Ab initio studies of aluminium fluoride surfaces

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antimony pentafluoride have recently been produced.5. However, large differences in catalytic reactivity are observed between the different phases of AlF3.

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www.rsc.org/materials | Journal of Materials Chemistry

Ab initio studies of aluminium fluoride surfaces A. Wander,a C. L. Bailey,a S. Mukhopadhyay,b B. G. Searlea and N. M. Harrisonab Received 9th January 2006, Accepted 24th March 2006 First published as an Advance Article on the web 7th April 2006 DOI: 10.1039/b600273k Solid aluminium fluorides have great potential for use in a range of reactions that are catalysed by strong Lewis acids. However, very little is known about the detailed atomic scale structure of their surfaces. We present new results for the surface structure of b-AlF3 based on first principles simulation and compare these with our earlier work on a-AlF3. On the basis of these simulations we can explain the observed reactivity of the aluminium fluoride materials. We can also use these results to postulate a mechanism for the observed high reactivity shown by amorphous, ‘high-surface area’ AlF3.

1. Introduction Aluminium fluorides (AlF3) have great potential in many Lewis acid catalysed reactions such as Cl/F exchange and the production of hydrofluorocarbons.1–4 High surface area aluminium fluorides that have Lewis acidity comparable to that of the widely used Swarts catalysts based on antimony pentafluoride have recently been produced.5 However, large differences in catalytic reactivity are observed between the different phases of AlF3. In the current paper we present new results for the structure of b-AlF3 and place these in context by reviewing our recent work on a-AlF3. These results are obtained from thermodynamics calculations based on first principles hybrid-exchange density functional theory. These results allow us to explain the different reactivity of aluminium fluoride phases in terms of the substantial differences in the accessibility of the reactive, co-ordinatively unsaturated aluminium sites at their respective surfaces. For crystalline a-AlF3 we have previously shown that the Al atoms are effectively covered by fluorine atoms6 leading to a surface that displays no Lewis acidity or catalytic activity. Conversely, in the current study we show that the structure of b-AlF3, which shows moderate Lewis acidity and catalytic activity, contains co-ordinatively unsaturated five fold aluminium ions at the surface. These structures are substantially different from those derived earlier.7 We also postulate that the highly reactive, amorphous ‘high-surface area’ AlF3 may display acidic sites similar to those found on the b-AlF3 surface.

2. Theoretical methodology The relative stability of a surface with variable stoichiometry is determined by minimisation of the surface free energy. A mechanism for computing the surface free energy from ab initio calculations has been developed8,9 and has been described recently by Reuter and Scheffler.10 Here, a a Computational Science and Engineering Department, CCLRC Daresbury Laboratory, Warrington, Cheshire, UK WA4 4AD b Department of Chemistry, Imperial College London, Exhibition Road, London, UK SW7 2AZ

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brief outline of the formalism as applied in these studies is presented. Modelling the aluminium fluoride surface as a slab of material periodic in two dimensions and of finite thickness in the third, the surface free energy may be defined as:11 c(T,P)A = Gslab(T,P) 2 NAlmAl(T,P) 2 NFmF(T,P) in which A is the surface area of the unit cell (counting both surfaces of the slab), Gslab is the Gibbs energy per unit cell of the slab, and NAl and NF are respectively the total number of aluminium and fluoride ions within the slab. mAl and mF are the chemical potentials per atom of the pure metal and the halide gas respectively. As the surface is in equilibrium with the bulk fluoride mAl and mF cannot vary freely as they are constrained to satisfy: gbulk = mAl + 3mF where gbulk is the Gibbs free energy per formula unit of the bulk crystal. Here, the variation of surface stoichiometry with mF is of interest so this constraint is used to eliminate mAl from the first equation. Defining the surface fluoride excess as: CF = (NF 2 3NAl) one may write the surface free energy as: c(T,P)A = Gslab(T,P) 2 NAlgbulk 2 CFmF(T,P) In practice the fluoride chemical potential is controlled by varying the fluoride partial pressure and temperature. Approximating the fluoride as an ideal gas its chemical potential is given by: mF(T,P) = mF(T,PO) + kTln(P/PO)/2 Thus the complete temperature and pressure dependence of the fluoride chemical potential is determined relative to its value at a reference pressure PO. The chemical potential must be defined with respect to an energy zero which is consistent with that used to compute the bulk and slab free energies. For the ideal gas a suitable reference energy is the athermal limit at which the chemical potential equals the energy of formation of a single This journal is ß The Royal Society of Chemistry 2006

