The Zeolite Conundrum: Why Are There so Many Hypothetical Zeolites

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The zeolite conundrum: Why are there so many hypothetical zeolites and so few observed? A possible answer from the zeolite-type frameworks perceived as packings of tiles Vladislav A. Blatov, Gregory D. Ilyushin, and Davide M. Proserpio Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/cm303528u • Publication Date (Web): 11 Jan 2013 Downloaded from http://pubs.acs.org on January 11, 2013

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Chemistry of Materials

The zeolite conundrum: Why are there so many hypothetical zeolites and so few observed? A possible answer from the zeolite-type frameworks perceived as packings of tiles Vladislav A. Blatov, a* Gregory D. Ilyushin, b Davide M. Proserpioc a

b

Samara State University, Ac. Pavlov St. 1, Samara 443011, Russia. [email protected]

Institute of Crystallography of RAS, Leninsky Pr., 59, Moscow 117333, Russia. [email protected] c

Università degli Studi di Milano, Dipartimento di Chimica, Via Golgi 19, 20133 Milano, Italy. [email protected]

*

Vladislav A. Blatov, Samara State University, Ac. Pavlov St. 1, 443011 Samara, Russia. Phone: +7-

8463345445, Fax: +7-8463345417, [email protected] ACS Paragon Plus Environment

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ABSTRACT: In the attempt to explain why there are so many hypothetical zeolites and so few observed, a model of assembling zeolite-type frameworks as a packing of natural building units (smallest cages) and/or essential rings (smallest windows) is proposed. The packing units have no common T atoms, hence, the model takes into account the process of polycondensation of T4+(OH)4 or [T3+(OH)4]– complex groups resulting in oligomeric TnOm(OH)k units, eliminating water molecules, and forming T–O–T bridges. The packings were modeled for all zeolite minerals and most of synthetic zeolite-type frameworks accounting for 163 zeolites of the 201 known. It is shown that the extraframework cations can play a role of templates for the packing units. Application of the model to 1220 hypothetical zeolites shows that only a small set could be explained as packing of tiles, suggesting a possible ranking of feasibility that may help to unravel the zeolite conundrum.

KEYWORDS: zeolites, hypothetical zeolites, self-assembly, computation methods, tilings

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Introduction Zeolite frameworks have always drawn attention of crystal chemists as an example of extended architectures, which, being chemically simple, provide a great diversity of topologies. Indeed, the frameworks are composed of only tetrahedrally coordinated T atoms, but even the number of their modeled energetically stable structures reaches millions.1,2 At the same time, not all of them can be experimentally obtained – only 201 natural or synthetic zeolite-type frameworks are structurally characterized so far.3 Although real number of zeolite frameworks is larger if one takes into account Xray amorphous zeolites, it hardly exceeds 1% of modeled frameworks. This is a conundrum of the zeolite crystal chemistry: why some frameworks are realized in nature, while many others being very close to them by energy remain hypothetical? Another open question in the zeolite chemistry is the mechanism of formation of the zeolite framework. In terms of building units, three mechanisms of the zeolite crystal growth were proposed up to date:4 from (i) simple olygomeric units like T tetrahedra, T2 diorthogroups or small 4-, 5-, or 6-rings;5 (ii) pre-fabricated polyhedral building units, or (iii) nano-sized building blocks. The second mechanism was proposed long ago6,7 and was disputed by Cundy and Cox5 in favor of mechanism (i) claiming that rather large polyhedral building units can hardly occur in the reaction gel and are difficult to transport during crystal growth. Thus the question about the existence of polyhedral building units is crucial since the mechanism (iii) should eventually apply to the first two at the stage of appearing nano-particles. Small polyhedral building units like cubes d4r, pentagonal d5r or hexagonal d6r prisms were evidenced by different spectroscopic methods4,8 and the upper limit of 20 T atoms was estimated in such prefabricated units.5 The concept of prenucleation building unit,9 which relates to polyhedral building units in crystal but can differ from them, renovated the idea of assembling mechanism (ii) with modern NMR data. Combinatorial reasoning of such kind of assembling was recently discussed in detail.10 It is possible that all mechanisms are correct and different zeolites can grow in accordance with different assembling schemes.


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At present, many kinds of the zeolite building units are catalogued;11-13 any zeolite framework can be described in terms of different building units. In the last ten years, great efforts to model zeolite frameworks and to solve the zeolite conundrum were undertaken,2,14-21 but new approaches that could explain formation of known zeolites and predict realizability of hypothetical ones are still required. In this paper, we draw attention mostly to the crystallochemical aspect of the problem. Known crystallochemical models of zeolites do not unravel the zeolite conundrum, they just systematize the building units that compose the obtained frameworks. Recently,22 we represented each of the 194 zeolite-type frameworks known at that time as a space partition, proposing a new kind of building unit, natural tile or natural building unit (NBU), where NBUs fill the whole space by sharing their faces. This method has an important advantage: the procedure of decomposing the whole framework into NBU is rigorous, algorithmized and implemented as a computer program in the program package TOPOS.23 NBUs correspond to minimal cages of the framework; every larger cage can be described as a sum of them, gluing tiles via common faces. The NBU faces correspond to windows of the cages; they form the set of essential rings of the zeolite framework. Not all possible rings in the framework are essential, but only those that are not sums of smaller rings, so the essential rings represent the smallest windows in the framework. The same kind of NBU can occur in different zeolites, so NBUs can be considered as “bricks”, which compose frameworks by combining in different ways. A crucial issue is to understand if these combinations take into account any physical process of assembling the framework, or NBUs are as formal objects as other kinds of zeolite building units.11-13 In this paper, we hope to answer this question at least partially. Experimental Section The natural packing model of zeolite-type frameworks Let us consider the process of formation of a zeolite framework as polycondensation of T4+(OH)4 or [T3+(OH)4]– complex groups resulting in oligomeric TnOm(OH)k units and eliminating water molecules. The oligomeric units composed with T–O–T bridges can be chains, rings or more complicated species ACS Paragon Plus Environment

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including polyhedral NBUs. In the quasi-equilibrium conditions, only the most stable units survive in the polycondensation. We consider the cations-templates as one of the main factors providing stability of the oligomeric units. Every cation tends to surround itself by oxygens of the T–O–T bridges in an appropriate configuration forming a distinct secondary building unit.10 These building units are then united by additional T–O–T bridges and assemble the whole framework. In what follows, we consider the zeolite framework as a T net, which consists of only T (tetrahedral) atoms with bridge oxygen atoms replaced by the edges of the net. One may suppose that the building units existing in the reaction mixture retain their form in the resulting framework and hold the cations-templates. With this hypothesis, the framework has the following features: (i) it can be decomposed into a set of building units; all atoms of the framework belong to these units; (ii) the building units have no common T atoms. We call such arrangement packing as the building units do not intersect each other in the T net; (iii) the building units should be connected to the cations that have played the role of templates during the framework formation. These features fit both two basic mechanisms of the zeolite crystal growth from simple olygomeric building units or from pre-fabricated polyhedral building units; further step is to restrict possible topologies of the building units. In this paper, we assume that the building units correspond to NBUs and/or to some essential rings (further we call them just rings). Although chains of T atoms can also compose the zeolite framework, we account that polyhedral or cyclic species should be especially suitable to shield the cations-templates; such units were found in the reaction gel by experimental methods.4,8 With this assumption, we have to select from the whole set of NBUs and/or their faces (rings) a subset of packing units (PU) that (a) have no common T-atoms, (b) compose the whole T net, and (c) include cations or other particles as templates. These three conditions define rules of assembly that we call the natural packing model of a zeolite-type framework. The conditions (a) and (b) lead to an important ACS Paragon Plus Environment

