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Using computational approaches to model hematite surfaces
Computational Materials Science 17 (2000) 243±248
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Using computational approaches to model hematite surfaces I. Lado-Touri~ no *, F. Tsobnang Institut Sup erieur des Mat eriaux du Mans, 44 Av. Bartholdi, 72000 Le Mans, France
Abstract Oxide surfaces are very important in many areas of science and technology. The development of both new experimental surface techniques and theoretical approaches, has allowed a better understanding of metal oxide surfaces. In this work, a force®eld-based method is applied to the calculation of some properties of the a-Fe2 O3 (0 0 1) and (0 1 2) surfaces, with the aim to obtain equilibrium structures (relaxed atomic positions of surface atoms) and some data on the energetics of the adsorption of H2 O and SO2 molecules on these surfaces. Ó 2000 Elsevier Science B.V. All rights reserved. Keywords: Hematite; Surfaces; Adsorption; Force®eld
1. Introduction Oxide surfaces are very important in many areas of science and technology including catalysis, microelectronics, corrosion, adhesion, etc. The possibility to simulate phenomena occurring at these surfaces (relaxation, adsorption and dissociation of molecules), as well as a detailed understanding of its properties on the atomic level, is scienti®cally and economically very useful and appealing. Experimentally, the development of new surface techniques has led to a wealth of experimental data [1,2]. At the same time, new theoretical approaches have been applied to the study of surfaces and interfaces [2±4]. The combination of both, theoretical and experimental results, has allowed a better understanding of metal oxide surfaces. * Corresponding author. Tel.: +33-0-2432-14000; fax: +33-02432-14039. E-mail address: [email protected] (I. Lado-TournÄo).
a-Fe2 O3 appears to be an active catalytic material for a great variety of reactions [5,6]. Other possible applications are in photoelectrodes [7] and nonlinear optics materials [8]. Although this oxide plays an important role in several processes, theoretical studies on the electronic and atomic properties of its surfaces are scarce. In this work, a force®eld-based method is applied to study the aFe2 O3 (0 0 1) and (0 1 2) surfaces, with the aim to obtain equilibrium structures (relaxed atomic positions of surface atoms), and some data on the adsorption of H2 O and SO2 molecules on them.
2. Model system and calculation method Two-dimensionally periodic slabs in the form of (1 1) (pure a-Fe2 O3 ) or (2 2) (a-Fe2 O3 + adsorbate) supercells were used to model the surfaces. The slab was repeated in the direction perpendicular to the surface. The thickness of the for both vacuum gap separating the slabs is 30 A surfaces. The thickness of the slab was varied (see
0927-0256/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 0 0 ) 0 0 0 3 2 - X
244
I. Lado-Touri~ no, F. Tsobnang / Computational Materials Science 17 (2000) 243±248
