- Email: [email protected]
Surface structure determination of zeolites
Studies in Surface Science and Catalysis, volume 154 E. van Steen, L.H. Callanan and M. Claeys (Editors) © 2004 Elsevier B.V. All rights reserved.
1197
SURFACE STRUCTURE DETERMINATION OF ZEOLITES Slater, B.**, Gale, J.D.^ Catlow, C.R.A.^'\ Ohsuna, T / ' ^ and Terasaki, O.^'^ 'Davy Faraday Research Laboratory, The Royal Institution of Great Britain, 21 Albemarle St, London, WIS 4BS U.K. E-mail: [email protected] ^Nanochemistry Research Institute, Department of Applied Chemistry, Curtin University of Technology, Perth 6845, Australia. Department of Chemistry, Imperial College of Science, Technology and Medicine, South Kensington, London, SW7 2AZ, U.K. ^Department of Chemistry, University College London, 20 Gordon Street, London, WCIH OAY, U.K. "^Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan. ^Structural Chemistry, Arrehenius Laboratory, Stockholm University, Sweden. ""Department of Physics, Tohoku University, Sendai 980-8578, Japan. ABSTRACT We present atomistic computer simulation results in combination with high resolution electron microscopy (HREM) images that provide convincing evidence of the atomically resolved surface structure of zeolites Beta C and L. The purpose of the surface structure determination is two-fold: firstly, in solving the surface structure, we gain insight into the crystal growth process, which allows us to propose mechanistic routes and agents for controlling crystal morphology. Secondly, knowledge of surface structure allows us to study processes such as transport and catalysis at the crystal surface that are notoriously difficult to probe using experimental methods. The latter point is clearly important in understanding how the external surface behaves in contrast to the internal surface, in order to rationalise and predict the behaviour of microporous membranes. In this work, we report how a combination of classical and periodic density functional theory calculations have been utilised to predict structure, and to reveal fundamental insights into the intrinsic crystal growth mechanisms for zeolite Beta C and L. INTRODUCTION A significant challenge in zeolite materials chemistry is determining the structure of microporous materials. The challenge is multifarious in origin; the presence of extra-frame work species with extremely small occupancies within the unit cell, the presence of defects, the absence of order within the silicon/aluminium framework in many materials, to name just some of the factors that conspire to make solving the crystal structure of nanoporous materials non-trivial. However, numerous crystal structures have been solved and a natural extension to mapping the bulk structure is the determination of the surface structure of this class of materials. In dense non-porous materials that have utility in catalysis, for example, knowledge of surface structure is vital if one is to understand a catalytic reaction mechanism at the atomic scale. The crystal bulk may impart electronic structural effects upon the surface species but atoms within the solid do not play any physical role within the reaction. In nanoporous materials where the average crystal size is » n m , much of the catalysis may take place within the crystal interior (assuming reagents and products can pass easily through the structural framework) because the external surface area to internal surface area is extremely low. However, nano-crystals are quite different in their potential reactive surface area, such as in lamellar materials, like ITQ2[1] materials, where the external surface area to internal surface area ratio is very high. In the nano-sized class of materials, it is important to understand how the external surface structure dictates the reactivity of the solid, since the surface largely governs the gross 'reactive properties' of the crystal. In larger crystals, the external surface structure also plays a role in determining the reactive properties of the crystal but to a generally unknown degree. The crystal surface may facilitate desirable or undesirable reactions, products, by-products, which can resuh in reduction of the materials lifetime through coking, for example. Given that the scientific motivation for undertaking a comprehensive study of zeolite surface structure is well grounded, it important to review what progress has been made in measuring, predicting and understanding surface structure within the nanoporous class of materials. Two techniques have proved
1198 invaluable in resolving atomistic detail in zeolites; Atomic Force Microscopy(AFM) and HREM. AFM has been widely utilised to study Heulandite[2], zeolite A[3], Y[4, 5], MFI[6], where studies have revealed characteristic step heights comparable with interlayer separations and fractions thereof, that correspond with secondary building units. In the systematic work of Agger, Anderson and their co-workers, studies of zeolite A and Y and MFI have been complemented by numerical simulation approaches. Their work has identified that zeolites appear to grow in the terrace-ledge-kink fashion in common with many inorganic materials, facilitated by multiple or unitary surface nucleation. HREM has been widely used to probe the surface structure of a wide variety of zeolites including Y[7], A[8], MCM-22[9] and L[10]. The largest body of work in this area is due to Terasaki and Ohsuna where the sub 2 Angstrom resolution of the HREM tool affords direct visualisation of the surface and bulk structure of microporous materials, revealing detail such as stacking faults and defects. To choose just one example, the HREM imaging of zeolite Y reveals that the crystal surface occurs with just two terminations; the D6R terminated (111) surface and a termination where the D6R is absent. This is quite distinct from non-polymeric inorganic materials that typically only expose one termination, except at high temperatures or at deviation from stoichiometry arising from changes in the chemical potential (such as the partial pressure of oxygen). The reason that two terminations are exposed is thought to be due to the pre-formation of a D6R unit in solution, which can then condense directly upon the surface. These studies offer insight into the nature of the true building blocks from which zeolites are formed. In the remainder of this paper, the results of calculations probing the surface structure and crystal growth mechanism of zeolite Beta C and zeolite L will be presented.
