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J. Phys. Chem. C 2009, 113, 4976–4983
Structure and Stability of r-AlF3 Surfaces C. L. Bailey,*,† S. Mukhopadhyay,‡ A. Wander,† B. G. Searle,† and N. M. Harrison†,‡ Computational Science and Engineering Department, Science and Technology Facilities Council, Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD, United Kingdom, and Department of Chemistry, Imperial College London, Exhibition Road, London, SW7 2AZ United Kingdom ReceiVed: December 5, 2008; ReVised Manuscript ReceiVed: January 23, 2009
An understanding of the phase stability of AlF3 surfaces as a function of their environment is an important prerequisite in the development of, and an ability to control, their catalytic properties. In this study, all electron hybrid-exchange density functional theory is used to calculate the structure and corresponding energies of several R-AlF3 surfaces. It is shown that the surfaces expose under-coordinated Al ions that are potential Lewis acid sites. The binding energy of NH3 to these sites is calculated and used to quantify their relative acidities. The Lewis acid sites are significantly weaker than the strongest sites predicted to occur on β-AlF3 surfaces. The equilibrium morphology of R-AlF3 crystallites is predicted from the construction of an approximate Wulff plot. The stabilities of two representative terminations of R-AlF3, as a function of HF and H2O chemical potentials are computed using ab initio thermodynamics. The geometries of their stable surfaces are found to be strongly dependent on the environmental conditions. I. Introduction There has been much recent interest in the use of aluminum fluoride (AlF3) as a strong Lewis acid catalyst. High surface area AlF3 can now be prepared that has a Lewis acidity comparable to that of the widely used Swarts catalysts based on antimony pentafluoride.1,2 Such material is of interest as strong Lewis acid catalysts are used in the large-scale production of chlorofluorocarbons and hydrofluorocarbons3-6 for a wide range of applications including aerosol propellants, refrigerants, and solvents. Many experimental studies have been performed to investigate the structure and chemical properties of AlF3, 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 science techniques used to determine surface structure require large, pure, crystalline samples. Unfortunately, producing suitable AlF3 crystals is very difficult. Consequently, very little is known about the detailed atomicscale surface structure of these fluorides. The various crystalline forms of AlF3 consist of arrangements of corner sharing AlF6 octahedra.18-20 The thermodynamically stable phase is R-AlF3. The bulk structure of R-AlF3 is closely related to the corundum structure adopted by R-Al2O3 but with one of the aluminum sites occupied in the oxide being vacant in the fluoride.18,19 The surfaces of R-AlF3 are known to be less catalytically active than the surfaces of the β phase (moderately catalytic) and the amorphous high surface area material (HSAlF3) which shows high catalytic activity.21 However, it is not understood how the surface structure of the different phases of AlF3 leads to the observed differences in their catalytic activity. We have previously quantified the strength of Lewis acid sites on β-AlF3 surfaces from calculations of the binding energy of the Lewis base, NH3, and the shift in the CO stretch frequency * To whom correspondence should be addressed. † Daresbury Laboratory. ‡ Imperial College London.
after adsorption to the surfaces.22,23 A strong Lewis acid is characterized by a large NH3 binding energy and a large blue shift in the CO stretch frequency. The strongest Lewis acid sites on β-AlF3 consist of under-coordinated Al ions bound to five bidentate F ions.22,23 X-ray diffraction studies have shown that crystallites of R-AlF3 predominately expose the (011j2) surface.24 We have previously shown that this surface consists of undercoordinated Al ions bound to five bidentate F ions.24 The structure of this surface and the binding energy of NH3 to it is very similar to the most Lewis acidic surface of β-AlF3.24,22 This result was not expected given that R-AlF3 is less catalytically active than β-AlF3.25 In this paper we revisit our previous study on the stability of the R-AlF3 (011j2) surface and show that there is a more stable and less Lewis acidic termination. We also consider the stability of the (0001), (101j1), (2j110), and (101j4) surfaces and use this data to construct a Wulff plot26 and predict the morphology of R-AlF3 crystallites. The relative Lewis acidities of the surfaces are characterized from calculations of the binding energies of NH3 to the under-coordinated Al ions. It is well-known that the surfaces of AlF3 strongly hydrolyze and adsorb water. Hydroxylated surfaces are expected to have different catalytic properties (possibly including Bro¨nsted acidity) to those of clean surfaces. HF is often used as a fluorination agent to refluorinate hydroxylated AlF3 surfaces. Examining the surface structure and stoichiometry under typical reaction conditions is therefore of great importance to enable a better understanding of the catalytic nature of AlF3 surfaces. In this study the hydroxylation of two R-AlF3 surfaces is considered along with the adsorption of H2O and HF. The relative energetics of these surfaces are used to predict the stability of the R-AlF3 surface as a function of HF and H2O chemical potential. II. Methodology Calculations were performed using the CRYSTAL code.27 The B3LYP hybrid exchange functional, which has been shown to provide reliable structures and energetics in a wide range of materials,28 was employed throughout. Polarized triple valence
10.1021/jp810719h CCC: $40.75 2009 American Chemical Society Published on Web 03/02/2009
Structure and Stability of R-AlF3 Surfaces
J. Phys. Chem. C, Vol. 113, No. 12, 2009 4977
TABLE 1: Oxygen and Hydrogen Basis Sets
The surface free energy of an AlF3 slab, including adsorbed HF, H2O and hydroxyl groups is defined as39
oxygen orbital
exp.
