J. Phys. Chem. C 2008, 112, 6515-6519
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Steps, Microfacets, and Crystal Morphology: An ab Initio Study of β-AlF3 Surfaces A. Wander,*,† C. L. Bailey,† S. Mukhopadhyay,‡ B. G. Searle,† and N. M. Harrison†,‡ Computational Science and Engineering Department, STFC Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD, United Kingdom, and Department of Chemistry, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom ReceiVed: October 29, 2007; In Final Form: January 21, 2008
First principles simulations of steps on the β-AlF3 (100) surface between two, previously identified, lowenergy terminations have been performed. The optimization of these structures leads to the formation of microfacets having the (010) orientation. The microfaceted surface is found to have a lower surface energy than either of the low-energy terminations used to construct the model stepped system. This suggests that the (100) surface is not, thermodynamically, the most stable termination of β-AlF3. We have therefore also investigated the structure and stability of the (010) and (001) surfaces and find that both of these surfaces are lower in energy than the (100) surfaces. The surface energies of these planes are used to construct an approximate Wulff plot and thus predict the equilibrium crystal morphology.
I. Introduction The catalytic fluorination of hydrocarbons produces a rich and diverse chemistry that is of great industrial importance. For many years these processes have facilitated the large-scale production of chlorofluorocarbons for a wide range of applications including aerosol propellants, refrigerants, and solvents. Fluorination is now playing a growing role in inorganic synthesis as it provides a powerful tool for tuning electronic, chemical, optical, and mechanical properties. Lewis acid catalysts are commonly used for fluorination reactions. Recently, high surface area aluminum fluoride (HSAlF3) has been prepared which has a Lewis acidity comparable to that of the widely used Swarts catalysts based on antimony pentafluoride.1,2 This makes HS-AlF3 a promising candidate for use in several Lewis acid-catalyzed reactions including Cl/F exchange3 and in the production of hydrofluorocarbons (HFCs).3-6 Fluorinated aluminas have been studied by a range of techniques, including solid-state NMR,7-9 powder X-ray diffraction,7,8,10-14 infrared spectroscopy,13-15 X-ray photoelectron spectroscopy,7,15,16 and temperature-programmed desorption.17 However, the majority of traditional surface structural probes would require the production of a large, pure, crystalline sample of AlF3. Consequently, very little is known about the detailed atomic-scale surface structure of these fluorides although models have been suggested on the basis of observations of chemical activity.18 These models are based on the (100) plane of β-AlF3. In a previous study19 we investigated the phase stability of β-AlF3 (100) as a function of F2 chemical potential and showed that two different surface terminations were stable and had virtually identical surface energies (∼0.85 J m-2). These surfaces are termed the T1 and T6 surfaces and are displayed in Figure 1. AlF3 is highly ionic, and consequently these surfaces are stoichiometric. Both surfaces display under-coordinated Al3+ ions which are thought to be responsible for the Lewis acidity * To whom correspondence should be addressed. † STFC Daresbury Laboratory. ‡ Imperial College London.
Figure 1. T1 (left) and T6 (right) terminations of the relaxed β-AlF3 (100) surface. The Al ions are shown as small white spheres and the F ions as large dark spheres.
of the material. However, the nature of the sites on the two surfaces is different. On the T1 surface the Al3+ ion is surrounded by bridging F- ions (F ions that are bound to two different Al ions) while on the T6 surface its neighbors consist of four bridging F- ions and one dangling F ion (an F ion that is bound to a single Al ion). As these surfaces have virtually identical surface energies, we might expect that the surface of a real material would display approximately equal amounts of the two terminations (dependent on the kinetics of the growth process), and hence we should expect a relatively high step density. Consequently, the surface chemistry of real samples might be strongly dependent on the nature and reactivity of sites at the step edges. In the current paper we investigate two model stepped systems: one consisting of a T1 upper terrace and a T6 lower terrace and a second system in which the character of the two terraces is reversed. In the case of the T6 upper and T1 lower terrace the optimized structure consists of microfacets of the (010) plane. We have therefore also investigated the (010) and (001) planes of β-AlF3, and on the basis of these calculations we have constructed an approximate Wulff plot20 enabling us to predict the equilibrium crystal morphology for this material.