METHODOLOGY The strategy used here to predict surface structure and growth mechanism is based upon two distinct approaches, exploiting classical simulation methods and two first-principle density functional methods. In the former methodology, the Born model of solids is invoked, where atoms are represented by point charges with extensions to describe the polarisability of the ions. Ions are kept at equilibrium distances by the presence of a short range potential, which in this instance is of Buckingham form. In the latter approach, a N^^ scaling (where N is the number of atoms) ultra-soft pseudopotential plane wave based technique (CASTEP[11]) and a N^ scaling local orbital based method (SIESTA[12]). The classical calculations are undertaken by optimising the crystal bulk at constant pressure, with a short-range cut-off of 12A using the lattice optimisation code GULP1.3[13]. The surface is then relaxed using the same minimisation procedure using a separate code, MARVIN[14], which has a 2D treatment of the Ewald summation, necessary for accurate calculation of the long ranged Coulombic component of the energy. In low-symmetry framework materials, many terminations are possible and indeed unique, therefore the stability of each terminating structure must be evaluated and its thermodynamic stability assessed. We have found that the surface energy, as defined in reference [14] gives a reliable indication of which terminations will be observed at the crystal surface. Terminating structures are generated using two conditions: the first is that the surface is charge neutral and the second is that the surface must have no net dipole normal to the crystal surface. The presence of a dipole indicates the existence of a field within the crystal slab that will polarise the atoms within the block. As the field increases, so does the polarisation, and both the structure and energy of the slab are scaled such that the energy per unit Si02 will uniformly rise. To achieve convergence of the self-energy of the crystal slab and therefore the surface energy, the surface is reconstructed so that the slab is non-polar. This is achieved by translating (in the case of purely siliceous zeolitic materials) either silicon or oxygen ions from the top of the crystal to the bottom to achieve stoichiometry on each face of the crystal slab. In general, a small number of terminations are observed experimentally, yet assessment of the thermodynamic stability of the possible terminating surfaces often reveals a larger number of equally stable terminations. The explanation for this is, we believe, intimately related to the mechanism of crystal growth in framework materials. It has been postulated that the spectrum of building blocks observed by detailed NMR studies, including double 4-membered rings, double-6 membered rings and lower symmetry species can react directly with the crystal surface. In order to calculate the viability of this process, one needs to calculate the condensation energy on the crystal surface directly. Clearly, only electronic structure methods have the required accuracy to probe this problem. In this instance we have used two distinct methods to look at the reaction enthalpy: a plane wave based method and a local orbital scheme. A significant difference between the codes lies in the treatment of void space. In CASTEP, all cell space is sampled, which is
1199 computationally expensive for porous materials. In SIESTA, on the other hand, the volume encapsulated by the orbitals only is considered, dramatically reducing the cost of treating zeolites. In the plane-wave calculations reported here, first reported elsewhere[15], the kinetic energy cutoff used was 260eV, which is rather low. However, the sensitivity of reaction enthalpy was checked by considering the condensation of two S4Rs to give a D4R as a function of kinetic energy cutoff, and a maximum variation of <8kJ mol-1 was found. This number is rather small in absolute magnitude and in terms of the solvation energy, a quantity excluded here which will undoubtedly be different for the various clusters sizes considered. Each H-bond lost in cyclising for example will cost approximately 15kJ mof^ therefore we consider the reaction enthalpy we quote to be indicative of the true reaction energies. RESULTS AND DISCUSSION We first examined the bulk and surface structure of zeolite Beta C, a material recently synthesised for the first time by Camblor et al.[16]. The material has a novel intersecting 12 membered ring structure that has potential utility in catalytic applications. Using the interatomic potential set due to Sanders and Catlow[17], we relaxed the purely siHceous cell of Beta C and obtained cell parameters of a = 12.636A, b = 12.632A, c = 13.030A, a = 90.003° p = 89.992° and y = 90.023°. These values are not in close agreement with the experimentally determined values, however, the as synthesised material contains flouride ions that would expand the lattice. Since the location of the fluoride is not precisely known, the exact relation between atomistic structure and cell parameters are not explored here. The terminations of the (100) face were explored using the atomistic methods described earlier in this article. The (100) face is the most morphologically important face - it dominates the crystal morphology. In this manner, many (in excess often) unique terminations can be generated. Each terminating structure is then relaxed in two states. In the first stage, we relax the structure in its stochiometric form. In the second stage, we consider the reaction of water with the under