1s
5484.6717 825.2349 188.0470 52.9645 16.8976 5.7996 15.5396 3.5999 1.0138 0.2742 0.538
2sp 3sp 3d
s co-eff
p co-eff
0.0018 0.0140 0.0684 0.2327 0.4702 0.3585 -0.1108 0.0709 -0.1480 0.3398 1.1308 0.7272 1.0 1.0 1.0 (d co-eff) hydrogen
orbital
exp.
s co-eff
1s
50362.3 29510.2 4251.44 827.084 193.406 50.0397 13.7402 3.9009 1.1397 0.346 0.109 0.1098
0.00000020 0.00000104 0.00001154 0.00007679 0.00043129 0.00219849 0.01055974 0.04760939 0.18487289 0.47812170 1.0 1.0 (p co-eff)
2s 3s 2p
Gaussian basis sets were used. The Al and F basis sets have been defined in our previous paper.29 The basis sets for O and H were obtained from previous studies30 and are displayed in Table 1. The H basis set used for NH3 was less diffuse than that used to define H2O, OH, and HF species due to numerical difficulties associated with strong H-F and H-H overlap at high coverage. The N and H basis sets used for molecular NH3 have been documented elsewhere.22 In CRYSTAL, the convergence of the real space summation of the Coulomb and exchange contributions to the Hamiltonian matrix are controlled by five overlap criteria. The values used in this study were 10-8, 10-8, 10-8, 10-8, 10-16. A pruned (75 974) integration grid consisting of 75 radial points and 974 angular points was used. More details about these approximations and the control of them is described elsewhere.27 We have previously performed a full geometry optimization of the bulk R-AlF3 crystal using the same computational parameters.31 Slabs periodic in two dimensions were cleaved from the bulk R-AlF3 crystal. The positions of the ions within the slabs were allowed to relax in all directions consistent with maintaining a glide symmetry operator in the plane of the surface. This was achieved using a combination of damped molecular dynamics and BFGS32 algorithms. Optimisation was considered complete when residual forces where below 1.0 × 10-4 Hartree Bohr-1. The surface energies of the slabs used in this study are converged to better than 0.01 J m-2 with respect to slab thickness. Calculations of molecular binding energies were corrected for basis set superposition error (BSSE) using the counterpoise scheme.33 The relative stability of surfaces with different stoichiometries is determined by the comparison of their surface free energy. The methodology used to calculate the surface free energy at a finite temperature and pressure has been developed for metal oxide systems34-36 and extended to multicomponent environments.37 The methodology used to evaluate the surface free energy of AlF3 in the presence of HF and H2O is outlined here, a full derivation is available elsewhere.38
1 [G (T, Ptot) 2A slab 1 1 NAl µAl(T, Ptot)-NF µF2(T, PF2) - NO µO2(T, PO2) 2 2 1 NH µH2(T, PH2)] (1) 2
γ(T, PF2, PO2, PH2, Ptot) )
where A is the surface area of the two-dimensional unit cell of the slab (the factor of 2 accounts for both sides of the slab). Gslab is the Gibbs free energy per unit cell of the slab and NAl, NF, NO, and NH are respectively the total number of aluminum, fluorine, oxygen and hydrogen ions within the unit cell of the slab. PF2, PO2, and PH2 are the partial pressures of the F2, O2, and H2 gaseous species respectively and Ptot is the total pressure of the system. µAl, µF2, µO2, and µH2 are the chemical potentials for aluminum, fluorine, oxygen, and hydrogen, respectively. It is assumed that bulk aluminum fluoride is in equilibrium with aluminum and fluorine in their natural states, consequently
3 Gbulk(T, Ptot) ) µAl(T, Ptot) + µF2(T, PF2) 2
(2)
where Gbulk is the Gibbs free energy per AlF3 formula unit of the bulk crystal. Similarly, HF and H2O are in equilibrium with their constituent atoms, hence
1 1 µ (T, PH2) + µF2(T, PF2) ) µHF(T, PHF) 2 H2 2
(3)
1 µH2(T, PH2) + µO2(T, PO2) ) µH2O(T, PH2O) 2
(4)
Using eqs 2-4, µAl, µF2, and µO2 can be eliminated from eq 1 to obtain
{
1 G (T, Ptot) 2A slab NAlGbulk(T, Ptot) - (NF - 3NAl)µHF(T, PHF) 1 NO µH2O(T, PH2O))- (3NAl - NF - 2NO + NH)µH2(T, PH2) 2 (5)
γ(T, PHF, PH2O, PH2) )
}