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property of PU set: the sum of numbers of atoms in the PUs multiplied by the multiplicities of the corresponding Wyckoff positions is equal to the number of T atoms in the unit cell. The last condition gives a criterion to choose from different packing models (if any) the model that reflects the assembling of the framework with PUs existing in the reaction gel. Note that this condition does not require cations to be allocated only in PUs; some other voids in the resulting framework can also be occupied during the polycondensation of PUs. To avoid confusion, we emphasize that NBUs or essential rings and PUs are not different units; PUs are selected from NBUs or essential rings in accordance with conditions (a)-(c). Note that namely essential rings are the primitives elements in the natural tiling model from which NBUs and the whole network are built.24 In many cases, NBUs can in turn be considered as packings of essential rings which obeys conditions (a) and (b): simplest examples are the d4r, d5r and d6r units mentioned above (Fig. 1). This means that rings can play an important role in assembling zeolite frameworks as we also showed for aluminophosphates.25 Such assembling schemes were also proposed basing on experimental data. For example, spectroscopic study of crystallization of FAU type (Zeolite X and Y)26,27 allowed the authors to propose a mechanism of forming t-toc (sod, sodalite) cages from 4rings or from 6-rings. Hereafter, to designate NBUs we use the t-xxx symbols.22

Figure 1. Representations of the natural building units t-hpr (d6r), t-kaa, and t-toc (sod), as packings of 6-rings (cf. Fig. 2). The pictures of tiles and tilings are made with the program 3dt (http://www.gavrog.org). According to the natural packing model, PUs contact to each other via T–O–T bridges, or in T net via T–T edges. If one replaces PUs with their centers, and connects the centers of contacting PUs with lines, a packing net will be obtained, which nodes and edges correspond to PUs centers and contacts between them. The topology of the packing net characterizes the method of assembling the zeolite framework with PUs. The topological types of packing nets are identified according to the RCSR three-lettersymbol nomenclature28 or TOPOS nomenclature.29 ACS Paragon Plus Environment

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Recently,25 we implemented a special procedure into the TOPOS program package to decompose T net into a set of PUs according to conditions (a) and (b) of the natural packing model. To check how the natural packing model fits the zeolite-type structures we have considered all 201 zeolite frameworks collected in the Zeolite Framework Database.3 We have already applied the model to aluminophosphate zeolite frameworks,25 for which only conditions (a) and (b) are valid (there are no extra-framework cations). Here we attend to those zeolites, where the positions of extra-framework cations are well-determined. In particular, we pay a special attention to zeolite-like minerals, since the natural conditions of crystallization can be considered most equilibrium and satisfying all three conditions (a)-(c) of the natural packing model. We do not consider in detail the zeolite materials containing organic structure-directing agents (OSDA)30 since organic molecules do not exist in minerals and usually are not well allocated in the framework cages in X-ray experiment. As we shown earlier,25 such zeolites, among which there are many aluminophosphates, can also be interpreted with the natural packing model if one ignores condition (c). To outline a possible way of solving the problem formulated in the title of the paper we explored if the natural packing model could be applied to rank feasible hypothetical zeolite frameworks. Complete treatment of all hypothetical zeolite frameworks generated up to date1,2,18 and extracting all robust ones is the subject of a separate work; in this paper, we will just outline possible usefulness of the model. For this purpose, methodologically is not so important what force field was used to refine the zeolite frameworks and which of known databases is chosen. More important is to explore all structures within a sample extracted from a database in accordance with some reasonable criteria. To do so, we analyzed the data on 274611 hypothetical zeolites from the BRONZE database1 that have

energy

less

than

0.2

eV

http://www.hypotheticalzeolites.net/DATABASE/BRONZE_CONFIRMED/index.html).

(see As

first

attempt, we restricted this dataset retrieving the T nets of 1220 hypothetical zeolites that contain strictly two non-equivalent T atoms, and have a topology that does not occur in the known 201 zeolite frameworks. Note that all uninodal (with one kind of T node) hypothetical zeolites correspond to already ACS Paragon Plus Environment

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synthesized zeolite-type frameworks, so we have considered topologically the simplest hypothetical frameworks. Results NBU packings Our analysis shows that 16 zeolite minerals and 5 synthetic zeolites can be constructed as packings only with NBUs (without ring-like PUs) and obey all (a)-(c) conditions of the natural packings model (Table 1). Table S1 of the Supporting Information contains the data for other 30 zeolites that are also built with NBUs only (16+5+30=51 in total); they are either neutral (i.e. they do not include extraframework cations), or the extra-framework cations were not allocated in them. These 30 frameworks obey conditions (a) and (b), but condition (c) could not be checked. The following features of the packings should be noted: (i) The kinds of packing units are essentially restricted: there are 16 PUs (Fig. 2) out of 40 NBUs existing in the 21 considered zeolites22 and only 12 PUs (excluding t-bal, t-cub, t-kzd, t-vsr) are associated with extra-framework cations (Table 2). Most of them (t-afo, t-ato, t-bal, t-can, t-cub, thpr, t-kaa, t-kzd, t-lau, t-opr, t-pes, t-srs) contain less than 20 T atoms so they are likely to exist in the reaction gel. Larger NBUs t-toc and t-grc can be assembled from 6- or 8-rings, respectively (cf. Fig. 1), and namely these rings are centered by cations (Table 2). The NBUs t-kzd and t-cub are too small to incorporate cations, but their simple topologies do not require templating (see discussion below). Large t-lio NBU includes sulfate anions, but the FAR framework where this unit exists has an alternative packing model with smaller t-can and t-toc NBUs (Table 2).

Figure 2. Packing natural building units that are associated with cation templates and occur in assembling schemes without participation of ring units. For each NBU its t-xxx symbol,22 number of vertices and composite building unit name3 (if any) are given.


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(ii) Each kind of PU is characterized by a pattern of connections which has common features in different zeolites. Let us consider the t-hpr (d6r) packings, which are most frequently observed for zeolite minerals and synthetic zeolites (10 out of 51). Such packings are also important since the existence of separate t-hpr (d6r) units was proved by in situ experiments.4,5,8 In all cases, every t-hpr PU is surrounded by six other PUs and contacts them via alternating edges of the hexagonal rings (Fig. 3). By this condition, there are two ways to connect the t-hpr prisms: when the contacting edges of the top and bottom hexagons of the central prism belong to adjacent (alternating) sides of square rings (Fig. 3a,b,d,e,f), or when the edges belong to the same square rings (Fig. 3c,g). In the first case, the centers of the six surrounding prisms form an octahedron, while in the second case a trigonal prism. As a result, the overall topologies of the packings are described by the packing nets with the corresponding coordination figures: pcu, sta, lon-e, or crs for octahedral arrangement, acs or flu-e for trigonal-prismatic arrangement, and binodal nia for mixed one, when two inequivalent prisms have different environment as in AFX.