coordinated sites upon the surface that are formed when the crystal is cleaved to generate the appropriate termination under investigation. Gaseous water is deemed to dissociatively react with the crystal surface, generating a structure that is generally fully hydroxylated. In the first stage, the structure can be though of as being unhydroxylated. By calculating the energy difference between the hydroxylated and unhydroxylated case, the enthalpy of reaction can be calculated. Knowledge of the chemical state of the surface is clearly vital if one is to correctly model the surface structure in contact with other media. In recent work, we have found that when the surface density is low, the surface is reactive with water, when the density is high, the surface tends to self-passivate or reconstruct and is unreactive with water. To classify the reactivity and stability of the surface we utilise the surface energy. A low surface energy indicates that the crystal surface is relatively stable, whilst a high surface energy indicates a relatively unstable surface. The surface energies for distinct terminations for given faces can be compared and utilised to make a prediction of the crystal shape by the Wulff theorem. The essence of Wulff theorem is that the equilibrium crystal shape will be that that minimises the surface energy of the crystal in three dimensions. In Beta C, we find three possible terminations of equal thermodynamic stability (surface energy) for the (100) surface that are depicted in figure 1. The terminations are shown in cross-section, the upper part of the figure being the terminating structure. The vertices represent the intersection between two silicon atoms i.e. the oxygen atoms have been removed from the figure for clarity. Recent HRTEM imaging of the surface, which is shown in figure 2, reveals that the crystal surface exposes two distinct terminating structures. The central structure (lb) predicted from classical simulation methods is not observed experimentally. In each case, the termination is predicted to be hydroxylated. Each of the three terminations predicted from classical calculations exposes an identical number of dangling bonds, hence the reactivity of each surface is governed by the precise configuration of dangling bonds. The enthalpy of reaction is found to be the same for each terminating structure, being -150 kJ m o r \ The surface energy of each of the three terminations is found to be 1.67 Jm"^, which is in the range that one would expect for stable surfaces - which typically have energies of substantially less than 5 Jm ^
1200
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Figure 1. a,b,c: Predicted terminations of zeolite Beta C (100) face. The surface is shown in cross section and only the siliconframeworkis shown. Looking in detail at both figure 1 and figure 2, it is tempting to forecast an elementary mode of crystal growth based upon the structural relations between the terminations. On the basis of the classical predictions, if the only building block for zeolite growth was a Si(OH)4 tetrahedron, one would expect to observe all three terminating structures, yet from figure 2, it is clear that only two are observed in the HREM. There are at least two possible explanations for the absence of the 'intermediate' termination, figure 1(b): firstly, the intermediate structure may be short lived and is therefore not observed. Secondly, the building unit that facilitates growth may be larger than the S4R structure that is necessary to facilitate growth from figure la to lb. For example, the building unit could be a D4R, in which case the intermediate structure would not be observed. Understanding the absence of the intermediate termination clearly requires knowledge of the constituent building blocks in solution, which is somewhat problematic. There are relatively few examples of investigation into the constituents of solution by experimental methods. Thus far, NMR has proved to be an important tool in the identification of growth/secondary building units. The largest unit identified in a mother liquor representative of the strongly basic solution that is typical of hydrothermal syntheses contains units comprised of just a few T sites. However, the work of Kirshhock et al.[18, 19] has identified strong evidence for a relatively large building block unit containing over forty atoms that is thought to be responsible for the growth of silicalite. Both S4R and D4R's have been observed as solution species and therefore it is reasonable to follow the reaction pathway of condensing both units on the Beta C (100) surface.
Figure 2. HREM images of zeolite Beta C (100): a-c. Simulation predicted images: d-
1201 Using the planewave approach, we optimised the unit cell of Beta C using ultrasoft pseudopotentials and the Perdew-Wang 91 exchange-correlation treatment. The cell was then cleaved parallel to the (100) surface to create three slabs corresponding with the three terminations seen in figure 1, with a vacuum gap of 6.9A. The slabs contained up to 132 atoms in the case of the termination shown in figure Ic. Each surface was then relaxed such that the forces on each atom were less than 10'^ eV/atom. The self-energy of a monomeric Si(OH)4 unit, a dimer, S4R, D4R and water was evaluated by optimising the structures within the cell used to relax the slab. The reaction enthalpy for the two mechanisms of growth is shown in figures 3 and 4, calculated using a Born-Haber cycle.
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Figure 3. S4R mediated reaction pathway for crystal growth on the (100) surface.