For a slab of stoichiometry AlF3-x(OH)x with or without molecular HF or H2O adsorbed at its surface, the term in eq 5 involving µH2 is equal to zero. If the stable surfaces only consist of such slabs their relative stabilities can be written as a function of µH2O and µHF. To illustrate this, consider a slab consisting of m AlF3-x(OH)x units and n HF and p H2O molecules; NAl ) m, NF ) m(3 - x) + n, NO ) mx + p, and NH ) mx + n + 2p; hence
3NAl - NF - 2NO + NH ) 3m - (m(3 - x) + n) 2(mx + p) + (mx + n + 2p) ) 0 (6) Treating the gaseous species as ideal gases, their chemical potential’s dependence on P and T is
4978 J. Phys. Chem. C, Vol. 113, No. 12, 2009
()
µX(T, PX) ) µX(T, PX°) + kT ln
PX PX°
Bailey et al.
(7)
The chemical potential can therefore be calculated at any pressure if the value of µX(T, PX) at a given pressure PX° is known. This chemical potential can be referred to the athermal limit and the energy from the density functional theory (DFT) calculations by rewriting eq 5 as
µX (T, PX) ) [µX(T, PX) - µX(0, PX°)] + EDFT(T ) 0) (8) µX′ is referred to here as the effective chemical potential. The gaseous species are treated as ideal gases in this derivation; hence, EDFT at T ) 0 is independent of pressure. The term in square brackets in eq 8 can be obtained from thermodynamical reference tables,40 as described previously.38 In the current study the Gibbs free energies of the slab and bulk crystal are computed at the athermal limit and their temperature and pressure dependence is ignored as it is negligible compared to that of the gaseous species. Equation 5 can be used along with eq 8 for HF and H2O to evaluate the surface energies of different clean and hydroxylated AlF3 surfaces as a function of the HF and H2O partial pressures at fixed temperature. The surface phase diagram is then obtained by determining the surfaces with the lowest free energy as a ′ and µH′ 2O. function of µHF To obtain an accurate phase diagram requires calculations of the free energies of every structure that may conceivably occur. Our previous studies on both R- and β-AlF3 surfaces have shown that the dominant theme governing the stability of AlF3 surfaces is stoichiometry The strong ionic character of Al3+ and F- ions implies that only stoichiometric slabs that maintain charge balance will be present in the phase diagram. OH- ions must, therefore, be substituted for F- ions, maintaining a stoichiometry of AlF3-x(OH)x. In this study we consider replacing up to three surface F ions for OH ions on each surface of interest. Thus the energies of all possible structures in which one, two, or three of the surface F ions are replaced by OH ions have been calculated. Adsorption of HF and H2O above the under-coordinated Al ions on each of the clean and hydroxylated surfaces must also be calculated. This requires a very large number of calculations. Therefore, approximate calculations using CRYSTAL, but with a lower level of numerical accuracy (the overlap criteria, the shrinking factors and the size of the integration grid were all reduced), were initially performed to predict which surfaces were candidates for inclusion in the phase diagrams. Tests showed that the accurate and approximate calculations gave relative differences in surface energies of structures with identical stoichiometries to within 0.005 J m-1. Accurate calculations were performed for each system that had a surface free energy within 0.01 J m-1 of the lowest energy surface for each possible stoichiometry. III. Results and Discussion A. Structures and Surface Energies of the Clean Surfaces. Previous X-ray diffraction studies have shown that crystallites of R-AlF3 predominantly expose the (011j2) surface.24 In our previous study, the structure of the (011j2) surface, calculated within a (1 × 1) unit cell, was shown to consist of alternating 6-fold and 5-fold coordinated Al ions, as shown in Figure 1a. The Al ions are each bound to five bidentate F ions, and the 6-fold Al ions, in addition are also coordinated to a monodentate
Figure 1. Structures of (a) the (011j2) (1 × 1) termination and (b) the (011j2) (2 × 2) termination. The F ions are represented by large spheres and the Al ions by small spheres.
