coordination number to oxygen is three ŽOC 1., and the tetrahedral Al’s under them, whose coordination number is also three ŽTE 1., are exposed. On the lower surface, tetrahedral Al’s, whose coordination number to oxygen is three ŽTE 4., are exposed. The coordination number and number of atoms being in the same layer is given in Table 5. The octahedral Al’s in bulk ŽOC 2, OC 3, OC 4. conserved their initial coordination number of six ŽTable 6.. About 60% of OC 1 moved down to the octahedral site in the bulk. But 40% of them remained on the surface. Most of TE 1 moved to the octahedral site. About half of TE 4 remained on the surface, which can be seen from the change in the coordination number to three ŽTable 6.. Some of the tetrahedral Al’s ŽTE 2, TE 3. moved to the octahedral site Ž63% for TE 2, 35% for TE 3.. Conclusively, when the Ž111. A-layer is exposed as a surface, the unsaturated octahedral Al’s on the surface may stay there. Tetrahedral Al’s on the surface of A-layer were found to move to the
Table 4 In Ž110. surface model The final distribution of the coordination number of Al’s in octahedral site Layer
4
5
6
OC 1 OC 2 OC 3 OC 4 OC 5 OC 6 OC 7 OC 8
75.000 1.786 0.000 0.000 7.143 1.786 7.143 71.429
23.214 0.000 0.000 0.000 0.000 0.000 7.143 21.429
0.000 98.214 100.000 100.000 92.856 98.214 83.929 7.143
The final distribution of the coordination number of Al’s in tetrahedral site Layer TE 1 TE 2 TE 3 TE 4
3 4.082 0.000 0.000 0.000
4 24.490 48.000 67.391 62.500
5 0.000 4.000 4.348 22.917
6 71.429 46.000 28.261 14.583
I. Gunji et al.r Applied Surface Science 130–132 (1998) 549–554
553
Table 5 In the Ž111. surface: number of aluminum in same octahedral and tetrahedral layer and the initial coordination number of aluminum to oxygen Layer
Number
First coordination number
OC 1 OC 2 OC 3 OC 4 TE 1 TE 2 TE 3 TE 4
44 132 43 140 36 38 40 39
3 6 6 6 3 4 4 3 Fig. 2. Relaxation energy scaled by surface area.
bulk octahedral site. Tetrahedral Al’s on the lower surface remained like the octahedral Al’s on the upper surface. Therefore the coordination number of Al to oxygen on Ž111. surface is mainly three. More number of tetrahedral Al’s in the bulk were found to move to the bulk octahedral site in comparison to other surface models. 3.4. Relaxation energy The relaxation energies scaled by the surface area of each model are given in Fig. 2. These values can be viewed as the average of the upper and lower surfaces of each model. The relaxation energy of Ž111. surface model was the largest among the three, which is consistent with the largest change in terms of the coordination number in this surface. This surface would thus be hardly exposed, or if exposed, it will be subjected to a considerable reconstruction which would yield the amorphous phase on the surface. The relaxation energy of Ž110. surface was Table 6 In Ž111. surface model: the final distribution of the coordination number of Al’s in octahedral and tetrahedral site Layer
3
4
5
6
OC 1 OC 2 OC 3 OC 4 TE 1 TE 2 TE 3 TE 4
0.000 0.000 0.000 38.636 8.333 0.000 0.000 53.846
0.714 2.326 3.030 2.273 5.556 26.316 57.500 7.692
8.571 6.977 2.273 2.273 5.556 10.526 7.500 12.821
90.000 90.698 94.697 56.818 80.556 63.158 35.000 25.641
found to be the smallest, which indicates that this plane is the most rigid. The relaxation energy of Ž100. surface was slightly larger than that of Ž110. surface. From this result and the previous one that the surface octahedral Al’s in Ž100. and Ž110. are stable, these two surfaces are expected to exposed. From the interpretation of the experimental infrared ŽIR. spectra of hydroxyl groups adsorbed on gAl 2 O 3 , it was proposed that only Ž110. surface is exposed w7x. On the other hand, transmission electron diffraction ŽTED. of g-Al 2 O 3 obtained by thermal oxidation of Al foil revealed that Ž100. orientation is dominant w8x. These two surfaces thus might be exposed depending on the preparation conditions.
