research papers\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

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ISSN: 2052-5206

Hypothetical binodal zeolitic frameworks

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aDavy–Faraday Research Laboratory, The Royal Institution of Great Britain, 21 Albemarle Street, London W1S 4BS, England, bDepartment of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287-1604, USA, cDepartment of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, England, and dDepartment of Chemistry, CICECO, University of Aveiro, Campus Universitário de Santiago, Aveiro 3810-193, Portugal
*Correspondence e-mail: jk18@cam.ac.uk

(Received 19 April 2005; accepted 27 April 2005)

Hypothetical binodal zeolitic structures (structures containing two kinds of tetrahedral sites) were systematically enumerated using tiling theory and characterized by computational chemistry methods. Each of the 109 refineable topologies based on `simple tilings' was converted into a silica polymorph and its energy minimized using the GULP program with the Sanders–Catlow silica potential. Optimized structural parameters, framework energies relative to α-quartz and volumes accessible to sorption have been calculated. Eleven of the 30 known binodal topologies listed in the Atlas of Zeolite Framework Types were found, leaving 98 topologies that were unknown previously. The chemical feasibility of each structure as a zeolite was evaluated by means of a feasibility factor derived from the correlation between lattice energy and framework density. Structures are divided into 15 families, based on common structural features. Many `feasible' structures contain only small pores. Several very open structures were also enumerated, although they contain three-membered rings which are thermodynamically dis­favoured and not found in conventional zeolites. We believe that such topologies may be realizable as framework materials, but with different elemental compositions to those normally associated with zeolites.

1. Introduction

Zeolites find many important applications in science and technology in areas as diverse as catalysis, chemical separation, water softening, agriculture, refrigeration and opto-electronics. There are 152 distinct structural types of zeolites which have now been identified (Baerlocher et al., 2001[Baerlocher, C., Meier, W. M. & Olson, D. H. (2001). Atlas of Zeolite Structure Types (updates at https://www.iza-structure.org/ ), 5th ed. London: Elsevier.]). The definition of a zeolite is based not on chemical composition or function, but rather on atomic scale geometry. In order to qualify as a zeolite or zeolite-type material (zeotype), a mineral or synthetic material must possess a framework composed of corner-sharing tetrahedra. There is an additional requirement of `openness', simultaneously dependent on density and smallest ring size, thus excluding denser minerals. Another way of expressing this is in terms of a four-connected net in which each vertex (in chemical terms the central atom of a tetrahedron) is connected to its four closest neighbours, normally via an oxygen bridge.

The enumeration of hypothetical zeolitic framework structures (Klinowski, 1998[Klinowski, J. (1998). Curr. Opin. Solid State Mater. Sci. 3, 79-85.]) is of considerable scientific and practical interest in terms of generating new nanoporous architectures. Enumeration originates with the work of Wells (1977[Wells, A. F. (1977). Three-Dimensional Nets and Polyhedra. New York: Wiley.], 1979[Wells, A. F. (1979). Further Studies of Three-Dimensional Nets, American Crystallographic Association Monograph No. 8, Vol. 9. Pittsburgh, PA: Polycrystal Book Service.], 1984[Wells, A. F. (1984). Structural Inorganic Chemistry, 5th ed. Oxford University Press.]) on three-dimensional nets and polyhedra. Smith and collaborators (Smith, 1988[Smith, J. V. (1988). Chem. Rev. 88, 149-182.], 1993[Smith, J. V. (1993). ACS Abstr. 205, 157-IEC.]; Alberti, 1979[Alberti, A. (1979). Am. Mineral. 64, 1188-1198.]; Sato, 1984[Sato, M. (1984). Framework Topology and Systematic Derivation of Zeolite Structures, edited by D. H. Olson and A. Bisio. In Proc. of the 6th Intl Zeolite Conference, Reno, USA, 10-15 July. Guildford: Butterworths.], 1987[Sato, M. J. (1987). Phys. Chem. 91, 4675-4681.]; Sherman & Bennett, 1973[Sherman, J. D. & Bennett, J. M. (1973). Molecular Sieves, edited by W. M. Meier and J. B. Uytterhoeven, Vol. 121, p. 52. Washington, DC: American Chemical Society.]; Barrer & Villiger, 1969[Barrer, R. M. & Villiger, H. (1969). Z. Kristallogr. 128, 352-370.]), O'Keeffe and collaborators (O'Keeffe & Hyde, 1996a[O'Keeffe, M. & Hyde, S. T. (1996a). Z. Kristallogr. 211, 73-78.],b[O'Keeffe, M. & Hyde, B. G. (1996b). Crystal Structures I: Patterns and Symmetry. Mineralogical Association of America Monograph, Washington, DC.]) and Akporiaye & Price (1989[Akporiaye, D. E. & Price, G. D. (1989). Zeolites, 9, 23-32.]) found many possible new structures by combining various structural subunits. More recent work involves computer search algorithms (Boisen et al., 1999[Boisen, M. B., Gibbs, G. V., O'Keeffe, M. & Bartelmehs, K. L. (1999). Micropor. Mesopor. Mater. 29, 219-266.]; Treacy et al., 1997[Treacy, M. M. J., Randall, K. H., Rao, S., Perry, J. A. & Chadi, D. J. (1997). Z. Kristallogr. 212, 768.]; Foster & Treacy, 2004[Foster, M. D. & Treacy, M. M. J. (2004). Hypothetical Zeolites: Enumeration Research; https://www.hypotheticalzeolites.net/ 2004 .]; Mellot-Draznieks et al., 2000[Mellot-Draznieks, C., Newsam, J. M., Gorman, A. M., Freeman, C. M. & Férey, G. (2000). Angew. Chem. Int. Ed. 39, 2270-2275.]).

Our work is based on advances in combinatorial tiling theory (Dress et al., 1993[Dress, A. W. M., Huson, D. H. & Molnár, E. (1993). Acta Cryst. A49, 806-817.]). A tiling is a periodic subdivision of three-dimensional space into connected regions, which we call tiles. If two tiles meet along a surface, the surface is called a face. If three or more faces meet along a curve, we call the curve an edge. If at least three edges meet at a point, we call that point a vertex. A network is thus formed by the vertices and edges. The configuration of edges, faces and tiles around a given vertex can be described via the so-called vertex figure, obtained by placing the centre of a small notational sphere at the vertex and considering the tiling of that sphere formed by the intersections with the different tiles touching that vertex. We have already enumerated all possible Euclidean uni-, bi- and trinodal tilings based on simple vertex figures and all uninodal tilings with vertex figures containing up to six extra edges (Delgado Friedrichs, 2001[Delgado Friedrichs, O. (2001). Discret. Comput. Geom. 26, 549-571.]), and the computer program used for this task is available from the authors upon request (olaf.delgado@asu.edu).

The tiling approach identified networks with one, two and three types of inequivalent vertices, which we call uninodal, binodal and trinodal (Delgado Friedrichs et al., 1999[Delgado Friedrichs, O., Dress, A. W. M., Huson, D. H., Klinowski, J. & Mackay, A. L. (1999). Nature, 400, 644-647.]). We have shown that there are exactly 9, 117 and over 1300 topological types of four-connected uninodal, binodal and trinodal nets, respectively, which are based on `simple' periodic tilings (as explained in Delgado Friedrichs et al., 1999[Delgado Friedrichs, O., Dress, A. W. M., Huson, D. H., Klinowski, J. & Mackay, A. L. (1999). Nature, 400, 644-647.]). The previously reported number of 926 for the trinodal simple tilings included, due to an error in the manual processing of the data files, only those nets for which the tiles have non-trivial site symmetry. In addition, there are at least 157 additional uninodal nets derived from `quasi-simple' tilings (the vertex figures of which are derived from tetrahedra, but contain double edges; Delgado Friedrichs et al., 1999[Delgado Friedrichs, O., Dress, A. W. M., Huson, D. H., Klinowski, J. & Mackay, A. L. (1999). Nature, 400, 644-647.]) and which have already been discussed elsewhere (Foster et al., 2001[Foster, M. D., Bell, R. G. & Klinowski, J. (2001). Stud. Surf. Sci. Catal. 136, 266.], 2003[Foster, M. D., Delgado Friedrichs, O., Bell, R. G., Almeida Paz, F. A. & Klinowski, J. (2003). Angew. Chem. Int. Ed. 42, 3896-3899.]; Foster, Friedrichs et al., 2004[Foster, M. D., Friedrichs, O. D., Bell, R. G., Almeida Paz, F. A. & Klinowski, J. J. (2004). Am. Chem. Soc. 126, 9769-9775.]; Foster, Simperler et al., 2004[Foster, M. D., Simperler, A., Bell, R. G., Delgado Friedrichs, O., Almeida Paz, F. A. & Klinowski, J. (2004). Nature Mater. 3, 234-238.]; Simperler et al., 2004[Simperler, A., Foster, M. D., Bell, R. G. & Klinowski, J. (2004). J. Phys. Chem. B, 108, 869-879.];). For example, zeolitic structure types SOD, LTA, RHO, FAU, KFI and CHA are all based on quasi-simple tilings. An example of a non-simple tiling is that of GIS, where the tile has some two-connected vertices.

Here we focus our attention on the binodal structures, i.e. those with two topologically inequivalent types of tetrahedral vertex (T-atom sites) derived only from simple tilings, meaning that they can be readily described by the packing of convex polyhedra, the vertices of which are all three-connected. Structures containing cages are thus found in abundance, while those with, for instance, more `cylindrical' channels are less common and tend to have lower framework density than the `quasi-simple' structures, with a greater proportion lying in the range of density where most known zeolites are found, as opposed to denser minerals. On the other hand, many of the known zeolite structure types cannot be constructed from simple tilings. Thus, simple tilings cannot generate the complete set of binodal zeolites. Seven of the 21 known uninodal zeolites correspond to simple tilings, and the remaining 14, together with several mineral structures (although not quartz) are constructed using quasi-simple tilings. We have found 11 of the 30 known binodal zeolite types, and the remaining 19 will be found by considering quasi-simple tilings, just as with the uninodal structures. The number of potential binodal networks thus generated will be enormous, and their enumeration will require the use of state-of-the-art computational facilities. However, only very few binodal structures have previously been enumerated, while nearly all uninodal structures derived from the tilings were previously known, either as crystal structures or as hypothetical nets. It is therefore of interest to describe the binodal structures derived only from simple tilings.

To characterize the structures, we follow procedures identical to those used in our previous work (Foster et al., 2003[Foster, M. D., Delgado Friedrichs, O., Bell, R. G., Almeida Paz, F. A. & Klinowski, J. (2003). Angew. Chem. Int. Ed. 42, 3896-3899.]; Foster, Simperler et al., 2004[Foster, M. D., Simperler, A., Bell, R. G., Delgado Friedrichs, O., Almeida Paz, F. A. & Klinowski, J. (2004). Nature Mater. 3, 234-238.]). These involve generating model SiO2 polymorphs from the tiling nets and optimizing them using lattice energy minimization. Apart from obtaining an optimized structure for each topology, we also calculate a lattice energy, which provides an accurate guide to the thermodynamic stability that such a phase might have. A `feasibility factor', ϑ, derived from the correlation between lattice energy and density calculated for known zeolite structure types, serves as a further measure of thermodynamic feasibility. We have also calculated the accessible volume for each pore system using a standard definition (Molecular Simulations Inc., 1999[Molecular Simulations Inc. (1999). Cerius2, Version 4.0. Molecular Simulations Inc., San Diego, USA.]).

In describing the structural characteristics of each framework, we have resorted to the `model building' approach (Baerlocher et al., 2001[Baerlocher, C., Meier, W. M. & Olson, D. H. (2001). Atlas of Zeolite Structure Types (updates at https://www.iza-structure.org/ ), 5th ed. London: Elsevier.]; Smith, 1988[Smith, J. V. (1988). Chem. Rev. 88, 149-182.]; Meier, 1986[Meier, W. M. (1986). Zeolites and Zeolite-Like Materials. 7th Int. Zeolite Conference, Tokyo, 17-22 August.]; Liebau et al., 1986[Liebau, F., Gies, H., Gunawardane, R. P. & Marler, B. (1986). Zeolites, 6, 373-377.]), which is consistent with descriptions found in the online zeolite database and allows structures to be classified into `families' if they share certain structural motifs. As part of this analysis we define as a composite building unit (CBU) every small finite unit from which a structure may be generated. These units can be corner-, edge- or face-sharing, or joined to one another by single linkages. The automated assembly of such units is also a potential method of structural enumeration, as demonstrated by Mellot-Draznieks (Mellot-Draznieks et al., 2000[Mellot-Draznieks, C., Newsam, J. M., Gorman, A. M., Freeman, C. M. & Férey, G. (2000). Angew. Chem. Int. Ed. 39, 2270-2275.], 2002[Mellot-Draznieks, C., Girard, S., Férey, G., Schön, J. C., Cancarevic, Z. & Jansen, M. (2002). Chem. Eur. J. 8, 4103-4113.]). Zeolite structures may also be described in terms of the strictly defined secondary building units (SBUs), one type of which may be used to build a unit cell of the zeolite, without sharing T atoms. Here, we have not used the SBU approach, finding it more informative to use alternative descriptions (in general, our building units tend to be larger). However, the SBUs involved may be readily identified, as may the infinite periodic building units (PerBUs). We note that none of the units discussed are intended to represent the precursors from which zeolite crystals grow; neither do they necessarily correspond to the tiles of the original nets.