Figure 2. Structures of the two (0001) terminations: (a) the lowest energy termination (type A) and (b) the higher energy termination (type B). The F ions are represented by large spheres and the Al ions by small spheres.
ion. The surface energy of this structure was calculated to be 0.94 J m-2.24 In this current study, we have considered a reconstruction of the surface that allows the formation of a surface structure similar to the lowest energy β-AlF3 surface.29 This reconstruction can be obtained within a (2 × 2) cell. The optimized structure, shown in Figure 1b, has a surface energy of 0.76 J m-2. It is more stable than the (1 × 1) termination. The surface Al ions on the (2 × 2) termination are bound to four bidentate F ions and one monodentate F ion. Our previous study of the R-AlF3 (0001) surface considered terminations within a (1 × 1) cell. It is not possible to obtain a stoichiometric surface within the (1 × 1) cell. The smallest cell required to obtain a stoichiometric termination is either a (1 × 2) or a (2 × 1) cell; these two cells are indistinguishable from one another. Two possible terminations, calculated within a (2 × 1) cell, were obtained and labeled type A and type B; both have very similar surface energies of 1.18 and 1.19 J m-2, respectively. Given this small difference in energies it is expected that both terminations will be occur on the (0001) surface. The structures of these two terminations are shown in Figure 2. Both terminations contain a 4-fold and a 5-fold coordinated surface Al ion. The 4-fold Al is almost perfectly tetrahedrally coordinated whereas the 5-fold Al ion is in either a distorted or truncated octahedral geometry. The differences between the two terminations arises from the rotation of the tetrahedral Al ion by approximately 60°; the Al ion binds to different F ions in the two structures. Two possible structures of the (101j1) surface have also been obtained, with energies of 1.15 and 1.20 J m-2. These structures are essentially equivalent to the (0001) type A and type B terminations respectively. The main difference between the (0001) and the (101j1) terminations is that the unit cell of the (101j1) surface is approximately 1.6% larger than the unit cell of the (0001) surface. The relaxed stoichiometric (2j110) termination, shown in Figure 3, has a surface energy of 1.04 J m-2. The surface Al ions are coordinated to four bidentate F ions and a monodentate F ion. The local structure of this surface is very similar to that
Structure and Stability of R-AlF3 Surfaces
Figure 3. Structure of the (2j110) termination (E ) 1.04 J m-2). The F ions are represented by large spheres and the Al ions by small spheres.
Figure 4. Equilibrium morphology of an R-AlF3 crystal predicted from the surface free energy of the {011j2}, {0001}, {101j1}, {2j110}, and {101j4} lowest energy surfaces.
of the (011j2) (2 × 2) termination. The most significant difference between the two surfaces is the density of Al ions. On the (011j2) termination there are 3.9 surface Al ions per nm2 compared with 5.5 per nm2 on the (2j110) termination. The ratio of the density of sites (3.9/5.5 ) 0.71) is similar to the ratio of the surface energies, (0.76/1.04 ) 0.73). We have previously suggested that the surface energies of AlF3 can be predicted by consideration of the density and local geometry of surface Al ions.29 The relaxed stoichiometric (101j4) termination has also been calculated and is essentially equivalent to the (2j110) termination, the difference being that the surface area of its unit cell is 1.2% smaller than that of the (2j110) termination and it has a surface energy of 1.06 J m-2. The predicted morphology of an R-AlF3 crystal, calculated from the lowest energy {011j2}, {0001}, {101j1}, {2j110}, and {101j4} surfaces is shown in Figure 4. The {0001} and {101j1} surfaces are very similar as are the {2j110} and {101j4} surfaces. The surface of the crystal is composed of approximately 82% {011j2} surfaces, 14% {2j110} and {101j4} surfaces, and 4% {0001} and {101j1} surfaces. In a previous study, Chaudhuri et al.41 used an atomistic molecular dynamics approach to study cubic nanoparticles of AlF3. In their study they started with a cubic nanoparticle displaying the {0001} surface and performed a molecular dynamics simulation in order to obtain an equilibrium morphology for an R-AlF3 nanoparticle. The dominance of the {0001} surface in their resultant structure is likely to be an artifact of their choice of initial geometry which prevented thermodynamic equilibrium from being reached during the time scale of the simulation. B. Characterization of the Lewis Acid Sites on the Clean Surfaces. The surfaces predicted to occur on R-AlF3 all expose under-coordinated Al ions. The local structure around these Al ions differs on the different surfaces. The Al ions on the low energy (011j2), (2j110), and (101j4) terminations are all coordinated to four bidentate F ions and a monodentate F ion. The (0001) and (101j1) terminations consist of both 4-fold Al ions and 5-fold Al ions. The 4-fold Al ions are tetrahedrally bound to three bidentate F ions and a monodenate F ion. The 5-fold Al ions are bound to either one or two monodentate F ions. The under-coordinated Al ions on the (011j2) (1 × 1) termination