below) to study its in¯uence on surface properties. In both cases, it is very important to ensure that the thickness is big enough to make interactions between opposite surfaces negligible. Cross-sections of the a-Fe2 O3 (0 0 1) and (0 1 2) surfaces are shown in Fig. 1. The (0 1 2) surface can be built up from neutral O±Fe±O±Fe±O units (three of these units are shown in the ®gure) and the (0 0 1) surface is built from Fe±O3 ±Fe±Fe±O3 ±Fe units. In this work, we only consider the neutral, nonpolar termination for both surfaces. Some other truncations of the bulk are, in general, unexpected because they give rise to high surface dipole moments, which imply electrostatically unfavorable situations. However, one must keep in mind that some surfaces can experience a signi®cant stabilizing relaxation and they should not be simply viewed as a truncated bulk. The potential energy of a system can be expressed as a sum of valence (bond), crossterm and nonbond interactions. A particular force®eld de®nes the functional form of each term in this sum. In this work, two dierent force®elds were used:
The Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force®eld [9] for describing the a-Fe2 O3 and absorbate + a-Fe2 O3 systems and the Universal Force®eld (UFF) [9] to treat the absorbate + aFe2 O3 systems. COMPASS is a condensed-phase, ab initio force®eld, which allows a fairly broad coverage of the periodic table and is well parameterized for the a-Fe2 O3 system. In order to describe dierent systems, COMPASS uses dierent models. For covalent bonded molecules the total energy is written as a combination of valence terms including diagonal and o-diagonal cross coupling terms plus nonbonded terms, which include the coulombic energy and the van der Waals interaction. For ionic systems, only these nonbonded terms are retained and all the atoms are treated as nonbonded. For semi-ionic systems the same nonbonded terms are used for atoms that are not in direct contact. For atoms that are bonded, the interaction energy is represented by an electrostatic term and a Morse-dispersion function. UFF is a purely diagonal harmonic force®eld (for a more detailed description of each energy term of both force®elds, see Ref. [9]). It has full coverage of the periodic table as the force®eld parameters are calculated by combining atomic parameters. Thus, force®eld parameters for any combination of atom types can be generated as required. The atomic positions were relaxed by the following procedure: For a-Fe2 O3 , the energy of the system was minimized with respect to atom positions and cell parameters using the Newton± Raphson method [9]. For the a-Fe2 O3 + adsorbate systems, we ®xed the entire surface and let the molecule move around on it by running a molecular dynamics simulation for 50 ps at 300 K. This probes the con®gurational states of the surface and molecule. Once the minimum structure was located by this procedure, the ®rst few surface layers were relaxed. 3. Results and discussion
Fig. 1. Cross-sections of a-Fe2 O3 (0 0 1) and (0 1 2) surfaces.
a-Fe2 O3 : The calculations were carried out for four dierent slab thickness (3, 9, 15 and 30 stacking units) to test convergence of slabsÕ
I. Lado-Touri~ no, F. Tsobnang / Computational Materials Science 17 (2000) 243±248
245
and ®vefold (0 1 2) coordinated surface iron. This is clearly seen in Figs. 2(c) and (d). The bond (Fig. distances to the formerly Fe atoms are 2.09 A 2(c)), 2.11 A (Fig. 2(d)) and 2.08 A (Fig. 2(e)). These results are in close agreement with those presented in Ref. [3]. The results obtained with the COMPASS force®eld are very dierent. The O atom of the water molecule coordinates several Fe surface atoms, and the mean distance to the sur Figs. 2(f) and (g) show the results face is 3.2 A. for the adsorption of a SO2 molecule. The two O atoms coordinate the same Fe atom in the (0 0 1) This can be surface. The distance O±Fe is 2.18 A. seen as a way to approach the sixfold coordination found in the bulk. For the (0 1 2) surface, a single O atom is sucient to obtain the sixfold coordination, so the two O atoms of the SO2 molecule point toward two dierent Fe surface atoms. The
