Symmetry Aspects of Zeolite Frameworks

3 Symmetry Aspects of Zeolite Frameworks W. M. MEIER

Downloaded by UNIV OF SYDNEY on August 26, 2013 | http://pubs.acs.org Publication Date: June 1, 1973 | doi: 10.1021/ba-1973-0121.ch003

Institut für Kristallographie und Petrographie der ETH, Zurich, Switzerland

Zeolite frameworks are variously pseudosymmetric. Reported structure determinations and refinements of most zeolites pertain to symmetrized structures in which bond distances tend to be too short, and structural details such as Si, Al order and cation distribution are more or less obscured. Distance least squares (DLS), a method for generating model structures (DLS models) with optimum interatomic distances, is useful for studying symmetry-dependent geometrical constraints in zeolite frameworks, determining probable space groups of desymmetrized structures, and for interpreting symmetrized structures. Using analcime and faujasite-type structures as examples, it is shown how evidence for (local) Si, Al order can be obtained from sufficiently refined symmetrized structures using DLS models.T-Odistances should not be used directly for determining the amount of Al in T sites in these high-symmetry structures.

n o t a b l e feature of most zeolite s t r u c t u r e s is t h e a p p a r e n t l y h i g h s y m m e t r y of t h e a l u m i n o s i l i c a t e f r a m e w o r k . I n e v i t a b l e d e v i a t i o n s f r o m the i d e a l i z e d s t r u c t u r e s a n d t h e i r a p p a r e n t s y m m e t r y are f r e q u e n t l y n o t r e a d i l y observable. A l l zeolites are i n fact m a r k e d l y p s e u d o s y m m e t r i c . T h e p s e u d o s y m m e t r y c a n arise for v a r i o u s reasons i n c l u d i n g S i , A l o r dering, bonding requirements, a n d geometrical constraints. x

T h e i d e a l i z e d h i g h - s y m m e t r y s t r u c t u r e ( A s t r u c t u r e ) a n d the p s e u d o s y m m e t r i c a c t u a l s t r u c t u r e ( H s t r u c t u r e ) m u s t be c l e a r l y d i s t i n g u i s h e d . T h e A s t r u c t u r e c a n be d e r i v e d f r o m the H s t r u c t u r e b y s y m m e t r i z a t i o n , i.e., b y a p p l y i n g the p s e u d o s y m m e t r y operation(s). T h i s is i l l u s t r a t e d i n F i g u r e 1. T h e H s t r u c t u r e i n t h i s s i m p l e e x a m p l e c o n t a i n s a f o u r f o l d p s e u d o r o t a t i o n . T h e s y m m e t r i z a t i o n is c a r r i e d o u t b y a p p l y i n g t h e o p e r a t i o n of t h i s f o u r f o l d r o t a t i o n t o t h e H s t r u c t u r e , a n d s y m m e t r i z e d positions (located a t the centers of the shaded areas i n F i g u r e 1) are t h e r e b y o b t a i n e d . T h e a t o m s i n the H s t r u c t u r e are t h u s d i s p l a c e d t o some extent w i t h respect t o t h e s y m m e t r i z e d positions. U n l i k e H s t r u c t u r e s , A s t r u c tures c a n i n general be d e t e r m i n e d r o u t i n e l y b y c o n v e n t i o n a l m e t h o d s of 39 In Molecular Sieves; Meier, W., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1973.

40

MOLECULAR SIEVES


s t r u c t u r e a n a l y s i s . T h e basic p r o b l e m i n the a n a l y s i s of p s e u d o s y m m e t r i c H s t r u c t u r e s is f i n d i n g the d i s p l a c e m e n t v e c t o r for each a t o m of the H s t r u c t u r e . F o u r i e r peaks of s y m m e t r i z e d s t r u c t u r e s c a n a t best r e v e a l t h e m a g n i t u d e b u t n o t t h e d i r e c t i o n of the d i s p l a c e m e n t vectors. The p r o b l e m of d e t e r m i n i n g these vectors is p a r t i c u l a r l y difficult w h e n the s y m m e t r i z e d peaks comprise more t h a n t w o c o m p o n e n t peaks a n d w h e n t h e displacements are s m a l l . F u r t h e r difficulties are encountered i n t h e absence of t r a n s l a t i o n a l p s e u d o s y m m e t r y operations. T h e s e give rise t o e x t r a reflections w h i c h d e p e n d o n t h e displacements a n d are t h u s v e r y useful.