4. Conclusion The structure and the stability of g-Al 2 O 3 surface corresponding to three plane indices, namely, Ž100., Ž110., and Ž111., were investigated by molecular dynamics method. From the analyses of the coordination number, surface tetrahedral Al’s were found to migrate. The octahedral Al’s with one or two dangling bond are stable and remained in the surface. The largest change of the coordination number was observed in the Ž111. surface, which is consistent with the largest relaxation energy. This surface would thus be hardly exposed. The relaxation energies of Ž100. and Ž110. surfaces were found to be almost equal, and the stability of the octahedral Al’s in these surface was shown from the analyses of the coordination numbers. Studies on the catalytic reactions or
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I. Gunji et al.r Applied Surface Science 130–132 (1998) 549–554
the deposition of metals on these surface are in progress.
References w1x H. Knozinger, P. Ratnasamy, Catal. Rev. Sci. Eng. 17 Ž1978. 31. w2x L.J. Alvarez, J.F. Aanz, M.J. Capitan, ´ M.A. Centeno, J.A. Odriozola, J. Chem. Soc. Faraday Trans. 89 Ž1993. 3623.
w3x L.J. Alvarez, L.E. Leon, ´ J.F. Sanz, M.J. Capitan, ´ J.A. Odriozola, J. Phys. Chem. 99 Ž1995. 17872. w4x L.J. Alvarez, L.E. Leon, ´ J.F. Sanz, M.J. Capitan, ´ J.A. Odriozola, Phys. Rev. B 50 Ž1994. 2561. w5x K. Kawamura, in: F. Yonezawa ŽEd.., Molecular Dynamics Simulations, Springer, Berlin, 1992 p. 88. w6x R. Miura, H. Yamano, R. Yamauchi, M. Katagiri, M. Kubo, R. Vetrivel, A. Miyamoto, Catal. Today 23 Ž1995. 409. w7x Y. Chen, L. Zhang, Catal. Lett. 12 Ž1992. 51. w8x B. Ealet, M.H. Elyakhloufi, E. Gillet, M. Ricci, Thin Solid Films 250 Ž1994. 92.
Molecular dynamics study on the stability of g-Al 2 O 3 surfaces Isao Gunji, Kazuo Teraishi, Akira Endou, Ryuji Miura, Xilin Yin, Ryo Yamauchi, Momoji Kubo, Abhijit Chatterjee, Akira Miyamoto ) Department of Materials Chemistry, Graduate School of Engineering, Tohoku UniÕersity, Aoba, Aramaki, Aoba-ku, Sendai 980-77, Japan
Abstract Molecular dynamics method was applied to investigate the structure and stability of g-Al 2 O 3 surface with reference to three plane indices, namely, Ž100., Ž110., and Ž111.. Analyses of coordination number shows that surface tetrahedral Al’s were found to have more mobility than octahedral Al’s. The largest change of the coordination number was observed in the Ž111. surface, which matches with the largest relaxation energy. The relaxation energies of Ž100. and Ž110. surfaces were found to be almost equal, and the stability of the octahedral Al’s in these surfaces were compared from the analyses of the coordination numbers. q 1998 Elsevier Science B.V. All rights reserved. Keywords: g-Al 2 O 3 ; Surface; Structure; Molecular dynamics; Hydroxyl group
1. Introduction Unique character of g-Al 2 O 3 , in terms of high surface area, acidity, and mechanical strength, has prompted its application in many catalysis processes like automobile exhaust treatment, hydrotreating, and combustion w1x. In these processes, g-Al 2 O 3 act directly as a catalyst or indirectly as a support. In case of its use as a catalyst, the catalytic reactions take place on the surface, and when in case of its use as a support, other catalytically active species like metals are impregnated on its surface. Therefore, understanding of the g-Al 2 O 3 surface is essential to rationalize its activity, or to design a new catalyst. Experimentally, however, it is difficult to characterize the )
Corresponding author. Tel.: q81-22-217-7233; fax: q81-22217-7235; e-mail: [email protected].
surface of g-Al 2 O 3 due to problem of getting a single crystal. Computational studies were also carried out to shed a light on the surface structure of g-Al 2 O 3 . Alvarez et al. w2x performed molecular dynamics simulation for bulk g-Al 2 O 3 and the layers corresponding to several plane indices were analyzed. Although they compared their results with IR spectra of hydroxyl groups adsorbed on g-Al 2 O 3 ; surface relaxation or reconstruction evidenced by the experiment w1x, was not taken into consideration in this simulation. Alvarez et al. w3,4x later simulated the reconstruction process of the Ž100. surface of gAl 2 O 3 . Porous amorphous-like structure was obtained after the simulation, which, in turn, indicated the instability of this surface. They infer that under this experimental condition of synthesis, Ž100. surface would never be exposed.
