Designer zeolitesIgor Rivin

Temple UniversityDepartment of Mathematics

All work joint with Mike Treacy (ASU)

What is a zeolite?

Zeolites (Greek, zein, "to boil"; lithos, "a stone") are hydrated aluminosilicate minerals and have a micro-

porous structure.

The term was originally coined in the 18th century by a Swedish mineralogist named

Axel Fredrik Cronstedt who observed, upon rapidly heating a natural mineral, that the stones began to

dance about as the water evaporated. Using the Greek words which mean "stone that boils," he called this

material zeolite.

We will describe what zeolites are to a mathematician shortly, but the important aspect of them for a

material scientist is that they are very porous, and that’s what is responsible for most of the uses described

below...

Summary• Zeolites are industrially important. There is a need for new zeolite structures.

• Zeolite frameworks can be represented as directed, or colored, graphs, that contain information about site symmetry and bonded neighbors.

• Given a space group, and number of unique T-atoms NT, all the possible graphs can be enumerated by a combinatorial analysis of all those site-site interconnections that are consistent with tetrahedral bonding.

• Graphs can be “embedded” in real space by various methods, such as simulated annealing, to find the regular tetrahedral SiO2 frameworks.

• A combinatorial explosion of graphs with increasing NT, limits the method as presently implemented, to NT ≤ 7 for high symmetry space groups. The percentage of viable frameworks drops off rapidly with increasing NT.

• Describe the methods used and highlight the problems with imbedding.

• Examples from high-symmetry space groups, Pm3m, P6/mmm, etc

• Can we predict how to make hypothetical zeolites?

What are zeolites good for

• Petrochemical industry

Synthetic zeolites are widely used as catalysts in the petrochemical industry, for instance in fluid catalytic cracking and hydro-cracking. Zeolites confine molecules in small spaces, which causes changes in their structure and reactivity. The hydrogen form of zeolites (prepared by ion-exchange) are powerful solid-state acids, and can facilitate a host of acid-catalyzed reactions, such as isomerisation, alkylation, and cracking. The specific activation modality of most zeolitic catalysts used in petrochemical applications involves quantum-chemical Lewis acid site reactions. Catalytic cracking uses a furnace and reactor. First crude oil distillation fractions are heated in the furnace and passed to the reactor. In the reactor the crude meets with a catalyst such as zeolite. It goes through this step three times, each time getting cooler. Finally it reaches a step known as separator. The separator collects recycled hydrogen. Then it goes through a fractionator and becomes the final item.

What are zeolites good for?

• Commercial and Domestic

Zeolites are widely used as ion-exchange beds in domestic and commercial water purification, softening, and other applications. In chemistry, zeolites are used to separate molecules (only molecules of certain sizes and shapes can pass through), as traps for molecules so they can be analyzed.

Zeolites have the potential of providing precise and specific separation of gases including the removal of H2O, CO2 and SO2 from low-grade natural gas streams. Other separations include: noble gases, N2, O2, freon and formaldehyde. However at present, the true potential to improve the handling of such gases in this manner remains unknown.

What are zeolites good for?

• Nuclear Industry

Zeolites have uses in advanced reprocessing methods, where their micro-porous ability to capture some ions while allowing others to pass freely allow many fission products to be efficiently removed from nuclear waste and permanently trapped. Equally important are the mineral properties of zeolites. Their alumino-silicate construction is extremely durable and resistant to radiation even in porous form. Additionally, once they are loaded with trapped fission products, the zeolite-waste combination can be hot pressed into an extremely durable ceramic form, closing the pores and trapping the waste in a solid stone block. This is a waste form factor that greatly reduces its hazard compared to conventional reprocessing systems.

What are zeolites good for?

• Agriculture

In agriculture, clinoptilolite (a naturally occurring zeolite) is used as a soil treatment. It provides a source of slowly released potassium. If previously loaded with ammonium, the zeolite can serve a similar function in the slow release of nitrogen. Zeolites can also act as water moderators, in which they will absorb up to 55% of their weight in water and slowly release it under plant demand. This property can prevent root rot and moderate drought cycles.