Figure 1.

Simple example of symmetrization

T h e space-group s y m m e t r y of t h e A s t r u c t u r e of a zeolite c a n be defined as t h e m a x i m u m t o p o l o g i c a l s y m m e t r y of t h e f r a m e w o r k . The space g r o u p of t h e H s t r u c t u r e m u s t t h e n be a s u b g r o u p thereof. The m a x i m u m s y m m e t r y of a r e p r e s e n t a t i v e n u m b e r of zeolites is g i v e n i n T a b l e I together w i t h t h e e s t i m a t e d degree of p s e u d o s y m m e t r y for each of these zeolites. T h e degree of p s e u d o s y m m e t r y , w h i c h varies considera b l y , s h o u l d i n d i c a t e the m a g n i t u d e of the recognizable d e v i a t i o n s f r o m t h e i d e a l i z e d h i g h - s y m m e t r y s t r u c t u r e . F o r the m a j o r i t y of zeolites the g e n e r a l l y a d o p t e d space g r o u p is i d e n t i c a l w i t h t h e m a x i m u m t o p o l o g i c a l s y m m e t r y . I n m a n y cases t h i s b r i n g s a b o u t a n u n r e a s o n a b l y h i g h degree of i d e a l i z a t i o n a n d false d e t a i l i n s t r u c t u r a l studies. U n u s u a l or even u n l i k e l y s t r u c t u r a l p a r t i c u l a r i t i e s , s u c h as p l a n a r 6-rings or S i - 0 - ( S i , A l ) b o n d angles a p p r o a c h i n g 180°, are n e a r l y a l w a y s caused b y s y m m e t r y a s s u m p t i o n s . M o r e o v e r , i n A s t r u c t u r e s S i a n d A l a t o m s (collectively c a l l e d T atoms) are as a r u l e n o t d i s t i n g u i s h a b l e , a n d S i , A l order is p r e c l u d e d i n these s y m m e t r i z e d s t r u c t u r e s . A t least p a r t i a l S i , A l o r d e r appears h i g h l y p r o b a b l e i n zeolites, a n d S i , A l d i s t r i b u t i o n s c a n be best d e t e r m i n e d o n the basis of observed T - 0

In Molecular Sieves; Meier, W., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1973.

3.

Table I.

41

Zeolite Frameworks

MEIER

Maximum Topological Symmetry of Some Zeolite Frameworks" Maximum Symmetry

Framework Type

Framework Type

1

Analcime Natrolite Socialite Cancrinite Gmelinite Chabazite

IaSd

(c)

I4i/amd

(a)

Erionite Gismondine Mordenite Ferrierite Faujasite Linde A

(b) P6z/mmc (b) P6z/mmc (c) RSm (c or d)

/43m

Maximum Symmetry^ P6z/mmc (c) I^i/amd (b or c) Cmcm (d) Immm (c or d) Fd3m (mostly d) Pm3m (c)

° See Ref. 17 for references. Degree of pseudosymmetry is given in parentheses, (a) Deviation from maximum symmetry readily observable (even by powder methods), (b) Deviation not so pronounced but in any case detectable by conventional single-crystal techniques, (c) Deviation only observable when suitable samples and special techniques are used, (d) Extreme cases of suspected pseudosymmetry based on slight indications only.


b

b o n d distances. pseudosymmetry,

Y e t because of t h e considerable difficulties caused almost

a l l the reported

zeolites p e r t a i n t o s y m m e t r i z e d s t r u c t u r e s .

structure determinations O n e s h o u l d therefore

by of

know

i n w h a t w a y b o n d distances (i.e., s p e c i f i c a l l y T - 0 distances) are affected by symmetrization.