energies and structures with respect to them. The results are presented in Tables 1 and 2. One can see that three stacking units are sucient for convergence for both energy and structure. Our calculations are, in general, in good agreement with previous calculations done by other methods. On the contrary, the values obtained for surface energies completely dier. Our results seem to be closer to experimental fracture surface energies, which range between 6 and 24 J/m2 for (0 1 2) and around 40 J/m2 for (0 0 1) [11]. a-Fe2 O3 + adsorbate (H2 O, SO2 ): The surface structures for the a-Fe2 O3 (0 0 1) and (0 1 2) + adsorbate systems are shown in Fig. 2. Figs. 2(a) and (b) show the results obtained with the COMPASS force®eld. Structures 2(c)±(g) were obtained with the UFF. For both molecules, the O atoms point toward the surface to adsorb the threefold (0 0 1)
Table 1 Interlayer relaxations of the a-Fe2 O3 (0 0 1) surface as a function of the number of stacking unitsa Bulk value (A) Fe O Fe Fe O Fe Fe O Fe Fe O Fe
0.79 0.79 0.64 0.79 0.79 0.64 0.79 0.79 0.64
References
3
9
15
30
0.41 ()48.10) 0.8 (1.26) 0.40 ()37.50) 0.96 (21.52) 0.83 (5.06) 0.62 ()3.12) 0.79 0.00 0.76 ()3.80)
0.42 ()46.83) 0.81 (2.53) 0.39 ()39.06) 0.96 (21.52) 0.83 (5.06) 0.61 ()4.69) 0.80 (1.26) 0.78 ()1.26) 0.66 (3.12) 0.78 ()1.26) 0.79 (0.00)
0.42 ()46.83) 0.81 (2.53) 0.39 ()39.06) 0.96 (21.52) 0.83 (5.06) 0.61 ()4.69) 0.80 (1.26) 0.78 ()1.26) 0.66 (3.12) 0.78 ()1.26) 0.79 (0.00)
0.42 ()46.83) 0.81 (2.53) 0.39 ()39.06) 0.96 (21.52) 0.83 (5.06) 0.61 ()4.69) 0.80 (1.26) 0.78 ()1.26) 0.66 (3.12) 0.78 ()1.26) 0.79 (0.00)
0.79 0.79
Surface energy (J/m2 ) a
Number of stacking units
22.34
22.50
22.53
[2]
22.53
[3]
()57.00) (7.00) ()33.00) (15.00)
[10]
0.44 ()49.00) 0.83 ()3.00) 0.39 ()41.00) 1.02 (21.00)
(1.00) (5.00) ()47.00) (20.00)
(5.00)
(3.00)
()3.00)
(2.00)
(1.00) (4.00)
1.52
1.65
1.53
The values in parenthesis represent the change in interlayer spacing as a percent of the bulk value. The surface energy is calculated from the formula E Eslab ÿ Ebulk =2 A, where A is the surface area and Ebulk is the energy of an equivalent number of Fe2 O3 molecules in the bulk.
246
I. Lado-Touri~ no, F. Tsobnang / Computational Materials Science 17 (2000) 243±248
Table 2 Interlayer relaxations of the a-Fe2 O3 (0 1 2) surface as a function of the number of stacking unitsa Bulk value (A) Number of stacking units O Fe O Fe O O Fe O Fe O
0.30 0.79 0.79 0.30 1.49 0.30 0.79 0.79
3
9
30
[3]
0.24 ()18.33) 0.69 ()12.66) 0.87 (9.75) 0.35 (16.67) 1.46 ()2.28) 0.32 (7.67) 0.78 ()1.01)
0.24 ()18.33) 0.69 ()12.66) 0.86 (9.37) 0.35 (16.67) 1.45 ()2.75) 0.32 (7.67) 0.79 (0.00) 0.77 ()1.90) 0.30 (0.00)
0.24 ()18.33) 0.69 ()12.66) 0.86 (9.37) 0.36 (19.00) 1.45 ()2.75) 0.33 (8.67) 0.79 (0.00) 0.77 ()1.90) 0.30 (0.00)
0.29 ()18.00) 0.66 ()18.00) 0.84 (5.00) 0.46 (34.00) 1.40 ()7.00)
0.30
Surface energy (J/m2 )
Reference
12.86
12.79
12.79
2.00
a
The values in parenthesis represent the change in interlayer spacing as a percent of the bulk value. The surface energy is calculated from the formula E Eslab ÿ Ebulk =2 A, where A is the surface area and Ebulk is the energy of an equivalent number of Fe2 O3 molecules in the bulk.