What are zeolites good for?

• Animal Welfare

In Concentrated Animal Growing facilities, the addition of as little as 1% of a very low sodium clinoptiloite was shown to improve feed conversion, reduce airborne ammonia up to 80%, act as a mycotoxin binder and improve bone density. See US Patents 4,917,045 and 6,284,232. Can be used in general odor elimination for all animal odors.

What are zeolites good for?

• Medical

Zeolite-based oxygen concentrator systems are widely used to produce medical grade oxygen. The zeolite is used as a molecular sieve to create purified oxygen from air using its ability to trap impurities, in a process involving the absorption of undesired gases and other atmospheric components, leaving highly purified oxygen and up to 5% argon. QuikClot® brand hemostatic agent, which continues to be used successfully to save lives by stopping severe bleeding, contains a calcium loaded form of zeolite.

What are zeolites good for?

• Heating and refrigeration

Zeolites can be used as solar thermal collectors and for adsorption refrigeration. In these applications, their high heat of adsorption and ability to hydrate and dehydrate while maintaining structural stability is exploited. This hygroscopic property coupled with an inherent exothermic (heat producing) reaction when transitioning from a dehydrated to a hydrated form, make natural zeolites useful in harvesting waste heat and solar heat energy.

What are zeolites good for?

• Detergents

The largest single use for zeolite is the global laundry detergent market. This amounted to 1.44 million metric tons per year of anhydrous zeolite A in 1992.

What are zeolites good for?

• Construction

Synthetic zeolite is also being used as an additive in the production process of warm mix asphalt concrete. The development of this application started in Europe (Germany) in the 1990s. It helps by decreasing the temperature level during manufacture and laying of asphalt concrete, resulting in lower consumption of fossil fuels, thus releasing less carbon dioxide,aerosols and vapours. Other than that the usage of synthetic zeolite in hot mixed asphalt leads to easier compaction and to a certain degree allows cold weather paving and longer hauls. When added to Portland Cement as a Pozzolan, it can reduce chloride permeability and improve workability. It reduces weight and helps moderate water content while allowing for slower drying which improves break strength.

What are zeolites good for?

• Aquarium keeping

Zeolites are marketed by pet stores for use as a filter additive in aquariums. In aquariums, zeolites can be used to absorb ammonia and other nitrogenous compounds. However, due to the high affinity of some zeolites for calcium, they may be less effective in hard water and may deplete calcium. Zeolite filtration is used in some marine aquaria to keep nutrient concentrations low for the benefit of corals adapted to nutrient-depleted waters.

Where and how the zeolite was formed is an important consideration for aquariums. Northern hemisphere natural zeolites were formed when molten lava came in contact with sea water, thereby 'loading' the zeolite with Na (sodium) sacrificial ions. These sodium ions will speciate with other ions in solution, thus the takeup of nitrogen in ammonia, with the release of the sodium. In southern hemisphere zeolites, such as found in Australia, which were formed with fresh water, thus the calcium uptake on formation.

Zeolite is an effective ammonia filter, but must be used with some care, especially with delicate tropical corals which are sensitive to water chemistry and temperature.

Space hardware testing

Zeolites can be used as a molecular sieve in cryosorption pumps for rough pumping of vacuum chambers which can be used to simulate space-like conditions in order to test hardware bound for space.

Cat litter

Non-clumping cat litter is often made of zeolite or diatomite.