A r e l a t e d q u e s t i o n is w h e t h e r s y m m e t r i z e d s t r u c -

tures c a n y i e l d a n y i n f o r m a t i o n at a l l o n possible S i , A l order a n d other s t r u c t u r a l details w h i c h are m o r e or less o b s c u r e d b y s y m m e t r i z a t i o n . C o m p u t e r - s i m u l a t e d m o d e l s t r u c t u r e s are of considerable interest i n t h i s respect.

T w o s t r u c t u r e t y p e s , a n a l c i m e a n d f a u j a s i t e , h a v e been chosen

i n t h i s p a p e r to d e m o n s t r a t e h o w t h i s m o d e l - o r i e n t e d a p p r o a c h c a n be u s e d t o i n v e s t i g a t e these s y m m e t r y - r e l a t e d p r o b l e m s .

Computer Optimized Model Structures D i s t a n c e least squares ( D L S ) , a m e t h o d d e v e l o p e d b y M e i e r a n d V i l l iger (1) for g e n e r a t i n g m o d e l s t r u c t u r e s ( D L S models) of p r e s c r i b e d s y m m e t r y a n d o p t i m u m i n t e r a t o m i c distances, c a n s u p p l y a t o m i c coordinates w h i c h closely a p p r o a c h t h e v a l u e s o b t a i n e d b y extensive s t r u c t u r e refinement.

D L S m a k e s use of t h e a v a i l a b l e i n f o r m a t i o n o n i n t e r a t o m i c d i s -

tances, b o n d angles, a n d other geometric features.

I t is p r i m a r i l y b a s e d

o n t h e fact t h a t t h e n u m b e r of c r y s t a l l o g r a p h i c a l l y n o n - e q u i v a l e n t i n t e r a t o m i c distances exceeds t h e n u m b e r of coordinates i n f r a m e w o r k - t y p e structures.

A general D L S p r o g r a m is a v a i l a b l e (2) w h i c h a l l o w s a n y

c o m b i n a t i o n of p r e s c r i b e d p a r a m e t e r s ( i n t e r a t o m i c distances, r a t i o s distances, u n i t cell constants etc).

of

I n a d d i t i o n , s u b s i d i a r y c o n d i t i o n s (as

discussed i n R e f s . 1 a n d 8) c a n also be p r e s c r i b e d . I n its simplest form D L S minimizes the residual function P« = E Z W / ' U W j ) - Do(j)V j m,n


42

MOLECULAR SIEVES

where D (j) is t h e i n t e r a t o m i c distance of t y p e , / between a t o m s m a n d n, a n d D (j) is the p r e s c r i b e d i n t e r a t o m i c distance of t y p e j. A l l prescribed p a r a m e t e r s a n d c o n d i t i o n s c a n be i n d i v i d u a l l y w e i g h t e d . T h e weights Wj are n o r m a l l y based o n b o n d i n g considerations or recorded v a r i a t i o n s i n b o n d l e n g t h v a l u e s . T h e prescribed distances a n d weights used i n t h i s w o r k are essentially based o n t h e reference v a l u e s b y R i b b e a n d G i b b s (4) a n d are g i v e n i n T a b l e I I . mn

0


Table II.

Prescribed Interatomic Distances

Z)o(T-O) Do(O-O) Z)o(T-Si) ° Distances in Angstroms.

0

T = Si

T = Al

1.605 (2.0) 2.621 (1.0) 3.10 (0.1)

1.757 (2.0) 2.869 (0.8) 3.25 (0.1)

Weights are given in parentheses.