respectively. distances Fe±O are 2.17 and 2.18 A, From the results obtained with the UFF, one can see that adsorption has only minor eect on the rest of the surface. However, this result must be regarded with caution, due to the simplicity of the terms used in this force®eld to describe the bond in a-Fe2 O3 . The UFF considers it as a covalent bond. Distortion of surface atoms is evident in the structures obtained with the COMPASS force®eld. However, this force®eld does not reproduce well the interaction between the adsorbate molecule and the surface. A combination of both force®elds may be a solution for this problem and some calculations are in progress. In Table 3, some results obtained for a-Fe2 O3 using the COMPASS, Universal and mixed force®elds are shown. The best results are obtained for the COMPASS force®eld, but an important improvement can be seen for the mixed approach. Unfortunately, we could not calculate adsorption energies for these molecules. An usual and
simple way of doing this calculation is by moving the molecule away from the surface by a distance that is sucient to eliminate the interaction between both the surface and molecule. Then the energies of both con®gurations (with and without interaction) are subtracted. We always observed an interaction, even for distances bigger than At this time, the reason for this is not 12±13 A. understood, but is a subject for future work. 4. Conclusions Qualitative results on relaxed a-Fe2 O3 surface structures as well as on the adsorption of H2 O and SO2 molecules on them were presented. On one hand, we found that the COMPASS force®eld reproduces quite well the relaxation occurring after the creation of a a-Fe2 O3 surface. On the contrary, it works less well for interfacial systems. On the other hand, the UFF is able to describe
I. Lado-Touri~ no, F. Tsobnang / Computational Materials Science 17 (2000) 243±248
247
Fig. 2. Adsorbate + a-Fe2 O3 surfaces (only the ®rst repeat unit and the top two layers of the second repeat unit are shown): (a) a-Fe2 O3 (0 0 1) + H2 O (COMPASS); (b) a-Fe2 O3 (0 1 2) + H2 O (COMPASS); (c) a-Fe2 O3 (0 0 1) + H2 O; (d) a-Fe2 O3 (0 1 2) + H2 O; (e) a-Fe2 O3 (0 0 1) + 2H2 O; (f) a-Fe2 O3 (0 0 1) + SO2 ; (g) a-Fe2 O3 (0 1 2) + SO2.
248
I. Lado-Touri~ no, F. Tsobnang / Computational Materials Science 17 (2000) 243±248
Table 3 Cell parameters, Fe1 Fe2 distance (the shortest Fe±Fe contact, parallel to the threefold c axis) and the Fe1 ±O±Fe2 angle associated to this distancea a, b (A) c (A) d Fe1 Fe2 (A) Fe1 O Fe2 (°) COMPASS Universal Mixed Experimental a
5.076 (0.81) 4.989 ()0.91) 5.241 (4.09) 5.035
13.334 ()3.00) 12.677 ()7.78) 13.727 ()0.14) 13.747
2.861 ()1.17) 2.521 ()12.92) 2.873 ()0.76) 2.895
87.00 (0.58) 79.7 ()7.86) 87.3 (0.92) 86.50
The values in parenthesis represent the change as a percent of the experimental value.
interfacial interactions, but does not perform so well for the a-Fe2 O3 system. Calculations that use a mixed approach are being carried out. Quantum mechanical simulations are superior to molecular mechanics and dynamics methods with parameterized potentials. However, they are computationally expensive. Parameterized potentials methods are, in general, less accurate, but results can be obtained in a realistic period of time. Structures obtained from this method could be used as a starting point for more sophisticated ab initio calculations. Ab initio [2] and experimental studies [1] have shown two possible terminations of the (0 0 1) surface under typical O2 pressure conditions. These two surfaces have been clearly identi®ed by STM. Future work must be done in this direction and studies on other surfaces and surface terminations must be carried out to completely under-
stand surface properties of a-Fe2 O3 . Other adsorbates must also be studied. References [1] C.M. Eggleston, M.F. Hochella, Am. Mineral. 77 (1992) 911. [2] X.G. Wang, W. Weiss, K. Sahikhutdinov, M. Ritter, M. Ptersen, F. Wagner, R. Schlogl, M. Scheer, Phys. Rev. Lett. 81 (1998) 1038. [3] E. Wasserman, Surf. Sci. 385 (1997) 217. [4] L. Armelao, J. Phys. Condens. Matter 7 (1995) L299. [5] K.E. Smith, V.E. Henrich, Phys. Rev. B 32 (1985) 5384. [6] W. Weiss, Catal. Lett. 52 (1998) 215. [7] L.L. Hu, T. Yoko, Thin Solid Films 219 (1992) 18. [8] T. Hashimoto, J. Ceram. Soc. Jpn. 101 (1993) 64. [9] Force®eld-based simulations, Molecular Simulations Inc., San Diego, April 1997. [10] W.C. Mackrodt, J. Cryst. Growth 80 (1987) 441. [11] J. Guo, D.E. Ellis, D.J. Lam, Phys. Rev. B 45 (1992) 13647.