molecule for any pressure; thus the reference energy for mF(T,P) is taken to be: mF(0,P) = (Etotal F2 )/2 ; 0 The chemical potential at a reference pressure may then be obtained from the measured variation of the free energy as: mF(T,PO) = mF(0,PO) + DG(DT,PO,F2)/2 = mF(0,PO) + [H(T,PO,F2) 2 H(0 K,PO,F2)] 2 T[S(T,PO,F2) 2 S(0 K,PO,F2)]/2 The enthalpy and entropy of gaseous fluorine at standard pressure are tabulated in thermochemical data tables12 and may be extrapolated to the athermal limit. Calculations were performed using a linear combination of atomic orbitals scheme as implemented in the CRYSTAL code.13 The B3LYP hybrid exchange functional, which has been shown to provide reliable structures and energetics in a wide range of materials,14 was employed to approximate electronic exchange and correlation. Local Gaussian basis sets for the Al3+ and F2 ions were obtained from standard sources.15 The basis set used for the fluorine has been modified since the publication of references 6 and 7. The modifications were made to improve the BSSE corrections when investigating the absorption of different molecules to the surfaces of these structures. Most significantly this involved adding a d orbital to the basis set.

3. a-AlF3(0001) It is known that the a-AlF3 surfaces are chemically inert. Geometrically, the surfaces of the a phase are far more simple than those of the b phase. In the current section we report on our study of the surface structure of a-AlF3 in an effort to understand why its surfaces are chemically inert and for comparison to the b-AlF3 phase. The bulk a-AlF3 structure is closely related to the corundum structure adopted by a-Al2O3 but with one of the aluminium sites occupied in the oxide being vacant in the fluoride. The surfaces of alumina have been widely studied and it is known that the basal plane (the (0001)) surface is very stable.16 In our earlier study we have proposed a structure for the basal plane (0001) of a-AlF3.7 Several terminations of a-AlF3 are possible and are displayed in Fig. 1. The crystal structure consists of planes containing 3F2 ions and planes containing a single Al3+ ion stacked along the c axis. Consequently two terminations of the crystal are achieved simply by termination on each such plane. In addition we have considered two further terminations created by successive removal of F2 ions from the fluorine terminated surface. For these surface calculations a periodic two-dimensional slab of material was used. The boundary condition perpendicular to the slab is that the wavefunction should decay to zero at infinity with no constraints on the electrostatic potential perpendicular to the slab. If the bulk stoichiometry is maintained these surfaces are polar and thus unstable due to the generation of a macroscopic electric field. In all cases here the surfaces are modelled using symmetric, non-stoichiometric slabs which are inherently non-polar. Calculations were This journal is ß The Royal Society of Chemistry 2006

Fig. 1 Possible terminations of the a-AlF3(0001) surface. a) The aluminium terminated SAl slab. b) The S3F slab. c) The S2F slab. d) The S1F slab.

performed for slabs with increasing numbers of layers, and the optimum geometry of the slab for each thickness was found by energy minimisation with respect to the atomic positions. The surface energy was found to be converged with respect to slab thickness to better than 0.01 J m22 while the Mulliken charges of the central two layers varied from the bulk charge density by less than 0.02|e|. We therefore treat the slab containing seven Al3+ ions per unit cell as converged with respect to slab thickness. Having fully optimised the geometry of these slabs, their free energies as a function of external partial pressure of fluorine can be compared. The resultant data are shown in Fig. 2. As can be seen, the S2F surface is stable at all realistic F chemical potentials and consequently, under reaction conditions, we would expect this surface to be terminated by a layer containing two F2 ions. The potentially chemically active SAl slab is the least stable of the four terminations examined here and consequently is unlikely to be observed in real systems under any reaction conditions.

Fig. 2 Surface energies of the six possible bulk terminations of the a-AlF3(0001) surface as a function of external fluorine partial pressure.

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Fig. 3 The optimised S2F slab. Left: plan view. Right: side view.

Fig. 3 shows the optimized structure of the 2F surface. It can clearly be seen that the surface does not expose any Al3+ ions. The relaxations of the other two F2 terminated surfaces also do not expose an Al3+ ion, it is thus only exposed on the SAl surface where its presence at the surfaces is unavoidable. This is of fundamental importance since it is the Al3+ ion that would be expected to form the surface Lewis acid centre essential to the surface catalysis.