We discuss the structures in terms of the component units, and relate these to the calculated stability and feasibility. Taken together, thermodynamic feasibilty and the nature of the building units can provide a good initial guide as to which of these structures could be most readily synthesized.

2. Energy minimization

The systematically enumerated nets (Delgado Friedrichs et al., 1999[Delgado Friedrichs, O., Dress, A. W. M., Huson, D. H., Klinowski, J. & Mackay, A. L. (1999). Nature, 400, 644-647.]) were first converted into atomistic models. This was done by inserting an Si atom at each vertex point in the network and placing a bridging oxygen between each pair of adjacent Si atoms. Each net was scaled such that the vertices were separated by ca 3.1 Å, a typical Si—Si distance. The resulting structure was then pre-optimized using the DLS (distance least squares) method (Meier & Villiger, 1969[Meier, W. M. & Villiger, H. (1969). Z. Kristallogr. 128, 352-370.]), which performs geometric refinement of the structure by fitting bond lengths and angles to the prescribed values, and reduces the amount of computer time needed for the subsequent minimization of lattice energy. This procedure was found to have no influence on the final result: using lattice energy minimization from the outset gives the same structure, but at greater computational expense. The lattice energy and crystallographic data are those extracted from the GULP minimizations, whereas coordination sequences, bond distances and angles were calculated with zeoTsites (Version 1.2; Sastre & Gale, 2001[Sastre, G. & Gale, J. D. (2001). Micropor. Mesopor. Mater. 43, 27-40.]). The connectivity was additionally checked with the software tool KRIBER (Version 1.1; Bialek, 1995[Bialek, R. (1995). KRIBER, Version 1.1. Institut für Kristallographie und Petrographie, ETH, Zürich, Switzerland.]). Additional calculations were carried out using Cerius2 software (Molecular Simulations Inc., 1999[Molecular Simulations Inc. (1999). Cerius2, Version 4.0. Molecular Simulations Inc., San Diego, USA.]). Structural figures were prepared using GDIS (SourceForge, 2004[SourceForge (2004). GDIS, Version 0.84. SourceForge.]) and POV-Ray (Persistence of Vision Raytracer Pty. Ltd, 2004[Persistence of Vision Raytracer Pty. Ltd (2004). POV-Ray, Version 3.6. Persistence of Vision Raytracer Pty Ltd.]; Henson et al., 1994[Henson, N. J., Cheetham, A. K. & Gale, J. D. (1994). Chem. Mater. 6, 1647-1650.]). The lattice energy, ΔEquartz, given in Table 1[link], is relative to that of α-quartz, calculated using the same potential model, and is thus analogous to the heat of transition reported for several high-silica zeolites (Henson et al., 1994[Henson, N. J., Cheetham, A. K. & Gale, J. D. (1994). Chem. Mater. 6, 1647-1650.]; Petrovic et al., 1993[Petrovic, I., Navrotsky, A., Davis, M. E., Zones, S. I. (1993). Chem. Mater. 5, 1805-1813.]; Navrotsky et al., 1995[Navrotsky, A., Petrovic, I., Hu, Y. T., Chen, C.-Y. & Davis, M. E. (1995). Micropor. Mater. 4, 95-98.]; Hu et al., 1995[Hu, Y. T., Navrotsky, A., Chen, C. Y. & Davis, M. E. (1995). Chem. Mater. 7, 1816-1823.]; Piccione et al., 2000[Piccione, P. M., Laberty, C., Yang, S. Y., Camblor, M. A., Navrotsky, A. & Davis, M. E. (2000). J. Phys. Chem. B, 104, 10001-10011.], 2001[Piccione, P. M., Woodfield, B. F., Boerio-Goates, J., Navrotsky, A. & Davis, M. E. (2001). J. Phys. Chem. B, 105, 6025-6030.], 2002[Piccione, P. M., Yang, S. Y., Navrotsky, A. & Davis, M. E. (2002). J. Phys. Chem. B, 106, 3629-3638.]; Moloy et al., 2002[Moloy, E. C., Davila, L. P., Shackelford, J. F. & Navrotsky, A. (2002). Micropor. Mesopor. Mater. 54, 1-13.]).

Table 1
Chemical feasibility factor, relative lattice energy, framework density and coordination sequences for 109 hypothetical binodal zeolites, optimized as purely siliceous structures

Structures are listed in order of increasing value of ϑ.