J. Phys. Chem. C, Vol. 113, No. 12, 2009 4979 are coordinated to five bidentate F ions, this termination is not predicted to be exposed at the crystalline surface but is included for completeness. In principle we might expect the 4-fold coordinated Al ions to be more reactive than the 5-fold Al ions. However, the coordination geometry, as well as the coordination number, will influence the reactivity of the sites. In metal oxide systems, tetrahedral coordination generally occurs for metal ions with radii less than 0.5 Å and octahedral coordination for radii between 0.5 and 0.8 Å.42 The ionic radius of F- is 1.33 Å compared to 1.36 Å for O2-,43 and so the coordination properties of metal halides are expected to be similar to those of their corresponding metal oxides. The ionic radii of Al3+ is 0.54 Å,43 which is close to the transition between tetrahedral and octahedral coordination and consequently the formation of tetrahedral AlF3 in the current system is not surprising. This observation is of great significance. Previously it has been suggested that the very strong Lewis acid sites on AlF3 materials may be due to under-coordinated 4-fold Al ions.41 However, formation of stable tetrahedral structures suggests that such sites may be relatively unreactive. Conversely, the 5-fold coordinated Al ions, in distorted or truncated octahedra may be expected to show moderate Lewis acidity. The binding energies of NH3 to the under-coordinated Al ions on the R-AlF3 terminations considered in section 3.1 are tabulated in Table 2. The binding energies to the (101j4) and (101j1) are not considered as these terminations are essentially identical to the (2j110) and (0001) terminations respectively. The under-coordinated Al sites on the metastable (011j2) termination bind NH3 significantly more strongly than the Al sites on the other terminations. Although this type of site is not predicted to occur on the R-AlF3 surface, it is expected to occur, in small quantities, on the β-AlF3 surface.29 This may explain why β-AlF3 is significantly more catalytically active than R-AlF3. The binding energy of NH3 to this type of site on the β-AlF3 surface, at full monolayer coverge, is -1.73 eV. One can speculate that this type of site may be present in much larger quantities on highly catalytic HS-AlF3. The binding energies of NH3 to the tetrahedral Al ions and the 5-fold Al ions bound to one or more monodentate F ions are all similar in magnitude. Given that the binding energy is also dependent on the overall coverage of NH3 (it decreases with increased coverage) and the formation of hydrogen bonds with nearby F ions22 it is not possible to distinguish the strength of these acid sites from the NH3 binding energies alone. C. Structures and Surface Energies of the Hydroxylated Surfaces. In this section the structure and stability of the R-AlF3 surfaces as a function of HF and H2O partial pressure is reported. The R-AlF3 (011j2) and (0001) terminations are considered as they are significant in the crystal morphology plot. The (2j110) termination has not been considered, even though it is predicted to occur on real crystallites, as its surface structure is similar to the (011j2) (2 × 2) termination. 1. (011j2) Termination. The phase diagram for the (011j2) (1 × 1) termination has been reported previously.44 In this study we have calculated the phase diagram for the (2 × 2) termination. This has been combined with the phase diagram for the (1 × 1) termination to produce a complete phase diagram for the (011j2) surface. The resultant phase diagram is shown in Figure 5. The clean (nonhydroxylated) termination is labeled the 3F termination, the hydroxylated surfaces are labeled according to the number of F ions that are replaced by OH ions per surface unit cell (i.e., 2F-1OH, 1F-2OH, and 3OH). The structures that appear in this phase diagram are all derived from
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TABLE 2: Binding Energy of NH3 to the Various r-AlF3 Terminationsa termination (011j2) (011j2) (2j110) (0001) (0001) (0001) (0001) a
(1 × 1) (2 × 2) (1 × 1) (1 × 2) type (1 × 2) type (1 × 2) type (1 × 2) type
A A B B
Al coordination
no. of monodentate F ions
density of NH3 (per nm2)
length of hydrogen bonds formed (Å)
NH3 binding energy (eV)
5 5 5 5 4 5 4
0 1 1 2 1 1 1
3.9 3.9 5.5 2.3 2.3 2.2 2.2
2.05, 2.05 1.92 1.64,2.06 1.76, 1.79 1.61 1.72 1.68
-1.79 -1.34 -1.38 -1.46 -1.56 -1.52 -1.44
The binding energies are corrected for BSSE using the counterpoise scheme.33
Figure 5. Stable R-AlF3 (011j2) surfaces, including terminations derived from the (1 × 1) and (2 × 2) 3F terminations, as a function of HF and H2O effective chemical potential (defined in eq 8) and partial pressure and temperature. The terminations derived from the (1 × 1) 3F termination are denoted by an asteric. The area within the small rectangle is the accessible region of the phase diagram at 300 K and the region within the large rectangle is the accessible region at 600 K (see text for details).