D L S is a n effective t o o l for s t u d y i n g s y m m e t r y - d e p e n d e n t g e o m e t r i c a l c o n s t r a i n t s i n c o m p l e x s t r u c t u r e s s u c h as zeolite f r a m e w o r k s . T h i s is of p a r t i c u l a r significance i n t h e d e t e r m i n a t i o n of the a c t u a l space g r o u p of zeolite s t r u c t u r e s w i t h ordered S i , A l d i s t r i b u t i o n . M o d e l s c o n n o t i n g possible subgroups of t h e m a x i m u m t o p o l o g i c a l s y m m e t r y are t h e r e b y s y s t e m a t i c a l l y tested b y D L S . A s a r u l e a n acceptable m o d e l s h o u l d r e fine to a w e i g h t e d m e a n r e s i d u a l of d i s t i n c t l y less t h a n 0.02 A i f the ass u m e d s y m m e t r y , cell parameters, a n d stereochemical r e q u i r e m e n t s are fully compatible. Analcime Framework A n a l c i m e is n o r m a l l y described as c u b i c w i t h space group IaSd a n d a = 13.73 A . O n the other h a n d , c r y s t a l s of a n a l c i m e are f r e q u e n t l y o p t i c a l l y a n i s o t r o p i c ( i n d i c a t i n g n o n c u b i c s y m m e t r y ) , a n d several v a r i a n t s h a v e been d i s t i n g u i s h e d o n t h i s basis. T h e S i / A l r a t i o of n a t u r a l a n a l cimes is r e m a r k a b l y c o n s t a n t , a n d there are o n l y slight v a r i a t i o n s f r o m t h e i d e a l c o m p o s i t i o n Nai Ali Si32096- 1 6 H 0 r e p r e s e n t i n g the u n i t cell contents. T h e r a t h e r c o m p l i c a t e d s t r u c t u r e of a n a l c i m e was first det e r m i n e d b y T a y l o r (5) a n d more r e c e n t l y refined b y several i n v e s t i g a t o r s (6, 7) a l l a s s u m i n g cubic s y m m e t r y Ia3d. D e t a i l s a n d f u r t h e r references c a n be f o u n d i n ref. 7. T h e c o n s t a n c y of t h e S i / A l r a t i o c a n n o t be e x p l a i n e d o n the basis of t h e cubic s t r u c t u r e . M o r e o v e r , S i , A l order of a n y k i n d is i n c o m p a t i b l e w i t h space group J a 3 d , t h e m a x i m u m t o p o l o g i c a l s y m m e t r y . T h e s e a n d other observations, i n c l u d i n g t h e o p t i c a l findings, i n d i c a t e t h a t the t r u e s y m m e t r y is p r o b a b l y t e t r a g o n a l as was a l r e a d y suspected b y T a y l o r (5) i n 1930. T h e highest r a n k i n g subgroup of IaSd p e r m i t t i n g S i , A l order is tei/acd. T h i s c a n be assumed to be the space group of the H s t r u c t u r e w h i l e the A s t r u c t u r e has IaSd s y m m e t r y . 6

6

2


3.

MEIER

43

Zeolite Frameworks

D L S of t h e A s t r u c t u r e w a s b a s e d o n a p r e s c r i b e d average T - 0 d i s tance of 1.656 A ( c o r r e s p o n d i n g t o S i / A l = 2) a n d proceeded t o a w e i g h t e d m e a n r e s i d u a l p of 0.030 A . T - 0 distances i n t h e r e s u l t a n t D L S m o d e l A are a l l s o m e w h a t t o o s m a l l . A c c o r d i n g t o D L S c o m p u t a t i o n s t h e c e l l c o n s t a n t a of t h e f u l l y disordered s t r u c t u r e s h o u l d b e a r o u n d 13.95, i n s t e a d of t h e o b s e r v e d 13.73 A (or less). D L S refinement of t h e H s t r u c t u r e p r o ceeded t o a r e m a r k a b l y l o w p of less t h a n 0.001 A , o n t h e other h a n d . T h e r e s u l t a n t D L S m o d e l B i s i n d e e d n e a r perfect w i t h respect t o b o n d distances a n d angles. T h e a t o m i c coordinates of t h e t w o D L S models a r e g i v e n i n T a b l e III. w


w

Table III.

Analcime.