4. b-AlF3(100) An understanding of the difference in reactivity between the a and b surfaces of the material may be of fundamental importance in any future attempts to design real catalysts based on AlF3. In the current section we examine the surface structure of b-AlF3 in an effort to understand why its surfaces are chemically active in contrast to the a phase. Six different (1 6 1) terminations of b-AlF3(100) can be produced by cleaving the bulk crystal on different layers. These terminations are denoted here as T1–T6. Obviously, the surface may undergo reconstruction, but in the absence of experimental data we will consider these (1 6 1) terminations here. For these surface calculations the same methodology was used as for the a-AlF3 calculations. The only exception was in the convergence tests with respect to slab thicknesses, as due to the large size of the unit cell, these calculations could not be performed. However, tests were carried out with the molecular modelling code GULP17 using potentials taken from the literature18 which indicated that slabs containing in excess of 25 atomic layers were sufficient to converge the surface structure. This leads to slab thicknesses of 25, 27, 29, 25, 27 and 29 layers for the T1–T6 surfaces respectively; this corresponds to a unit cell containing 26 Al ions for surfaces T1–T3 and 28 Al ions for surfaces T4–T6. The optimum geometry of each of these slabs was found by energy minimisation with respect to the atomic positions. The geometry optimisation was assumed to have converged when the residual forces along all allowed symmetry directions were below 5 6 1024 Hartrees Bohr21. The relative stability of these terminations as a function of fluorine chemical potential is shown in Fig. 4. A chemical potential of zero for fluorine represents the point at which fluorine condenses onto the surface of the material (very high pressure) while the left hand limit on the graph is set at a pressure of approximately 102200 Torr at 300 K. In principle, the left-hand limit can be defined by setting up an equilibrium 1908 | J. Mater. Chem., 2006, 16, 1906–1910

Fig. 4 Surface energies of the six possible bulk terminations of the b-AlF3(100) surface as a function of fluorine partial presssure.

between the slab and bulk aluminium. However, within the current calculation scheme (B3LYP functional and local Gaussian basis sets) it is not sensible to evaluate this point. As can be seen, the T6 slab is stable at all fluorine chemical potentials. In addition, a second termination, T1 (high sym), is also relatively stable across most realistic fluorine chemical potentials likely to be encountered in real applications of such materials and therefore these two surfaces are worthy of further investigation. These surfaces were therefore subsequently optimised with all symmetry operators, other than top bottom symmetry, removed within the same (1 6 1) unit cell. The T1 surface undergoes a reconstruction. The resultant structure has a surface energy of 0.85 J m22 compared to 1.35 J m22 for the higher symmetry T1 surface. This result is new and updates our earlier results for this system which were obtained under the symmetry constraint.19 The T6 surface did not reconstruct using reduced symmetry operators. The bulk terminated T1 and T6 surfaces are shown in Fig. 5a and c. In both cases, the resultant structure exposes co-ordinatively unsaturated Al ions to the surrounding environment and should therefore be active for Lewis acid catalysis. However, the nature of the sites on the two terminations is very different. The reconstruction of the T6 surface gives rise to true five-fold co-ordinated Al ions at the surface. We will use the term type 1 sites to describe this situation. The reconstruction of the T1 surface is more complicated. The bulk terminated surface exposes four-fold co-ordinated top layer Al ions to the surrounding environment. Either side of the top layer of Al ions is a row of 2nd layer Al ions, each 6-fold co-ordinated in the bulk. After surface relaxation the fluorine ions above one of the 2nd layer Al ions move towards the 1st layer Al ions to lie approximately equidistant between the two rows of Al ions. Every alternate fluorine on the other 2nd layer of Al ions moves away from the Al ions to the first layer Al ions. The result of this surface reconstruction is that every alternate top layer Al ion becomes 5-fold co-ordinated and every alternate Al ion on every alternate 2nd layer Al ions is 5-fold co-ordinated. All other Al ions are 6-fold co-ordinated. This results in two different types of Lewis acid sites, those above This journal is ß The Royal Society of Chemistry 2006

Fig. 5 The b-AlF3(100) structures. (a) T1 bulk cleaved. (b) T1 reconstructed. (c) T6 bulk cleaved. (d) T6 reconstructed. The large, pale spheres represent F ions while the small, dark objects are Al ions.