[edit]

Zeolites Are Important for Synthesis, Refining, and Environmental Processes

1995 2000 2005

Chemical (1) 180 280 350

Refining (2) 650 930 1,130

Environmental (3) 150 410 530

Notes

1) Aromatics and specialty organic synthesis

2) USY in FCC, hydrocracking, Other zeolites in FCC additives, saturation,

isomerization and lubes

3) VOC, automotive Source: The Catalyst Group

Zeolite Catalyst Sales, $M, Constant $

Are there Opportunities for New Structures? C

um

ula

tive N

o. of

Zeolit

e P

ate

nts

and P

ublic

ati

on

s (N

ew

Str

uct

ure

s, S

yn

thesi

s, C

ata

lysi

s, S

orb

ents

)/Year

1965 1985 1990 1995 2000 20051970 1975 1980

Publications Patents

Why zeolite catalysts?• Significantly better product selectivity • Greater activity – leading to higher throughputs and debottlenecking.• Environmental compatibility– Catalyst disposal– Reduction of byproducts• Growth in the variety of available zeolite structures and compositions.• Improved understanding of diffusivity and structure – property – function

relationships.

Advances in zeolite catalyst technology have changed the nature of the refining and petrochemical processes – requiring

less separation, less energy, smaller reactors, and often simpler process configurations

sPA-Based Cumene Process In 1986 (US only) • Generated 250M lbs of heavy aromatics as a cumene byproduct - put into

gasoline

• Generated 5M lbs of spent SPA catalyst as solid waste

Special Handling Requirements• SPA catalyst disposal involves drying and directed explosive charges to dislodge

it from reactors

• Requires precise H2O addition

Cumene Process

ZeoliteZeolite

Cumene Purity 99.97%Cumene Yield 99.7%Bz/Propylene 3:1 Catalyst Life 5 yrs +

sPA sPA

Cumene Purity 99.0%Cumene Yield 95%Bz/Propylene 8:1 Catalyst Life 12-18 mo.

http://internet-mobil.na.xom.com/mobil_research/mapped/cumene.html

There are Five “Big” Zeolites

Attests to the versatility of these materials and the exceptional selectivity provided by the specific crystal structure

12-MR, 1-dimensional

12-MR, 3-dimensional

10-MR, 3-dimensional

10- &12-MR, 2-dimensional

12-MR, 3-dimensional

Faujasite (FAU) MCM-22 (MWW)

Beta (BEA)

ZSM-5 (MFI)

Mordenite (MOR)

Factors Contributing to the Predominance of These Five Structures

• Early discovery and development

• Scaleability and low cost of manufacture

• Early structure resolution – allows modelling

• Hydrothermal stability - regenerability

• Compositional and morphological versatility

• Understanding the underlying catalytic chemistry and implications of

molecular transport

• Inability of other materials to match the broad selectivity advantages

and activity of these structures

Are there Opportunities for New Structures?The Answer is Yes!

Most Likely:– Supplementing existing catalysts to tailor selectivity– In new applications driven by changes in product demand or regulatory

changes (e.g., benzene alkylation)– At the intersection of petroleum refining and petrochemical manufacturing– Where the materials provide new routes to existing processes (e.g.,

reaction and separation) – In specialty chemicals production where product margins can justify the

cost of catalyst development and scale-up– Where there are needs for processing non-conventional feedstocks (e.g.

biomass; heavy/dirty feedstocks; natural gas)

– In advanced environmental catalysts (e.g. NOX and SOX reduction)

However, almost all new zeolites are discovered by serendipity – by unpredictable synthetic methods, or as new minerals.

The number of known zeolites is growing

LTL Framework

Pt/ K-zeolite L converts n-hexane to benzene with high yield and efficiency

Construction of LTL Model

ConstructCancrinite

cages

StackCancrinite cages

Cross-connectCancrinite columns

LTL Framework

But instead…

ConstructCancrinite

cages

StackCancrinite cages

Cross-connectCancrinite columns

Definitely Not LTL

191_2_13

Rotated Cancrinite Columns

LTLCross-linking creates 8-rings

apertures are sinusoidal12-ring 18-ring channelsa = 18.0 Å, c = 7.50 Å

NOT-LTLCross-linking creates 4-rings

apertures are smooth18-ring channels

a = 21.4 Å, c = 7.66 Å

191_2_14 191_2_13

A simple connection error produceda new and interesting structure

Defects in Zeolites RepresentNew Local Topologies

M. Audier, J, M,. Thomas, J. Klinowski, D. A. Jefferson and L. Bursill, J. Phys. Chem. 1982, 86, 581. The elusive “Breck’s structure 6”

Faujasite with a stacking fault

Challenge!