Atomic Coordinates for the Framework

Atoms Derived by D L S H Structure, I4i/acd (origin at 1), a = c = 13.73 A Displace-

A Structure. IaSd. a = 13.73 A

Atoms T

x y z

DLS Model A 0.66109 0.58891 1/8

Symmetrized DLS Model B 0.66190 0.58810 1/8

Atoms Al

x y z

Si

X

y z O

x

y z

0.10649 0.13456 0.72105

0.10795 0.13200 0.72102

0(1)

X

y z 0(2)

X

y z 0(3)

X

y z

DLS Model B

ments from Symmetrized Position, A

0.17076 0.07924 1/8 0.09229 0.12618 0.34276 0.10165 0.11265 0.22726 0.15329 0.04492 0.40016 0.13320 0.23071 0.37451

0.172

0.088

0.292

0.366

0.276

T h e r e is o n l y one possible S i , A l o r d e r i n g scheme i n t h e s t r u c t u r e w h e n t h e s y m m e t r y is t a k e n t o be I^i/acd. T h e ordered a l u m i n o s i l i c a t e f r a m e w o r k consists of (near p a r a l l e l ) 4-rings c o n t a i n i n g S i o n l y w h i c h a r e i n terconnected t h r o u g h single A l t e t r a h e d r a as s h o w n s c h e m a t i c a l l y i n F i g u r e 2b. T h i s s t r u c t u r e is o b v i o u s l y t e t r a g o n a l , a n d i n order t o a c c o u n t f o r the f r e q u e n t l y observed i s o t r o p i c properties one h a s t o assume s u b m i c r o scopic t w i n n i n g . I n a n y one d o m a i n t h e f o u r - m e m b e r e d S i rings m a y b e o r i e n t e d i n one of three possible d i r e c t i o n s . T h e c u b i c A s t r u c t u r e , w h i c h is i l l u s t r a t e d i n F i g u r e 2 a , demonstrates t h a t t h e three possible o r i e n t a t i o n s of t h e 4-rings of S i are e q u a l l y p r o b a b l e . T r u e long-range S i , A l order


44

MOLECULAR SIEVES

appears r a t h e r u n l i k e l y u n d e r these circumstances. T h e observed v a r i a t i o n s of the o p t i c a l properties c o u l d be r e a d i l y e x p l a i n e d i n t e r m s of s u b m i c r o s c o p i c t w i n n i n g due t o l o c a l S i , A l order.


T h e p o s t u l a t e d l o c a l S i , A l o r d e r i n g i n a n a l c i m e resembles t h e o b s e r v e d S i , A l d i s t r i b u t i o n i n the s t r u c t u r e of l a u m o n t i t e (8, 9) w h i c h is also c o m posed of f o u r - m e m b e r e d S i - r i n g s l i n k e d to each other t h r o u g h A l t e t r a h e d r a . A n a l c i m e p s e u d o m o r p h s after l a u m o n t i t e h a v e been recorded (10). A l l 4-rings i n l a u m o n t i t e are near p a r a l l e l , a n d t w i n n i n g of t h e t y p e j u s t described is n o t possible.

Figure 2. Framework topology of analcime: (a) Diagrammatic representation of the 4-rings in the symmetrized framework structure with T atoms occupying the corners of the squares, (b) Proposed Si, Al ordering scheme using the same diagrammatic representation. 4-Rings containing Si are linked to each other through single tetrahedra containing Al (marked by circles) T h e d i s p l a c e m e n t s of t h e f r a m e w o r k a t o m s i n t h e H s t r u c t u r e of a n a l c i m e f r o m t h e s y m m e t r i z e d positions are l i s t e d i n T a b l e I I I . T h e y are c o n s i d e r a b l y larger t h a n t h e displacements of 0.02-0.07 A f o u n d i n s y n t h e t i c zeolite N a A (3) w h i c h are t h e smallest displacements recorded so f a r i n a p s e u d o s y m m e t r i c s t r u c t u r e . T h e d i s p l a c e m e n t v e c t o r s i n a n a l c i m e c a n be r e l a t e d t o t h e a p p a r e n t t e m p e r a t u r e p a r a m e t e r s of t h e A s t r u c t u r e . F i g u r e 3 shows t h e e x p e r i m e n t a l l y d e t e r m i n e d " v i b r a t i o n " ellipsoids of o p t i c a l l y i s o t r o p i c a n a l c i m e (7). T h e s t r o n g l y a n i s o t r o p i c ellipsoids are i n r e a s o n a b l y g o o d a c c o r d w i t h the d i s p l a c e m e n t v e c t o r s obtained independently b y D L S . T h e a t o m i c coordinates of D L S m o d e l A a n d of the s y m m e t r i z e d D L S m o d e l B (listed i n T a b l e I I I ) differ i n some measure. T h e e x p e r i m e n t a l l y d e t e r m i n e d a t o m i c p o s i t i o n s i n o p t i c a l l y isotropic a n a l c i m e (7) d e v i a t e o n l y b y 0.025 A ( T ) a n d 0.027 A (O) f r o m t h e positions i n t h e s y m -