Figure 3. Local configurations (ensembles) of packing natural building units in the t-hpr packings of zeolite minerals or synthetic zeolites: (a) AEI (pcu); (b) AFT (sta), AFX (nia), CHA (pcu); (c) AFX (nia), GME (acs); (d) EMT (lon-e), FAU (crs); (e) KFI (pcu); (f) SAV (pcu); (g) TSC (flu-e). The topologies of the packing nets are given in parentheses. Different orientation of the t-hpr prisms can lead to the same packing net for different zeolites depending on the method of interconnecting the local configurations (ensembles of packing units).31 Thus, AEI, CHA, EMT, and KFI have the same pcu packing net, but quite different geometry of the local configurations. On the contrary, EMT and FAU have similar local t-hpr configurations, but different methods of their assembling (see item (v) below).


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(iii) In most cases, the packing is composed of one topological kind of PU even if there are two geometrically inequivalent PUs as in EMT or LIO. Only in FAR and TSC there are two ways to build packings both with one and with two kinds of PU. (iv) 11 of the 21 zeolite frameworks (EMT, FAR, FAU, KFI, LAU, LTA, LTL, OFF, RHO, THO, TSC) can be represented as NBU packings in more than one way. These ways are not independent; for instance, in EMT, FAU, or TSC, a special arrangement of t-hpr PUs forms the t-toc cages (Fig. 3). However, not all NBU packings obey condition (c) of the packing model; and this allows us to choose among different packings (this will be considered in more detail below). (v) In some cases, the local arrangement of PUs is the same in different zeolites, but the packing net topologies are different. A remarkable example is the pair EMT – FAU, where the local configurations of the t-hpr PUs are the same (Fig. 3), but the t-hpr packing gives different nets lon-e and crs, respectively. This difference becomes clearer if one considers the alternative t-toc packings of the lonsdaleite (lon) and diamond (dia) topologies, respectively. Indeed, in both EMT and FAU, the hexagonal prisms can be considered as links between the t-toc cages; these links correspond to edges of lonsdaleite and diamond underlying nets, respectively (Fig. 4). The figure shows also the other zeolite (LTA) that can be described with t-toc PU only.

Figure 4. The t-toc packings in EMT (lon), FAU (dia), and LTA (pcu). The topologies of the packing nets are given in parentheses. The crucial point for selecting the NBU packings model is to determine if extra-framework cations are allocated according to condition (c). The data of Table 1 show that in the 21 zeolites the cations occupy the positions in the centers or near the faces (rings) of the PUs. Note that we took into account all extraframework ions that fully occupy their positions. Obviously, the size of NBU is crucial; thus, sodium cations prefer to occupy the positions near plane 6-rings (like in t-hpr), undulated 8-rings (like in t-kaa ACS Paragon Plus Environment

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(Fig. 2), t-ste, or t-pau (Fig. 5)), or in the center of such NBUs as t-afo or t-toc (Fig. 2). In some cases (LAU, LTA, TSC), there are several packings, some of which obey condition (c), but some do not. We then use this information to select the most likely kind of packing. For instance, the t-cub PUs in LTA are too small to include Na cations, but these PUs are formed as a result of the t-toc packing (Fig. 4).

Figure 5. Some NBUs that are not packing units but have been observed as host for the cation templates. For each NBU its t-xxx symbol,22 number of vertices and composite building unit name3 (if any) are given. An exception is the group of zeolites composed of the smallest NBU t-kzd (see Fig. 2): thomsonite (THO), natrolite (NAT) and edingtonite (EDI), where the cations are allocated in the centers or near the surface of larger NBUs (t-kdt, t-krr, t-nat, t-krq, Table 1, Fig. 5). Obviously, small rings consisting of three or four T atoms do not require any cation templates: they can be easily assembled with ortho- (T) or diorthogroups (T2). In this case, the template role of cations consists in arranging the small NBUs into a 3D framework as is shown for THO (Fig. 6). NAT and EDI are considered below; an additional decrease of symmetry is required for their frameworks to be assembled of PUs.

Figure 6. (left) Arrangement of four t-kzd NBUs around a Ca atom in the crystal structure of THO.32 T atoms of one t-kzd unit are connected by red lines; (right) assembling THO framework with the t-kzd NBUs and the positions of Ca atoms. Packings of rings or NBUs + rings As we have said above, cations are often allocated near centers of rings (NBU faces) that allows one to treat rings as packing units and consider sets of rings or combinations of rings and NBUs in the natural packing model.


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We allowed then our computation to look for rings and/or NBUs and we found that other 82 zeolite frameworks (in addition to the 51 zeolites assembled with NBUs only) can be represented as packing of rings or combinations NBUs + rings (Table S2). Many of them were considered in detail in our paper on aluminophosphates,25 but minerals were not treated yet. This sample contains 19 zeolite minerals for each of which we found at least one model, where the rings composing the packing are associated with the extra-framework cations. In details the sets of PUs are: 4-rings build the structures of BRE (brewsterite), GIS (gismondine), MON (montesommaite), -PAR (parthéite), PHI (phillipsite), YUG (yugawaralite). Since the 4-ring is too small to include alkali or alkaline-earth metals, the cations are allocated not in the centers of 4-rings, but anyway link to the rings. 6-rings build the structures of AFG (afghanite), BOG (boggsite), CAN (cancrinite), FRA (franzinite), GIU (giuseppettite), LEV (levyne), -LIT (lithosite), LOS (bystrite), MAR (marinellite), TOL (tounkitelike). The rings are centered by Na, K or Ca cations. CAN, LOS, MAR, and TOL can be constructed uniquely from one, two, two, or three types of 6-rings, respectively. There are two inequivalent ways to assemble the LEV framework (R 3 m) with 6-rings, centers of which are allocated in Wyckoff positions 9d or 3b+6c. Only the latter case obeys condition (c): the positions 6c are completely occupied by Ca, while the mixed Na/K/Ca positions are allocated in 3b.33 AFG (P63/mmc) and –LIT (Pnma) can also be assembled in two ways, but they are equivalent and fit condition (c); the centers of two rings occupy the positions 2a+6h or 2b+6g in AFG34 and 4b or 4c in –LIT.35 The BOG (Imma), FRA (P 3 m1), and GIU (P63/mmc) frameworks can also be constructed in two ways from three different 6-rings (8g+8h or 16j for BOG, 1a+3f+6i or 1b+3e+6i for FRA, and 2a+2d+12k or 4f+6g+6h for GIU); both ways are equivalent since all 6-rings are centered by cations.36-38

4- and 6-rings build the structure of MAZ (mazzite); the 6-rings are occupied by Mg atoms in the dehydrated form.39

8-rings form the framework in ETR (zeolite ECR-34) and they encompass the potassium cations.40 Mixed packings, where both NBUs and rings play the role of PUs, are rare in zeolites. We found only one mineral in this group, paulingite (PAU, Im 3 m), where PUs are two NBUs t-oto and t-gsm as well ACS Paragon Plus Environment

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as one 6-ring with the center in 8c. The three PUs are occupied by Na, K, Ca and Ba cations. The selfassembly of the PAU framework from the PUs is considered in detail elsewhere.41 In many cases, NBUs are the same as shown in Fig. 2 and they are usually combined with 4- or 6-rings. In particular, the combination t-hpr + 6-ring occurs in three zeolites (EAB, LEV and SAT) which differ by methods of packing of hexagonal prisms and 6-rings (Fig. 7). Packing nets for EAB, LEV and SAT are all 6coordinated (each PU, hexagonal prism or 6-ring, is connected to six other PUs), but topologies are different: they are nia, pcu and stb, respectively. This example demonstrates that typical packing nets, like pcu or nia, that were already found in t-hpr packings (Fig. 3), are realized also for NBUs + rings packings, i.e. PUs tend to be arranged in space in accordance with one of simple topologies, moreover, these packing nets are typical also for packings of atoms or molecules. Thus, nia and pcu packing nets mean that PUs in EAB and LEV are arranged like atoms in NiAs and NaCl; in both cases t-hpr units form a close packing (hexagonal-type for EAB and cubic-type for LEV).