How many ways can two Si atoms be interconnectedin space group P6/mmm to produce regular tetrahedralzeolitic frameworks?

• Billions+ ? – the combinations are almost infinite.

• A handful ? – the combinations being limited by symmetry.

It took 10 years to get an answer – there are exactly 48!31 of which are close to regular tetrahedral.

Methods For Finding New Frameworks• Synthesis + Direct experimental methods (Single crystal, Rietveld, TEM).

– MFI, beta (+ many others)• Modification of existing structures.

– ALPO-8• Model building – trial and error.

– FAU framework• Permutation of connections between sheets, polyhedra.

– Many examples by J. V. Smith• Applying symmetry operators to secondary building units.

– Akporiaye & Price, Shannon• Distance least squares, simulated annealing.

– DLS-76 (Hepp Baerlocher, Meier), ZEFSA (Deem & Newsam)• Permutation of symmetry operators.

– Fischer et al. (1993) - search for low-density frameworks• Dense grid search.

– O'Keeffe & Brese (1990)• Symmetry-Constrained Intersite Bonding Search (SCIBS).

– Treacy et al. (1993, 1997, 2004), Klein (1996)• Polyhedral tiling.

– Andries & Smith (1996), Delgado-Friedrichs (1999)

The LTL framework has P6/mmm symmetry

36 T-atoms and 72 oxygen atoms per unit cell

The LTL framework has P6/mmm symmetry

All of the symmetry operations can be generated by mirrors

LTL Framework

Each T-atom isconnected to fouroxygens

The LTL framework is generated bythe action of the mirror planes,much in the same way as akaleidascope works.

LTL fundamental region contains 2 T-atoms and 6 unique Oxygen atoms,and is bounded by 5 mirror planes.

The general site has 3 choices

LTL

• 2 must connect directly to 1, and to the top and side faces to ensure3-D connectivity.

• This leaves one free bond, and three connectible faces.Permutation over the three available bonds gives 3 new structures

1

2

The basal mirror site has 3 choices

• 1 must connect directly to 2.

• Two of the oxygens attached to 1 must lie on the edges defined byintersecting (perpendicular) mirror planes to preserve regular tetrahedral symmetry.

• The fourth bond to 1 is generated by reflection in the basal mirror plane.

1

2 T-atom 2 is insidethe fundamental region

= 3 possibilities for atom 132 = 3.2.1

1.2.1There are only

Nine topologies with T-atoms on the same sites as LTL

There are exactly 48 binodal topologies in P6/mmm, 31 of which refine well

Generalizing to other space groups

“Roadmap” viewgraph from 1991

Colored Graph Description – LTL

Oxygen atoms are implied by the Si–Si bonds, and are therefore redundant.

Colored (or directed) graph. The “color” is the bond operator type

Atom id operator Atom idAtom site list

o o’’

Mirror sites o ando’ are topologicallydistinct.

Space groupNumber of unique T-atoms

Another Example – FER

Surprisingly, most of the effort is in refining the graphs

Imbedding the graphs in real space – refining them – has been arduous, and is an ongoing struggle.

Speed and efficiency are low.

The effort planned assumedthat the refining would bequick and easy

Regular tetrahedral force model

This is an empirical model with lowest cost for the cubic diamond structure

€

U = K1 dTT − 3.05( )2

€

+ K2 αTTT −1.91063( )3

Ångstrom

radian

This formula attempts to force T-atoms into a regular tetrahedralarrangement with TTT angles of 109.47°

This generates reasonable approximations to zeolite frameworks.

Predicts that cristobalite has lower energy than quartz, because realzeolites do not favor tetrahedral TTT angles because of the bridgingoxygen atoms

Out of 6,471 uninodal graphs, only one was new!