Structure ϑ ΔEquartz (kJ mol−1) FD (T sites per 1000 Å3) Coordination sequence
2_87 0.10 15.91 16.86 4 9 17 30 49 72 96 121 150 187
        4 10 20 33 49 69 94 125 160 197
2_89 (ERI) 0.12 16.39 16.51 4 9 17 30 50 75 98 118 144 185
        4 10 20 32 46 64 90 126 164 196
2_84 (EAB) 0.12 16.41 16.49 4 9 17 30 49 71 92 115 147 190
        4 10 20 32 46 66 94 128 162 192
2_90 (SAT) 0.18 15.72 16.91 4 9 17 30 50 75 100 126 157 194
        4 10 20 33 50 71 95 124 158 197
2_103 0.30 16.80 16.04 4 10 17 30 52 70 107 128 166 208
        4 11 20 33 51 73 103 136 169 207
2_88 (AWW) 0.32 15.03 17.25 4 9 17 30 50 74 97 123 158 198
        4 10 20 33 50 72 98 128 162 200
2_86 0.37 15.54 16.85 4 9 17 30 49 72 96 121 150 186
        4 10 20 33 49 68 92 122 155 191
2_83 (LEV) 0.42 16.00 16.48 4 9 17 30 49 71 92 114 143 183
        4 10 20 32 46 64 90 124 156 184
2_85 0.69 16.03 17.57 4 9 17 30 49 71 95 125 161 201
        4 10 20 33 50 73 100 131 168 208
2_107 (LOS) 0.91 13.86 17.47 4 10 20 34 52 74 102 136 172 210
        4 10 20 34 54 78 104 134 168 210
2_74 (TSC) 0.94 19.47 13.55 4 9 16 25 37 53 74 99 125 151
        4 9 17 28 41 56 73 93 117 146
2_110 0.94 13.82 17.47 4 9 17 30 50 74 97 123 158 198
        4 10 20 33 50 72 98 128 162 200
2_106 0.97 13.79 17.46 4 10 20 34 52 74 100 130 166 208
        4 10 20 34 53 76 103 135 170 209
2_95 0.93 17.49 16.80 4 9 18 32 52 75 99 133 171 207
        4 10 19 32 52 76 103 136 172 213
2_108 0.97 13.77 17.47 4 10 20 34 53 76 102 132 167 208
        4 10 20 34 53 76 103 135 170 208
2_81 (SAS) 0.98 15.88 16.00 4 9 17 30 48 68 87 109 142 184
        4 10 19 30 45 65 90 118 145 175
2_91 0.95 17.12 17.07 4 9 17 31 54 82 108 137 176 223
        4 11 22 35 55 81 107 143 184 222
2_78 (AFX) 1.00 16.41 15.61 4 9 17 29 45 64 85 110 141 178
        4 9 17 29 45 65 89 116 144 175
2_101 (AST) 0.99 18.14 16.41 4 9 19 34 48 66 96 127 151 183
        4 12 18 28 52 78 88 112 162 204
2_117 1.22 11.58 18.74 4 11 24 41 64 93 127 163 205 255
        4 12 22 44 64 94 124 164 206 252
2_114 2.17 11.15 18.09 4 11 21 36 64 93 120 156 202 255
        4 11 23 40 62 88 123 162 202 249
2_47 3.02 24.55 14.00 4 9 17 28 41 56 74 97 125 158
        4 8 14 24 37 54 75 97 121 148
2_54 3.18 24.09 14.47 4 8 14 25 40 57 76 96 119 150
        4 9 17 27 38 54 76 101 128 154
2_112 4.66 20.19 18.66 4 10 22 40 60 95 121 165 212 258
        4 12 21 41 67 90 128 168 211 263
2_50 (AFY) 5.03 27.27 14.12 4 8 14 25 39 53 71 96 124 152
        4 9 16 23 34 57 82 98 115 141
2_53 5.11 26.05 15.05 4 7 12 24 39 60 79 110 168 250
        4 10 19 27 39 62 92 137 202 275
2_51 5.18 27.49 14.12 4 8 14 25 39 53 72 100 130 157
        4 9 16 23 34 57 82 98 118 153
2_59 5.25 23.49 16.96 4 9 18 32 52 75 99 133 171 207
        4 10 19 32 52 76 103 136 172 213
2_113 5.32 18.94 20.19 4 10 23 38 60 86 118 154 195 244
        4 11 21 39 61 86 118 154 195 243
2_96 5.45 24.88 16.21 4 9 18 32 52 75 105 144 181 217
        4 11 21 35 54 80 113 145 182 228
2_57 5.51 25.91 15.54 4 8 14 26 44 63 80 97 122 164
        4 10 19 28 39 57 82 112 139 159
2_109 5.67 21.61 18.68 4 10 20 34 53 76 102 133 170 212
        4 10 20 34 53 77 106 139 174 212
2_58 6.04 24.64 16.95 4 8 14 26 45 67 89 115 149 188
        4 10 20 32 47 68 93 122 157 196
2_102 6.08 26.50 15.70 4 9 19 34 48 73 98 125 167 197
        4 11 18 31 54 72 96 128 160 204
2_55 7.61 29.43 15.20 4 8 14 26 44 62 91 121 144 181
        4 11 19 29 47 67 91 121 153 188
2_82 9.41 27.74 18.17 4 9 17 30 48 69 92 119 153 192
        4 10 20 32 46 66 94 126 158 194
2_67 10.27 33.41 15.11 4 8 16 28 42 60 84 108 136 170
        4 9 16 27 43 62 83 109 139 171
2_99 10.53 30.91 17.10 4 9 18 34 55 76 103 144 187 229
        4 9 20 34 54 81 110 144 185 229
2_35 10.69 41.65 9.82 4 8 13 20 28 36 46 62 83 104
        4 9 15 21 28 37 49 65 85 108
2_62 10.97 33.96 15.43 4 8 14 27 48 70 91 116 146 185
        4 9 19 32 45 67 92 124 165 209
2_43 11.62 41.22 11.05 4 8 14 21 34 53 71 90 108 133
        4 8 16 27 35 48 66 83 113 146
2_64 12.15 41.09 11.67 4 8 15 25 37 52 71 95 120 148
        4 8 16 27 37 53 71 89 116 144
2_45 12.91 40.22 13.03 4 8 14 23 34 49 67 87 111 139
        4 9 16 25 37 52 70 91 114 140
2_31 13.16 48.71 7.40 4 8 12 17 24 31 36 42 54 72
        4 9 15 20 24 29 37 48 60 73
2_24 13.28 43.16 11.36 4 7 12 22 32 41 56 80 106 125
        4 9 15 22 32 46 63 81 100 122
2_19 13.39 47.93 8.17 4 7 10 16 22 26 34 48 63 76
        4 8 12 16 21 28 37 49 64 80
2_73 13.62 38.71 14.78 4 9 15 21 37 59 104 138 182 199
        4 11 20 36 52 77 121 155 192 236
2_68 13.82 41.46 13.08 4 8 17 28 45 66 88 114 141 182
        4 9 16 28 48 66 84 115 150 178
2_39 13.86 39.83 14.25 4 8 13 22 36 53 72 94 122 156
        4 9 16 25 38 56 78 103 129 157
2_17 13.96 51.80 6.05 4 7 9 13 19 23 25 30 41 55
        4 8 12 15 17 21 28 36 44 53
2_70 14.33 41.70 13.42 4 8 17 32 46 71 95 129 166 199
        4 9 18 32 50 70 95 128 166 212
2_40 14.97 40.32 15.02 4 8 13 22 37 56 76 98 126 158
        4 9 16 26 41 60 80 101 126 158
2_27 15.42 42.76 13.78 4 7 12 24 38 50 68 94 122 153
        4 9 16 26 40 57 78 103 130 159
2_23 15.97 51.69 8.14 4 7 12 20 26 32 44 68 90 108
        4 8 13 17 24 34 49 67 82 101
2_20 16.11 50.76 8.93 4 7 10 17 27 35 41 52 73 100
        4 9 15 20 25 33 47 66 84 98
2_97 16.99 40.46 16.94 4 9 18 32 52 76 106 147 188 229
        4 11 21 35 55 81 117 152 188 238
2_71 17.07 39.95 17.38 4 8 19 39 58 83 118 160 193 232
        4 10 21 38 58 91 117 158 195 244
2_26 17.51 50.60 10.44 4 7 12 22 34 46 58 76 107 139
        4 8 14 21 32 48 65 86 111 138
2_25 17.56 50.63 10.47 4 7 12 22 33 44 58 80 104 125
        4 8 14 21 32 48 65 85 106 132
2_37 18.50 48.93 12.58 4 8 12 17 24 31 36 42 54 72
        4 9 15 20 24 29 37 48 60 73
2_21 18.85 49.90 12.26 4 7 10 18 32 47 59 71 91 121
        4 9 16 24 34 48 66 89 117 149
2_32 19.04 49.98 12.40 4 8 12 18 29 44 60 77 98 125
        4 9 16 24 33 45 62 85 113 143
2_48 19.09 45.87 15.29 4 8 14 25 38 50 70 100 125 147
        4 9 16 24 36 56 76 92 120 159
2_41 19.44 55.48 8.99 4 8 14 19 26 40 52 70 88 100
        4 8 14 20 29 42 52 68 89 109
2_69 20.57 49.50 14.25 4 8 17 29 46 68 91 117 154 184
        4 9 17 28 49 69 92 119 151 184
2_65 20.64 52.45 12.28 4 8 15 28 47 66 86 118 155 181
        4 8 16 26 48 66 88 120 142 200
2_33 20.83 49.10 14.80 4 8 12 18 30 49 71 92 114 143
        4 9 16 25 38 56 77 99 121 147
2_52 20.93 48.51 15.30 4 7 10 16 25 34 43 58 75 90
        4 7 11 16 24 35 46 59 75 93
2_100 22.42 45.32 19.00 4 9 18 34 58 86 113 146 194 248
        4 11 22 38 61 88 120 157 199 246
2_79 23.48 45.37 20.03 4 9 17 29 46 69 98 133 174 221
        4 10 21 37 58 84 114 148 186 229
2_77 24.27 47.94 19.04 4 9 16 26 41 61 84 110 140 175
        4 9 17 28 42 61 85 114 146 179
2_44 24.31 60.53 10.36 4 8 14 21 36 55 75 94 120 154
        4 8 16 20 34 64 72 96 128 146
2_46 24.45 57.04 12.91 4 8 14 24 36 48 64 90 118 136
        4 9 15 22 34 52 71 87 106 136
2_61 25.45 53.55 16.33 4 8 14 26 46 70 91 113 149 197
        4 10 19 30 45 68 94 122 152 186
2_22 26.31 64.37 9.70 4 7 11 18 28 42 56 68 85 111
        4 8 14 21 29 41 57 77 99 121
2_92 26.57 53.08 17.78 4 9 17 31 54 82 109 139 182 233
        4 11 22 35 55 82 110 146 188 230
2_13 26.62 61.44 12.04 4 6 15 28 34 60 69 96 126 142
        4 9 16 25 39 57 75 96 120 150
2_93 28.25 60.99 13.98 4 10 20 31 50 71 104 134 176 210
        4 9 18 30 48 70 94 134 180 213
2_12 29.67 65.74 12.11 4 6 15 20 30 50 67 90 115 126
        4 8 13 22 32 47 71 91 108 132
2_30 33.21 64.55 16.47 4 8 12 16 26 42 56 72 102 140
        4 8 13 20 30 41 56 80 111 138
2_94 33.62 58.11 21.34 4 9 18 31 55 88 121 157 194 236
        4 11 23 41 63 88 123 162 207 262
2_16 36.19 72.38 14.02 4 6 17 32 49 65 92 135 167 183
        4 11 20 28 50 81 102 117 159 222
2_34 36.28 76.83 11.03 4 8 13 19 26 38 55 74 95 115
        4 9 16 24 34 47 61 78 100 126
2_14 36.36 72.96 13.79 4 6 16 31 48 57 77 116 154 161
        4 11 19 26 42 70 93 103 128 182
2_98 37.01 63.95 20.69 4 9 18 33 51 72 105 147 184 230
        4 9 18 33 53 78 108 143 184 232
2_56 38.29 72.66 15.93 4 8 14 26 44 62 93 122 145 182
        4 11 19 29 47 68 94 123 155 193
2_116 43.29 71.75 21.56 4 11 22 39 65 96 134 175 223 280
        4 11 23 41 65 94 133 177 230 284
2_111 43.36 69.96 22.87 4 10 20 46 70 94 140 206 264 308
        4 12 25 47 74 108 155 203 262 334
2_18 44.29 89.79 10.06 4 7 10 14 17 24 37 48 57 70
        4 8 8 10 20 24 28 50 64 64
2_28 45.34 88.96 11.69 4 7 13 18 33 44 66 72 110 118
        4 8 12 21 30 50 58 82 98 138
2_15 46.13 89.89 11.83 4 12 10 28 52 34 84 124 74 172
        4 6 17 27 31 64 75 81 143 146
2_75 50.08 80.91 22.01 4 7 13 25 39 56 87 107 148 182
        4 8 14 25 40 59 84 110 147 180
2_29 50.83 93.06 14.34 4 10 18 30 45 59 103 165 219 314
        4 10 20 31 49 80 103 164 269 289
2_10 51.21 104.88 6.53 4 6 12 16 24 32 44 55 68 80
        4 6 12 17 24 31 44 55 68 82
2_5 52.01 104.95 7.28 4 5 9 14 13 16 26 34 36 44
        4 8 10 11 16 22 24 28 42 60
2_115 52.70 88.37 19.46 4 11 21 36 64 94 123 165 214 272
        4 11 23 40 63 91 126 167 213 265
2_7 53.66 105.42 8.60 4 5 10 20 26 24 44 80 98 93
        4 9 14 16 22 40 58 72 83 109
2_8 54.06 110.45 5.39 4 6 7 12 19 21 22 30 46 58
        4 8 12 13 16 22 30 36 44 56
2_6 56.38 102.26 13.51 4 5 10 19 22 25 40 62 80 90
        4 9 13 16 23 36 50 58 68 94
2_104 64.22 107.73 17.56 4 10 17 30 52 72 108 130 167 208
        4 11 20 33 52 76 105 138 173 213
2_105 65.06 106.55 19.22 4 6 9 15 28 43 65 92 134 172
        4 7 11 20 31 47 74 99 133 196
2_76 68.64 110.29 20.21 4 9 16 25 38 58 87 124 165 209
        4 10 20 34 53 78 109 146 191 245
2_63 73.83 116.23 21.28 4 8 14 27 50 80 114 153 200 258
        4 11 23 39 62 93 130 174 223 275
2_9 73.85 127.41 13.56 4 6 8 14 20 30 45 54 73 98
        4 7 10 14 22 34 42 58 78 94
2_60 79.89 131.67 16.65 4 8 14 26 45 68 93 125 171 223
        4 11 22 35 52 76 109 148 189 232
2_80 87.12 142.73 16.21 4 9 17 29 48 70 100 138 175 222
        4 11 20 36 58 81 112 146 189 240
2_42 104.27 164.99 17.94 4 8 14 21 32 48 67 91 117 149
        4 10 18 28 42 59 80 105 134 168
2_4 107.62 186.37 6.48 4 5 8 16 18 24 36 48 63 72
        4 8 10 15 22 26 38 54 64 80
2_36 166.29 262.64 12.30 4 8 13 20 29 41 56 72 89 110
        4 9 16 24 33 44 58 76 97 120
2_69 189.35 292.92 14.38 4 8 17 29 46 68 91 117 154 184
        4 9 17 28 49 69 92 119 151 184

2.1. The feasibility factor

The well established relationship between framework density and calculated lattice energy (Foster et al., 2001[Foster, M. D., Bell, R. G. & Klinowski, J. (2001). Stud. Surf. Sci. Catal. 136, 266.], 2003[Foster, M. D., Delgado Friedrichs, O., Bell, R. G., Almeida Paz, F. A. & Klinowski, J. (2003). Angew. Chem. Int. Ed. 42, 3896-3899.]; Foster, Friedrichs et al., 2004[Foster, M. D., Friedrichs, O. D., Bell, R. G., Almeida Paz, F. A. & Klinowski, J. J. (2004). Am. Chem. Soc. 126, 9769-9775.]; Foster, Simperler et al., 2004[Foster, M. D., Simperler, A., Bell, R. G., Delgado Friedrichs, O., Almeida Paz, F. A. & Klinowski, J. (2004). Nature Mater. 3, 234-238.]; Simperler et al., 2004[Simperler, A., Foster, M. D., Bell, R. G. & Klinowski, J. (2004). J. Phys. Chem. B, 108, 869-879.]) was confirmed experimentally (Henson et al., 1994[Henson, N. J., Cheetham, A. K. & Gale, J. D. (1994). Chem. Mater. 6, 1647-1650.]) for known zeolites. Using the standard least-squares technique, a straight line was fitted to 145 data points obtained from minimizing quartz and all the known zeolite topologies in a purely siliceous form (Fig. 1[link]). We excluded the four non-silicate structure types which substantially deviate from the rest: WEI (calcium beryllophosphate), CZP (sodium zincophosphate), OSO (potassium berylosilicate) and RWY (gallium germanium sulfide). The line of best fit has the formula y = −1.4433x + 40.3904, where x is the framework density (FD) and y is ΔEquartz. The feasibility factor, ϑ, is then simply the dimensionless deviation of a data point (x1, y1) from the line of best fit, given by the vertical offset [\vartheta = \left| {1.4433x_1 + y_1 + 40.3904} \right| / 1.4433]. Being formally independent of the framework density, the feasibility factor ϑ is thus a convenient way of discriminating between candidate structures and can be compared with the values obtained from known zeolite structures. We minimized all the known zeolite topologies as silica polymorphs, regardless of the actual composition in which they occur. We believe that ϑ is a better gauge of the feasibility of the structure than ΔEquartz alone, as evidenced by the fact that seven of the ten lowest ϑ values in Table 1[link] belong to structures with known zeolite topologies. A ranking in order of ascending ΔEquartz would, in contrast, produce only four values. Virtually all of the topologies which are known in the form of silicates, aluminosilicates or aluminophosphates, including those with low levels of heteroatom substitution, have ϑ < 5. This reflects the similarity of the preferred geometry between (alumino)silicates and AlPOs. The highest values of ϑ are 5.03 for AFY (Co-AlPO-50), which has 19% framework cobalt, and 5.18 for AHT, only known as the thermally unstable material AlPO-H2. By analogy, we define structures with ϑ < 5 as feasible `conventional' zeolites, i.e. those for which natural zeolites along with high-silica and AlPO forms are known. Framework types with more `exotic' compositions have ϑ > 5. For example, the zincosilicates VNI, VSV and RSN have ϑ of 5.75, 6.07 and 6.09, respectively. Beryllosilicates, generally containing three rings, also have higher ϑ, e.g. LOV (6.51), NAB (10.99) and OSO (23.30), while the beryllophosphate weinebeneite has ϑ = 12.24 and the zincophosphate CZP ϑ = 20.92. We therefore propose that ϑ values up to 25 indicate that the topology may be feasible in the form of an `oxide' material. Above this, we note that for RWY, the only zeotype structure known solely as a framework sulfide, ϑ = 51.69. Many other compositions, such as metal-organic frameworks, are of course possible. This means that although a structure may be deemed highly unfeasible as a zeolite, it may exist in other chemical forms. Also, the precise value of ϑ will be an unreliable guide in the high region, since it is based only on a silica model. In order to gauge the feasibility of a particular topology in a different composition, it would be necessary to carry out separate series of computations, taking into account the actual composition.