3.

MEIER

Zeolite Frameworks

45

Figure 3. Analcime. Apparent thermal-motion probability ellipsoids of the T and 0 atoms in the A structure and the displacements from the symmetrized position obtained by DLS. Ellipsoids are based on thermal parameters reported by Knowles, Rinaldi, and Smith (7) and are scaled to enclose 50% probability. The diagrams were generated with the aid of computer program ORTEP by C.K. Johnson

metrized D L S model B .

O f p a r t i c u l a r interest a r e t h e i n t e r a t o m i c d i s -

tances i n t h e s y m m e t r i z e d D L S m o d e l B w h i c h are l i s t e d i n T a b l e I V .

Table IV. Analcime. Interatomic Distances i n Symmetrized D L S M o d e l and Expected Average Values Corresponding to S i / A l = 2 D(T-0),A 1.628 (2) 1.633 (2)

Expected Value 1.656

D(0-0)> A 2.644 2.666 (2) 2.666 2.668 (2)

Expected Value 2.704

T h e s e distances are a l l c o n s i d e r a b l y b e l o w t h e average T - 0 a n d 0 - 0 d i s tances based o n the S i / A l r a t i o . T h i s exemplifies the fact t h a t i n t e r a t o m i c distances are i n v a r i a b l y shortened o n s y m m e t r i z a t i o n . A l l e x p e r i m e n t a l l y d e t e r m i n e d T - 0 distances i n a n a l c i m e (6, 7) are also s i g n i f i c a n t l y shorter t h a n 1.656 A . T h i s m u s t be because of s y m m e t r i z a t i o n , a n d t h i s f i n d i n g represents i n itself evidence of p s e u d o s y m m e t r y .


46

MOLECULAR SIEVES

Faujasite Framework F a u j a s i t e - t y p e zeolite s t r u c t u r e s h a v e m a x i m u m s y m m e t r y

Fd3m,

a n d a l l t h e 192 T a t o m s per u n i t c e l l of t h e A s t r u c t u r e are s y m m e t r i c a l l y equivalent.

T h e o b s e r v e d S i / A l r a t i o s of s y n t h e t i c f a u j a s i t e - t y p e species

v a r y w i t h i n a range f r o m s l i g h t l y over 1 u p t o 2.5 ( a n d o c c a s i o n a l l y a b o v e ) . U n m o d i f i e d species t h u s n o r m a l l y c o n t a i n b e t w e e n 48 a n d a l m o s t 96 A l a t o m s per u n i t cell.

T h e a l m o s t c o n t i n u o u s range i n A l c o n t e n t does n o t

b y itself r u l e o u t a n y k i n d of S i , A l order.

D i s c o n t i n u i t i e s i n t h e p l o t of

t h e c e l l d i m e n s i o n s a g a i n s t t h e n u m b e r of A l a t o m s per u n i t c e l l h a v e been r e p o r t e d b y s e v e r a l i n v e s t i g a t o r s (11, 12).