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Using computational approaches to model hematite surfaces I. Lado-Touri~ no *, F. Tsobnang Institut Sup erieur des Mat eriaux du Mans, 44 Av. Bartholdi, 72000 Le Mans, France
Abstract Oxide surfaces are very important in many areas of science and technology. The development of both new experimental surface techniques and theoretical approaches, has allowed a better understanding of metal oxide surfaces. In this work, a force®eld-based method is applied to the calculation of some properties of the a-Fe2 O3 (0 0 1) and (0 1 2) surfaces, with the aim to obtain equilibrium structures (relaxed atomic positions of surface atoms) and some data on the energetics of the adsorption of H2 O and SO2 molecules on these surfaces. Ó 2000 Elsevier Science B.V. All rights reserved. Keywords: Hematite; Surfaces; Adsorption; Force®eld
1. Introduction Oxide surfaces are very important in many areas of science and technology including catalysis, microelectronics, corrosion, adhesion, etc. The possibility to simulate phenomena occurring at these surfaces (relaxation, adsorption and dissociation of molecules), as well as a detailed understanding of its properties on the atomic level, is scienti®cally and economically very useful and appealing. Experimentally, the development of new surface techniques has led to a wealth of experimental data [1,2]. At the same time, new theoretical approaches have been applied to the study of surfaces and interfaces [2±4]. The combination of both, theoretical and experimental results, has allowed a better understanding of metal oxide surfaces. * Corresponding author. Tel.: +33-0-2432-14000; fax: +33-02432-14039. E-mail address: [email protected] (I. Lado-TournÄo).
a-Fe2 O3 appears to be an active catalytic material for a great variety of reactions [5,6]. Other possible applications are in photoelectrodes [7] and nonlinear optics materials [8]. Although this oxide plays an important role in several processes, theoretical studies on the electronic and atomic properties of its surfaces are scarce. In this work, a force®eld-based method is applied to study the aFe2 O3 (0 0 1) and (0 1 2) surfaces, with the aim to obtain equilibrium structures (relaxed atomic positions of surface atoms), and some data on the adsorption of H2 O and SO2 molecules on them.
2. Model system and calculation method Two-dimensionally periodic slabs in the form of (1 1) (pure a-Fe2 O3 ) or (2 2) (a-Fe2 O3 + adsorbate) supercells were used to model the surfaces. The slab was repeated in the direction perpendicular to the surface. The thickness of the for both vacuum gap separating the slabs is 30 A surfaces. The thickness of the slab was varied (see
0927-0256/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 0 0 ) 0 0 0 3 2 - X
244
I. Lado-Touri~ no, F. Tsobnang / Computational Materials Science 17 (2000) 243±248
below) to study its in¯uence on surface properties. In both cases, it is very important to ensure that the thickness is big enough to make interactions between opposite surfaces negligible. Cross-sections of the a-Fe2 O3 (0 0 1) and (0 1 2) surfaces are shown in Fig. 1. The (0 1 2) surface can be built up from neutral O±Fe±O±Fe±O units (three of these units are shown in the ®gure) and the (0 0 1) surface is built from Fe±O3 ±Fe±Fe±O3 ±Fe units. In this work, we only consider the neutral, nonpolar termination for both surfaces. Some