[Figure 1]
Figure 1
Framework energy, EF (kJ mol−1), with respect to α-quartz, versus framework density, FD (Si atoms per 1000 Å3), for (a) and (b) all known zeolitic structure types; (c) and (d) hypothetical binodal zeolitic structures.

The Cerius2 software suite (Molecular Simulations Inc., 1999[Molecular Simulations Inc. (1999). Cerius2, Version 4.0. Molecular Simulations Inc., San Diego, USA.]) was used for visualizing and manipulating the structures and for calculating free volumes, space-group symmetry and other parameters. In addition to calculating the energetics of the hypothetical structures, it is important to compare the calculated values with the values for all known zeolite frameworks. Thus, all relevant properties were also calculated for the purely siliceous forms of all known zeolite topologies. Lattice energies were calculated relative to α-quartz, the most stable form of the mineral at ambient temperature.

The `available volume', defined as the difference between the volume of the unit cell and the effective volume of all the atoms, depends on the van der Waals radius used for each atom. `Occupiable volume' is the volume which can be occupied by a probe molecule with a given radius as it probes the surface of the structure. The `accessible volume' is determined by tracing out the volume by the centre of the probe molecule as it follows the structure contours, but with the extra requirement that the probe must enter the unit cell from the outside via sufficiently wide pores or channels. The accessible volume gives an indication of the space available within each structure for applications in molecular sieving and catalysis. The calculations of the accessible volume were performed using the Free Volume module of the Cerius2 package, which applies the Connolly (1985[Connolly, M. L. (1985). J. Am. Chem. Soc. 107, 1118-1124.]) method consisting of `rolling' a probe molecule with a given radius over the van der Waals surface of the framework atoms. We have used a probe molecule with a radius of 1.4 Å (such as water) and 1.32 and 0.9 Å for the radii of O and Si atoms, respectively. The void volume, enclosed within the Connolly surface, was calculated first. The accessible volume was then calculated by requiring the probe molecule to enter the unit cell from the outside.

3. Results and discussion

Of the 117 structures, eight could not be optimized, either because refinement was not possible or because of failure during minimization, usually resulting in loss of the original network topology. The remaining 109 structures are described below. For the most part, these minimized smoothly without any loss of symmetry, although there are a few whose low-energy symmetry is lower than that of the original space group. In these instances, the original space group is shown in parentheses in Table 2[link].

Table 2
Space groups and unit-cell dimensions of 109 hypothetical binodal zeolites, optimized as purely siliceous structures

Structure Space-group symbol Space-group number a (Å) b (Å) c (Å) α (°) β (°) γ (°)
2_4 Im[\bar 3]m 229 24.5550 24.5550 24.5550 90 90 90
2_5 Im[\bar 3]m 229 23.6252 23.6252 23.6252 90 90 90
2_6 Pn[\bar 3]m 224 19.2265 19.2265 19.2265 90 90 90
2_7 P[\bar 4]3m 215 14.0784 14.0785 14.0785 90 90 90
2_8 Im[\bar 3]m 229 29.9045 29.9046 29.9046 90 90 90
2_9 R[\bar 3]m 166 20.6871 20.6871 10.7470 90 90 120
2_10 Im[\bar 3]m 229 30.8610 30.8610 30.8610 90 90 90
2_12 I41/amd 141 15.1769 15.1769 17.2033 90 90 90
2_13 Fm/m 225 17.4521 17.4521 17.4521 90 90 90
2_14 I4/mmm 139 11.5929 11.5929 12.9540 90 90 90
2_15 Pm/n 223 13.6367 13.6367 13.6367 90 90 90
2_16 P42/mnm 136 10.2171 10.2171 16.3964 90 90 90
2_17 Im[\bar 3]m 229 31.6666 31.6666 31.6666 90 90 90
2_18 Im[\bar 3]m 229 18.1332 18.1332 18.1332 90 90 90
2_19 Im[\bar 3]m 229 26.0211 26.0211 26.0211 90 90 90
2_20 Pm[\bar 3]m 221 17.5191 17.5191 17.5191 90 90 90
2_21 Fm[\bar 3]m 225 31.5256 31.5256 31.5256 90 90 90
2_22 Pm[\bar 3]m 221 19.5087 19.5087 19.5087 90 90 90
2_23 Fm[\bar 3]m 225 32.8255 32.8255 32.8255 90 90 90
2_24 Pm[\bar 3]m 221 14.6896 14.6986 14.6896 90 90 90
2_25 Fm[\bar 3]m 225 30.1897 30.1897 30.1897 90 90 90
2_26 Fm[\bar 3]m 225 30.2151 30.2151 30.2151 90 90 90
2_27 Fm[\bar 3]m 225 27.5480 27.548 27.5480 90 90 90
2_28 Im[\bar 3] 204 16.0155 16.0155 16.0155 90 90 90
2_29 Fd[\bar 3]c 228 29.9172 29.9172 29.9172 90 90 90
2_30 Pn[\bar 3]m 224 15.3879 15.3879 15.3879 90 90 90
2_31 R[\bar 3]m (Fd[\bar 3]m) 166 (227) 26.3028 26.3028 64.9314 90 90 120
2_32 Im[\bar 3]m 229 24.9270 24.9270 24.9270 90 90 90
2_33 R[\bar 3]m 166 13.1741 13.1741 32.3570 90 90 120
2_34 Im[\bar 3]m 229 25.9183 25.9183 25.9183 90 90 90
2_35 Fd[\bar 3]m 227 30.8413 30.8416 30.8413 90 90 90
2_36 Pm[\bar 3]m 221 19.8342 19.8342 19.8342 90 90 90
2_37 Pn[\bar 3]m 224 19.6887 19.6887 19.6887 90 90 90
2_39 P1 (Im[\bar 3]m) 1 (229) 21.5940 21.6260 21.6370 90.1262 89.9558 90.0775
2_40 R[\bar 3]m 166 13.2084 13.2084 23.8034 90 90 120
2_41 Im[\bar 3]m 229 25.2127 25.2127 25.2127 90 90 90
2_42 Im[\bar 3]m 229 20.0209 20.0209 20.0209 90 90 90
2_43 Fm[\bar 3]m 225 25.9040 25.9040 25.9040 90 90 90
2_44 P[\bar 4]3m 215 11.3123 11.3124 11.3124 90 90 90
2_45 Pm[\bar 3]m 221 17.6786 17.6786 17.6786 90 90 90
2_46 Pn[\bar 3]m 224 15.4919 15.4919 15.4919 90 90 90
2_47 Pm[\bar 3]m 221 19.0003 19.0003 19.0003 90 90 90
2_48 Pm[\bar 3]n 223 16.7613 16.7613 16.7613 90 90 90
2_50 P[\bar 3]1m 162 12.3351 12.3351 8.6007 90 90 120
2_51 P63/mcm 193 12.3340 12.3340 17.2043 90 90 120
2_52 Pn[\bar 3]m 224 16.7584 16.7584 16.7584 90 90 90
2_53 Pn[\bar 3]m 224 18.5448 18.5448 18.5448 90 90 90
2_54 I4/mmm 139 14.8438 14.8438 20.0782 90 90 90
2_55 P63/mcm 193 13.7562 13.7562 19.2727 90 90 120
2_56 P[\bar 3]1m 162 13.7003 13.7003 9.2686 90 90 120
2_57 I4/mmm 139 14.0993 14.0993 15.5435 90 90 90
2_58 I4/mmm 139 13.5265 13.5265 20.6385 90 90 90
2_59 P4/nmm 129 13.5133 13.5133 10.3319 90 90 90
2_60 Im[\bar 3]m 229 17.9320 17.9320 17.9320 90 90 90
2_61 I41/amd 141 16.3875 16.3875 10.9441 90 90 90
2_62 Pm[\bar 3]m 221 14.5985 14.5985 14.5985 90 90 90
2_63 I[\bar 4]m2 119 12.6142 12.6142 9.4486 90 90 90
2_64 Pm[\bar 3]m 221 18.3419 18.3419 18.3419 90 90 90
2_65 Ia[\bar 3] 206 18.0311 18.0311 18.0311 90 90 90
2_67 Ia[\bar 3]d 230 19.9520 19.9520 19.9520 90 90 90
2_68 I41/amd 141 15.1043 15.1043 10.7274 90 90 90
2_69 R[\bar 3]m 166 16.6853 16.6853 20.9554 90 90 120
2_70 Pm[\bar 3]m 221 13.8940 13.8940 13.8940 90 90 90
2_71 P213 198 14.0298 14.0298 14.0298 90 90 90
2_73 Fd[\bar 3]m 227 29.6184 29.6184 29.6184 90 90 90
2_74 Fm[\bar 3]m 225 30.4872 30.4872 30.4872 90 90 90
2_75 Fd[\bar 3]m 227 25.9368 25.9368 25.9368 90 90 90
2_76 P[\bar 4]3m 215 13.3418 13.3418 13.3418 90 90 90
2_77 Pn[\bar 3]m 224 15.5787 15.5787 15.5787 90 90 90
2_78 P63/mmc 194 13.5479 13.5479 19.3503 90 90 120
2_79 Im[\bar 3]m 229 21.2424 21.2424 21.2424 90 90 90
2_80 Im[\bar 3]m 229 18.0938 18.0938 18.0938 90 90 90
2_81 I4/mmm 139 13.9993 13.9993 10.2051 90 90 90
2_82 Pn[\bar 3]m 224 15.8240 15.8240 15.8240 90 90 90
2_83 R[\bar 3]m 166 12.9786 12.9786 22.4610 90 90 120
2_84 P63/mmc 194 12.9887 12.9887 14.9436 90 90 120
2_85 I4/mmm 139 13.2812 13.2812 15.4875 90 90 90
2_86 P[\bar 3]m1 164 12.7931 12.7931 10.0490 90 90 120
2_87 P63/mmc 194 12.7982 12.7982 20.0706 90 90 120
2_88 P4/nmm 129 13.5200 13.5199 7.6115 90 90 90
2_89 P63/mmc 194 12.9122 12.9122 15.1051 90 90 120
2_90 R[\bar 3]m 166 12.7260 12.7259 30.3678 90 90 120
2_91 I4/mcm 140 13.9768 13.9768 19.1953 90 90 90
2_92 P4/nbm 125 13.9490 13.9490 9.2497 90 90 90
2_93 Im3m 229 17.2697 17.2697 17.2697 90 90 90
2_94 C2 (Fd[\bar 3]m) 5 (227) 29.4382 29.3841 20.7989 90 90 90
2_95 I4/mmm 139 12.2058 12.2058 19.1794 90 90 90
2_96 Im[\bar 3] 204 16.4413 16.4413 16.4413 90 90 90
2_97 Pm3n 223 16.1973 16.1973 16.1973 90 90 90
2_98 P4132 213 11.5642 11.5642 11.5642 90 90 90
2_99 Pm3 200 12.8171 12.8171 12.8171 90 90 90
2_100 I[\bar 4]m2 119 12.8690 12.8691 7.6292 90 90 90
2_101 Fm3m 225 13.4592 13.4592 13.4592 90 90 90
2_102 R[\bar 3]m 166 12.6141 12.6141 16.6417 90 90 120
2_103 P63/mcm 193 13.6152 13.6152 13.9813 90 90 120
2_104 P[\bar 3]1m 162 13.4810 13.4810 6.5129 90 90 120
2_105 P1 (R[\bar 3]c) 1 (167) 10.6747 16.8789 16.9018 67.8079 86.0781 86.1532
2_106 P63/mmc 194 12.4093 12.4093 15.4571 90 90 120
2_107 P63/mmc 194 12.3972 12.3972 10.3205 90 90 120
2_108 R[\bar 3]m 166 12.4186 12.4186 30.8573 90 90 120
2_109 Pn[\bar 3]m 224 17.2562 17.2562 17.2562 90 90 90
2_110 R[\bar 3]m 166 12.4060 12.4060 23.1948 90 90 120
2_111 P4132 213 11.6324 11.6324 11.6324 90 90 90
2_112 P213 198 13.7019 13.7019 13.7019 90 90 90
2_113 Fddd 70 7.4170 13.5469 23.6645 90 90 90
2_114 I4/mcm 140 13.7055 13.7055 14.1225 90 90 90
2_115 P4/nbm 125 13.4128 13.4128 6.8567 90 90 90
2_116 I432 211 16.4510 16.4519 16.4510 90 90 90
2_117 P42/mnm 136 7.1839 7.1839 12.4079 90 90 90

Figs. 1[link](a) and (b) show plots of framework energy relative to α-quartz, EF, versus the framework density, FD, for all known zeolites. Relative framework energies of the hypothetical binodal frameworks range from 11.15 kJ mol−1 (structure 2_114) to as much as 515.43 kJ mol−1 (structure 2_72) (Fig. 1[link]c). Fig. 1[link](d) plots the framework energy versus the framework density for the hypothetical binodal structures with energies below 30 kJ mol−1, the range considered as the most `desirable', and with framework densities typical of the known zeolites.