T h e observed discontinuity


at a r o u n d 64 A l , i n p a r t i c u l a r , has been r e l a t e d t o S i , A l o r d e r i n g (12). F u l l details a n d references o n f a u j a s i t e - t y p e zeolite s t r u c t u r e s c a n be f o u n d i n t h e c o m p r e h e n s i v e a n d c r i t i c a l r e v i e w b y S m i t h (13).

Figure 4- Probable Si, Al ordering schemes in double 6-ring unit of faujasitetype structures. Al positions are marked by circles. B requires 96 AVs and C and D require 64 AVs per unit cell. The space group symmetry of the framework is given for each arrangement of the Al atoms. Numbering refers to the nonequivalent T atoms in the common subgroup F222 T h e present s t u d y is r e s t r i c t e d t o l i k e l y S i , A l o r d e r i n g schemes of relatively high symmetry.

O n l y f r a m e w o r k s c o n t a i n i n g either 96 or 64

A P s per u n i t c e l l h a v e been considered.

T h e p a r t i c u l a r a r r a n g e m e n t s of

S i a n d A l d e a l t w i t h i n t h i s p a p e r are s h o w n i n F i g u r e 4.

T h e r e is o n l y

one possible o r d e r i n g scheme i n a f r a m e w o r k c o n t a i n i n g 96 A P s per u n i t cell i f a r r a n g e m e n t s w i t h 2 A P s s h a r i n g t h e same o x y g e n a t o m are r u l e d out.

T h i s possible f r a m e w o r k w i t h a l t e r n a t e S i a n d A l t e t r a h e d r a has

b e e n f o u n d t o exist (14) a n d w i l l be d e n o t e d m o d e l B . schemes are possible i n case of 64 A l ' s per u n i t cell. cussed t o some extent b y D e m p s e y (15).

Several ordering

T h e s e were first d i s -

M o d e l C represents t h e o n l y

possible s t r u c t u r e c o n t a i n i n g 6-rings w i t h t w o A P s p a r a .

Other arrange-

m e n t s of s u c h 6-rings are i n c o m p a t i b l e either w i t h t h e A l - O - A l a v o i d a n c e


3.

MEIER

Zeolite Frameworks

47

r u l e or w i t h a face-centered l a t t i c e ( w h i c h is c l e a r l y observed). Model D represents t h e m o s t l i k e l y a r r a n g e m e n t w i t h a l l 6-rings c o n t a i n i n g t w o A P s i n meta positions. T h e m a x i m u m s y m m e t r y of these ordered f r a m e w o r k s is Fd3 ( m o d e l B ) , F 4 2 2 (model C ) , a n d Fddd (model D ) . T h e c o m m o n s u b g r o u p of these space groups is F222. T h e d o u b l e 6 - r i n g u n i t s h o w n i n F i g u r e 4 represents t h e a s y m m e t r i c u n i t of t h e s t r u c t u r e f o r F 2 2 2 a n d has been f o u n d t o be t h e m o s t c o n v e n i e n t u n i t f o r d i s c u s s i n g S i , A l o r d e r i n g schemes. T h e T a t o m s h a v e c o n s e q u e n t l y been assigned n u m b e r s c o r r e s p o n d i n g t o t h e positions i n t h i s d o u b l e 6 - r i n g u n i t .


X

A l l these models r e p r e s e n t i n g possible H s t r u c t u r e s h a v e been refined b y D L S . F o r c o m p a r i s o n , t h e a v e r a g e d disordered s t r u c t u r e w i t h m a x i m u m s y m m e t r y FdSm (model A ) has also been o p t i m i z e d b y D L S . T h e a d o p t e d u n i t c e l l constants were 25.132 A f o r models w i t h 96 A P s a n d 24.808 A f o r 64 A P s {12). T h e D L S refinements proceeded t o w e i g h t e d m e a n residuals p ( i n angstroms) of 0.006 f o r A , 0.010 for B , 0.005 f o r C , a n d 0.011 f o r D . T h e m e a n r e s i d u a l s f o r t h e T - 0 distances alone were a l l less t h a n 0.001 A except for m o d e l D (0.003 A ) . R e f i n e m e n t s i n t h e l o w e r s y m m e t r y F222 gave essentially t h e same results, a n d i t w a s t h u s c o n firmed b y D L S t h a t t h e assigned space g r o u p of each m o d e l is c o m p a t i b l e w i t h g e o m e t r i c a l r e q u i r e m e n t s . T h e a t o m i c coordinates of t h e r e s u l t a n t D L S models, B , C , a n d D are l i s t e d i n T a b l e V , a n d those of D L S m o d e l A are l i s t e d i n T a b l e V I . w