TABLE 3: Binding Energy of H2O and HF to the Various r-AlF3 3F Terminationsa termination (011j2) (1 × 1) (011j2) (2 × 2)
H2O binding energy (eV)
HF binding energy (eV)
-1.60 -1.06
-1.26 -0.81
a The binding energies are corrected for BSSE using the counterpoise scheme.33
Figure 6. Structures of (a) HF and (b) H2O adsorbed on the (011j2) (1 × 1) 3F termination.
the (2 × 2) 3F termination, except for the 3F+H2O and 3F+HF terminations, which are derived from the (1 × 1) 3F termination. The structures of the 2F-1OH, 1F-2OH, and 3OH terminations, that occur in the phase diagram, are shown in Figure 6. The bidentate F ions are preferentially substituted for OH ions. Furthermore, it is preferable to replace F ions at positions where the Al-F-Al angle is relatively small (≈140°).
Replacing an F ion where the Al-F-Al angle is larger (≈165°) is energetically unfavorable as it results in a large distortion of the surface, forming an Al-O-Al angle of approximately 140°. HF and H2O bind more strongly to the (1 × 1) 3F termination than the (2 × 2) 3F termination, as can be seen from Table 3, consequently, the (1 × 1) 3F terminations with adsorbed HF or H2O are more stable than the corresponding structures derived from the (2 × 2) 3F termination. This observation is consistent with the larger binding energies of NH3 to the (1 × 1) termination and the prediction that the Al ions on this termination are more reactive. Stronger hydrogen bonding also
Structure and Stability of R-AlF3 Surfaces occurs on the (1 × 1) termination compared to the (2 × 2) termination. The H2O molecule hydrogen bonds via both of its hydrogens on the (1 × 1) termination. After adsorption of HF, the HF bond length and its hydrogen bond with a nearby F ion are of the same length, 1.15 Å. That is, an FHF- species is formed. This behavior has previously been seen after adsorption of HF on β-AlF3 surfaces.45 The structures of the (1 × 1) 3F termination after adsorption of HF and H2O are shown in panels a and b in Figure 7, respectively. Adsorbed HF acts as a strong Bro¨nsted acid as it can easily give up its proton, for instance to protonate nearby OH- groups. It may be that the catalysis of some reactions requires the availability of both a strong Lewis acid site and a Bro¨nsted acid site. The phase diagram in Figure 5 is plotted for effective chemical potentials ranging from 0.0 to -2.9 eV. The corresponding partial pressures at 300 and 600 K are also displayed. The full range of the phase diagram, shown in Figure 5, is not practically accessible at any given temperature. Regions of the phase diagram that are accessible at 300 and 600 K are marked by boxes in Figure 5. The lower limits for the H2O and HF partial pressures are set at 10-10 and 10-15, respectively. These values are estimates of typical partial pressures expected under UHV conditions The upper limits are obtained from the vapor pressure of H2O and HF. At 300 K the vapor pressures of H2O and HF are 0.036 and 1.3 atm, respectively. The vapor pressure of H2O at 600 K is 0.12 atm. The upper HF partial pressure is limited by experimental procedures and safety concerns; a maximum pressure of 5 atm is assumed. At 300 K the (1 × 1) 3F+H2O termination is predicted to be the thermodynamically stable surface at most relevant HF and H2O partial pressures. The reactive Al ions on this termination are shielded by adsorbed H2O molecules. At 600 K the (2 × 2) 3F termination is expected to dominate, unless the HF partial pressure is low and the H2O partial pressure is high, under which circumstances the surface is predicted to be hydroxylated. At very low partial pressures of HF and high partial pressures of H2O the surface is unstable with respect to complete hydroxylation of the crystallite; such instabilities have been observed.46,47 It is important to note that the phase diagram is only based on thermodynamic considerations. The kinetic barriers to phase transitions are not considered. For instance, there is likely to be a considerable barrier to the transition from the (1 × 1) to the (2 × 2) structure. R-AlF3 is usually synthesized at elevated temperatures, at which the (2 × 2) 3F termination will dominate. It may be that the transition to the (1 × 1) 3F+H2O termination upon cooling to room temperature is kinetically hindered. Conversely, catalytically active HS-AlF3 is synthesized using sol-gel methods that proceed at lower temperatures.1,2 Under these conditions the (2 × 2) 3F termination does not form and so one can speculate that