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Figure 4. D4R mediated reaction pathways for crystal growth on the (100) face. Consideration of the reaction energetics suggests two possible reasons for the absence of the intermediate termination. Firstly, the two-step S4R reaction consists of an energetically unfavourable and a favourable step. Under reaction conditions, and in the absence of information on the nature of the free-energy barriers of activation for the reactions we cannot disclude the possibility that both reactions occur, however there is and indication that if the intermediate structure is formed, it is short-lived, indeed kinetically unstable with respect to the formation of the D4R terminated structure. The other one-step reaction incurs, in essence, no thermodynamic penalty and would be expected to proceed. Clearly this mechanism precludes the possibility of observing the intermediate structure. Since both the S4R and D4R species can be formed in solution, both reactions may well occur but given the arguments presented above, there is a rationale for the absence of the intermediate structure in both mechanistic pathways. We have subsequently repeated our calculations at a higher energy cutoff and using the SIESTA software, and found that the predicted mechanism is consistent in each approach. This finding demonstrates that the surface structure of zeolites is determined by the reaction enthalpy of attaching preformed building blocks to the crystal surface. We note in passing that the energetics of assembling the D4R at the crystal surface is quite different to that in solution and indeed will be system
1202 specific. Therefore, we cannot a-priori reliably speculate on the reaction enthalpy of attaching fragments to the crystal surface without a rigorous quantum mechanical investigation. We next report details of an investigation into the surface structure of zeolite L (LTL). The structure of zeolite L is shown in figure 5a and b and shows the 12MR ring that gives access to the crystal interior and also the columnar structure of LTL, which can be thought of as containing cancrinite (CAN) and D6R structures. The morphology of zeolite L is typically cylindrical and essentially dominated by two surfaces: the (11.0) and the (001), the (11.0) being the most morphologically prevalent surface. Using the same approach as described above, we considered a large number of terminating structures, and identified 1 uniquely stable termination for the (11.0) face and two terminating structures for the (001) face. In figure 6, the predicted termination of the (001) face is shown next to an HREM image taken from the work of Ohsuna and Terasaki [10]. In addition to the D6R termination shown, we find that thermodynamic stability of the surface in the absence of the D6R is identical to that with the D6R (2.12Jm'^). For brevity the surface is not depicted here, but by reference to figure 5b, the reader will infer that the termination exposes a half CAN cage. The intermediate ("S6R") termination, is much higher in energy and has a surface energy of 2.6 Jm'^ and hence would not be expected to be observed. A thorough HREM inspection of the sample of zeolite L indicates that the S6R and half CAN terminated structures are not observed. Therefore, we infer that the structures are kinetically unstable with respect to the formation of the D6R structure, or the surfaces are not observed because of the mechanistic pathway of assembly.
^'^i%^^$^'
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Figure 5. a,b: A view down the [001] axis of LTL exposing the 12 MR (left) and the columnar filament (right) of LTL. We have undertaken a thorough investigation of the stability of zeolite L secondary building units using both SIESTA and CASTEP. The results of this investigation are the subject of a forthcoming paper[20] but in essence, the calculations suggest that the D6R is least likely to form in solution and hence the mechanism of columnar assembly is dictated by the condensation of CAN cages and half CAN cages and is no way reliant upon the D6R secondary building unit. We believe that the D6R evidenced at the surface is actually formed by condensing a S6R onto the base of a CAN or half CAN cage since our calculations suggest this reaction is extremely favourable. The base of a CAN or half CAN cage is actually a S6R, hence fiising a further S6R upon this structure generates a D6R. This leads us to speculate on the way in which the morphology of zeolite L can be controlled by slowing down the rate of columnar assembly.
Figure 6. Simulated (left and middle) and HREM image (right) of the (001) face of LTL.
1203 CONCLUSION A combination of classical surface simulation methods, aperiodic and periodic density functional based methods prove to be a reliable tool for investigating the surface structure of zeolites. Aside from the predictive capacity of this simulation protocol, the investigations into zeolite Beta C and zeolite L reveal mechanistic information into the nature of crystal growth for frameworks materials by comparison with HREM data. In addition to the two materials described here, we have also investigated a wide range of materials, including complex natural zeolites[21] and low symmetry materials such as MFI[22]. These studies have indicated that in order to understand the mechanism of growth to the atomic level, the contents of the mother liquor must be known, in addition to the geometry of the crystal growth surface. These calculations also provide a platform to undertake kinetic studies of growth and also provide the necessary structural information that allows one to simulate processes at surfaces. Indeed, in ongoing work, we are using our surface structural models to understand the rate of ion-exchange at zeolite interfaces, realistic modelling of zeolite membranes and pore-mouth catalysis. REFERENCES 1. 2. 3. 4.