10.1021/jp710433n CCC: $40.75 © 2008 American Chemical Society Published on Web 04/03/2008
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TABLE 1: Basis Sets Used for Aluminum and Fluorine aluminum orbital exponent 1s
2sp
3sp 4sp 3d
70510 10080 2131 547.5 163.1 54.48 19.05 5.402 139.6 32.53 10.23 3.810 1.517 0.59 0.35 0.51
s coeff 0.000226 0.0019 0.0110 0.0509 0.1697 0.3688 0.3546 0.0443 -0.01120 -0.1136 -0.0711 0.5269 0.7675 1.0 1.0 1.0 (d co-eff.)
fluorine p coeff exponent 13770 1589 327.6 91.46 30.50 11.46 4.66 0.0089 0.0606 0.1974 0.3186 0.2995 1.0 1.0
27.802 6.8982 2.095 0.6723 0.217 1.28
s coeff
p coeff
0.000877 0.00195 0.0486 0.1691 0.3707 0.4165 0.1316 -0.16 -0.5333 1.362
Figure 3. As-cleaved T1/T6 (left) and T6/T1 slabs (right).
0.123 0.6004 1.509
1.0 1.0 1.0 1.0 1.0 (d co-eff.)
Figure 4. Relaxed T1/T6 (left) and T6/T1 (right) surfaces.
II. Methodology Calculations were performed using the CRYSTAL code,21 and the B3LYP hybrid exchange functional, which has been shown to provide reliable geometric and electronic structures and energetics in a wide range of materials,22 was used to approximate electronic exchange and correlation. Triple-valence local Gaussian basis sets for Al and F have been obtained from standard sources.23 The F basis set has been modified, most significantly, by the addition of d orbitals. These basis sets are given in Table 1. Geometry optimization was performed by energy minimization using a damped molecular dynamics algorithm as implemented in CRYSTAL. The atomic positions were allowed to relax in all directions consistent with symmetry. The structures were taken to be converged when the residual forces on all atoms was below 1 × 10-4 Hartree Bohr-1. The very similar surface energies of the β-AlF3 T1 and T6 surfaces suggest that the surface of a real sample should contain roughly equal amounts of the two terminations. Consequently, we should expect relatively high concentrations of steps. To investigate the structure of the steps, we construct a (2 × 1) supercell in which one half of the unit cell consists of the T1 surface and the other half contains the T6 surface, as shown in Figure 2. Our previous work on both R- and β-AlF319,24-27 has shown that the dominant theme governing surface stability is stoichiometry. For every Al ion present in the slab there should be three negative ions present allowing the formation of Al3+ and 3 F- ions. Hence, the steps were constructed by removing sufficient F and Al ions at the interface between the two terminations to leave a stoichiometric slab. The two unit cells considered here are shown in Figure 3 before optimization. We have also considered the relaxation of surfaces derived from the bulk cleaved (010) and (001) terminations. Although
Figure 2. Bulk β-AlF3 structure. The horizontal lines indicate the T6 (upper) and T1 (lower) terminations. The T6 upper/T1 lower surface is created by cutting a slab along the T6 plane in the outer two unit cells and the T1 in the central unit cell.