Figure 7. Packings of t-hpr units (d6r hexagonal prisms) and 6-rings (yellow) in EAB, LEV and SAT. In mutinaite (MFI, Pnma)42 Na and Ca cations are strongly disordered and for this framework is difficult to check condition (c).

Low-symmetry packings While constructing a packing one should take into account the symmetry of the real zeolite framework. The natural and synthetic zeolites often have a lower symmetry than the idealized framework, for which the NBUs are tabulated; this decrease of symmetry is often caused by a special arrangement of extra-framework species. A simple example is shown in Fig. 1 right: the maximum symmetry of t-toc is m 3 m (the symmetry of a cube) but in this case all 6-rings are equivalent and cannot form a packing since they share edges. To construct a packing one has to reduce the symmetry down to 4 3m (the symmetry of a tetrahedron) that results in splitting the set of 6-rings into two non-equivalent subsets, one of which is colored in blue in Fig. 1 right. It is noteworthy that the extra-framework Ca2+


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cations in mineral tschörtnerite (TSC, Table 1) exactly occupy positions near the centers of only one set of the 6-rings, following the packing rules. The same concerns sodalite (SOD) composed of only t-toc units: decrease of symmetry from maximum Im 3 m to P 4 3n allows sodium cations to occupy half of 6rings; for example, the blue ones as in Fig. 1 right. The symmetry of the packing of the 6-rings is even lower (R 3 m, Table S3). Alternative packing of 4-rings can be realized in the P 4 3m symmetry (Table S3) but it does not fit condition (c). One more example is the zeolite RHO (Table 1), where both of the two independent NBU (t-opr and

t-grc) have common T-atoms in maximum framework symmetry (they share faces, Fig. 8 left). However, reducing symmetry of the framework from Im 3 m down to Pm 3 m one can distinguish the corner and central t-grc cages in the unit cell and represent the framework in two alternative ways: as a packing with half of the t-grc set (Fig. 8 middle), or with half of the t-opr set (Fig. 8 right).

Figure 8. (left) Natural tiling of the zeolite RHO framework; (middle) packing of the yellow t-grc cages; (right) packing of the blue t-opr cages. Two minerals, natrolite (NAT, I41/amd) and edingtonite (EDI, P 4 m2), can be constructed from t-kzd, but unlike THO illustrated in Fig. 6, they can be represented as packings of the t-kzd NBUs only in a low-symmetrical form: indeed, the highest symmetry for natural natrolite and edingtonite is I 4 2d and

P 4 21m, respectively (Fig. 9).

Figure 9. Assembling zeolite frameworks with the t-kzd NBUs: NAT (left), EDI (right). Only T nets are shown. The mineral wenkite (-WEN, P 6 2m) admits the packing of hexagonal prisms (t-hpr) and tiles formed by three 10-rings (t-srs) in the same space group but with a doubled unit cell (Fig. 10). The 6-rings of the hexagonal prisms and the t-srs 10-rings are centered by K/Ba and Ca cations, respectively.43 ACS Paragon Plus Environment

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Figure 10. Packing units t-hpr and t-srs assembling the -WEN framework. The bikitaite framework (BIK, Cmcm) can be represented as a packing of t-pes PUs in a tripled unit cell (a, b, 3c) (Fig. 11 left; Table 1). The lithium atoms in the bikitaite mineral with a lower symmetry P21 or P144,45 are allocated on the boundary of the t-pes PUs near the centers of 6-rings.

Figure 11. (left) The BIK framework as a packing of t-pes packing units; (right) connection of two t-euo NBUs and two 3-rings in the VSV framework. One t-euo NBU and one 3-ring are shown by red lines. Packing of PUs in NES (Fmmm) also includes t-pes NBU, but in combination with t-euo NBU and 5rings (Table S3). The cations in mineral gottardiite with the NES framework (Cmce)46 are not well allocated. The framework in VSV (I41/amd) can be assembled with t-euo NBU and 3-rings in the I41md symmetry; both packing units are too small to incorporate cations. Sodium cations in mineral gaultite (VSV framework, Fdd2)47 are connected to both t-euo and 3-rings (Fig. 11 right) and provide their assembling as in other similar cases (cf. Fig. 6). Analcime (ANA, Ia 3 d) can be composed of 6-rings in the Ia 3 (or lower) subgroup. In the highest symmetry (Ia 3 d) the positions of the Na templates are occupied by 2/3,48 so the cations are arranged according to the packing motif. The framework of nabesite (NAB, I 4 m2) can be assembled with 3- and 4-rings, which do not require templates, but the symmetry of the packing cannot be higher than P 4 m2. The structure of natural mineral nabesite has even a lower symmetry (P212121).49 The same PUs are realized for weinebeneite (WEI, Cccm) in the Pmna symmetry. The structure of weinebeneite50 belongs to the Cc space group that is a general subgroup of Pmna. Lovdarite (LOV, P42/mmc) can be constructed as a packing of 3- and 6-rings or t-kaa NBUs in the class-equivalent subgroup P42/mnm with a doubled unit cell.


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The similar frameworks of dachiardite (DAC, C2/m) and mordenite (MOR, Cmcm) can be assembled with one 4- and two 5-rings packed in different ways in doubled unit cells (class-equivalent subgroups) of the symmetry C2/m and Cmce, respectively. Ferrierite (FER, Immm) is constructed as a packing of 5- and 8-rings in the Fddd (or lower) symmetry. The 8-rings are centered by potassium cations.51 Heulandite (HEU, C2/m) and stilbite (STI, Fmmm) are examples of the framework that is constructed in a lower symmetry (C2/m)52,53 with both NBUs (t-bru, bre) and 4-rings. Note that STI can be represented in a lower symmetry also as a packing of NBUs t-bru and t-kuo, but this method of assembling does not obey condition (c) (Ca cations in stilbite lie outside these NBUs.53 Instead, the assembling scheme t-bru+4-rings is observed in four zeolites: besides HEU and STI it is realized in CON (Table S2) and RRO (Table S3). In total, 30 zeolite frameworks can be described as packings of NBUs and/or rings in a lowsymmetrical form (Table S3), while eight (AST, ASV, BIK, EDI, NAT, RHO, SZR, and VET) are composed of NBUs only as given in Tables 1 and S1.

Other packing units So far our model is accounted for 163 (=51+82+30) zeolites; for the remaining 38 zeolite frameworks we did not find a packing solution with NBUs or rings. It is noteworthy that among them there are only three minerals (goosecreekite, GOO, melanophlogite, MEP, and terranovaite, TER) and only GOO and TER contain alkali or alkaline-earth cations. The positions of cations in terranovaite are not well determined that hinders a valid separation of PUs. To assemble the GOO and MEP frameworks we need to consider other kinds of packing units. (i) Additional T tetrahedra that link other PUs. This is observed for the MEP clathrasil framework that can be constructed as a packing of pentagonal dodecahedra (t-red, mtn) (that are occupied by template molecules) linked by T tetrahedra (Fig. 12).