5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Corma, A., et al., Microporous Mesoporous Mat, (2000). 38(2-3): p. 301-309. Yamamoto, S., et al., Microporous Mesoporous Mat, (1998). 21(1-3): p. 1-6. Agger, J.R., et al., J. Am. Chem. Soc, (1998). 120(41): p. 10754-10759. Agger, J.R. and M.W. Anderson, Crystal growth of zeolite Y studied by computer modelling and atomic force micoscopy, in Impact of Zeolites and Other Porous Materials on the New Technologies at the Beginning of the New Millennium, Pts a and B. 2002. p. 93-100. Anderson, M.W., etaL, Angew. Chem.-Int Edit Engl., (1996). 35(11): p. 1210-1213. Agger, J.R., et al., J. Am. Chem. Soc, (2003). 125(3): p. 830-839. Alfredsson, V., et al., Angew. Chem.-Int Edit Engl., (1993). 32(8): p. 1210-1213. Terasaki, O., J. Electron Microsc, (1994). 43(6): p. 337-346. Gonzalez-Calbet, J.M. and S. Nicolopoulos. Solid State Ion., (1997). 101: p. 975-983. Ohsuna, T., et at, Chem. Mat, (1998). 10(3): p. 688-+. Segall, M.D., et al., J. Phys.-Condes. Matter, (2002). 14(11): p. 2717-2744. Soler, J.M., et at, J. Phys.-Condes. Matter, (2002). 14(11): p. 2745-2779. Gale, J.D. J. Chem. Soc.-Faraday Trans. (1997). 93(4), 629-637 Gay, D.H. and A.L. Rohl. J. Chem. Soc.-Faraday Trans., (1995). 91(5): p. 925-936. Slater, B., et at, Angew. Chem.-Int Edit, (2002). 41(7): p. 1235-+. Liu, Z., et at, J. Am. Chem. Soc, (2001). 123(22): p. 5370-5371. Sanders, M.J., M. Leslie, and C.R.A. Catlow. J. Chem. Soc-Chem. Commun., (1984)(19): p. 1271-1273. Kirschhock, C.E.A., et at, J. Phys. Chem. B, (2002). 106(19): p. 4897-4900. Kirschhock, C.E.A.,et al., J. Phys. Chem. B, (1999). 103(50): p. 11021-11027. Slater, B., et at, Manuscript in preparation, (2003). Mistry, M., B. Slater, and C.R.A. Catlow. submitted, (2003). Ramsahye, N. and B. Slater. Unpublished results, (2003).
1197
SURFACE STRUCTURE DETERMINATION OF ZEOLITES Slater, B.**, Gale, J.D.^ Catlow, C.R.A.^'\ Ohsuna, T / ' ^ and Terasaki, O.^'^ 'Davy Faraday Research Laboratory, The Royal Institution of Great Britain, 21 Albemarle St, London, WIS 4BS U.K. E-mail: [email protected] ^Nanochemistry Research Institute, Department of Applied Chemistry, Curtin University of Technology, Perth 6845, Australia. Department of Chemistry, Imperial College of Science, Technology and Medicine, South Kensington, London, SW7 2AZ, U.K. ^Department of Chemistry, University College London, 20 Gordon Street, London, WCIH OAY, U.K. "^Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan. ^Structural Chemistry, Arrehenius Laboratory, Stockholm University, Sweden. ""Department of Physics, Tohoku University, Sendai 980-8578, Japan. ABSTRACT We present atomistic computer simulation results in combination with high resolution electron microscopy (HREM) images that provide convincing evidence of the atomically resolved surface structure of zeolites Beta C and L. The purpose of the surface structure determination is two-fold: firstly, in solving the surface structure, we gain insight into the crystal growth process, which allows us to propose mechanistic routes and agents for controlling crystal morphology. Secondly, knowledge of surface structure allows us to study processes such as transport and catalysis at the crystal surface that are notoriously difficult to probe using experimental methods. The latter point is clearly important in understanding how the external surface behaves in contrast to the internal surface, in order to rationalise and predict the behaviour of microporous membranes. In this work, we report how a combination of classical and periodic density functional theory calculations have been utilised to predict structure, and to reveal fundamental insights into the intrinsic crystal growth mechanisms for zeolite Beta C and L. INTRODUCTION A significant challenge in zeolite materials chemistry is determining the structure of microporous materials. The challenge is multifarious in origin; the presence of extra-frame work species with extremely small occupancies within the unit cell, the presence of defects, the absence of order within the silicon/aluminium framework in many materials, to name just some of the factors that conspire to make solving the crystal structure of nanoporous materials non-trivial. However, numerous crystal structures have been solved and a natural extension to mapping the bulk structure is the determination of the surface structure of this class of materials. In dense non-porous materials that have utility in catalysis, for example, knowledge of surface structure is vital if one is to understand a catalytic reaction mechanism at the atomic scale. The crystal bulk may impart electronic structural effects upon the surface species but atoms within the solid do not play any physical role within the reaction. In nanoporous materials where the average crystal size is » n m , much of the catalysis may take place within the crystal interior (assuming reagents and products can pass easily through the structural framework) because the external surface area to internal surface area is extremely low. However, nano-crystals are quite different in their potential reactive surface area, such as in lamellar materials, like ITQ2[1] materials, where the external surface area to internal surface area ratio is very high. In the nano-sized class of materials, it is important to understand how the external surface structure dictates the reactivity of the solid, since the surface largely governs the gross 'reactive properties' of the crystal. In larger crystals, the external surface structure also plays a role in determining the reactive properties of the crystal but to a generally unknown degree. The crystal surface may facilitate desirable or undesirable reactions, products, by-products, which can resuh in reduction of the materials lifetime through coking, for example. Given that the scientific motivation for undertaking a comprehensive study of zeolite surface structure is well grounded, it important to review what progress has been made in measuring, predicting and understanding surface structure within the nanoporous class of materials. Two techniques have proved