it would be possible to perform a full analysis of all terminations of these surfaces and investigate the phase stability as a function of fluorine chemical potential, we again use the fact that stable terminations are always stoichiometric and consequently only consider such terminations here. Within a (1 × 1) unit cell there are two stoichiometric terminations of the (010) surface (labeled S1 and S2) and three stoichiometric terminations of the (001) surface (labeled R1, R2, and R3). These structures are shown in Figure 5 before optimization. The bulk unit cell of β-AlF3 has Cmcm symmetry. However, it is very close to the higher symmetry P6322 group. Therefore, to a very good approximation the (100) plane is equivalent to the (130) and (1h30) planes of P6322 symmetry. These planes are shown in Figure 8. Similarly, the (010) plane is almost identical to the (110) and (1h10) planes. We can therefore approximate the energies of these surfaces to be the same as their (100) and (010) counterparts. These surface energies are used to calculate an approximate Wulff plot20 for β-AlF3. III. Results and Discussion Both stepped surfaces undergo large-scale reconstructions. The relaxed geometries are shown in Figure 4. The T1 upper terrace/T6 lower terrace stepped surface converges to a structure little different from a straight superposition of the two relaxed individual surfaces. The surface energy, despite the presence of the step edges, is very similar to that of the T1 and T6 surfaces individually at 0.85 J m-2. The two types of Al sites having five nearest neighbors present on the T1 and T6 surfaces are still present. The surface with a T6 upper terrace/T1 lower terrace is more interesting. In this case the optimized structure appears to show the formation of microfacets along the (010) direction. The surface Al ions that are obtained from the T1 cut of the slab all have six nearest-neighbor F ions and form four-member rings, containing two Al ions (-F-Al-F-Al-). On the T1 surface only half of the surface groups form such rings, as can be seen in Figure 1. The other surface Al ions alternate between 5- and 6-fold coordination, as it is energetically unfavorable to form these four-member rings close to one another. The 5-fold Al site present on the T6 surface is still present on this reconstructed surface. This surface has an energy slightly lower than the other surfaces so far considered at 0.84 J m-2, suggesting that the presence of (010) microfacets leads to a stabilization of the surface. It should be noted that the nature of these reconstructions leads to final structures in which parts of the slab are rather
Ab Initio Study of β-AlF3 Surfaces
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Figure 5. As-cleaved stoichiometric (010) and (001) surfaces.
Figure 6. Relaxed stoichiometric (010) surfaces.
thin, and consequently the surface energies are unlikely to be fully converged with respect to slab thickness. However, despite this, the formation of the microfaceted structure does suggest that the (010) surface may be lower in energy than the (100) surface. Furthermore, although it is not initially obvious, the T1 and T6 surfaces also show microfaceting to the (010) plane. The high periodicity of these surfaces results in microfaceting occurring on a smaller scale; it simply becomes much more obvious on the T6/T1 stepped surface. This behavior is commonly seen at the surface of many metals where the {110} surface spontaneously reconstructs, giving rise to the (1 × 2) missing row reconstruction. Removal of the close-packed rows from the {110} surface produces ribbons of {111}-like microfacets across the surface, although the initial structure also shows small microfacets of the {111} surface. The relaxed geometries of the (010) terminations are shown in Figure 6. The surface energies of these terminations are 0.74 and 0.93 J m-2 for the S1 and S2 surfaces, respectively. As the S1 surface is significantly lower in energy, it is expected that this surface will dominate on real crystals. The surface Al ions on the S1 termination all have five nearest neighbors. Their local geometries are almost identical to those of the Al ions on the T6 surface; however, the orientation of the Al-F groups is different on the two surfaces. On the S1 surface the bond between the Al and the dangling F ion is perpendicular to the surface, while on the T6 surface the bond makes an angle of ∼60° to the surface and the dangling F ions along adjacent rows point toward one another. There are 3.9 under coordinated Al sites per nm2 on the S1 surface compared to 4.5 per nm2 on the T6 surface. It is likely that this is, at least in part, why the S1 surface is more stable than the T6 surface. The S2 surface consists of a checkerboard-like pattern in which the Al ions alternate between having five and six nearest-neighbor F ions. The local geometries of these Al ions are similar to the