Out of 6,471 uninodal graphs, ~300 were plausible tetrahedralarrangements, and only one was truly new! mmt in O'Keeffe's database

Space group #56. Pccn.a = 8.02 Å, b = 4.43 Å, c = 8.68 ÅT-atom at:x = 0.071, y = 0.126, z = 0.151T/1000 = 25.92

High density phase – “ −silica”

• Related to O'Keeffe's –Si, bcc(8)

• Post-diamond high-pressure form of carbon

FD = 26.76 T-atoms/1000Å3

TD10 = 1165.0

Coordination Sequence1 4 12 27 49 77 109 148 194 244 301

Vertex Symbol 6.62.6.62.6.62

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Ia3

206_1_170

γ

γ

Next steps

• Find a way to efficiently imbed graphs with NT ≥ 2 – increases the number of graphs exponentially.

• Find a way to efficiently include the bridging oxygen atoms – potentially triples the degrees of freedom.

Both of these goals dramatically increase the complexity of the problemto be solved.

We have an enormous number of graphs out to NT ≤ 7, but had succeeded only in imbedding the uninodal (NT = 1) graphs withoutthe oxygen atoms.

Boisen-Gibbs-Bukowinski force model

Empirical force field derived from ab-initio modellingof Si2O7, and fitting to quartz compressibility data.

Most terms relate to the local T2O7 cluster.

The non-codimer repulsion terms (dOO) arecomputationally expensive.

M. B. Boisen, G.V. Gibbs and M.S.T. Bukowinski, Phys. Chem. Minerals (1994) 21 269 – 284

€

UBGB = A L −L0( )2

O

∑

+ B OTO −OTO0( )2

T

∑

+ C TO −TO0( )2

T

∑

+ D L −L0( ) TO −TO0( )O

∑T

∑

+ E exp(−FdOO +G)d

OO>4Å

∑

Stages of refinementExample, LTL, space group P6/mmm (191) two unique T-atoms

Place atoms at thegeometric center oftheir neighbors (barycentering).Refine unit cellusing T-atoms

Refine T-atoms andunit cell parametersusing “regulartetrahedral” forceson T-atoms

Refine T-atoms,O-atoms andunit cell parametersUsing Boisen-Gibbs-Bukowinski force model

Refine T-atoms,O-atoms andunit cell usingGULP (J. Gale)

Refinement MethodParallel tempering with selective inheritance

Parallel simulated annealing runs, with temperature swappingand with elements of a genetic algorithm

• Temperatures are decreased, and swapped according to a Boltzmann factor• If logjammed, parameter lists are compared, and favorable “genetic” traits are selected from other annealing results

Inherited “genes”

Unpredictable Convergence Rates

Preconditioning the frameworks for refinement

SiGH – Silica General Handler (S. A. Wells)

• SiGH is a symmetry-aware ‘offspring’ of GASP. It finds rapidly the conformations that preserve best the rigid tetrahedra.

SiGH as an efficient filter

• SiGH finds rapidly the implausible frameworks – i.e. those for which there is no hope of ever identifying a tetrahedral flexibility window.

SiGH speeds up the rate of framework discovery by a factor of ~10

• It appears that there are very few “babies in the bathwater”, but it seems likely that some good frameworks will be discarded inadvertently

Combinatorial ExplosionThe number of graphs tends to increase exponentially with increasing n

N =A× Bn

Combinatorial ExplosionThe number of graphs tends to increase exponentially with increasing n

(225)

The number of viable frameworks does not increase as rapidlywith increasing n

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Pm3 m

Spacegroup Pm3m is “productive”

225_1_1

225_1_2

225_1_3

3 out of 3 uninodal graphs refine well

UBGB = 0.007605 eV

UGULP = -128.504213 eV

UBGB = 0.026605 eV

UGULP = -128.562527 eV

UBGB = 0.021484 eV

UGULP = -128.382971 eV

LTA SOD KFI

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Pm3 m,1T- atom

Spacegroup Pm3m is “productive”12 out of 13 binodal graphs refine well

€

Pm3 m, 2 T- atoms

GULP evaluates stability from phonon eigenvalues

225_2_13

Tetrapod of double 3-ring prisms

Some phonon eigenvalues are complex indicating that the framework isunstable in this space group and composition.