1198 invaluable in resolving atomistic detail in zeolites; Atomic Force Microscopy(AFM) and HREM. AFM has been widely utilised to study Heulandite[2], zeolite A[3], Y[4, 5], MFI[6], where studies have revealed characteristic step heights comparable with interlayer separations and fractions thereof, that correspond with secondary building units. In the systematic work of Agger, Anderson and their co-workers, studies of zeolite A and Y and MFI have been complemented by numerical simulation approaches. Their work has identified that zeolites appear to grow in the terrace-ledge-kink fashion in common with many inorganic materials, facilitated by multiple or unitary surface nucleation. HREM has been widely used to probe the surface structure of a wide variety of zeolites including Y[7], A[8], MCM-22[9] and L[10]. The largest body of work in this area is due to Terasaki and Ohsuna where the sub 2 Angstrom resolution of the HREM tool affords direct visualisation of the surface and bulk structure of microporous materials, revealing detail such as stacking faults and defects. To choose just one example, the HREM imaging of zeolite Y reveals that the crystal surface occurs with just two terminations; the D6R terminated (111) surface and a termination where the D6R is absent. This is quite distinct from non-polymeric inorganic materials that typically only expose one termination, except at high temperatures or at deviation from stoichiometry arising from changes in the chemical potential (such as the partial pressure of oxygen). The reason that two terminations are exposed is thought to be due to the pre-formation of a D6R unit in solution, which can then condense directly upon the surface. These studies offer insight into the nature of the true building blocks from which zeolites are formed. In the remainder of this paper, the results of calculations probing the surface structure and crystal growth mechanism of zeolite Beta C and zeolite L will be presented.
METHODOLOGY The strategy used here to predict surface structure and growth mechanism is based upon two distinct approaches, exploiting classical simulation methods and two first-principle density functional methods. In the former methodology, the Born model of solids is invoked, where atoms are represented by point charges with extensions to describe the polarisability of the ions. Ions are kept at equilibrium distances by the presence of a short range potential, which in this instance is of Buckingham form. In the latter approach, a N^^ scaling (where N is the number of atoms) ultra-soft pseudopotential plane wave based technique (CASTEP[11]) and a N^ scaling local orbital based method (SIESTA[12]). The classical calculations are undertaken by optimising the crystal bulk at constant pressure, with a short-range cut-off of 12A using the lattice optimisation code GULP1.3[13]. The surface is then relaxed using the same minimisation procedure using a separate code, MARVIN[14], which has a 2D treatment of the Ewald summation, necessary for accurate calculation of the long ranged Coulombic component of the energy. In low-symmetry framework materials, many terminations are possible and indeed unique, therefore the stability of each terminating structure must be evaluated and its thermodynamic stability assessed. We have found that the surface energy, as defined in reference [14] gives a reliable indication of which terminations will be observed at the crystal surface. Terminating structures are generated using two conditions: the first is that the surface is charge neutral and the second is that the surface must have no net dipole normal to the crystal surface. The presence of a dipole indicates the existence of a field within the crystal slab that will polarise the atoms within the block. As the field increases, so does the polarisation, and both the structure and energy of the slab are scaled such that the energy per unit Si02 will uniformly rise. To achieve convergence of the self-energy of the crystal slab and therefore the surface energy, the surface is reconstructed so that the slab is non-polar. This is achieved by translating (in the case of purely siliceous zeolitic materials) either silicon or oxygen ions from the top of the crystal to the bottom to achieve stoichiometry on each face of the crystal slab. In general, a small number of terminations are observed experimentally, yet assessment of the thermodynamic stability of the possible terminating surfaces often reveals a larger number of equally stable terminations. The explanation for this is, we believe, intimately related to the mechanism of crystal growth in framework materials. It has been postulated that the spectrum of building blocks observed by detailed NMR studies, including double 4-membered rings, double-6 membered rings and lower symmetry species can react directly with the crystal surface. In order to calculate the viability of this process, one needs to calculate the condensation energy on the crystal surface directly. Clearly, only electronic structure methods have the required accuracy to probe this problem. In this instance we have used two distinct methods to look at the reaction enthalpy: a plane wave based method and a local orbital scheme. A significant difference between the codes lies in the treatment of void space. In CASTEP, all cell space is sampled, which is
1199 computationally expensive for porous materials. In SIESTA, on the other hand, the volume encapsulated by the orbitals only is considered, dramatically reducing the cost of treating zeolites. In the plane-wave calculations reported here, first reported elsewhere[15], the kinetic energy cutoff used was 260eV, which is rather low. However, the sensitivity of reaction enthalpy was checked by considering the condensation of two S4Rs to give a D4R as a function of kinetic energy cutoff, and a maximum variation of <8kJ mol-1 was found. This number is rather small in absolute magnitude and in terms of the solvation energy, a quantity excluded here which will undoubtedly be different for the various clusters sizes considered. Each H-bond lost in cyclising for example will cost approximately 15kJ mof^ therefore we consider the reaction enthalpy we quote to be indicative of the true reaction energies. RESULTS AND DISCUSSION We first examined the bulk and surface structure of zeolite Beta C, a material recently synthesised for the first time by Camblor et al.