alternating rows of 5- and 6-fold coordination on the T1 surface. There are 3.9 under-coordinated Al sites per nm2 on the S2 surface compared to 2.3 per nm2 on the T1 surface. Again, this may explain, at least in part, why the surface energy of the S2 termination is greater than that of the T1 termination. As can be seen, the comparison of the density of under-coordinated sites explains, at least in part, the relative stability of surfaces which have the same local structure (S1/T6 and S2/T1). The relative energetics of surfaces with different local structures will be discussed later. The relaxed structures of the stoichiometric (001) surfaces are shown in Figure 7. The surfaces are perpendicular to the channels that run through the β-AlF3 structure. The surface energies of these terminations are 0.79, 0.93, and 1.24 J m-2 for the R1, R2, and R3 surfaces, respectively. It is therefore expected that the R1 surface will dominate. The outermost Al ions on this surface all display tetrahedral coordination. Half of the outermost Al ions are bound to three bridging and one dangling F ion each, while the other Al ions are bound to two bridging and two dangling F ions each. The R2 surface consists of equal amounts of 5- and 6-fold surface Al ions. This surface has similarities to the T1 and S2 surfaces. It has a density of 3.5 Al sites with 5 neighboring F ions per nm2. The high-energy R3 surface consists of two Al ions per unit cell in its outermost layer. These both have four nearest-neighbor F ions, one type bound to one dangling F ion and the other to two dangling F ions. These species are approximately tetrahedral, although significantly more distorted than those found on the stable R1 surface. Analysis of these surfaces suggests that a simple model could be used to predict their surfaces energies. We define the Al effective coordination number as the number of bridging F ions it is bound to multiplied by one-half added to the number of dangling F ions it is bound to. For example, an Al ion with six nearest-neighbor F ions, one of which is dangling, has an effective coordination number of 3.5 (5 × 0.5 + 1). Three factors contribute to the surface energies. These are the density of 5- and 4-fold Al ions and the density of Al ions that do not have an effective coordination number of three. Analysis of our data shows that the surface energies can be estimated using
1 E ) {19.0 × (no. of 5-fold Als) + 27.4 × A (no. of 4-fold Als) + 2.6 × (no. of Al eff coord * 3)} (1) where A is the area of the surface and the prefactors are obtained from numerical fits to the data.
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Figure 7. Relaxed stoichiometric (001) surfaces.
Figure 8. Bulk β-AlF3 structure. The lines indicate the (100), (130), and (1h30) planes.
TABLE 2: Parameters Used To Predict the Surface Energies of the Surfaces Using Eq 1; Predicted Energies and Those Calculated from Our DFT Energy Calculations Are Also Displayed surface β(100) T1 β(100) T6 β(010) S1 β(010) S2 β(001) R1 β(001) R2 β(001) R3 R(011h2) R(0001) I R(0001) II
surface no. of no. of no. of eff predicted calculated area 5-fold Als 4-fold Als coord * 3 energy energy 88.5 88.5 51.1 51.1 85.7 85.7 85.7 25.7 44.0 44.0
2 4 2 2 0 3 1 1 1 1
0 0 0 0 2 0 3 0 1 1
4 0 0 4 2 6 2 2 2 2
0.55 0.86 0.74 0.95 0.70 0.85 1.24 0.94 1.17 1.17
0.85 0.86 0.74 0.95 0.79 0.93 1.24 0.94 1.18 1.19
The results from this analysis are shown in Table 2. We have also included three surfaces of R-AlF325,27 in this table. The two R (0001) surfaces appear identical from this analysis but are structurally different. Both surfaces contain two dangling F ions. In one case they are both attached to the same Al ion, while on the other each is attached to a separate Al ion. It can be seen that this model can accurately predict the surface energies. The only large discrepancy is for the (100) T1 surface. This is most probably because the model does not take into account the distorted four-member rings that occur on this surface. The (001) R1 and R2 surface energies are overestimated by around 10%. These surfaces cut perpendicularly through the channels of β-AlF3; hence, the problem may be in the nonuniform distribution of the atoms in the surface plane. The accurate prediction of the (001) R3 surface may be due to this error being canceled by the neglect of the distorted nature of its Al tetrahedra. The predicted equilibrium morphology of a β-AlF3 crystal, calculated from the lowest energy {100}, {010}, and {001} planes and assuming P6322 symmetry, as discussed in section II, is shown in Figure 9. The surface area of the crystal is composed of 4% {001} surface, 59% {010} surface, and 38% {001} surface. From this predicted morphology the {100} surfaces will make very little contribution to the surface area of a crystallite; however, we have seen that the {010} surfaces display similar local structures. It is hence likely that the properties of these two surfaces are similar. The remaining 38%
Figure 9. Morphology of a β-AlF3 crystal predicted form the approximate Wulff plot of the {100}, {010}, and {001} lowest energy surfaces.