Figure 12. Assembling the MEP framework with t-red PUs and T tetrahedra (red balls). ACS Paragon Plus Environment

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(ii) The PUs are combinations of rings and ortho- or diorthogroups. The example is goosecreekite (GOO), whose framework is composed of 6-rings added with T2 diorthogroups. This unusual structure of the T8 PUs is caused by an asymmetric force field of the [Ca(H2O)5]2+ templates (Fig. 13).54 The remaining 36 zeolite frameworks (Table S4) do not contain metal cations and their assembling mechanisms lie beyond the scope of this paper. At the same time, we can suppose that such mechanisms could follow Cundy and Cox’s scheme5 when distinct natural building units are being assembled on the surface of a growing zeolite crystal from small oligomeric units thanks to metal cations or OSDAs.

Figure 13. T8 packing units assembling the GOO framework and the [Ca(H2O)5]2+ templates.

Discussion Natural packing model: principles of assembling The zeolite models discussed in the previous part allow us to formulate some principles that restrict possible assembling schemes and could be used in the synthesis of new zeolites. We realize that these principles being topological cannot fit all possible ways of synthesis; some special hydrothermal conditions or SDA templates could result in an exclusive framework. However, if the framework obeys these principles, it should have a high probability to be obtained. (i) The framework should fit the natural packing model, which obeys the main mechanisms of the zeolite crystal growth, both from oligomeric units5 and from secondary building units,4 as it is not important for packing schemes if PUs are assembled on the surface of the crystal (as the first mechanism assumes) or in the reaction gel (as the second one does). (ii) Packing units that form zeolite frameworks are not numerous. Although we cannot list all those of them that obey condition (c) due to lack of data on cation positions in some zeolites, a quick look at Fig. 2, Table 2 and S1 Tables shows that the number of polyhedral PUs does not exceed 30-40, i.e. ten times less than the total number of NBUs (308).22 Most typical ring PUs are 4-, 6-, or 8-rings; the last two are usually formed with cation templates while 4-rings are too small to incorporate cations and are ACS Paragon Plus Environment

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spontaneously assembled in the reaction gel.5 Accordingly, polyhedral PUs can be of three types: (a) small PUs with 5-10 vertices (like t-kzd or t-cub), which are composed of a few 3-, 4-, or 5-rings and do not require any template when forming in the reaction gel; (b) medium PUs, which bear up to 20 vertices, contain 6-, or 8-rings and can still occur in the reaction gel but should be stabilized by cations (like t-hpr, t-can, or t-opr); large PUs with more than 20 vertices, which should in turn be assembled as a packing of the 6-, or 8-rings stabilized by cation templates (like t-toc or t-grc). Strictly speaking, the natural packing model, dealing with final stage of the assembling process, does not prove templating effect, but it gives additional arguments for the role of cations as templates. (iii) The number of topologically different PUs (NBUs or rings) in zeolite framework is typically equal to 1 or 2. Hence, the zeolite packing nets prefer to have simple uninodal or binodal topology like primitive cubic (pcu), body-centered cubic (bcu) or hexagonal close packing (hcp) (Table 1). (iv) Typical PUs mentioned in (ii) and packing nets (methods of assembling PUs) mentioned in (iii) can combine in different ways to give the zeolite framework diversity. The same PUs can be differently assembled (as was shown for t-hpr), but also different PUs can follow the same assembling scheme (e.g. the pcu scheme is realized for seven zeolites from Table 1). (v) For most frameworks there are several methods of decomposing to PUs (Table 1 and Tables S1S3); all of them could be useful even when they do not obey condition (c) because they indicate genetic relations between different frameworks: similar frameworks can be built from the same PUs and/or with the same assembling schemes (packing nets). For example, all the 10 zeolites composed with t-hpr units (Fig. 3) could be considered similar. One can expect their mutual transformation thanks do different SDAs; they can coexist in nature (like faujasite and chabazite).55 These principles are supported by experimental data for most typical and well-determined zeolite frameworks. Tables 1, S2, S3 contain packing models for 16+19+12=47 zeolite minerals, i.e. for all structurally characterized minerals (except GOO and TER, which were discussed separately) that were reported by Commission on New Minerals and Mineral Names of the International Mineralogical Association.56 The 38 zeolite frameworks from Table S4 remain a challenge for the natural packing ACS Paragon Plus Environment

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model. Some of them (EON, EUO, IMF, SFS, STO, STT, SVR, TUN, UTL) are too complicated to enumerate all possible assembling schemes. For others a deep decreasing of symmetry is probably required that also leads to combinatorial explosion of the number of assembling schemes.

Outlook for hypothetical zeolites In this section we briefly discuss the results obtained with the natural packing model for 1220 hypothetical zeolites from the BRONZE database.1 A detailed analysis of all zeolites of this group lies beyond the scope of the paper, but we would like to mention some important cases that show potential usefulness of the model to essentially restrict the set of feasible hypothetical frameworks and to explain why some of them can hardly be ever synthesized. (i) For 85 zeolites no proper tiling can be constructed. The reason is that the rings in the T nets of these zeolites are intersected or catenated by other rings (Fig. 14); as a result, these rings cannot be tile faces since tiles (cages) must not intersect each other.24 So these zeolites are less likely to be synthesized. Remember that a proper tiling can be constructed for any of 201 known zeolite frameworks.

Figure 14. A fragment of T net with two catenated 8-rings in the hypothetical zeolite 192_2_239769. (ii) For 45 zeolites there are several possible proper tilings and no unique (natural) tiling can be chosen. This means that some cages cannot be unambiguously selected owing to tiny intersections of some cages. In turn, the intersections appear thanks to much distorted rings and cages (Fig. 15). Again, for this set the ambiguity in the tiling may hamper the synthesis.

Figure 15. One of two possible proper tilings (top) and three types of tiles (bottom) in the hypothetical zeolite 15_2_93461.


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(iii) For the remaining 1090 zeolites the natural tilings were constructed and for 237 frameworks were possible to construct a packing of NBUs that obey conditions (a) have no common T atoms and (b) compose the whole T net. All other 853 hypothetical zeolites cannot be represented as a packing of NBUs, i.e. they disobey condition (a). We have not considered possible ways to represent them as packings of rings or low-symmetrical embeddings; we leave this for a further study. Importantly, none of these hypothetical zeolites has been yet synthesized. Table 3 contains the occurrences of NBU packings in the 237 hypothetical zeolites with a given type or a combination of types of NBUs. We considered only those packings where all NBUs had combinatorial types of known zeolite cages.22 The following features of the packings are noteworthy: (i) Most of the packings (189 out of 237) are composed of NBUs that occur in real zeolites. Some frameworks can be represented as packings in several ways, therefore the total occurrence in Table 3 (249) exceeds the number of frameworks. One can expect that the remaining 237-189=48 zeolite frameworks can hardly be obtained with alkali or alkaline-earth cations; other templates should found to stabilize such unusual cages. (ii) A comparison with Table 2 shows that only four out of 31 PUs listed in Table 3 (t-opr, t-toc, t-

hpr, t-kaa) are realized in zeolite minerals, moreover, the occurrence of these four types is low. One can conclude that most of the packings are not suitable to be stabilized by alkali or alkaline-earth cations. At the same time, some other PUs (t-lov, t-cub, t-gme, t-tes, t-kah) occur in synthetic zeolites containing no inorganic cations (see the Supporting Information). (iii) The local configurations (ensembles) of NBUs are quite different in zeolite minerals (Fig. 3) and in hypothetical zeolites (Fig. 16) even for the packings of the same NBUs. For example, there are three packing of t-hpr: in 65_2_57 the NBUs contact by only one vertex; in 65_2_80 the NBUs are connected by edges, but two of the edges of each hexagonal prism belong to square rings. In 194_2_24 the method of connecting NBUs is quite different: the upper hexagonal ring is connected to only one t-hpr prism resulting to a tetrahedral t-hpr configuration and the lonsdaleite (lon) packing net topology. Obviously, in this case, the alkali or alkaline-earth cations cannot be coordinated to this ring since they would fall ACS Paragon Plus Environment

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into too small t-hpr cage clamped between the pair of contacting NBUs.