J. Phys. Chem. C, Vol. 113, No. 12, 2009 4981 structures that are similar to those found on the (1 × 1) 3F termination form. 2. (0001) Termination. The phase plot for the (0001) (1 × 2) surface is shown in Figure 8. This surface hydroxylates more readily than the (011j2) termination. The 2F-1OH termination, shown in Figure 9a, is based on the type B structure; the bidentate F ion is substituted for an OH group. The OH group points toward a nearby monodentate F ion, with which it forms a hydrogen bond. The flexibility of the monodentate F ions on this surface facilitates the formation of hydrogen bonds, and this explains, at least in part, why the surface is easily hydroxylated. Subsequent hydroxylation of the surface occurs via substitution of the two monodentate F ions for OH ions. Hydroxylation of F ions below the surface Al ions was not considered. It is interesting to note that while the 3F type A termination is more stable than the type B termination, the hydroxylated type B terminations are more stable than their type A counterparts. This is due to the formation of a bridging OH ion on the type B termination. There are both 5-fold and 4-fold Al ions exposed at the (0001) surface. It is possible to adsorb up to three molecules per unit cell; two to the 4-fold Al and one to the 5-fold Al. This leads to a very large number of possible permutations of molecular adsorption geometries. The most stable surfaces that involve adsorbed molecules are those where the molecules form strong hydrogen bonds to surface F and OH ions. Such bonds are usually formed to monodentate ions due to their greater flexibility compared to bidentate F ions. Consequently, in almost all cases, the stable surfaces involving adsorbed molecules are based on the type A structure. The structures of the 3F terminations after adsorption of two H2O and two HF molecules are shown in panels b and c in Figure 9, respectively. After adsorption of two HF molecules to the 3F termination, one of the molecules forms an FHF- species, where the two H-F bonds are of equal length, while the other forms a strong hydrogen bond. In the later case the HF bond length is 1.05 Å and the hydrogen bond is of length 1.30 Å. The (0001) surface generally adsorbs HF and H2O molecules more strongly than the (011j2) (2 × 2) termination, due to the formation of hydrogen bonds. The stoichiometry of an x F-(3 - x)OH + HF (x ) 0, 1, or 2) termination is the same as an (x +1)F-(2 - x)OH + H2O termination and it is always energetically favorable to form the termination consisting of an adsorbed H2O molecule, consequently hydroxylated surfaces with adsorbed HF are not present in the phase diagram. At 300 K a range of terminations can be expected, depending on the HF and H2O partial pressures. Under normal laboratory conditions, three H2O molecules are predicted to adsorb on the 3F termination. At 600 K, a large number of different terminations occur. Under typical reaction conditions, for instance 20%
Figure 7. Structures of (a) the 2F 1OH, (b) the 1F 2OH and (c) the 3OH R-AlF3 (011j2) (2 × 2) terminations. The F ions are represented by large spheres and the Al ions by small spheres.
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Figure 8. Stable R-AlF3 (0001) surfaces as a function of HF and H2O effective chemical potential (defined in eq 8) and partial pressure and temperature. The area within the small rectangle is the accessible region of the phase diagram at 300 K and the region within the large rectangle is the accessible region at 600 K (see text for details).
Figure 9. Structures derived from the (0001) surface. (a) The 2F-1OH termination, (b) HF adsorbed on the 3F termination, and (c) H2O adsorbed on the 3F termination. The F ions are represented by large spheres and the Al ions by small spheres.