Fig. 2[link](a) shows a plot of accessible volume versus framework density for the known structural types and Figs. 2[link](b) and (c) the corresponding plot for hypothetical binodal zeolites. Low framework density structures are of particular interest as they have very high accessible free volumes. Of the structures with framework densities below 18 Si atoms/1000 Å3, structures 2_57, 2_58, 2_59, 2_82, 2_85, 2_86, 2_87, 2_91, 2_95, 2_96, 2_102, 2_103, 2_106, 2_108, 2_109, 2_110, 2_112, 2_113, 2_114 and 2_117 are energetically stable (Fig. 1[link]c). Many hypothetical structures have dense frameworks, which are largely inaccessible. However, as many known zeolite topologies have low accessible volumes (Fig. 2[link]a), a structure cannot be ruled out as a feasible topology on the basis of a low accessible free volume, even though it may be of no interest to scientists studying sorption, ion exchange or catalysis. A plot of framework density for known zeolites and for dense silicate frameworks against the size of the smallest ring in the structure (Brunner & Meier, 1989[Brunner, G. O. & Meier, W. M. (1989). Nature, 337, 146-147.]) shows that very open frameworks with low FD have the largest number of four- and three-membered rings and that there is a gap in FD between compact minerals, such as quartz and tridymite, and the zeolite frameworks. The lower boundary of FD for known zeolites is from about 11 tetrahedral atoms per 1000 Å3 in materials with four-membered rings to about 17 tetrahedral atoms in materials with 5+ rings, where the plus sign signifies that some tetrahedral atoms are associated only with the larger rings.

[Figure 2]
Figure 2
Accessible volume (Å3 per Si atom) versus framework density for (a) all known zeolitic structure types; (b) hypothetical binodal zeolitic structures; (c) structures with accessible volumes below 40 Å3 per Si atom.

Fig. 3[link] plots the framework energy with respect to α-quartz for the known zeolitic structures and the hypothetical binodal structures versus the accessible volume, thus combining information contained in Figs. 1[link] and 2[link]. Structures of the greatest practical interest are those with low energies and large volumes (see inset in Fig. 3[link]b). Full details of all the structures have recently been published elsewhere (Foster, Simperler et al., 2004[Foster, M. D., Simperler, A., Bell, R. G., Delgado Friedrichs, O., Almeida Paz, F. A. & Klinowski, J. (2004). Nature Mater. 3, 234-238.]). Crystallographic CIF files from which powder X-ray diffraction patterns can be easily calculated are given as supplementary information.1

[Figure 3]
Figure 3
Framework energy with respect to α-quartz versus accessible volume (Å3 per Si atom) for (a) all known zeolitic structure types; (b) hypothetical binodal zeolitic structures. Hypothetical structures of particular chemical interest are identified in the inset.

The structures have been divided into 15 families, the members of which share a common building scheme or structural unit. As explained above, the building units used do not necessarily equate to SBUs or PerBUs in the strict sense. We also note that the allocation of a structure to a certain family is not unequivocal: there are several structures which could equally well be assigned to more than one family. The order in which the various families are discussed is dictated by the feasibility factor of the most feasible structure in that family. Selected members of a particular family are shown in Figs. 4–9[link][link][link][link][link][link] in the same order, whereas a full description of all members is available in the electronic supplement. The more feasible structures will thus be encountered earlier in the following sections, with the exception of the `orphan family' which contains several chemically feasible members. In describing the various structures, we use standard nomenclature from the zeolite literature. For instance, `D6R' refers to a double six-ring unit. In describing polyhedral cages or units, the [MxNy] system adopted by Smith (1988[Smith, J. V. (1988). Chem. Rev. 88, 149-182.]) is also used, where (M, N) is the number of edges defining a given face and (x, y) is the number of times that face appears in the polyhedron. Results are also tabulated in Table 1[link] (in order of ϑ) and Table 2[link] (in numerical order of the structures). Table 1[link] gives ϑ, ΔEquartz, the framework density and the coordination sequences of the T sites. Table 2[link] gives the crystallographic data.

[Figure 4]
Figure 4
Molecular graphic illustrations of some structures from the ABC-6 and [3256] families.
[Figure 5]
Figure 5
Molecular graphic illustrations of some structures from the AWW and supercage families.
[Figure 6]
Figure 6
Molecular graphic illustrations of structures from the SAS, [4258] and AST families.
[Figure 7]
Figure 7
Molecular graphic illustrations of some structures from the D8R family, AFY structures and the D6R family.
[Figure 8]
Figure 8
Molecular graphic illustrations of structures from the three- and four-ring family, the D3R family and the three-ring family.
[Figure 9]
Figure 9
Molecular graphic illustrations of structures from the [34] family and of some of the orphan structures.

3.1. ABC-6 family

Of the 109 refinable binodal structures, 13 can be described using the building scheme for the ABC-6 family (van Koningsveld, 2004[Koningsveld, H. van (2004). Schemes for Building Zeolite Structure Models, in Database of Zeolite Structures; https://topaz.ethz.ch/IZA-SC/ModelBuilding.htm .]). Six of these are known frameworks: 2_89 = ERI, 2_84 = EAB, 2_90 = SAT, 2_83 = LEV, 2_107 = LOS and 2_78 = AFX. The PerBU of the family consists of a hexagonal array of isolated six-membered rings, which are related by pure translations along [100] and [010]. A three letter code (A, B and C) gives the connection mode of the layers along [001]. The six-membered rings of A are centred at (0,0), while layer B is shifted by (+2/3a,+1/3b) and layer C by (+1/3a,+2/3b). The connection between six-rings in adjacent layers is invariably via four-rings. In the (001) projection, there is a close similarity between all the structures of this family, epitomized by that of 2_106 (Fig. 4[link]a), where the hexagonal array of six-rings, interspersed by four-rings, is clearly evident. Each structure is uniquely characterized by its [001] stacking sequence and the stacking sequences of the 13 structures (in order of their `thermodynamic feasibility') are ABBACBBC(A) for 2_87, ACAABA(A) for 2_89 (ERI), ACCABB(A) for 2_84 (EAB), AABABBCBCCAC(A) for 2_90 (SAT), ABBC(A) for 2_86, AACBBACCB(A) for 2_83 (LEV), ABAC(A) for 2_107 (LOS), ACABABCBC(A) for 2_110, ACABCB(A) for 2_106, ACACBABACBCB(A) for 2_108, ACCAABBA(A) for 2_78 (AFX), ACCCBBBAA(A) for 2_40, and AAAACCCCBBBB(A) for 2_33. 2_87, 2_89, 2_84, 2_107, 2_106 and 2_78, which have hexagonal symmetry, space group P63/mmc, while 2_90, 2_83, 2_110, 2_108, 2_40 and 2_33 (all R[\bar 3]m) and 2_86 (P[\bar 3]m1) are trigonal. The ABC-6 structures, both known and hypothetical, are among the most thermodynamically favoured as silica polymorphs and, as can be seen from Table 1[link], have high chemical feasibilities (0.08 < ϑ < 0.98), except for 2_40 and 2_33 which have ϑ of 14.97 and 20.83, respectively. The ABC-6 structures may also be thought of in terms of stacks, or chains, of cages linked parallel to the [001] direction through six-rings and, depending on symmetry, there are either one or two distinct types of stack. For example, the most feasible structure 2_87 (Figs. 4[link]b and c) contains both the [496283] gmelinite cages and [496883] EAB cages, which alternate along (001) (Fig. 4[link]c). Parallel to these are stacks of alternating sodalite cages and double six-rings (D6R). The structure 2_40, which is less dense, is quite interesting as it has large cages linked through elongated 10- and 12-rings, respectively (Fig. 4[link]d and e).

3.2. [3256] family

Four structures (2_103, 2_55, 2_56 and 2_104) are built up from columns of [3256] polyhedral units (Fig. 4[link]g) arranged hexagonally so as to give 12-membered ring channels along the c direction (Fig. 4[link]f). The [3256] units are linked by sharing their `terminal' three-membered ring windows (Fig. 4[link]h) in structures 2_103 and 2_104, while in structures 2_55 and 2_56 these small cage units are separated by a [3243] unit (i.e. a trigonal prism or D3R; Fig. 4[link]i). None of these four are known structures, although 2_103 is expected to be highly chemically feasible (ϑ = 0.30). Three further members of this family, 2_112, 2_102 and 2_80, also contain the [3256] unit (Fig. 4[link]g), but with different building patterns. For example, in 2_112 the [3256] units are linked via single oxygen bridges, while in 2_102 and 2_80 the units are linked via double oxygen bridges (Fig. 4[link]j). Both 2_112 and 2_102 are highly feasible, with ϑ = 4.66 and 6.08, respectively, as opposed to 2_80 which has ϑ = 87.12.

3.3. AWW family

The nine structures which we describe as members of the `AWW family' share a small [4664] cage as the common building unit (Fig. 5[link]a). Six of these structures, 2_88 (which has the actual AWW topology), 2_85, 2_59, 2_58, 2_100 and 2_63, are tetragonal, with columns of larger cages parallel to [001] and having eight-ring windows as the maximum pore diameter in that direction. The archetypal example is the AWW [486882] cage (Fig. 5[link]b), which stacks through shared eight-rings. Fig. 5[link](c) shows the [001] projection of 2_85, which is typical of this series.

Depending on the linkage pattern of the [4664] building units along [001], different types of large cage are defined. AWW, 2_59, 2_100 and 2_63 have only one type of eight-ring channel cage each, whilst in 2_85 two alternating types of larger cage are thus defined, [4861282] and [486482] (also found in the structures SAS and ATN respectively). Structures AWW, 2_58, 2_59 and 2_85 fall within the feasible range, with ϑ = 0.32–6.04, while 2_100 (ϑ = 22.42) and 2_63 (ϑ = 73.83) are less feasible.

There are also three cubic structures, which contain the same building unit (2_109, 2_97 and 2_60), with 2_109 being by far the most feasible of the three (ϑ = 5.67). For these three structures, the [4664] units alternate with sodalite or beta cages in a chain along [100]. Structure 2_97 (ϑ = 16.99) falls within the extended range of oxide feasibility, whereas 2_60 (ϑ = 80.04) does not.

3.4. Supercage family

There are 11 structures which contain sodalite or LTA (alpha) cages linked by smaller prismatic units in such a way that it also generates much larger cages. All the structures have cubic or pseudo-cubic symmetry, as can be seen in the [100] view of 2_45 (Fig. 5[link]e). Structure 2_74 has the framework of the mineral tschörtnerite (TSC) with both sodalite and alpha cages linked via D6R (Fig. 5[link]f), thus defining the large TSC cage (Fig. 5[link]g). The remaining structures will be discussed with respect to structural similarities and not by their chemical feasibility factor, ϑ.

Structures 2_35 (Fig. 5[link]h) and 2_31 are composed of sodalite cages linked tetrahedrally via D6R and thus form a series together with the FAU structure. 2_35 and 2_31 are both feasible as oxide materials, with ϑ of 10.69 and 13.16, respectively. 2_45 (Fig. 5[link]i) and 2_36 can similarly be imagined as belonging to a series with RHO, a structure formed by alpha cages linked octahedrally via D8R. Both have Pm[\bar 3]m symmetry and 2_45 is relatively feasible (ϑ = 12.91). 2_24 (Fig. 5[link]j) and 2_20 are related to the LTA structure, since they can be generated by linking sodalite cages and D4R. They also have the same supercages as 2_45 and 2_36 and similar ϑ of 13.28 and 16.11, respectively. Structures 2_27 (Fig. 7[link]k) and 2_21 can also be considered part of a series with LTA, except in this case it is the alpha cages which are retained and the linkages between them expanded. The final pair, 2_39 (Fig. 5[link]l) and 2_32, form a series derived from KFI, containing alpha cages which are connected via shared D6R and are replaced by stacks of two and three D6R.