One more possible

explanation of preferring methods of connecting t-hpr NBUs is requirement of flexibility of the zeolite framework.20,21 The connections between all atoms of 4- or 6-rings of neighboring t-hpr NBUs (see for example 65_2_57 and 194_2_24 in Fig. 16) should lead to rigid local configurations that are not favorable according to the flexibility concept. We may extend this observation speculating that only the ensembles of NBUs that preserve the flexibility will likely be feasible as a crystal; this hypothesis needs further exploration with the set of feasible hypothetical zeolites recently reported by Dawson et al.21

Figure 16. Local configurations (ensembles) of packing natural building units in the t-hpr packings of hypothetical zeolites: (a) 65_2_57 (pcu); (b) 65_2_80 (pcu); (c) 194_2_24 (lon). The packing nets are given in parentheses. All these arguments prove that the most of the 1220 low-energy hypothetical zeolite frameworks can hardly be realized with alkali or alkaline-earth cations due to assembling (kinetic) reasons; no new minerals of those T net topologies should be discovered. Thus, the natural packing model allows one to consider the zeolite conundrum from a new point of view. When modeling zeolite frameworks, the framework free energy is used as the main criterion of stability, without taking into account the kinetic factors (including the methods of its self-assembly). At the same time, even a thermodynamically stable framework could not be ever obtained if its building units are not stable in the reacting system, or cannot be assembled in a proper way. Resting upon the NBU model we can formulate additional criteria to be applied in the design of new zeolite materials: (i) the zeolite framework, at least that is formed with metal cation templates, should be representable as a packing of building units that can be stable in the reacting mixture; the building units should not touch, intersect or catenate each other; (ii) the building units should fit the extra-framework species (cations, anions, or molecules) that play the role of templates; ACS Paragon Plus Environment

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(iii) ensembles of the building units should have some favorable topologies (methods of connection of PUs) to be similar to those in natural zeolite frameworks. Again, we emphasize that these criteria are not strict, but they could help to select most feasible and easy to synthesize zeolite frameworks. The detailed elaboration of these criteria requires a critical analysis of all data on hypothetical zeolites and is a matter of a future work. In this paper, we have merely considered a specification of these criteria. In particular, the building units were assumed to be NBU and only extra-framework alkali or alkaline-earth cations were taken into account. However, even this limited consideration shows that many hypothetical zeolite frameworks, like mentioned in Figs. 1416, should be discarded as unrealizable despite they have low free energy. Our preliminary screening of 1220 hypothetical structures is able to extract 189 zeolite frameworks as most possible targets for synthesis (Table S5).

Conclusion We started this paper with a conundrum: why there are so many hypothetical zeolites and so few observed. The results obtained show that most of zeolite frameworks can be assembled with a limited set of natural building units (cages) and essential rings (mainly 4- or 6-membered) according to the packing conditions. The complete set of NBUs and rings can be unambiguously obtained for a given zeolite framework (both natural and hypothetical) with a strict algorithm.24 The packing units are either quite simple (3-, 4-, or 5-rings or small cages bounded by these rings) or stabilized by extra-framework cations that play the role of templates. The packing units as well as assembling schemes repeat in different zeolite frameworks that facilitates search for genetic relations in the zeolite realm. Hence we may suppose that the natural packing model takes into account the results of polycondensation processes in the reaction system, although this hypothesis needs further experimental check. Using the model one might find a way to solve the zeolite conundrum: one could apply additional criteria to select the hypothetical zeolite frameworks that obey both thermodynamic and kinetic restrictions, and this would greatly restrict the list of feasible new zeolites. Although the strict mechanism of the zeolite growth is not ascertained yet, the natural packing model is flexible enough to adjust all the basic mechanisms ACS Paragon Plus Environment

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proposed.5-7 Indeed, the full list of the model conditions (a)-(c) fits the mechanism of assembling zeolite structure from pre-fabricated packing units, however, the method and TOPOS tools can also be used to search for possible building schemes of zeolites composed of simple olygomeric units if condition (c) about templating agents is ignored.

Supporting Information Available: Tables S1-S4 contain the packing models for all the zeolites not reported in Table 1, Table S5 lists the code-names of 189 hypothetical binodal zeolite framework. Shape of all the NBUs could be found in the supplementary material22 and in the Zeolite Framework Database. This information is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENTS: We thank Martin D. Foster for providing data from the Database on Prospective Zeolite Structures. V.A.B and G.D.I. are grateful to Russian Foundation for Basic Research for grant No. 12-02-00493. V.A.B. thanks the 2011/2012 Fellowship from Cariplo Foundation & Landau Network - Centro Volta (Como - Italy).


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REFERENCES (1) The Database on Prospective Zeolite Structures, http://www.hypotheticalzeolites.net/. (2) Pophale, R.; Cheeseman, P. A.; Deem, M. W. Phys. Chem. Chem. Phys., 2011, 13, 12407; http://www.hypotheticalzeolites.net/DATABASE/DEEM/index.php. (3) The Zeolite Framework Database, http://www.iza-structure.org/databases/. (4) Aerts, A; Kirschhock, C. E. A.; Martens, J. A. Chem. Soc. Rev. 2010, 39, 4626. (5) Cundy, C. S.; Cox, P. A. Microporous Mesoporous Mater. 2005, 82, 1. (6) Barrer, R.M.; Baynham, J.W.; Bultitude, F.W.; Meier, W.M. J. Chem. Soc. 1959, 195. (7) Breck, D.W. Zeolite Molecular Sieves, Wiley, New York, 1974. (8) Fan, F.; Feng, Z.; Li, C. Chem. Soc. Rev. 2010, 39, 4794. (9) Taulelle, F. Curr. Opin. Solid State Mater. Sci. 2001, 5, 397. (10) Ilyushin, G. D. Struct Chem. 2012, 23, 997. (11) Smith, J. V. Microporous and other Framework Materials with Zeolite-Type Structures; LandoltBörnstein New Series IV/14 Subvolume A: Tetrahedral Frameworks of Zeolites, Clathrates and Related

Materials; Springer, Berlin 2000. (12) Fischer, R. X.; Baur, W. H. Microporous and other Framework Materials with Zeolite-Type

Structures; Landolt-Börnstein New Series IV/14 Subvolumes B: Zeolite Structure Codes ABW to CZP, C: Zeolite-Type Crystal Structures and their Chemistry. Framework Type Codes DAC to LOV, D:

Zeolite-Type Crystal Structures and their Chemistry. Framework Type Codes LTA to RHO; Springer: Berlin, 2000, 2002, 2006. (13) Van Königsveld, H. Compendium of Zeolite Framework Types; Elsevier: London, 2007. ACS Paragon Plus Environment

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(14) Zwijnenburg, M.A.; Bell, R.G. Chem. Mater. 2008, 20, 3008. (15) Zwijnenburg, M.A.; Bromley, S.T. Phys. Chem. Chem. Phys. 2010, 12, 14579. (16) Bushuev, Yu.G.; Sastre, G. J. Phys. Chem. C 2010, 114, 19157. (17) Deem M. W.; Pophale, R.; Cheeseman, P. A.; Earl, D. J. J. Phys. Chem. C 2009, 113, 21353. (18) Treacy, M. M. J.; Rivin, I.; Balkovsky, E.; Randall, K. H. Foster, M. D. Micropor. Mesopor.