0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 1 1 3 - 5
550
I. Gunji et al.r Applied Surface Science 130–132 (1998) 549–554
In this study, the structure and the stability of g-Al 2 O 3 surface corresponding to several plane indexes, namely Ž100., Ž110., and Ž111., are investigated by molecular dynamics method. Prior to this, bulk g-Al 2 O 3 was simulated to test the validity of the potential parameters used here and to compare with the results obtained from the surface simulations. The mechanism of the reconstruction was analyzed by the change of the coordination number. Larger change in the coordination number corresponds to the higher degree of reconstruction, which further indicates the instability of the surface. Also the relaxation energies were calculated by subtracting the initial energy from the final energy. Here also a large relaxation energy is expected from the unstable surface. The most stable surface which is subjected to the least relaxation is determined. The results are in company with earlier observations.
2. Computational details Molecular dynamics calculations were performed using MXDORTO program w5x, in which Coulombic interaction is calculated by Ewald method and the periodic boundary condition is applied to all directions. Potential parameters developed to simulate a-Al 2 O 3 is also used in the present g-Al 2 O 3 simulations. Therefore, at first, we tested the validity of parameters for bulk g-Al 2 O 3 . Initial structure of the bulk model was constructed by eliminating Al atoms from the perfect spinel randomly but is retained the condition that 10% of tetrahedral and 46.7% of octahedral sites are occupied. Cubic box consisting of 864 Oxygen atoms and 576 Aluminum atoms was taken as a simulation cell. During 20 ps of simulation, jumps of Al’s from one site to neighboring vacant site were observed, but the oxygen’s positions and the tetrahedral Alroctahedral Al ratio were well preserved. The potential parameters are thus proved to be valid for g-Al 2 O 3 simulations. Three kind of surfaces, namely Ž100., Ž110., and Ž111., were expressed by the slab models extracted from the bulk ŽFig. 1.. Each model consists of four tetrahedral Al layers as well as four Žin the cases of Ž100. and Ž111.. or eight Žin the case of Ž110.. octahedral Al layers and appropriate number of oxygen layers. The upper and lower surfaces of Ž110.
Fig. 1. The g-Al 2 O 3 slab models extracted from the bulk. AlŽoct. means Al’s in octahedral site in initial state. AlŽtet. means Al’s in tetrahedral site in initial state.
model correspond to C-layer and D-layer, respectively. In case of Ž111. surface, the concentration of Al in the upper surface ŽA-layer. becomes very high, and the simulation resulted in the destruction of the lattice structure, and therefore 1r3 of Al’s in the Ž111. A surface are moved to the bottom surface. These slabs are placed inside the boxes whose base plane has the same size as that of the exposed ˚ . to surface and the height is large enough Ž95 A consider the surface as being exposed to the void. For this box, periodic boundary condition was applied to all directions. The variation of the coordination number was analyzed for each layer by tracing the Al’s in each layer and monitoring their coordination numbers to oxygen. The degree of the reconstruction was then
I. Gunji et al.r Applied Surface Science 130–132 (1998) 549–554
evaluated by the change of the coordination number. Also the relaxation energy of the surface was calculated by the energy difference between initial and final configuration. Now, as the surface area of the models are different, the relaxation energies were scaled in terms of surface area for comparison. MD simulations were carried out for 25 000 steps with a time interval of 0.4 ps. The temperature and pressure are kept at a constant of 300 K and 0.1 MPa, respectively through the calculation. RYUGA package w6x was employed for the visualization of the simulated result.