of a β-AlF3 crystal is predicted to consist of the {001} R1 surface. The local structure around the Al ions on this surface is significantly different to those previously seen on β-AlF3. In particular, it exposes tetrahedral Al ions at its surface. It will be of great interest to compare the properties of this surface to the T1 and T6 surfaces. It may be that the reactivity of this surface is significantly different than that of the previously studied surfaces. IV. Conclusions We have shown that the clean (100) surface is unstable with respect to the formation of microfacets consisting of the (010) crystallographic plane. We have consequently calculated the surface structure of the lowest energy (010) surface and for completeness the (001) surface. The energetics of these surfaces have been used to predict the morphology of a β-AlF3 crystal. We have shown that only a small amount of the {100} surface is expected to be exposed on such crystals. There are many similarities between many of the stoichiometric {100}, {010}, and {001} surfaces. However, the lowest energy {001} surface has a significantly different structure than any of the {100} and {010} surfaces. Furthermore, the analysis of these surfaces reveals that their energies can be approximately predicted from their surface structure alone. To enable a full understanding of the catalytic properties of β-AlF3 and related high surface area AlF3 materials, it is imperative that future studies and models of chemical reactivity consider all of these different low-energy surfaces. Acknowledgment. We thank the EU for support of this work through the 6th Framework Programme (FUNFLUOS, Contract NMP3-CT-2004-5005575). The calculations were performed in part on the STFC’s SCARF and NW-Grid systems and in part on the HPCx system where computer time has been provided via our membership of the UK’s HPC Materials Chemistry Consortium and funded by the EPSRC (portfolio grant EP/ D504872). References and Notes (1) Ruediger, S. K.; Gross, U.; Feist, M.; Prescott, H. A.; Chandra Shekar, S.; Troyanov, S. I.; Kemnitz, E. J. Mater. Chem. 2005, 15, 588.
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J. Phys. Chem. C, Vol. 112, No. 16, 2008 6519 (18) Kemnitz, E.; Kohne, A.; Grohmann, I.; Lippitz, A.; Unger, W. E. S. J. Catal. 1996, 159, 270. (19) Wander, A.; Bailey, C. L.; Mukhopadhyay, S.; Searle, B. G.; Harrison, N. M. Phys. Chem. Chem. Phys. 2005, 7, 3989. (20) Wulff, G. Z. Kristallogr. 1901, 34, 449. (21) Dovesi, R.; Saunders, V. R.; Roetti, C.; Orlando, R.; ZicovichWilson, C. M.; Pascale, F.; Civalleri, B.; Doll, K.; Harrison, N. M.; Bush, I. J.; D’Arco, P.; Llunell, M. CRYSTAL 2006 Users’s Manual; University of Torino: Torino, 2007. (22) Muscat, J.; Wander, A.; Harrison, N. M. Chem. Phys. Lett. 2001, 342, 397. (23) Basis sets are available from http://www.crystal.unito.it/Basis_Sets/ ptable.html. (24) Wander, A.; Searle, B. G.; Bailey, C. L.; Harrison, N. M. J. Phys. Chem. B 2005, 109, 22935. (25) Wander, A.; Bailey, C. L.; Mukhopadhyay, S.; Searle, B. G.; Harrison, N. M. J. Mater. Chem. 2006, 16, 1906. (26) Bailey, C. L.; Mukhopadhyay, S.; Wander, A.; Harrison, N. M. Accepted in J. Phys.: Conf. Ser. (27) Mukhopadhyay, S.; Bailey, C. L.; Wander, A.; Searle, B. G.; Muryn, C. A.; Schroeder, S. L. M.; Lindsay, R.; Weiher, N.; Harrison, N. M. Surf. Sci. 2007, 601, 4433.