other truncations of the bulk are, in general, unexpected because they give rise to high surface dipole moments, which imply electrostatically unfavorable situations. However, one must keep in mind that some surfaces can experience a signi®cant stabilizing relaxation and they should not be simply viewed as a truncated bulk. The potential energy of a system can be expressed as a sum of valence (bond), crossterm and nonbond interactions. A particular force®eld de®nes the functional form of each term in this sum. In this work, two dierent force®elds were used:
The Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS) force®eld [9] for describing the a-Fe2 O3 and absorbate + a-Fe2 O3 systems and the Universal Force®eld (UFF) [9] to treat the absorbate + aFe2 O3 systems. COMPASS is a condensed-phase, ab initio force®eld, which allows a fairly broad coverage of the periodic table and is well parameterized for the a-Fe2 O3 system. In order to describe dierent systems, COMPASS uses dierent models. For covalent bonded molecules the total energy is written as a combination of valence terms including diagonal and o-diagonal cross coupling terms plus nonbonded terms, which include the coulombic energy and the van der Waals interaction. For ionic systems, only these nonbonded terms are retained and all the atoms are treated as nonbonded. For semi-ionic systems the same nonbonded terms are used for atoms that are not in direct contact. For atoms that are bonded, the interaction energy is represented by an electrostatic term and a Morse-dispersion function. UFF is a purely diagonal harmonic force®eld (for a more detailed description of each energy term of both force®elds, see Ref. [9]). It has full coverage of the periodic table as the force®eld parameters are calculated by combining atomic parameters. Thus, force®eld parameters for any combination of atom types can be generated as required. The atomic positions were relaxed by the following procedure: For a-Fe2 O3 , the energy of the system was minimized with respect to atom positions and cell parameters using the Newton± Raphson method [9]. For the a-Fe2 O3 + adsorbate systems, we ®xed the entire surface and let the molecule move around on it by running a molecular dynamics simulation for 50 ps at 300 K. This probes the con®gurational states of the surface and molecule. Once the minimum structure was located by this procedure, the ®rst few surface layers were relaxed. 3. Results and discussion
Fig. 1. Cross-sections of a-Fe2 O3 (0 0 1) and (0 1 2) surfaces.
a-Fe2 O3 : The calculations were carried out for four dierent slab thickness (3, 9, 15 and 30 stacking units) to test convergence of slabsÕ
I. Lado-Touri~ no, F. Tsobnang / Computational Materials Science 17 (2000) 243±248
245
and ®vefold (0 1 2) coordinated surface iron. This is clearly seen in Figs. 2(c) and (d). The bond (Fig. distances to the formerly Fe atoms are 2.09 A 2(c)), 2.11 A (Fig. 2(d)) and 2.08 A (Fig. 2(e)). These results are in close agreement with those presented in Ref. [3]. The results obtained with the COMPASS force®eld are very dierent. The O atom of the water molecule coordinates several Fe surface atoms, and the mean distance to the sur Figs. 2(f) and (g) show the results face is 3.2 A. for the adsorption of a SO2 molecule. The two O atoms coordinate the same Fe atom in the (0 0 1) This can be surface. The distance O±Fe is 2.18 A. seen as a way to approach the sixfold coordination found in the bulk. For the (0 1 2) surface, a single O atom is sucient to obtain the sixfold coordination, so the two O atoms of the SO2 molecule point toward two dierent Fe surface atoms. The