humidity and an HF partial pressure between 10-1 and 10-5 atm two H2O molecules are predicted to adsorb on the 3F termination. IV. Conclusions The structure and energetics of stoichiometric surfaces of R-AlF3 have been calculated and the morphology of R-AlF3 crystallites has been predicted. It is shown that the (011j2) surface dominates for crystallites in thermodynamic equilibrium. Undercoordinated Al ions are always exposed at the surface of R-AlF3 crystallites. These Al ions are either coordinated to four or five F ions. It has previously been suggested that the most reactive Al ions will be those that are 4-fold coordinated. We have characterized the reactivity of the 4 and 5-fold coordinated Al ions via the calculation of their NH3 binding energies and shown that 4-fold Al ions are not the most reactive sites. It is suggested that this is because the coordination geometries exert a strong
influence on the reactivity of the Al ions. The 4-fold Al ions form stable tetrahedral structures, while the 5-fold Al ions are in a distorted or truncated octahedral environment. The most reactive surface Al ions were bound to five bidentate F ions in truncated octahedra. The surface displaying this type of Al site is not predicted to be exposed on crystalline R-AlF3 samples. Previous studies suggest that a small number of such sites may be present on β-AlF3 crystallites and it is speculated that they occur in higher quantities on high surface area materials. This result may explain the different reactivity of R-, β-, and HSAlF3. The surface structure of the stoichiometric (011j2) and (0001) terminations of R-AlF3 were calculated as a function of HF and H2O chemical potentials. The phase diagrams for the two surfaces showed many similarities. The formation of hydrogen bonds between the OH-, HF, and H2O species to nearby F and O ions occurred readily and the stable surfaces always maxi-
Structure and Stability of R-AlF3 Surfaces mized such bonding. Under standard atmospheric conditions the surfaces were predicted to adsorb water above under-coordinated Al ions. To expose the under-coordinated Al ions it is shown that the surfaces must be heated and put under conditions of low H2O partial pressures and high HF partial pressures. The phase diagram for the (011j2) termination contains phase boundaries between the structures derived from the (1 × 1) and the (2 × 2) surfaces. The (1 × 1) 3F termination consists of very strong Lewis acid sites; however, it is only thermodynamically stable when its Lewis acid sites are saturated by HF or H2O. This suggests that to obtain catalytically active AlF3 it is necessary to desorb these molecules at a temperature below that at which the surface reconstructs to form the inactive (2 × 2) phase. The sol-gel process used to obtain catalytically active HS-AlF3 satisfies this condition.1,2 Acknowledgment. We would like to thank the EU for support of the part of this work through the 6th Framework Programme (FUNFLUOS, Contract No. NMP3-CT-2004-5005575). The calculations were performed in part on the STFC’s SCARF and NW-Grid systems, in part on resources provided by the High Performance Computing Service at Imperial College and in part on the HPCx system where computer time has been provided via our membership of the U.K.’s HPC Material Chemistry Consortium and funded by the EPSRC (Portfolio Grant EP/ D504872). References and Notes (1) Ru¨diger, S. K.; Groβ, U.; Fiest, M.; Prescott, H. A.; Shekar, S. C.; Troyanov, S. I.; Kemnitz, E. J. Mat. Chem. 2005, 15, 588. (2) Kemnitz, E.; Groβ, U.; Ru¨diger, S.; Shekar, S. C. Angew. Chem. 2003, 115, 4383. (3) Kemnitz, E.; Menz, D. H. Prog. Solid State Chem. 1998, 26, 97. (4) Manzer, L. E.; Rao, V. N. M. U.S. Patent, 4,902,838, 1990. (5) Manzer, L. E.; Rao, V. N. M. AdV. Catal. 1993, 39, 329. (6) Corbin, D. R.; Rao, V. N. M. U.S. Patent, 6,040,486, 2000. (7) DeCanio, E.; Bruno, J. W.; Nero, V. P.; Edwards, J. C. J. Catal. 1993, 140, 84. (8) Chupas, P. J.; Ciraolo, M. F.; Hanson, J. C.; Grey, C. P. J. Am. Chem. Soc. 2001, 123, 1694. (9) Fischer, L.; Harl, V.; Kastelan, S.; d’Espinose de la Caillerie, J. B. Solid State Nucl. Mag. 2000, 16, 85. (10) McVicker, G. B.; Kim, C. J.; Eggert, J. J. J. Catal. 1983, 80, 315. (11) Saniger, M.; Sanchez, N. A.; Flores, J. O. J. Fluorine Chem. 1998, 88, 117. (12) Skapin, T. J. Mater. Chem. 1995, 5, 1215. (13) Vimont, A.; Lavalley, J. C.; Francke, L.; Demourgues, A.; Tressaud, A.; Daturi, M. J. Phys. Chem. B 2004, 108, 3246. (14) Demourgues, A.; Francke, L.; Durant, E.; Tressaud, A. J. Fluorine Chem. 2002, 114, 229. (15) Hess, A.; Kemnitz, E. J. Catal. 1994, 149, 449. (16) Hess, A.; Kemnitz, E.; Lippitz, A.; Unger, W. E. S.; Menz, D. H. J. Catal. 1994, 148, 270. (17) Deshmukh, S. S.; Kovalchuk, V. I.; Borovkov, V. Y.; Deitri, J. L. J. Phys. Chem. B 2000, 104, 1277.
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