3.5. SAS family

These structures are analogous to the AWW family as they contain stacks of large cages linked unidirectionally by eight-rings. Fig. 6[link](a) shows the [001] projection of structure 2_54, typical of all four tetragonal structures belonging to this family and having I4/mmm space-group symmetry [2_54, 2_57, 2_81 (SAS) and 2_95]. The basic building units may be thought of as smaller polyhedra arranged in parallel chains: in the case of 2_81 the basic units are D6R hexagonal prisms, which form a chain by sharing four-rings, 2_95 is a highly feasible (ϑ = 0.93) structure in which [4454] units are linked into chains via four-rings (Fig. 6[link]b); in 2_57 an additional D4R is interposed between the alternating D6R and 2_54 is built analogously from chains of alternating D8R and D4R. Aside from SAS and 2_95, both 2_54 and 2_57 are also quite feasible as zeolites (ϑ = 3.18 and 5.51, respectively).

3.6. [4258] family

These structures have a small [4258] cage as the building unit (Fig. 6[link]d). In four of the structures, these units are linked into chains through the four-rings which cap the cages. The structures are tetragonal with [4258] chains running along [001] and have large cages accessible through eight-rings. The projection of 2_91 along [001] is typical of this family (Fig. 6[link]c). Structure 2_91 is the most feasible of these structures (ϑ = 0.95) and has [4258] cages linked through D4R, with a chain repeat motif of two cages and two D4R. In 2_114, another highly feasible structure with ϑ = 2.17, the cages are directly linked through a shared four-ring. Structures 2_92 and 2_115 are analogous to structures 2_91 and 2_114, respectively, but with only half the chain repeat distance. Both structures are far less feasible, as is a fifth structure, 2_116 (Figs. 6[link]e and f), in which the [4258] units are linked into chains via pairs of T—O—T linkages (Fig. 6[link]f). In the latter, the chains are interconnected so as to run in all three directions of the cubic lattice and the structure also contains sodalite cages, each of which shares its four-ring windows with [4258] units.

3.7. AST family

Structure 2_101 (Fig. 6[link]gi) is topologically identical to the known zeolite AST (AlPO-16).33,34 The structure contains the characteristic [46610] cages (Fig. 6[link]i), but may also be thought of in terms of D4R units connected through O—T—O bridges (Fig. 6[link]h). In 2_73 the D4R connect through single oxygen bridges and, apart from containing sodalite cages, the structure also possesses large tetrahedral cages with 12-ring apertures. Structure 2_61 is tetragonal containing cages with oval-shaped ten-rings as their largest apertures. Topologically, 2_13 (Figs. 6[link]j and l) is a variation of the AST structure in which those T atoms which do not form part of D4R are replaced by the [34] tetrahedra of T sites, a structural feature not found in aluminosilicate zeolites, although present, for instance, in the zeotypic sulfide RWY.

3.8. D8R family

This family is formed by four structures which contain the double eight-ring (D8R) as a structural unit. Structure 2_47 has a cubic structure in which the building unit may be thought of as a D8R with four D4R attached to alternate four-ring faces (Fig. 7[link]a). The units do not link directly to one another, but are arranged so as to define the large [42468818] (TSC) cages (Fig. 7[link]b). Structures 2_19 and 2_17 form part of a homologous series of structures, together with the uninodal structure 1_11 (Foster et al., 2003[Foster, M. D., Delgado Friedrichs, O., Bell, R. G., Almeida Paz, F. A. & Klinowski, J. (2003). Angew. Chem. Int. Ed. 42, 3896-3899.]), one of the nine simple uninodal tilings. The latter structure has a body-centered cubic framework based on chains of D8R and D4R, and 2_19 has the same structure, except that the D4R in 1_11 are replaced in 2_19 by pairs of face-sharing D4R (Fig. 7[link]c) and in 2_17 by groups of three D4R. The more complex 2_34 structure also contains the D8R/D4R units, but with the addition of [4664] AWW cages forming large cages with 12-rings as the maximum aperture (Fig. 7[link]d). Topologically, the tile which corresponds to this cage is the largest among this set of binodal frameworks, with 74 faces, 144 vertices and 216 edges. Structure 2_34 shares the space group Im[\bar 3]m with both 2_19 and 2_17. Structure 2_47 is thermodynamically feasible (ϑ = 3.02), while 2_17 and 2_19 have ϑ = 13.96 and 13.39, respectively, despite having extremely low framework densities of 8.17 and 6.05T per 1000 Å3, respectively.

3.9. AFY family

Structure 2_50 is topologically identical to the known structural type AFY (AlPO-50). The secondary building unit of this family is a D4R, which in AFY form hexagonal layers (Fig. 7[link]e) and are tilted with respect to the (001) plane. These layers then repeat through simple translation along c, most clearly seen in the (120) projection (Fig. 7[link]f; van Koningsveld, 2004[Koningsveld, H. van (2004). Schemes for Building Zeolite Structure Models, in Database of Zeolite Structures; https://topaz.ethz.ch/IZA-SC/ModelBuilding.htm .]; Baelocher & McCusker, 2004[Baerlocher, C. & McCusker, L. B. (2004). https://www.iza-structure.org/databases .]). If, instead, the layers alternate in orientation by means of a mirror plane (i.e. ABA rather than AA), the hypothetical framework 2_51 is formed. Both have low ϑ values: 5.03 and 5.18 for 2_50 and 2_51, respectively, making 2_51 virtually as feasible as AFY.

3.10. D6R family

This family comprises seven structures (2_6, 2_30, 2_53, 2_75, 2_76, 2_77 and 2_82) which have in common D6R hexagonal prisms as building units. These structures are all cubic, space group Pn[\bar 3]m, with the exception of 2_76 and 2_75, for which D6R (i.e. 6–6) may be strictly defined as a secondary building unit. The first five members of the group may be thought of in terms of chains running along [110] in which the D6R are linked by various combinations of rings. In the most feasible member of the family, 2_53 (ϑ = 5.11), the link unit includes D4R, giving rise to the characteristic motif shown in Fig. 7[link](g), where four D6R are connected to a single D4R. This structure also contains FAU supercages linked via the [41886122] cages (Fig. 7[link]h). Structure 2_82 is quite similar to 2_53, whereas in 2_77 the D6R chains are linked by units of three four-rings and in 2_30 a spiro-5 unit links the D6R into chains. Structure 2_6 also contains three-rings linked into [34] tetrahedra which connect the D6R. Finally, structures 2_75 and 2_76 are the `odd ones' of the family since it is not possible to describe them using the D6R chain model. Structure 2_75 is very unusual as it contains both `regular' and flattened sodalite cages connected through six-rings (Fig. 7[link]i). Structure 2_76 contains (differently) distorted beta cages as well as larger cages accessible through both approximately planar six-rings and highly curved eight-rings. Structures 2_75, 2_6 or 2_76 are not expected to be chemically feasible.

3.11. Three- and four-ring family

These eight structures are grouped together because they contain both three- and four-membered rings, although in other ways they are fairly different. Seven structures are cubic and five have framework densities lower than 14 T per 1000 Å3. Structure 2_99, the most feasible structure of this family with ϑ = 10.53, can be described as a network of corner-sharing three- and four-rings, part of which is the unit shown in Fig. 8[link](a). Three types of cages are found, one of which is the [3886] (truncated cube, Fig. 8[link]b). The somewhat similar 2_62, which has ϑ = 10.97, also exhibits the truncated cube cage. Structure 2_68 has a low framework density of 13.08 T per 1000 Å3 and ϑ = 13.82. Structures 2_70 and 2_93 have similar framework densities to that of 2_68 (13.42 and 13.98, respectively) and ϑ = 14.33 and 28.25, making these three structures interesting candidates as zeotypes. Structure 2_93 contains [3464] cages, i.e. truncated tetrahedra (Fig. 8[link]c), which link through shared three-rings to form a body-centred cubic structure. Structures 2_18, 2_28 and 2_5 have much lower framework densities (10.06, 11.69 and 7.28, respectively) than conventional zeolites, and are thus much less feasible as zeotype materials.

3.12. [3243] D3R family

The common feature is a trigonal prism (a [3243] unit) and we have assigned nine structures to this family. As in the previous family, many are of interest due to their low density, with the presence of small polyhedra being compensated by large supercages. While we believe that none is feasible in a traditional zeolite or AlPO composition, they may be of interest in several areas of chemistry, for instance if it were possible to form the D3R unit as a precursor. All the structures are cubic and have at least m[\bar 3]m symmetry. Structure 2_43 (Figs. 8[link]df) is the most feasible (ϑ = 11.62) and has D3R units attached to [3464] truncated tetrahedra to form tetrahedral units (Fig. 8[link]e). `Truncated cube' cages are present, as are the large [42468818] cages shown in Fig. 8[link](f). In 2_64 the D3R are also attached to truncated cube cages, but the structure additionally contains alpha and [42468818] tschörtnerite (TSC) cages. Structure 2_23 has beta cages linked via D3R–four-ring–D3R bridging units and 2_26 also has the same unit of two D3R linked though a four-ring (as do 2_25 and 2_22), with alpha cages present. Structure 2_25 has a pore system connected through 12-ring apertures and contains, besides FAU supercages and LTA alpha cages, the large [42486128] cages found in the RWY structure. Structure 2_41 is similar to 2_43, as the D3R form an alternating network with truncated tetrahedra (as in Fig. 8[link]e). Structure 2_22 is also of very low density (FD = 9.70 T per 1000 Å3) and has the D3R connected so as to define D8R. Finally, 2_4 and 2_8 are among the least dense of all the binodal simple tile structures, with FD of 5.39 and 6.48 T per 1000 Å3, respectively. The basic building unit of 2_8 is two D3R stacked with an intervening D4R (Fig. 8[link]g). In 2_4 the intermediate unit is absent and D3R units join directly through a shared four-ring. In both cases, very open cavity systems are constructed by connection of these units (Fig. 8[link]h).

3.13. Three-ring family

This family of eight structures is characterized by the presence of three-rings. Five structures contain pairs, or longer chains, of three-rings which share one T atom and therefore contain the spiro-5 unit (Baerlocher et al., 2001[Baerlocher, C., Meier, W. M. & Olson, D. H. (2001). Atlas of Zeolite Structure Types (updates at https://www.iza-structure.org/ ), 5th ed. London: Elsevier.]). Two of the structures also contain four-rings. As expected, several of the structures are of low density, but none would be expected to be realisable as a conventional zeolite. In 2_71, the most feasible with ϑ = 17.07, three-rings themselves form rings of six (Fig. 8[link]i), with the structure also containing elongated cages having eight-rings as their largest pore. The basic unit of 2_69 is a pair of edge-sharing three-rings (or bridged four-ring, Fig. 8[link]j). These larger units then connect to define a hexagonal channel system. Structure 2_65 also contains loops of six three-rings, virtually identical in structure to those in 2_71. However, the structure is much more open (FD = 12.28, compared with 17.38 for 2_71), containing a three-dimensional network of 10- and 12-ring pores. Structure 2_44 is another very open structure (FD = 10.36), with a three-dimensional network of corner-sharing three-rings defining the small [3464] cages shown in Fig. 8[link](k), as well as large cavities linked through 12-rings. Structure 2_12 has unusual chains built up from pairs of edge-sharing three-rings and has large cross-linked channels extending in two dimensions, delineated by puckered 14-membered rings (Fig. 8[link]l). Structure 2_29 is an unusually complex cubic structure, with three- and four-rings linked together (Fig. 8[link]m): pairs of edge-sharing three-rings are formed (there are no spiro-5 units) and these pairs are further connected by distorted four-rings. Uniquely for this family, in 2_105 the three-rings do not directly link into chains or pairs through the sharing of T atoms, but rather connect through oxygen bridges to define five-rings. Finally, 2_9 has H-shaped building units in which four-rings share edges with pairs of three-rings (Fig. 8[link]n).