energies and structures with respect to them. The results are presented in Tables 1 and 2. One can see that three stacking units are sucient for convergence for both energy and structure. Our calculations are, in general, in good agreement with previous calculations done by other methods. On the contrary, the values obtained for surface energies completely dier. Our results seem to be closer to experimental fracture surface energies, which range between 6 and 24 J/m2 for (0 1 2) and around 40 J/m2 for (0 0 1) [11]. a-Fe2 O3 + adsorbate (H2 O, SO2 ): The surface structures for the a-Fe2 O3 (0 0 1) and (0 1 2) + adsorbate systems are shown in Fig. 2. Figs. 2(a) and (b) show the results obtained with the COMPASS force®eld. Structures 2(c)±(g) were obtained with the UFF. For both molecules, the O atoms point toward the surface to adsorb the threefold (0 0 1)
Table 1 Interlayer relaxations of the a-Fe2 O3 (0 0 1) surface as a function of the number of stacking unitsa Bulk value (A) Fe O Fe Fe O Fe Fe O Fe Fe O Fe
0.79 0.79 0.64 0.79 0.79 0.64 0.79 0.79 0.64
References
3
9
15
30
0.41 ()48.10) 0.8 (1.26) 0.40 ()37.50) 0.96 (21.52) 0.83 (5.06) 0.62 ()3.12) 0.79 0.00 0.76 ()3.80)
0.42 ()46.83) 0.81 (2.53) 0.39 ()39.06) 0.96 (21.52) 0.83 (5.06) 0.61 ()4.69) 0.80 (1.26) 0.78 ()1.26) 0.66 (3.12) 0.78 ()1.26) 0.79 (0.00)
0.42 ()46.83) 0.81 (2.53) 0.39 ()39.06) 0.96 (21.52) 0.83 (5.06) 0.61 ()4.69) 0.80 (1.26) 0.78 ()1.26) 0.66 (3.12) 0.78 ()1.26) 0.79 (0.00)
0.42 ()46.83) 0.81 (2.53) 0.39 ()39.06) 0.96 (21.52) 0.83 (5.06) 0.61 ()4.69) 0.80 (1.26) 0.78 ()1.26) 0.66 (3.12) 0.78 ()1.26) 0.79 (0.00)
0.79 0.79
Surface energy (J/m2 ) a
Number of stacking units
22.34
22.50
22.53
[2]
22.53
[3]
()57.00) (7.00) ()33.00) (15.00)
[10]
0.44 ()49.00) 0.83 ()3.00) 0.39 ()41.00) 1.02 (21.00)
(1.00) (5.00) ()47.00) (20.00)
(5.00)
(3.00)
()3.00)
(2.00)
(1.00) (4.00)
1.52
1.65
1.53
The values in parenthesis represent the change in interlayer spacing as a percent of the bulk value. The surface energy is calculated from the formula E Eslab ÿ Ebulk =2 A, where A is the surface area and Ebulk is the energy of an equivalent number of Fe2 O3 molecules in the bulk.
246
I. Lado-Touri~ no, F. Tsobnang / Computational Materials Science 17 (2000) 243±248
Table 2 Interlayer relaxations of the a-Fe2 O3 (0 1 2) surface as a function of the number of stacking unitsa Bulk value (A) Number of stacking units O Fe O Fe O O Fe O Fe O
0.30 0.79 0.79 0.30 1.49 0.30 0.79 0.79
3
9
30
[3]
0.24 ()18.33) 0.69 ()12.66) 0.87 (9.75) 0.35 (16.67) 1.46 ()2.28) 0.32 (7.67) 0.78 ()1.01)
0.24 ()18.33) 0.69 ()12.66) 0.86 (9.37) 0.35 (16.67) 1.45 ()2.75) 0.32 (7.67) 0.79 (0.00) 0.77 ()1.90) 0.30 (0.00)
0.24 ()18.33) 0.69 ()12.66) 0.86 (9.37) 0.36 (19.00) 1.45 ()2.75) 0.33 (8.67) 0.79 (0.00) 0.77 ()1.90) 0.30 (0.00)
0.29 ()18.00) 0.66 ()18.00) 0.84 (5.00) 0.46 (34.00) 1.40 ()7.00)
0.30
Surface energy (J/m2 )
Reference
12.86
12.79
12.79
2.00
a
The values in parenthesis represent the change in interlayer spacing as a percent of the bulk value. The surface energy is calculated from the formula E Eslab ÿ Ebulk =2 A, where A is the surface area and Ebulk is the energy of an equivalent number of Fe2 O3 molecules in the bulk.