the 1st layer Al ions and those above the 2nd layer Al ions. We have labelled these Lewis acid sites as type 2 and type 3 respectively. The optimised structures of these two surfaces are displayed in Fig. 5b and d. Tables of displacements of all atoms within the unit cell away from their ideal bulk terminated positions are available from the authors upon request. The bulk unit cell is displayed in Fig. 6 with the cleavage planes that produce the T1 and T6 surface indicated. The other terminations are produced by cleaves along planes intermediate between these two. The T1 and T6 surfaces have almost identical surface energies (0.85 J m22 and 0.86 J m22 respectively). Therefore it

is likely that both surfaces are exposed in real crystalline samples of pure b-AlF3. Temperature programmed desorption studies of ammonia from crystalline b-AlF3 show one main peak as well as shoulders either side of this.19 It would be of great interest to attempt to extract the relative Lewis acidity of the three acidic sites which is critical for practical catalytic applications such as Cl/F exchange reactions. The TPD data for HS-AlF3 show many similarities to the b-AlF3 data, therefore it seems likely that by studying b-AlF3 we may also improve our understanding of the HS-AlF3 phase. To clarify this issue work on the binding energy of NH3 to these three sites is ongoing within our group.20 Clearly, it is of interest to attempt to verify the current results experimentally. One mechanism for detection of these sites would be surface core level X-ray spectroscopy. Analysis of the eigenvalues for the converged system suggests that the outermost F2 ion in the type 1 site should exhibit a large shift in its 1s binding energy. The eigenvalue within our calculations is shifted by 3.42 eV towards lower binding energy relative to the other fluorine ions of the slab. The outermost F2 ion above the 1st layer of Al ions exhibits a shift of 3.99 eV towards a lower binding energy relative to the other F2 ions in the slab and the outermost F2 ion above the 2nd layer of Al ions exhibits a shift of 3.79 eV. However, it is important to emphasise that the shifts reported here are shifts in eigenvalues and neglect any possible final state effects. Given that the outermost F2 ions on the surface are in very different environments to the other F2 ions of the slabs it is likely that final state relaxation effects will also be very different for that atom. As the eigenvalues show very large shifts they should be relatively easy to detect experimentally. The environment of the outermost F2 ions over the proposed Lewis acid sites is interesting. A Mulliken partition of the total charge density has been used to calculate the relative charges on the atoms. This is no unique method of performing this partition of the charge method, however the choice of a given scheme is still very useful in comparing results of calculations performed using similar basis sets.21 The Mulliken charges suggest that this ion is in the formal charge state of F2, there is also a large increase in the bond overlap population between this ion and the first layer Al ion. In the bulk material the bond overlap population is 0.1|e|, a value typical of a range of ionic materials such as corundum (Al2O3); however, at the surface this rises to 0.2|e|. For comparison the overlap population in bulk silicon is 0.35|e|. Although it is important to be aware that the co-ordination of the F2 ions can affect the Mulliken analysis, this result is indicative of a degree of covalent bonding between the Al ion and the F2 ion.

5. Conclusions

Fig. 6 The bulk unit cell. The cuts that produce the T1 and T6 surfaces are indicated. The large, pale spheres represent F ions while the small, dark objects are Al ions.

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The above series of calculations provides an explanation for the observed reactivity of the a and b phases of AlF3. We show that the surface of crystalline a-AlF3 contains 6-fold co-ordinated Al ions, hence no Lewis acidic sites are available for reactions catalysed by strong Lewis acids. Conversely we find three different types of co-ordinatively unsaturated Al ions are exposed on the b-AlF3 surface, giving an explanation for its high catalytic properties. These observations provide a J. Mater. Chem., 2006, 16, 1906–1910 | 1909

possible explanation for the observed reactivity of the amorphous ‘high-surface area’ AlF3 phase. At the detailed atomic scale there is currently little information available about the surface structure of AlFs. Given the importance of the surface in potential applications of these materials, such knowledge is essential in the development of a full understanding and successful exploitation of these materials. The lack of detailed information from surface science experiments is primarily caused by the difficulty of handling and preparing these materials. Theoretical studies do not suffer from sample preparation problems and are therefore ideally suited to complement existing experimental research efforts on these systems. The highly parallel CRYSTAL software has proved a reliable and efficient way to study the complex surface structures of these materials on massively parallel high performance computers.

Acknowledgements We would like to thank the EU for support of part of this work through the 6th Framework Programme (FUNFLUOS, Contract No. NMP3-CT-2004-5005575) and the EPSRC for provision of access to the HPCx facility under the Materials Chemstry Consortium Grant (GR/S13422/01).

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