3.14. [34] family

The common feature of this family is a [34] unit, sometimes known as the `supertetrahedron' or `tetrahedron of tetrahedra'. This unit is unknown in zeolitic oxide materials, but is present in some sulfides, including the zeotypic RWY structure and the compound Na2Si2S5. Structure 2_16 (Figs. 9[link]a and b), one of the few structures containing seven-rings, is characterized by its [38427884] cage (Fig. 9[link]b). Each of the eight three-rings forms part of a [34] unit, shared with three other cages. This structure is the most feasible of this family, with ϑ = 36.19. Similarly, 2_14 has only one type of `larger' cage, [38426488], and the whole structure can be thought of in terms of the sodalite framework, but with one third of the T sites replaced by [34] supertetrahedra. Structure 2_15 is also related to the sodalite structure, although now with half of the original T sites replaced by the [34] units, creating [3126698] cages. Structure 2_10 can be derived from the RHO zeolite structure by replacement of all T sites by [34] tetrahedra. As a result, it possesses very large cages linked via double 16-membered rings (Fig. 9[link]c). Finally, structure 2_7, being the least dense of this family (FD = 8.60), has [3464] units (`truncated tetrahedra') linked via chains of four-rings and [34] units (Fig. 9[link]d). This very open cubic structure has 16-MR pores in all three dimensions.

3.15. Orphan structures

We show three selected structures out of the 12 which cannot be categorized in our `family' system.

  • Structure 2_96, a feasible zeolite structure (ϑ = 5.45), is unusual as it contains small [455262] cage units (Fig. 9[link]e) interconnected through shared four-rings to form a three-dimensional network (Fig. 9[link]f), thereby defining the [512620] cage which also appears in structure 2_97.

  • Structure 2_37 (Figs. 9[link]hj): the basic building unit is the D4R, which links via four-rings to create double 12-membered rings (Fig. 9[link]i), which are in turn linked into large [43684128] supercages with tetrahedral symmetry, with four puckered 12-rings and four 12-rings which are almost planar (Fig. 9[link]j). This cubic structure is quite open with FD = 12.58 T per 1000 Å3, but is of intermediate feasibility (ϑ = 18.50).

  • Structure 2_94 (Figs. 9[link]k and l) contains [3464] truncated tetrahedra, distorted sodalite cages, and larger cages with three- and six-rings (Fig. 9[link]l). The ideal symmetry of the structure is Fd[\bar 3]m. However, in silica form it appears highly strained in this symmetry, preferring to minimize in space group C2, giving rise to its somewhat distorted appearance.

4. Conclusions

We have evaluated and characterized 109 hypothetical zeolite structures, of which 98 do not correspond to known zeotype frameworks. Among these are many promising candidates for zeolite synthesis. Some of the most feasible as conventional aluminosilicates or AlPOs are those in the ABC-6 family, composed principally of four- and six-rings, although from the point of view of porosity, the more likely structures will be at best small-pore zeolites, having no aperture larger than the eight-ring. Other promising candidates come from structures which similarly have features in common with known zeolites, such as those in the AWW and SAS families (Figs. 5[link] and 6[link]), where cages stack through shared eight-rings. Again, four- and six-rings predominate, with the eight-ring being the limiting aperture in all cases, as it is for the more feasible structures in the [4256] family. At the other end of the scale, many very open structures also exist. These illustrate well the principle (Brunner & Meier, 1989[Brunner, G. O. & Meier, W. M. (1989). Nature, 337, 146-147.]) that less dense structures require a greater proportion of small (three- or four-membered) rings. Here, we can extend this to state that larger cavities also require the presence of much smaller cages. Hence, we find large-pore structures containing [34] units (Fig. 9[link]), double three-rings (Fig. 8[link]) and three-rings, as well as pairs and chains of three- and four-rings. In terms of aluminosilicate and aluminophosphate zeolites, these structural units, particularly those containing three-rings, are by and large disfavoured due to the strain imposed on the TO4 tetrahedra. In fact, it is apparent that feasibility decreases markedly as more three-rings are connected together with, for example, structures containing [34] units having higher values than those containing only spiro-5 units. The most viable three-ring structures are those in which the three-rings are isolated from one another. The best example is 2_103 which contains the [3256] unit (Fig. 4[link]g), reminiscent of the [314353] units in the MEI structure. Structure 2_103 is the most feasible large-pore zeolite among our 109 structures. Similarly, although four-rings are found in the most feasible structures, agglomerations of these units, obtained by stacking prismatic units such as D4R and D6R, result in decreasing likelihood (although individual D4R and D6R are tolerated, unlike D3R).

Having discounted many of the more open structures as potential zeolites on account of the presence of these small units, we do not exclude the possibility that these topologies could be possible in other chemical compositions where the local coordination environments are less constrained. Indeed, if we could construct units such as the D3R or the supertetrahedron as precursor species, many open framework architectures could be synthesized.