3. Results and discussion 3.1. (100) surface On the upper surface of Ž100. model, uppermost octahedral Al’s, whose coordination number to oxygen is five ŽOC 1., are exposed. The lowest tetrahedral Al’s whose coordination number to oxygen is two ŽTE 4., and the octahedral Al’s above them, which are coordinated to five oxygens ŽOC 4., are exposed to the lower surface. The coordination number and number of atoms being in same layer is given in Table 1. The unsaturated coordination numbers are due to dangling bond. The coordination number of Al’s to oxygen was monitored during the simulation and their final distribution is given in Table 2. The coordination number of OC 1 is unchanged during the simulation, which indicates stability of this layer. Next tetrahedral Al’s ŽTE 1. are initially coordinated to four oxygen, same as bulk,
551
Table 2 In Ž100. surface model: the final distribution of the coordination number of Al’s in octahedral and tetrahedral site Layer
4
5
6
OC 1 OC 2 OC 3 OC 4 TE 1 TE 2 TE 3 TE 4
1.449 3.704 9.231 5.926 64.815 75.000 61.667 25.000
97.826 10.370 2.308 93.333 35.185 0.000 23.333 66.667
0.725 85.926 88.462 0.741 0.000 25.000 15.000 8.333
but about 35% of them moved to the surface which is observed from the change in the coordination number from four to five ŽTable 2.. The octahedral Al’s in the middle layers ŽOC 2, OC 3. are quite stable, and the coordination numbers were constant during the simulation. The tetrahedral Al’s in the middle layers ŽTE 2, TE 3., on the other hand, changed their coordination number significantly. This implies that tetrahedral Al’s are less stable than octahedral ones. The coordination number of OC 4 was also constant during the simulation. In case of TE 4 Al’s moved to either second lowest octahedral site, or inner octahedral or tetrahedral site. Conclusively, when the octahedral layer is exposed as a surface, the five coordinated Al’s in the surface are fairly stable, where as the tetrahedral Al’s near the surface were found to move to the surface octahedral site, which increases the density of Al near the surface. This may be responsible for the activity of g-Al 2 O 3 . 3.2. (110) surface
Table 1 In Ž100. surface model: number of Aluminum in same octahedral and tetrahedral layer and the initial coordination number of aluminum to oxygen Layer
Number
First coordination number
OC 1 OC 2 OC 3 OC 4 TE 1 TE 2 TE 3 TE 4
138 135 130 135 54 56 60 60
5 6 6 5 4 4 4 2
On the upper surface of Ž110. surface C-layer, tetrahedral Al’s ŽTE 1., whose coordination number to oxygen is three and the octahedral Al’s ŽOC 1. under them, which are coordinated to four oxygens, are exposed. On the lower surface D-layer, octahedral Al’s whose coordination number to oxygen is four ŽOC 8. are exposed. The coordination number and number of atoms being in the same layer is given in Table 3. The octahedral Al’s in the bulk ŽOC 2–7. maintained their initial coordination number of six during the simulation ŽTable 4.. The octahedral Al’s which are located on or near the
I. Gunji et al.r Applied Surface Science 130–132 (1998) 549–554
552
Table 3 In the Ž110. surface model: number of aluminum in same octahedral and tetrahedral layer and the initial coordination number of aluminum to oxygen Layer
Number
First coordination number
OC 1 OC 2, 3, 4, 5, 6, 7 OC 8 TE 1 TE 2 TE 3 TE 4
56 56 56 49 50 46 48
4 6 4 3 4 4 4
face were found to move to the bulk octahedral or tetrahedral site, which decreases the density of Al near the surface. 3.3. (111) surface
surface ŽOC 1, OC 8. remained on the surface, but about 1r5 of OC 8 Al’s move to the neighboring site whose coordination number is five. Most of the TE 1 are migrated to tetrahedral or octahedral sites in the bulk, and only a few of them remained on surface ŽTable 4.. Some of the tetrahedral Al’s in the bulk ŽTE 2, TE 3, TE 4. moved to octahedral site while others stayed at their initial site. Five coordination is observed in case of TE 4. The examination of the structure using the computer graphics revealed that these tetrahedral Al’s did not expose to surface but the lattice oxygen at the surface moved. Conclusively, when the Ž110. C-layer or D-layer is exposed to the surface, the unsaturated octahedral Al’s in the surface remains there. Tetrahedral Al’s on the sur-
On the upper surface, the octahedral Al’s, whose coordination number to oxygen is three ŽOC 1., and the tetrahedral Al’s under them, whose coordination number is also three ŽTE 1., are exposed. On the lower surface, tetrahedral Al’s, whose coordination number to oxygen is three ŽTE 4., are exposed. The coordination number and number of atoms being in the same layer is given in Table 5. The octahedral Al’s in bulk ŽOC 2, OC 3, OC 4. conserved their initial coordination number of six ŽTable 6.. About 60% of OC 1 moved down to the octahedral site in the bulk. But 40% of them remained on the surface. Most of TE 1 moved to the octahedral site. About half of TE 4 remained on the surface, which can be seen from the change in the coordination number to three ŽTable 6.. Some of the tetrahedral Al’s ŽTE 2, TE 3. moved to the octahedral site Ž63% for TE 2, 35% for TE 3.. Conclusively, when the Ž111. A-layer is exposed as a surface, the unsaturated octahedral Al’s on the surface may stay there. Tetrahedral Al’s on the surface of A-layer were found to move to the
Table 4 In Ž110. surface model The final distribution of the coordination number of Al’s in octahedral site Layer
4
5
6
OC 1 OC 2 OC 3 OC 4 OC 5 OC 6 OC 7 OC 8
75.000 1.786 0.000 0.000 7.143 1.786 7.143 71.429
23.214 0.000 0.000 0.000 0.000 0.000 7.143 21.429
0.000 98.214 100.000 100.000 92.856 98.214 83.929 7.143
The final distribution of the coordination number of Al’s in tetrahedral site Layer TE 1 TE 2 TE 3 TE 4
3 4.082 0.000 0.000 0.000
4 24.490 48.000 67.391 62.500
5 0.000 4.000 4.348 22.917
6 71.429 46.000 28.261 14.583
I. Gunji et al.r Applied Surface Science 130–132 (1998) 549–554
553
Table 5 In the Ž111. surface: number of aluminum in same octahedral and tetrahedral layer and the initial coordination number of aluminum to oxygen Layer
Number
First coordination number
OC 1 OC 2 OC 3 OC 4 TE 1 TE 2 TE 3 TE 4
44 132 43 140 36 38 40 39
3 6 6 6 3 4 4 3 Fig. 2. Relaxation energy scaled by surface area.