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Pm3 m, 2 T- atoms

Some construction themes are obvious (with hindsight)

225_3_8

Sodalite cages connected bychains of cubes. The chainlength can be varied indefinitely

Coordination sequences1 4 7 8 10 17 27 35 39 40 42 53 78 110 137 154 1 4 7 10 15 20 25 31 36 41 51 68 89 110 127 139 1 4 9 15 20 23 24 26 33 47 67 88 104 111 112 115 Vertex symbols4.4.4.4.4.244.4.4.4.4.244.6.4.6.4.24

UGULP = -128.1129 eV/TO2

UBGB = 0.08123 eV/TO2

FD = 5.83 T-atoms/1000 Å3

Density = 0.5817 g.cm-3

TD10 = 245.667

Parent member of the progression is sodalite

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Pm3 m, 3 T- atoms

Framework density tends to increase with increasing refinement energy

P6 / mmm, 3 T-atoms

659 graphs out of 1150 refined with energy ≤ 1.0 eV/TO2 (BGB)The distribution of frameworks over energy is not uniform.

P6/mmm produces some very pretty frameworks

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P6/ mmm,3 T - atoms

191_3_123

[001]

[100]

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[11 0]

Enormous channels are possible

[100]

[001]

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P6/ mmm,4 T - atoms

a = 41.1Åc = 9.7 Å

FD = 6.75 T-atoms/10003

191_4_1955

Delicate low-density structures

[001]

FD = 10.88 T-atoms/10003

a = 26.5 Åc = 7.26 Å

This representationis cell-doubled191_4_3295

Assembly of decorated 12-ringsor decorated 24-rings

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P6/ mmm, 3 T - atoms

Likely candidate

[001]

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P6/ mmm,4 T - atoms a = 18.35Åc = 17.56 Å

FD = 16.4 T-atoms/10003

191_4_5828

Cancrinite and D8R

4.4.4.6.8.124.4.4.6.6.84.4.6.6.6.64.6.4.6.6.12

Vertex symbolssuggest simplepolyhedra

UBGB = 0.005 eV/TO2

Higher energy structures are also interesting

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Pm3 m, 3 T- atoms

191_3_786

Many beautiful, but improbable frameworks emerge at higher energies

UBGB = 0.5 eV/TO2

Unembeddable frameworks are also interesting

In ten, The smallest ring size is 10!

Another structure, elv, has smallest ring size is 11. It cannot be drawn (yet!)

ten

Our database is online and searchable

Several characterization tools have been implemented, including• Interactive graphics• Powder pattern simulation• Bond lengths, angles, topology• Pore characteristics (by Delaunay triangulation)

• http://www.hypotheticalzeolites.net

Spheres tell us a lot about zeolites

229_5_8058871

Packing: He, Ne, Ar, Kr, XeMaximum included sphereLargest freesphere

Sphere packing

Sphere packing

What is next?• Extend method out to NT = 12 (ie MFI) and beyond.

– Improved graph-filtering based on graph topology is needed.– Rapid graph-refinement strategies are still needed.– Computer cluster working on the problem.

• Improve framework topology microporous properties tools to help identify appropriate synthetic targets.

• Implement search algorithms based on pore characteristics.

• Can Delaunay triangulation work on a torus?

• Solve the Apollonian problem. This will accommodate the different van der Waals radii of the framework atoms.

• Implement search algorithms against powder patterns.

• Do all ‘real’ zeolites have a flexibility window? (Thorpe, Kapko)

→

“Real” zeolites are flexible

A. Sartbaeva, S. A. Wells, M. M. J. Treacy and M. F. Thorpe, The flexibility window in zeolites,Nature Materials 5 962–965 (2006).