Supporting information


Computing details top

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
[Figure 4]
[Figure 5]
[Figure 6]
[Figure 7]
[Figure 8]
[Figure 9]
(2_10) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Im3mV = ? Å3
a = 30.86100 ÅZ = ?
b = 30.86100 Å? radiation, λ = ? Å
c = 30.86100 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Im3mV = ? Å3
a = 30.86100 ÅZ = ?
b = 30.86100 Å? radiation, λ = ? Å
c = 30.86100 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.388740.950490.23571
Si20.364020.883620.29377
O10.359170.934280.27725
O20.618730.000000.77745
O30.561000.061000.25000
O40.377070.916310.19606
O50.645720.145720.25000
O60.666000.128760.66600
(2_100) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, I4m2V = ? Å3
a = 12.86907 ÅZ = ?
b = 12.86907 Å? radiation, λ = ? Å
c = 7.62915 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, I4m2V = ? Å3
a = 12.86907 ÅZ = ?
b = 12.86907 Å? radiation, λ = ? Å
c = 7.62915 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.268430.375730.66505
Si20.381440.618560.00000
O10.655640.844360.25000
O20.343340.333210.81858
O30.692260.692260.50000
O40.272320.500000.62435
O50.353130.500000.98438
(2_101) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Fm3mV = ? Å3
a = 13.45924 ÅZ = ?
b = 13.45924 Å? radiation, λ = ? Å
c = 13.45924 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Fm3mV = ? Å3
a = 13.45924 ÅZ = ?
b = 13.45924 Å? radiation, λ = ? Å
c = 13.45924 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.250000.250000.25000
Si20.385580.114420.11442
O10.317930.182070.18207
O20.500000.138100.86190
(2_102) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, R3mV = ? Å3
a = 12.61409 ÅZ = ?
b = 12.61409 Å? radiation, λ = ? Å
c = 16.64170 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, R3mV = ? Å3
a = 12.61409 ÅZ = ?
b = 12.61409 Å? radiation, λ = ? Å
c = 16.64170 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.793050.206950.78819
Si20.589180.178350.05806
O10.791470.791470.50000
O20.533590.466410.12084
O30.767500.232500.69912
O40.527250.263630.07142
(2_103) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, P63/mcmV = ? Å3
a = 13.61516 ÅZ = ?
b = 13.61516 Å? radiation, λ = ? Å
c = 13.98130 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, P63/mcmV = ? Å3
a = 13.61516 ÅZ = ?
b = 13.61516 Å? radiation, λ = ? Å
c = 13.98130 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.461180.790850.75000
Si20.668300.539100.04416
O10.468540.140330.15828
O20.336480.780090.75000
O30.415560.584440.50000
O40.585190.792600.50000
O50.372540.372540.98395
(2_104) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, P31mV = ? Å3
a = 13.48100 ÅZ = ?
b = 13.48100 Å? radiation, λ = ? Å
c = 6.51286 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, P31mV = ? Å3
a = 13.48100 ÅZ = ?
b = 13.48100 Å? radiation, λ = ? Å
c = 6.51286 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.407080.814160.00000
Si20.533170.661090.59486
O10.461640.730820.00000
O20.395680.504940.17752
O30.579310.789660.50000
O40.408040.816080.50000
O50.371740.371740.47879
(2_105) top
Crystal data top
O2Siβ = 86.07812°
Mr = ?γ = 86.15317°
?, P1V = ? Å3
a = 10.67472 ÅZ = ?
b = 16.87892 Å? radiation, λ = ? Å
c = 16.90175 Å × × mm
α = 67.80785°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 86.07812°
Mr = ?γ = 86.15317°
?, P1V = ? Å3
a = 10.67472 ÅZ = ?
b = 16.87892 Å? radiation, λ = ? Å
c = 16.90175 Å × × mm
α = 67.80785°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.416670.666670.16998
Si20.105280.301890.83346
Si30.766320.966910.50123
Si40.420890.204150.14625
Si50.086830.870660.81340
Si60.749850.541060.48475
Si70.410700.189030.69840
Si80.072700.855950.36965
Si90.738960.521540.02869
Si100.579570.388220.82629
Si110.240850.062940.49218
Si120.902260.725670.16157
Si130.585750.847670.84833
Si140.255280.508380.51358
Si150.918500.176860.18045
Si160.597020.861130.28038
Si170.266170.526680.95119
Si180.935920.192690.60669
Si190.374950.323830.75045
Si200.033910.991070.42082
Si210.699540.653050.08896
Si220.371420.780770.99420
Si230.048230.424300.66098
Si240.712730.094140.33007
Si250.405750.018480.22854
Si260.075670.684760.89746
Si270.743370.351730.55674
Si280.465650.361830.58207
Si290.127900.030510.25386
Si300.794470.698830.92022
Si310.434960.113150.33385
Si320.096140.781480.00173
Si330.770130.440280.66814
Si340.445410.610620.02919
Si350.141840.259230.69030
Si360.804110.929180.35612
Si370.632440.717020.24162
Si380.306820.384850.90275
Si390.971240.047700.56792
Si400.632870.268160.99883
Si410.294810.946970.66639
Si420.956650.616170.33763
Si430.604220.031560.74757
Si440.265100.697080.42484
Si450.930190.362040.07948
Si460.541890.689280.40802
Si470.210050.351070.06841
Si480.881560.020280.73264
Si490.574040.919590.65964
Si500.233840.593350.32897
Si510.909890.249170.99130
Si520.554360.437050.96277
Si530.202640.114840.62711
Si540.868130.784600.29320
O10.410590.588670.12925
O20.107280.225840.79277
O30.766170.893160.45848
O40.400380.192710.24700
O50.058580.858130.91382
O60.727300.523500.58671
O70.416520.265660.60282
O80.084320.932800.27438
O90.746850.603490.93701
O100.437560.105510.14921
O110.106480.771930.81651
O120.768590.444440.48190
O130.405070.760010.09504
O140.078700.398420.76168
O150.744280.064940.43132
O160.411560.221190.77915
O170.070110.889140.44975
O180.735840.550760.11281
O190.583540.468500.85935
O200.241420.143470.52514
O210.901370.809510.19142
O220.597440.843350.75214
O230.272900.513120.41387
O240.935930.174420.08383
O250.582320.789150.37783
O260.246760.449790.04520
O270.915510.121460.70402
O280.564030.949910.83004
O290.231140.608900.50329
O300.889990.279050.16225
O310.584120.291930.90266
O320.251410.967760.56892
O330.919680.632490.23997
O340.595760.819990.20660
O350.275840.487920.87311
O360.934280.150370.53305
O370.570930.664310.18736
O380.254620.323490.84718
O390.918820.983600.51538
O400.545460.230450.08568
O410.211430.901260.75364
O420.871830.574850.42461
O430.522680.120310.72160
O440.179130.783800.40127
O450.854250.453440.05240
O460.301660.269890.11850
O470.970330.938770.78484
O480.631610.608240.46041
O490.311630.617740.23921
O500.004770.258690.90973
O510.666800.924970.57795
O520.258080.170630.68764
O530.921250.840600.35318
O540.596560.496940.01328
O550.428420.380650.80673
O560.087550.050040.47620
O570.752350.706610.14844
O580.467360.829290.91667
O590.139000.475880.58058
O600.803810.147450.25015
O610.492120.933650.24025
O620.155260.596210.91163
O630.836210.269520.56499
O640.709840.787040.87867
O650.382150.449520.53919
O660.045290.118550.20966
O670.692520.412200.75813
O680.348840.091190.42039
O690.008420.755640.08837
O700.750780.876880.29192
O710.402620.552860.97403
O720.088330.206670.62453
O730.484960.366260.67522
O740.145020.034800.34746
O750.808560.699920.01529
O760.355790.693290.97732
O770.034910.334370.64638
O780.697600.005520.31288
O790.425940.024390.31990
O800.099650.691820.98788
O810.760550.353610.65008
O820.526460.673870.31973
O830.200560.338830.97773
O840.865960.003260.64450
O850.659190.360100.00409
O860.312220.040630.67185
O870.977290.711240.33957
O880.594470.013060.66116
O890.258570.684320.33560
O900.921440.343280.99324
O910.254630.329150.68876
O920.916780.996780.35553
O930.579080.660230.02833
O940.232360.818890.00145
O950.912180.469120.66284
O960.577160.139350.33466
O970.260220.021590.20705
O980.929120.692780.87545
O990.598080.351120.53539
O1000.755250.714130.30048
O1010.427240.380930.96586
O1020.087660.047350.63288
O1030.766640.222410.98998
O1040.428160.900580.65815
O1050.089270.567650.33657
O1060.746360.027100.77664
O1070.406980.698490.45196
O1080.072380.355640.10992
(2_106) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, P63/mmcV = ? Å3
a = 12.40926 ÅZ = ?
b = 12.40926 Å? radiation, λ = ? Å
c = 15.45706 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, P63/mmcV = ? Å3
a = 12.40926 ÅZ = ?
b = 12.40926 Å? radiation, λ = ? Å
c = 15.45706 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.586640.919650.58300
Si20.252800.001530.25000
O10.546700.093410.40593
O20.000000.659190.50000
O30.667630.988990.66630
O40.433720.216860.42777
O50.107420.214830.75000
O60.869980.130020.75000
(2_107) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, P63/mmcV = ? Å3
a = 12.39718 ÅZ = ?
b = 12.39718 Å? radiation, λ = ? Å
c = 10.32054 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, P63/mmcV = ? Å3
a = 12.39718 ÅZ = ?
b = 12.39718 Å? radiation, λ = ? Å
c = 10.32054 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.918920.332060.25000
Si20.746560.000000.50000
O10.009640.675720.62471
O20.224170.775830.75000
O30.462290.924590.75000
O40.118110.236230.48402
(2_108) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, R3mV = ? Å3
a = 12.41855 ÅZ = ?
b = 12.41855 Å? radiation, λ = ? Å
c = 30.85728 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, R3mV = ? Å3
a = 12.41855 ÅZ = ?
b = 12.41855 Å? radiation, λ = ? Å
c = 30.85728 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.666100.584800.62520
Si20.665050.080820.45895
O10.545970.091930.04936
O20.780890.219110.03414
O30.646890.650350.58397
O40.655680.655680.00000
O50.774020.548030.20409
O60.672630.005960.16667
O70.537120.462880.20898
(2_109) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Pn3mV = ? Å3
a = 17.25621 ÅZ = ?
b = 17.25621 Å? radiation, λ = ? Å
c = 17.25621 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Pn3mV = ? Å3
a = 17.25621 ÅZ = ?
b = 17.25621 Å? radiation, λ = ? Å
c = 17.25621 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.077140.663000.45976
Si20.756120.501630.37322
O10.750000.437510.06249
O20.406990.880500.11950
O30.154290.653840.51213
O40.500000.000000.37170
O50.766750.923160.07684
O60.754950.075420.07542
O70.798490.003800.20151
(2_110) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, R3mV = ? Å3
a = 12.40595 ÅZ = ?
b = 12.40595 Å? radiation, λ = ? Å
c = 23.19481 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 120°
?, R3mV = ? Å3
a = 12.40595 ÅZ = ?
b = 12.40595 Å? radiation, λ = ? Å
c = 23.19481 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.748070.748070.00000
Si20.748400.746940.22165
O10.783890.216110.34379
O20.682750.668820.27831
O30.774750.549490.11515
O40.592080.796040.44379
O50.673390.666670.16667
(2_111) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, P4132V = ? Å3
a = 11.63239 ÅZ = ?
b = 11.63239 Å? radiation, λ = ? Å
c = 11.63239 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, P4132V = ? Å3
a = 11.63239 ÅZ = ?
b = 11.63239 Å? radiation, λ = ? Å
c = 11.63239 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.875000.772520.97748
Si20.827500.177260.02147
O10.962110.838280.64201
O20.782580.875000.96742
O30.966010.216790.01311
O40.664220.914220.62500
(2_112) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, P213V = ? Å3
a = 13.70190 ÅZ = ?
b = 13.70190 Å? radiation, λ = ? Å
c = 13.70190 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, P213V = ? Å3
a = 13.70190 ÅZ = ?
b = 13.70190 Å? radiation, λ = ? Å
c = 13.70190 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.037700.066170.20272
Si20.208550.868400.91167
Si30.566160.797280.03769
Si40.291450.631600.58833
O10.007920.154930.12940
O20.066950.111570.30639
O30.950470.992600.22009
O40.199160.915360.80436
O50.304350.800840.91536
O60.111570.806390.93305
O70.654930.870590.00792
O80.492610.779910.95047
(2_113) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, FdddV = ? Å3
a = 7.41702 ÅZ = ?
b = 13.54690 Å? radiation, λ = ? Å
c = 23.66447 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, FdddV = ? Å3
a = 7.41702 ÅZ = ?
b = 13.54690 Å? radiation, λ = ? Å
c = 23.66447 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.698520.462530.68821
Si20.500000.500000.10086
O10.824810.507080.64016
O20.231940.344880.18906
O30.750000.995860.75000
O40.500000.500000.67290
(2_114) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, I4/mcmV = ? Å3
a = 13.70551 ÅZ = ?
b = 13.70551 Å? radiation, λ = ? Å
c = 14.12245 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, I4/mcmV = ? Å3
a = 13.70551 ÅZ = ?
b = 13.70551 Å? radiation, λ = ? Å
c = 14.12245 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.348700.557280.00000
Si20.400590.261510.80067
O10.556020.624330.50000
O20.418450.282970.91017
O30.500000.231330.75000
O40.642320.642320.75000
O50.671410.828590.21090
(2_115) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, P4/nbmV = ? Å3
a = 13.41282 ÅZ = ?
b = 13.41282 Å? radiation, λ = ? Å
c = 6.85666 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, P4/nbmV = ? Å3
a = 13.41282 ÅZ = ?
b = 13.41282 Å? radiation, λ = ? Å
c = 6.85666 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.115650.115650.00000
Si20.393920.257230.38273
O10.866550.811690.81976
O20.000000.863400.00000
O30.139760.360240.63353
O40.687270.687270.50000
O50.500000.267190.50000
(2_116) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, I432V = ? Å3
a = 16.45100 ÅZ = ?
b = 16.45100 Å? radiation, λ = ? Å
c = 16.45100 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, I432V = ? Å3
a = 16.45100 ÅZ = ?
b = 16.45100 Å? radiation, λ = ? Å
c = 16.45100 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.506610.371410.76034
Si20.561920.333980.93621
O10.084320.923660.23154
O20.717750.500000.28225
O30.516190.374250.85891
O40.500001.000000.19981
O50.250000.898450.60155
O60.116030.883970.50000
(2_117) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, P42/mnmV = ? Å3
a = 7.18391 ÅZ = ?
b = 7.18391 Å? radiation, λ = ? Å
c = 12.40787 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, P42/mnmV = ? Å3
a = 7.18391 ÅZ = ?
b = 7.18391 Å? radiation, λ = ? Å
c = 12.40787 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.847540.847540.62703
Si21.000000.500000.75000
O11.000001.000000.66022
O20.351090.096600.32664
O30.171450.171450.50000
(2_12) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, I41/amdV = ? Å3
a = 15.17688 ÅZ = ?
b = 15.17688 Å? radiation, λ = ? Å
c = 17.20330 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, I41/amdV = ? Å3
a = 15.17688 ÅZ = ?
b = 15.17688 Å? radiation, λ = ? Å
c = 17.20330 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.250000.688900.37500
Si20.273170.600580.52420
O10.283640.627150.30268
O20.666960.249690.84646
O30.240570.500000.20104
O40.375700.875700.75000
(2_13) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Fm3mV = ? Å3
a = 17.45206 ÅZ = ?
b = 17.45206 Å? radiation, λ = ? Å
c = 17.45206 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Fm3mV = ? Å3
a = 17.45206 ÅZ = ?
b = 17.45206 Å? radiation, λ = ? Å
c = 17.45206 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.307430.692570.80743
Si20.588120.911880.58812
O10.356280.750000.75000
O20.359470.640530.85947
O30.393590.893590.50000
(2_14) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, I4/mmmV = ? Å3
a = 11.59288 ÅZ = ?
b = 11.59288 Å? radiation, λ = ? Å
c = 12.95395 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, I4/mmmV = ? Å3
a = 11.59288 ÅZ = ?
b = 11.59288 Å? radiation, λ = ? Å
c = 12.95395 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.309820.500000.00000
Si20.377630.000000.67290
O10.385810.385810.00000
O20.265760.000000.39701
O30.613560.886440.25000
O40.500000.000000.39214
(2_15) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Pm3nV = ? Å3
a = 13.63666 ÅZ = ?
b = 13.63666 Å? radiation, λ = ? Å
c = 13.63666 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Pm3nV = ? Å3
a = 13.63666 ÅZ = ?
b = 13.63666 Å? radiation, λ = ? Å
c = 13.63666 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.750000.500000.00000
Si20.396630.675830.00000
O10.307530.601780.00000
O20.903630.403630.25000
O30.500000.614460.00000
(2_16) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, P42/mnmV = ? Å3
a = 10.21713 ÅZ = ?
b = 10.21713 Å? radiation, λ = ? Å
c = 16.39642 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, P42/mnmV = ? Å3
a = 10.21713 ÅZ = ?
b = 10.21713 Å? radiation, λ = ? Å
c = 16.39642 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.892610.892610.90445
Si20.365460.033210.18878
O10.244480.062190.13189
O20.125110.125110.00000
O31.000000.000000.88229
O40.500000.000000.13664
O50.406300.155300.24995
(2_17) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Im3mV = ? Å3
a = 31.66657 ÅZ = ?
b = 31.66657 Å? radiation, λ = ? Å
c = 31.66657 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Im3mV = ? Å3
a = 31.66657 ÅZ = ?
b = 31.66657 Å? radiation, λ = ? Å
c = 31.66657 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.452500.949380.61453
Si20.453340.949640.79440
O10.500000.065700.39671
O20.548520.000000.38400
O30.438410.930760.66085
O40.579240.068680.42076
O50.567690.067690.75000
O60.544000.000000.20923
O70.500000.069980.20292
(2_18) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Im3mV = ? Å3
a = 18.13320 ÅZ = ?
b = 18.13320 Å? radiation, λ = ? Å
c = 18.13320 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Im3mV = ? Å3
a = 18.13320 ÅZ = ?
b = 18.13320 Å? radiation, λ = ? Å
c = 18.13320 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.500000.250000.00000
Si20.583370.000000.88793
O10.500000.922810.29804
O20.500000.585840.00000
O30.574310.574310.88011
(2_19) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Im3mV = ? Å3
a = 26.02111 ÅZ = ?
b = 26.02111 Å? radiation, λ = ? Å
c = 26.02111 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Im3mV = ? Å3
a = 26.02111 ÅZ = ?
b = 26.02111 Å? radiation, λ = ? Å
c = 26.02111 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.440360.250000.05964
Si20.639540.558240.93847
O10.745990.928940.50000
O20.304760.080830.41868
O30.360620.442000.00000
O40.370070.500000.08145
O50.405240.405240.08371
(2_20) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Pm3mV = ? Å3
a = 17.51913 ÅZ = ?
b = 17.51913 Å? radiation, λ = ? Å
c = 17.51913 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Pm3mV = ? Å3
a = 17.51913 ÅZ = ?
b = 17.51913 Å? radiation, λ = ? Å
c = 17.51913 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
Si10.000000.419520.87393
Si20.000000.254180.87321
O10.000000.500000.82472
O20.000000.337790.83046
O30.074530.420340.92547
O40.809000.000000.19100
O50.925080.244640.92508
(2_21) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Fm3mV = ? Å3
a = 31.52555 ÅZ = ?
b = 31.52555 Å? radiation, λ = ? Å
c = 31.52555 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Fm3mV = ? Å3
a = 31.52555 ÅZ = ?
b = 31.52555 Å? radiation, λ = ? Å
c = 31.52555 Å × × mm
α = 90°
Data collection top
Refinement top
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzBiso*/Beq
O10.328950.232310.50000
O20.390830.308490.50000
O30.570530.795920.29592
O40.545770.782480.21752
O50.559880.851990.14801
O60.574130.925870.18239
Si10.452440.182760.74611
Si20.449980.118360.81176
O70.432460.140820.76800
(2_22) top
Crystal data top
O2Siβ = 90°
Mr = ?γ = 90°
?, Pm3mV = ? Å3
a = 19.50871 ÅZ = ?
b = 19.50871 Å? radiation, λ = ? Å
c = 19.50871 Å × × mm
α = 90°
Data collection top
h = ??l = ??
k = ??
Refinement top
Crystal data