bulk octahedral site. Tetrahedral Al’s on the lower surface remained like the octahedral Al’s on the upper surface. Therefore the coordination number of Al to oxygen on Ž111. surface is mainly three. More number of tetrahedral Al’s in the bulk were found to move to the bulk octahedral site in comparison to other surface models. 3.4. Relaxation energy The relaxation energies scaled by the surface area of each model are given in Fig. 2. These values can be viewed as the average of the upper and lower surfaces of each model. The relaxation energy of Ž111. surface model was the largest among the three, which is consistent with the largest change in terms of the coordination number in this surface. This surface would thus be hardly exposed, or if exposed, it will be subjected to a considerable reconstruction which would yield the amorphous phase on the surface. The relaxation energy of Ž110. surface was Table 6 In Ž111. surface model: the final distribution of the coordination number of Al’s in octahedral and tetrahedral site Layer
3
4
5
6
OC 1 OC 2 OC 3 OC 4 TE 1 TE 2 TE 3 TE 4
0.000 0.000 0.000 38.636 8.333 0.000 0.000 53.846
0.714 2.326 3.030 2.273 5.556 26.316 57.500 7.692
8.571 6.977 2.273 2.273 5.556 10.526 7.500 12.821
90.000 90.698 94.697 56.818 80.556 63.158 35.000 25.641
found to be the smallest, which indicates that this plane is the most rigid. The relaxation energy of Ž100. surface was slightly larger than that of Ž110. surface. From this result and the previous one that the surface octahedral Al’s in Ž100. and Ž110. are stable, these two surfaces are expected to exposed. From the interpretation of the experimental infrared ŽIR. spectra of hydroxyl groups adsorbed on gAl 2 O 3 , it was proposed that only Ž110. surface is exposed w7x. On the other hand, transmission electron diffraction ŽTED. of g-Al 2 O 3 obtained by thermal oxidation of Al foil revealed that Ž100. orientation is dominant w8x. These two surfaces thus might be exposed depending on the preparation conditions.
4. Conclusion The structure and the stability of g-Al 2 O 3 surface corresponding to three plane indices, namely, Ž100., Ž110., and Ž111., were investigated by molecular dynamics method. From the analyses of the coordination number, surface tetrahedral Al’s were found to migrate. The octahedral Al’s with one or two dangling bond are stable and remained in the surface. The largest change of the coordination number was observed in the Ž111. surface, which is consistent with the largest relaxation energy. This surface would thus be hardly exposed. The relaxation energies of Ž100. and Ž110. surfaces were found to be almost equal, and the stability of the octahedral Al’s in these surface was shown from the analyses of the coordination numbers. Studies on the catalytic reactions or
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the deposition of metals on these surface are in progress.
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w3x L.J. Alvarez, L.E. Leon, ´ J.F. Sanz, M.J. Capitan, ´ J.A. Odriozola, J. Phys. Chem. 99 Ž1995. 17872. w4x L.J. Alvarez, L.E. Leon, ´ J.F. Sanz, M.J. Capitan, ´ J.A. Odriozola, Phys. Rev. B 50 Ž1994. 2561. w5x K. Kawamura, in: F. Yonezawa ŽEd.., Molecular Dynamics Simulations, Springer, Berlin, 1992 p. 88. w6x R. Miura, H. Yamano, R. Yamauchi, M. Katagiri, M. Kubo, R. Vetrivel, A. Miyamoto, Catal. Today 23 Ž1995. 409. w7x Y. Chen, L. Zhang, Catal. Lett. 12 Ž1992. 51. w8x B. Ealet, M.H. Elyakhloufi, E. Gillet, M. Ricci, Thin Solid Films 250 Ž1994. 92.