A set of simple rules helps limit the numberof combinatorial possibilities

(1) No T-atom can lie on a 6-fold axis

(2) No T-atom, or T-atom vertex, can lie on a vertex of the fundamental region

(3) If a T-atom lies on a face of the fundamental region, then two (and only two)of the T-atom vertices lie on that same face. (otherwise it is planar))

• Connections to atoms outside the fundamental region must involve either aT-atom, or one of its vertices, that lies on a mirror (or on an edge defined bytwo perpendicular mirrors).

(5) All T-atoms are connected to four other T-atoms.

(6) Tetrahedra are denied edge- and face-sharing connectivities.

• Each of the five faces of the fundamental region must have at least one bondconnecting through it. (For 3-dimensional connectivity)

"γ-silica" comprises chiral space-filling units

There are equal numbers of left- and right-handed units

One of the TOT bond angles is ~180°

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206_1_170

Sphere packing

Pores are characterized automatically by Delaunay Triangulation Methods

Delaunay triangulation identifies the empty circumspheres in an arrayof points. It is a natural and convenient method for identifying and characterizing the empty spaces (pores and channels) in zeolites.It also allows us to estimate pore opening diameters.

Empty circumspheres in SOD

Zeolites as Colored Graphs

• Frameworks are represented as graphs with four edges (bonds) from each vertex.• All 4-connected uninodal graphs look the same – the clover-leaf shape.• There are four distinct 4-connected binodal graphs.• Edges (bonds) are "colored" by the crystallographic operator (and its inverse)

that defines the connection.• A combinatorial search is performed on all possible permutations of edge colorings.

Interthreaded Cristobalite

Two frameworks do not cross-connect

Interthreaded Δ1 cristobalite framework

This framework exists! [Sn5S9O2] . [HN(CH3)3]2 — Parise and Ko (1995)

Interthreaded FAU framework

Coordination Sequence• The coordination sequence for a T-atom Sk is the number of T-atoms

in the shell that is k bond lengths away.• Topological density TD10 can be defined simply as the sum of the first

10 entries of the coordination sequence

Count T-atomson expanding shell

Faujasite fragment

Coordination sequence is not necessarilyunique to each framework.

Circuit Symbols and Vertex Symbols

• Each T-atom has 6 interbond angles

• Describe each of the six shortest loops connecting any pair of bonds

• Example FAU – has one unique T-atom

• Circuit/Vertex symbols are not necessarily unique to each framework.

Issues when atoms are not pointsApollonian triangulation

Eight solutions exist for circles, sixteen solutions for spheres.We believe that we have this problem solved (in principle!)

Lowest-energy 6 T-atom structure

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Pm3 m, 6 T- atoms

UGULP = -128.5184 eV/TO2

Clathrated assembly of sodalite cages (in a sodaliticarrangement), cancrinite cages double 6-ring prisms and cubes.Modified SOD + LTA + LTL.225_6_22665

Family of 3D defect structures

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Pm3 m, 6 T- atoms

225_6_22665225_6_22585a = 41.285 Å (doubled cell)UGULP= -128.4852 eV/TO2

a = 41.633 ÅUGULP = -128.5184 eV/TO2 (More stable!)

• The third end-member of this particular series, ALL CAN/D6R units, has not yet been located in the data (confident it is there).• The SOD ⇐⇒ CAN/D6R transformation can occur in local pockets of 8 units at a time

Framework of ZSM-10

There were 18.4 million graphs with 6 unique T-atoms.This is the one!

Known to be in P6/mmm with 6 unique T-atoms

Visual Comparison of Powder Patterns Favors Model A

It is difficult to remove all extraframework K cations.A recent Rietveld refinement by D.L Dorset confirms A as the best fit.

ZSM-10: plausible low-energy frameworks

Two frameworks with 5-rings have even lower energy than LTLWhen refined as pure SiO2

Correlation between BGB and GULP framework energies is linear at low energies

• Some of the scatter may be related to the vagaries of simulated annealing• The gradient is 1:6 at low energies, 1:1 at higher energies (EGULP > 0.7 eV).

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P6/ mmm, 3 T - atoms

Delaunay Triangulation of a set of points

The perpendicular bisectors define the Voronoi cells

The edges of the Voronoi cell are equidistant from two points.Each Voronoi cell “belongs” to one point.