[16]. The material has a novel intersecting 12 membered ring structure that has potential utility in catalytic applications. Using the interatomic potential set due to Sanders and Catlow[17], we relaxed the purely siHceous cell of Beta C and obtained cell parameters of a = 12.636A, b = 12.632A, c = 13.030A, a = 90.003° p = 89.992° and y = 90.023°. These values are not in close agreement with the experimentally determined values, however, the as synthesised material contains flouride ions that would expand the lattice. Since the location of the fluoride is not precisely known, the exact relation between atomistic structure and cell parameters are not explored here. The terminations of the (100) face were explored using the atomistic methods described earlier in this article. The (100) face is the most morphologically important face - it dominates the crystal morphology. In this manner, many (in excess often) unique terminations can be generated. Each terminating structure is then relaxed in two states. In the first stage, we relax the structure in its stochiometric form. In the second stage, we consider the reaction of water with the under coordinated sites upon the surface that are formed when the crystal is cleaved to generate the appropriate termination under investigation. Gaseous water is deemed to dissociatively react with the crystal surface, generating a structure that is generally fully hydroxylated. In the first stage, the structure can be though of as being unhydroxylated. By calculating the energy difference between the hydroxylated and unhydroxylated case, the enthalpy of reaction can be calculated. Knowledge of the chemical state of the surface is clearly vital if one is to correctly model the surface structure in contact with other media. In recent work, we have found that when the surface density is low, the surface is reactive with water, when the density is high, the surface tends to self-passivate or reconstruct and is unreactive with water. To classify the reactivity and stability of the surface we utilise the surface energy. A low surface energy indicates that the crystal surface is relatively stable, whilst a high surface energy indicates a relatively unstable surface. The surface energies for distinct terminations for given faces can be compared and utilised to make a prediction of the crystal shape by the Wulff theorem. The essence of Wulff theorem is that the equilibrium crystal shape will be that that minimises the surface energy of the crystal in three dimensions. In Beta C, we find three possible terminations of equal thermodynamic stability (surface energy) for the (100) surface that are depicted in figure 1. The terminations are shown in cross-section, the upper part of the figure being the terminating structure. The vertices represent the intersection between two silicon atoms i.e. the oxygen atoms have been removed from the figure for clarity. Recent HRTEM imaging of the surface, which is shown in figure 2, reveals that the crystal surface exposes two distinct terminating structures. The central structure (lb) predicted from classical simulation methods is not observed experimentally. In each case, the termination is predicted to be hydroxylated. Each of the three terminations predicted from classical calculations exposes an identical number of dangling bonds, hence the reactivity of each surface is governed by the precise configuration of dangling bonds. The enthalpy of reaction is found to be the same for each terminating structure, being -150 kJ m o r \ The surface energy of each of the three terminations is found to be 1.67 Jm"^, which is in the range that one would expect for stable surfaces - which typically have energies of substantially less than 5 Jm ^
1200
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Figure 1. a,b,c: Predicted terminations of zeolite Beta C (100) face. The surface is shown in cross section and only the siliconframeworkis shown. Looking in detail at both figure 1 and figure 2, it is tempting to forecast an elementary mode of crystal growth based upon the structural relations between the terminations. On the basis of the classical predictions, if the only building block for zeolite growth was a Si(OH)4 tetrahedron, one would expect to observe all three terminating structures, yet from figure 2, it is clear that only two are observed in the HREM. There are at least two possible explanations for the absence of the 'intermediate' termination, figure 1(b): firstly, the intermediate structure may be short lived and is therefore not observed. Secondly, the building unit that facilitates growth may be larger than the S4R structure that is necessary to facilitate growth from figure la to lb. For example, the building unit could be a D4R, in which case the intermediate structure would not be observed. Understanding the absence of the intermediate termination clearly requires knowledge of the constituent building blocks in solution, which is somewhat problematic. There are relatively few examples of investigation into the constituents of solution by experimental methods. Thus far, NMR has proved to be an important tool in the identification of growth/secondary building units. The largest unit identified in a mother liquor representative of the strongly basic solution that is typical of hydrothermal syntheses contains units comprised of just a few T sites. However, the work of Kirshhock et al.[18, 19] has identified strong evidence for a relatively large building block unit containing over forty atoms that is thought to be responsible for the growth of silicalite. Both S4R and D4R's have been observed as solution species and therefore it is reasonable to follow the reaction pathway of condensing both units on the Beta C (100) surface.
Figure 2. HREM images of zeolite Beta C (100): a-c. Simulation predicted images: d-
1201 Using the planewave approach, we optimised the unit cell of Beta C using ultrasoft pseudopotentials and the Perdew-Wang 91 exchange-correlation treatment. The cell was then cleaved parallel to the (100) surface to create three slabs corresponding with the three terminations seen in figure 1, with a vacuum gap of 6.9A. The slabs contained up to 132 atoms in the case of the termination shown in figure Ic. Each surface was then relaxed such that the forces on each atom were less than 10'^ eV/atom. The self-energy of a monomeric Si(OH)4 unit, a dimer, S4R, D4R and water was evaluated by optimising the structures within the cell used to relax the slab. The reaction enthalpy for the two mechanisms of growth is shown in figures 3 and 4, calculated using a Born-Haber cycle.