Mater. 2004, 74, 121. (19) Martin, R. L.; Smit, B.; Haranczyk, M. J. Chem. Inf. Model. 2012, 52, 308. (20) Sartbaeva, A.; Wells, S. A.; Treacy, M. M. J.; Thorpe, M. F. Nature Mater. 2006, 5, 962. (21) Dawson, C. J.; Kapko, V.; Thorpe, M. F.; Foster, M. D.; Treacy, M. M. J. J. Phys. Chem. C,

2012, 116, 16175. (22) Anurova, N. A.; Blatov, V. A.; Ilyushin, G. D.; Proserpio, D. M. J. Phys. Chem. C, 2010, 114, 10160. (23) Blatov, V.A. Struct. Chem. 2012, 23, 955; http://www.topos.samsu.ru (24) Blatov, V.A.; Delgado-Friedrichs O.; O’Keeffe M.; Proserpio D. M. Acta Cryst. 2007, A63, 418. (25) Peskov, M.V.; Blatov, V.A.; Ilyushin, G.D.; Schwingenschlögl, U. J. Phys. Chem. C, 2012, 116, 6734. (26) Xiong, G.; Yu, Y.; Feng Z.-C.; Xin, Q.; Xiao, F.-S.; Li, C. Microporous Mesoporous Mater.

2001, 42, 317. (27) Dutta, P. K.; Shieh, D. C.; Puri, M. J. Phys. Chem. 1987, 91, 2332. (28) O'Keeffe, M.; Peskov, M.A.; Ramsden, S.J.; Yaghi, O. M. Acc. Chem. Res., 2008, 41, 1782; http://rcsr.anu.edu.au/ ACS Paragon Plus Environment

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(29) Alexandrov, E.V.; Blatov, V.A.; Kochetkov, A.V.; Proserpio, D.M. CrystEngComm, 2011, 13, 3947. (30) Wang, Z.; Yu, J.; Xu, R. Chem. Soc. Rev. 2012, 41, 1729. (31) Blatov, V. A.; Proserpio, D. M. Ch. 1 in Modern Methods of Crystal Structure Prediction, ed. A. R. Oganov, Wiley-VCH, Weinheim, 2011. (32) Pluth, J.J.; Smith, S.V.; Kvick, A. Zeolites, 1985, 5, 74. (33) Merlino, S.; Galli, E.; Alberti, A. Tsch. Mineral. Petrogr. Mitt. 1975, 22, 117. (34) Ballirano, P.; Bonaccorsi, E.; Maras, A.; Merlino, S. Eur. J. Mineral. 1997, 9, 21. (35) Pudovkina, Z.V.; Solov'eva, L.P.; Pyatenko, Yu.A. Dokl. Akad. Nauk SSSR, 1986, 291, 1370. (36) Zanardi, S.; Cruciani, G.; Alberti, A.; Galli, E. Am. Mineral.2004, 89, 1033. (37) Ballirano, P.; Bonaccorsi, E.; Maras, A.; Merlino, S. Can. Mineral. 2000, 38, 657. (38) Bonaccorsi, E. Microp. Mesop. Mater. 2004, 73, 129. (39) Rinaldi, R.; Pluth, J.J.; Smith J.V. Acta Cryst. 1975, B31, 1603. (40) Strohmaier, K.G.; Vaughan, D.E.W. J. Am. Chem. Soc. 2003, 125, 16035. (41) Ilyushin, G.D.; Blatov, V.A. Cryst. Rep. 2011, 56, 75. (42) Vezzalini, G.; Quartieri, S.; Galli, E.; Alberti, A.; Cruciani, G.; Kvick, A. Zeolites, 1997, 19, 323. (43) Merlino, S. Acta Cryst. 1974, B30, 1262. (44) Kocman, V.; Gait, R.I.; Rucklidge, J.C. Am. Mineral. 1974, 59, 71. (45) Ferro, O.; Quartieri, S.; Vezzalini, G.; Ceriani, C.; Fois, E.; Gamba, A.; Cruciani, G. Am.

Mineral. 2004, 89, 94. ACS Paragon Plus Environment

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(46) Alberti, A.; Vezzalini, G.; Galli, E.; Quartieri, S. Eur. J. Mineral. 1996, 8, 69. (47) Ercit, T.S.; van Velthuizen, J. Can. Mineral. 1994, 32, 855. (48) Ferraris, G.; Jones, D.W.; Yerkess, J. Z. Kristallogr. 1972, 135, 240. (49) Petersen, O.V.; Giester, G.; Brandstaetter, F.; Niedermayr, G. Can. Mineral. 2002, 40, 173. (50) Walter, F. Eur. J. Mineral. 1992, 4, 1275. (51) Pickering, I.J.; Maddox, P.J.; Thomas, J.M.; Cheetham, A.K. J. Catal. 1989, 119, 261. (52) Alberti, A. Tsch. Miner. Petrogr. Mitt. 1973, 19, 173. (53) Galli, E. Acta Cryst. 1971, B27, 833. (54) Rouse, R.C.; Peacor, D.R. Am. Mineral. 1986, 71, 1494. (55) Gottardi, G.; Galli, E. Natural Zeolites, Springer-Verlag, Berlin, 1985. (56) Coombs, D. S.; Alberti, A.; Armbruster, T.; Artioli, G.; Colella, C.; Galli, E.; Grice, J. D.; Liebau, F.; Mandarino, J. A.; Minato, H.; Nickel, E. H.; Passaglia, E.; Peacor, D. R.; Quartieri, S.; Rinaldi, R.; Ross, M.; Sheppard, R. A.; Tillmanns, E.; Vezzalini, G. Mineral. Mag. 1998, 62, 533.


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Table 1. Zeolite minerals (16) or synthetic zeolites (5) fitting all conditions of the natural packing model Zeolite code

Framewor k sp. gr.

Packi ng NBU (net)

Type material (mineral name)

Type material sp. gr.