respectively. distances Fe±O are 2.17 and 2.18 A, From the results obtained with the UFF, one can see that adsorption has only minor eect on the rest of the surface. However, this result must be regarded with caution, due to the simplicity of the terms used in this force®eld to describe the bond in a-Fe2 O3 . The UFF considers it as a covalent bond. Distortion of surface atoms is evident in the structures obtained with the COMPASS force®eld. However, this force®eld does not reproduce well the interaction between the adsorbate molecule and the surface. A combination of both force®elds may be a solution for this problem and some calculations are in progress. In Table 3, some results obtained for a-Fe2 O3 using the COMPASS, Universal and mixed force®elds are shown. The best results are obtained for the COMPASS force®eld, but an important improvement can be seen for the mixed approach. Unfortunately, we could not calculate adsorption energies for these molecules. An usual and
simple way of doing this calculation is by moving the molecule away from the surface by a distance that is sucient to eliminate the interaction between both the surface and molecule. Then the energies of both con®gurations (with and without interaction) are subtracted. We always observed an interaction, even for distances bigger than At this time, the reason for this is not 12±13 A. understood, but is a subject for future work. 4. Conclusions Qualitative results on relaxed a-Fe2 O3 surface structures as well as on the adsorption of H2 O and SO2 molecules on them were presented. On one hand, we found that the COMPASS force®eld reproduces quite well the relaxation occurring after the creation of a a-Fe2 O3 surface. On the contrary, it works less well for interfacial systems. On the other hand, the UFF is able to describe
I. Lado-Touri~ no, F. Tsobnang / Computational Materials Science 17 (2000) 243±248
247
Fig. 2. Adsorbate + a-Fe2 O3 surfaces (only the ®rst repeat unit and the top two layers of the second repeat unit are shown): (a) a-Fe2 O3 (0 0 1) + H2 O (COMPASS); (b) a-Fe2 O3 (0 1 2) + H2 O (COMPASS); (c) a-Fe2 O3 (0 0 1) + H2 O; (d) a-Fe2 O3 (0 1 2) + H2 O; (e) a-Fe2 O3 (0 0 1) + 2H2 O; (f) a-Fe2 O3 (0 0 1) + SO2 ; (g) a-Fe2 O3 (0 1 2) + SO2.
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Table 3 Cell parameters, Fe1 Fe2 distance (the shortest Fe±Fe contact, parallel to the threefold c axis) and the Fe1 ±O±Fe2 angle associated to this distancea a, b (A) c (A) d Fe1 Fe2 (A) Fe1 O Fe2 (°) COMPASS Universal Mixed Experimental a
5.076 (0.81) 4.989 ()0.91) 5.241 (4.09) 5.035
13.334 ()3.00) 12.677 ()7.78) 13.727 ()0.14) 13.747
2.861 ()1.17) 2.521 ()12.92) 2.873 ()0.76) 2.895
87.00 (0.58) 79.7 ()7.86) 87.3 (0.92) 86.50
The values in parenthesis represent the change as a percent of the experimental value.
interfacial interactions, but does not perform so well for the a-Fe2 O3 system. Calculations that use a mixed approach are being carried out. Quantum mechanical simulations are superior to molecular mechanics and dynamics methods with parameterized potentials. However, they are computationally expensive. Parameterized potentials methods are, in general, less accurate, but results can be obtained in a realistic period of time. Structures obtained from this method could be used as a starting point for more sophisticated ab initio calculations. Ab initio [2] and experimental studies [1] have shown two possible terminations of the (0 0 1) surface under typical O2 pressure conditions. These two surfaces have been clearly identi®ed by STM. Future work must be done in this direction and studies on other surfaces and surface terminations must be carried out to completely under-
stand surface properties of a-Fe2 O3 . Other adsorbates must also be studied. References [1] C.M. Eggleston, M.F. Hochella, Am. Mineral. 77 (1992) 911. [2] X.G. Wang, W. Weiss, K. Sahikhutdinov, M. Ritter, M. Ptersen, F. Wagner, R. Schlogl, M. Scheer, Phys. Rev. Lett. 81 (1998) 1038. [3] E. Wasserman, Surf. Sci. 385 (1997) 217. [4] L. Armelao, J. Phys. Condens. Matter 7 (1995) L299. [5] K.E. Smith, V.E. Henrich, Phys. Rev. B 32 (1985) 5384. [6] W. Weiss, Catal. Lett. 52 (1998) 215. [7] L.L. Hu, T. Yoko, Thin Solid Films 219 (1992) 18. [8] T. Hashimoto, J. Ceram. Soc. Jpn. 101 (1993) 64. [9] Force®eld-based simulations, Molecular Simulations Inc., San Diego, April 1997. [10] W.C. Mackrodt, J. Cryst. Growth 80 (1987) 441. [11] J. Guo, D.E. Ellis, D.J. Lam, Phys. Rev. B 45 (1992) 13647.