The empty circumcircles reveal the empty space

Each circle touches three points, but does not enclose any points.These circles thus delineate the empty space – i.e. the pores!

Typo at a recent conference:Zeoltie?

A combinatorial permutation of zeolite.

ZeoTileIs more appropriate for a polyhedral tilings(O. Delgado Friedrichs & M. O’Keeffe?)

OzEliteJ. C. H. Spence and D. J. Smith?

Cross-link defect that connects the interthreaded cristobalite frameworks

“Wormhole” defect that cross-connects two parallel frameworks

Cogwheels of double 3-ring prisms

225_3_32

225_3_27

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Pm3 m, 3 T- atoms

Establishing Connectedness in the General Case is Time-Consuming.

For connectedness, there must exist a path of bonds connecting each atom Ato its translated image A' in an adjacent unit cell.

Further, there must exist a path connecting all dissimilar atoms.

To prove that A and its image A'are not connected can involve(2n+1)3 unit cells, where n isthe number of unique atoms inthe unit cell.

Significant speed-up is obtainedby restricting the search toadjacent unit cells only.

Some legitimate structures willbe overlooked.

Comparison of GULP and BGB RefinementsThe GULP program and the Boisen-Gibbs-Bukowinski (BGB)

Refinements produce subtle differences in frameworks

BGB is a bonded-neighbour-only force-field

Correlation between topological density and framework density

Correlation is strongest for lowest energy refinements

Comparison of two combinatorial methods

O. Delgado Friedrichs et al (Nature 400 644 (1999)) demonstrated acombinatorial method based on tilings of polyhedra.

Since many important zeolites can be thought of as being built fromsimple polyhedral units, the tiling method effectively pre-selects theconnected sub-units (tiles) based on their likelihood of formingregular tetrahedral frameworks.

In our method, the sub-unit is the isolated T-atom. ALL possible graphsare found for a given space group and number of unique T-atom bypermuting all possible arrangements of T-atoms on special crystallographicsites. However, many of these graphs cannot be arranged as regularTetrahedral frameworks. The likely topologies (ie based on the polyhedraimplicit in the graph) are filtered out after each graph is created.

The two methods must converge on the same frameworks, but from differentstarting points.

What is next?• The Structure Commission of the International Zeolite Association is

planning to create a database of hypothetical zeolite frameworks that will be available to researchers on the web (perhaps by mid-2004).– Data of Smith, O’Keeffe/Delgado-Friedrichs, Bell/Foster, Deem, Treacy.

• Extend method out to NT = 12 (ie MFI) and beyond.

– Improved graph-filtering based on graph topology is needed.– Rapid graph-refinement strategies are needed.– Computer cluster working on the problem (plus Martin Foster).

• Improved tools for cataloging frameworks (O’Keeffe leads the way)• Improve graphics tools for visualizing results!

• Needed: Improved framework topology → microporous properties tools to help identify appropriate synthetic targets.

• O’Keeffe, Treacy, Foster and Delgado-Friedrichs are all at ASU

Outstanding issues for the database• Solve the Apollonian problem. This will accommodate the

different van der Waals radii of the framework atoms.

• How to handle elliptical apertures?

• Implement search algorithms based on pore characteristics.

• Implement search algorithms against powder patterns

Combinatorics of connections between crystallographic sites

There are 14 connectable sites for tetrahedra in the P6/mmmfundamental region. The rules for interconnections depend on the site.

A Venn Diagram Framework!

Tetragonal trihedronA 3-fold “paddle wheel”of bent 4-rings.

I4/mmm (139) 3 unique T-atoms-128.238 eV/TO2 (from GULP)

1 4 8 13 22 36 52 69 86 98 1121 4 9 16 24 35 52 67 78 101 1381 4 9 18 30 39 46 60 86 121 160

4.42.4.62.62.261024

4.4.4.82.4.82

4.42.8.8.8.8

€

P4 / mmm, 3 T- atoms