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Figure 4. D4R mediated reaction pathways for crystal growth on the (100) face. Consideration of the reaction energetics suggests two possible reasons for the absence of the intermediate termination. Firstly, the two-step S4R reaction consists of an energetically unfavourable and a favourable step. Under reaction conditions, and in the absence of information on the nature of the free-energy barriers of activation for the reactions we cannot disclude the possibility that both reactions occur, however there is and indication that if the intermediate structure is formed, it is short-lived, indeed kinetically unstable with respect to the formation of the D4R terminated structure. The other one-step reaction incurs, in essence, no thermodynamic penalty and would be expected to proceed. Clearly this mechanism precludes the possibility of observing the intermediate structure. Since both the S4R and D4R species can be formed in solution, both reactions may well occur but given the arguments presented above, there is a rationale for the absence of the intermediate structure in both mechanistic pathways. We have subsequently repeated our calculations at a higher energy cutoff and using the SIESTA software, and found that the predicted mechanism is consistent in each approach. This finding demonstrates that the surface structure of zeolites is determined by the reaction enthalpy of attaching preformed building blocks to the crystal surface. We note in passing that the energetics of assembling the D4R at the crystal surface is quite different to that in solution and indeed will be system
1202 specific. Therefore, we cannot a-priori reliably speculate on the reaction enthalpy of attaching fragments to the crystal surface without a rigorous quantum mechanical investigation. We next report details of an investigation into the surface structure of zeolite L (LTL). The structure of zeolite L is shown in figure 5a and b and shows the 12MR ring that gives access to the crystal interior and also the columnar structure of LTL, which can be thought of as containing cancrinite (CAN) and D6R structures. The morphology of zeolite L is typically cylindrical and essentially dominated by two surfaces: the (11.0) and the (001), the (11.0) being the most morphologically prevalent surface. Using the same approach as described above, we considered a large number of terminating structures, and identified 1 uniquely stable termination for the (11.0) face and two terminating structures for the (001) face. In figure 6, the predicted termination of the (001) face is shown next to an HREM image taken from the work of Ohsuna and Terasaki [10]. In addition to the D6R termination shown, we find that thermodynamic stability of the surface in the absence of the D6R is identical to that with the D6R (2.12Jm'^). For brevity the surface is not depicted here, but by reference to figure 5b, the reader will infer that the termination exposes a half CAN cage. The intermediate ("S6R") termination, is much higher in energy and has a surface energy of 2.6 Jm'^ and hence would not be expected to be observed. A thorough HREM inspection of the sample of zeolite L indicates that the S6R and half CAN terminated structures are not observed. Therefore, we infer that the structures are kinetically unstable with respect to the formation of the D6R structure, or the surfaces are not observed because of the mechanistic pathway of assembly.
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Figure 5. a,b: A view down the [001] axis of LTL exposing the 12 MR (left) and the columnar filament (right) of LTL. We have undertaken a thorough investigation of the stability of zeolite L secondary building units using both SIESTA and CASTEP. The results of this investigation are the subject of a forthcoming paper[20] but in essence, the calculations suggest that the D6R is least likely to form in solution and hence the mechanism of columnar assembly is dictated by the condensation of CAN cages and half CAN cages and is no way reliant upon the D6R secondary building unit. We believe that the D6R evidenced at the surface is actually formed by condensing a S6R onto the base of a CAN or half CAN cage since our calculations suggest this reaction is extremely favourable. The base of a CAN or half CAN cage is actually a S6R, hence fiising a further S6R upon this structure generates a D6R. This leads us to speculate on the way in which the morphology of zeolite L can be controlled by slowing down the rate of columnar assembly.
Figure 6. Simulated (left and middle) and HREM image (right) of the (001) face of LTL.
1203 CONCLUSION A combination of classical surface simulation methods, aperiodic and periodic density functional based methods prove to be a reliable tool for investigating the surface structure of zeolites. Aside from the predictive capacity of this simulation protocol, the investigations into zeolite Beta C and zeolite L reveal mechanistic information into the nature of crystal growth for frameworks materials by comparison with HREM data. In addition to the two materials described here, we have also investigated a wide range of materials, including complex natural zeolites[21] and low symmetry materials such as MFI[22]. These studies have indicated that in order to understand the mechanism of growth to the atomic level, the contents of the mother liquor must be known, in addition to the geometry of the crystal growth surface. These calculations also provide a platform to undertake kinetic studies of growth and also provide the necessary structural information that allows one to simulate processes at surfaces. Indeed, in ongoing work, we are using our surface structural models to understand the rate of ion-exchange at zeolite interfaces, realistic modelling of zeolite membranes and pore-mouth catalysis. REFERENCES 1. 2. 3. 4.
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