Catio n

Position of ICSD cation Collecti on Code

BIK

Cmcm

t-pes

Li2(H2O)2(Al2Si4O12]

P1

Li

29551

(hcp)

(bikitaite)

t-pes/t-bik, 6-ring

t-afo

K7Na7(Be14P14O56)(H2O)20

P321

Na1

t-afo

36583

(bnn)

(synthetic, beryllophosphate-H) Na2

t-bph/

BPH

P 6 2m

t-bpa, 12-ring K1,2

t-bpa, 8-rings

CHA

R3m

t-hpr

KCa(Al3Si3O12)(H2O)5

(pcu)

(chabazite)

P1

Ca

t-hpr/

30873

t-cha, 6-ring

EDI

EMT

P 4 m2

P63/mmc

t-kzd

Ba2(H2O)8(Al4Si6 O20)

(pcu)

(edingtonite)

t-hpr Na5(Al5Si19O48) + t(synthetic, EMC-2) hpr

P2 1 2 1 2

Ba

t-krq/t-krq, 29516 8-rings

P63/mmc

Na1-3

t-hpr/

92903

t-toc, 6-rings

(lone) Na4

t-toc

P63/mmc

Ca

t-can

23491

P6 3 / m

K1, Na14

t-can/

155057

t-toc (lon) ERI

FAR

P63/mmc

P63/mmc

t-can

Ca(Al2Si16O36)(H2O)2

(hex)

(erionite)

t-can Na35.65K9.18Ca8.52(Al42Si42O168) +t-toc (SO4)10.73F0.16Cl0.48(H2O)3.03 (tcj)

(farneseite)


t-lio, 6-rings

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Na2,7

t-lio (hcp)

t-toc/ t-toc, 6-rings

Na6,

t-can/

Na11

t-toc, 6-rings

Na13

t-can/ t-can, 6-ring

Na14

t-toc/ t-lio, 6-ring

SO4

t-toc, t-lio

FAU

Fd 3 m

t-hpr

Na57(Si135Al57O384)

(crs)

(faujasite)

Fd 3 m

Na2,3

t-hpr/

22278

t-toc, 6-ring Na1

t-toc (dia)

t-toc/ t-fau, 6-ring

GME

P63/mmc

t-hpr

Na2(Al2Si4O12)(H2O)5

(acs)

(gmelinite)

P63/mmc

Na

t-hpr/

31240

t-gme, 6-ring

KFI

Im 3 m

t-hpr

Na21.2H1.4(Al22.4Si73.6O192)

(pcu)

(synthetic, ZK-5)

Im 3 m

Na1,2

t-hpr/

67761

t-grc, 6-ring Na3

t-grc (bcu)

t-pau/ t-grc, 8-ring


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LAU

C2/m

t-lau

Ca(Al2Si4O12)(H2O)2

(pcu)

(laumontite)

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C2

Ca

t-lau/

20473

t-kah, 6-ring

t-bal (bct) LIO

P 6 m2

tcan+ t-can

Na10K6Ca8(Si18Al18O72)(SO4)5 Cl3.5F0.5

P6

Ca1,2

Pm 3 m

t-toc

Na12(Al12Si12O48)(H2O)27

(pcu)

(synthetic, zeolite A)

82468

t-can,

(liottite)

6-rings

(hcp)

LTA

t-can/

Fm 3 c

Cl1,2

t-can

Na

t-toc/

24901

t-grc, 6-ring

t-cub (reo) LTL

P6/mmm

t-kaa

K4.63Na6(Al10.63Si25.38O72)

(kag)

(H2O)19.32 (synthetic, zeolite L)

P6/mmm

t-can

K2

t-kaa

K1

t-can

Na

t-kaa/

69414

(bnn)

t-ste, 8-ring MER

I4/mmm

t-opr

K11.5(Al11.5Si20.5O64)

(bcu)

(merlinoite)

Pnnm

K1

t-opr

K2,3

t-ste/

93958

t-pau, 8-rings NAT

OFF

I41/amd

P 6 m2

t-kzd

Na16(H2O)16(Al16Si24O80)

(bsn)

(natrolite)

t-can

KCa1.4Mg(Al5.24Si12.76O36)

Fdd2

Na

t-nat/t-nat, 8-rings

48139

P 6 m2

K

t-can

85549


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(hex)

(H2O)13.5 (offretite) Ca1,2

t-ato

Mg

t-gme

Im 3 m

Na/Cs

t-opr

62691

Pnna

Ca

t-kdt/

61166

t-ato (hex)

RHO

Im 3 m

t-opr

(Na, Cs)12(H2O)44(Al12Si36O96)

(reo)

(synthetic, related to mineral pahasapaite)

t-grc (pcu) THO

Pmma

t-kzd

NaCa2(Al5Si5O20)(H2O)6

(pcu)

(thomsonite)

t-krr, 8-ring Ca/Na t-krr

t-kzd (pcu) TSC

Fm 3 m

t-hpr (flue)

Ca4Sr1.03K0.65Ba1.32Cu3(Si12Al12 Fm 3 m O48)(OH)8(H2O)20.465Cl0.056

Ca1,2

t-hpr/

85550

t-toc;

(tschörtnerite)

t-hpr/ t-grc, 6-rings

t-toc+ t-grc

Cu, Cl

t-grc

K/Ba

t-hpr

Ca

t-srs

(flu)

t-opr (reo)

t-vsr (fcu) -WEN

P 6 2m

thpr+ t-srs

(Ba3.5K0.5)(Ca5.5Na0.5)

P 6 2m

2083

(Si11Al9O41)(OH)2(SO4)3

(9,12T2) (wenkite)


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Table 2. NBUs obeying the conditions of the natural packing model NBU

Ion

Position

Zeolites

t-afo

Na

center

BPH

t-ato

Ca

center

OFF

t-can

K, Ca, Cl

center

ERI, LIO, LTL, OFF

Na, K, Ca

6-ring

FAR, LIO

Cu, Cl

center

TSC

Na

8-ring

KFI

t-hpr

Ca, Na

6-ring

CHA, EMT, FAU, GME, KFI, TSC, WEN

t-kaa

K

center

LTL

Na

8-ring

LTL

t-lau

Ca

6-ring

LAU

t-lio

SO4

center

FAR

Na

6-ring

FAR

t-opr

K, Cs

center

MER, RHO

t-pes

Li

6-ring

BIK

t-srs

Ca

10-ring

WEN

t-toc

Na, SO4

center

EMT

Na

6-ring

FAR, FAU, LTA

t-grc


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Table 3. Occurrence of NBU packings in 237 hypothetic zeolites Packing natural building unit

Face symbol

Occurrence

t-lov

[42.62]

88

t-whw

[34.62]

26

t-cub

[46]

21

t-tes

[54]

14

t-ctn-e

[32.83]

11

t-ste

[42.84]

11

t-afi

[65]

9

t-sod-a-1

[34]

9

t-aww

[46.64]

9

t-kah

[63]

6

t-oop

[64.82]

5

t-opr

[48.82]

4

t-toc

[46.68]

4

t-npo

[32.63]

4

t-apf

[66.122]

4

t-hpr

[46.62]

3

t-ffb

[412.122]

3

t-ber

[68]

2

t-sod-a-1+t-hpr

[34]+[46.62]

2

t-trc+t-cub

[38.86]+[46]

2

t-gie-1

[44.122]

2

t-kaa

[62.82]

1

t-mla

[512.62]

1

t-kno

[43.83.122]

1

t-gme

[49.62.83]

1

t-trc+t-trc

[38.86]+[38.86]

1

t-fau

[418.64.124]

1


33


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t-vsr

[424.68.818]

1

t-hpr+t-opr

[46.62]+[48.82]

1

t-sod-a-1+t-cub

[34]+[46]

1

t-sod-a-1+t-sod-a-1

[34]+[34]

1


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TABLE OF CONTENTS GRAPHIC


35


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180x59mm (300 x 300 DPI)


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191x123mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

201x117mm (300 x 300 DPI)


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180x58mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

170x35mm (300 x 300 DPI)


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133x60mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

180x71mm (300 x 300 DPI)


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172x62mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

154x65mm (300 x 300 DPI)


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118x47mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

145x63mm (300 x 300 DPI)


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93x81mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

90x127mm (300 x 300 DPI)


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80x69mm (300 x 300 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

109x62mm (300 x 300 DPI)


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170x54mm (300 x 300 DPI)


The Zeolite Conundrum: Why Are There so Many Hypothetical Zeolites

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