T h e i n t e r a t o m i c distances i n D L S m o d e l D are a l l s l i g h t l y t o o large w h i c h i n d i c a t e s a l i k e l y decrease i n t h e c e l l c o n s t a n t . I n fact, D L S y i e l d s a n o p t i m u m c e l l c o n s t a n t f o r m o d e l D of 24.781 A i n s t e a d of 24.808 A w h i l e m o d e l C is f u l l y c o m p a t i b l e w i t h t h e p r e s c r i b e d v a l u e of 24.808 A . T h e difference of 0.027 A is i n r e m a r k a b l y g o o d agreement w i t h t h e m a g n i t u d e of t h e observed d i s c o n t i n u i t y a t 64 A P s (12). T h e s e findings i n d i c a t e t h a t Y - t y p e species c o n t a i n i n g u p t o 64 A P s p e r t a i n t o m o d e l C ( p a r a form) whereas t h e t r a n s i t i o n - t y p e species c o n t a i n i n g a t least 64 A P s m u s t be r e l a t e d t o m o d e l D (meta f o r m ) . T h i s agrees w i t h t h e fact t h a t f u r t h e r s u b s t i t u t i o n of S i b y A l is o n l y possible i n m o d e l D . M o d e l s B a n d D a r e t h e t w o e n d m e m b e r s of a c o n t i n u o u s s u b s t i t u t i o n a l series. T h e a t o m i c coordinates of D L S models B , C , a n d D h a v e been s y m m e t r i z e d t o FdSm ( T a b l e V I ) for c o m p a r i s o n w i t h e x p e r i m e n t a l l y d e t e r m i n e d coordinates based o n FdSm s y m m e t r y a n d for d e t e r m i n i n g t h e displacements (listed i n T a b l e V ) . C o o r d i n a t e s of t h e s y m m e t r i z e d s t r u c tures differ s i g n i f i c a n t l y . T h i s suggests t h a t e v e n short-range o r d e r i n g schemes c a n p o s s i b l y b e detected i f d i s t o r t i o n of t h e f r a m e w o r k f r o m c a t i o n s or sorbate c a n b e neglected. T h i s is done b y c o m p a r i n g t h e c o n v e n t i o n a l l y refined A s t r u c t u r e w i t h s y m m e t r i z e d D L S models. A s a n example, t h e f o l l o w i n g m e a n d e v i a t i o n s f r o m t h e s y m m e t r i z e d D L S models of T a b l e V I h a v e been o b t a i n e d for t h e A s t r u c t u r e of n a t u r a l faujasite d e t e r m i n e d b y


48

MOLECULAR SIEVES

B a u r (16): 0.129 A ( A ) , 0.144 A ( s y m B ) , 0.096 A ( s y m C ) , a n d 0.036 A ( s y m D ) . T h i s a n d m o r e d e t a i l e d c o m p a r i s o n s show c l e a r l y t h a t B a u r ' s results o b t a i n e d f o r n a t u r a l faujasite c o u l d be i n t e r p r e t e d i n t e r m s of m o d e l D , a n d short-range disorder, i n p a r t i c u l a r , appears most u n l i k e l y o n t h i s basis. O f considerable interest, f u r t h e r m o r e , a r e t h e i n t e r a t o m i c Table V . Faujasite. Atomic Coordinates of D L S Models with Ordered S i / A l Distributions and Displacements (A) from the Symmetrized Positions 0


DLS Model B, Al Alternating with Si, FdS (Origin at 3), a = 25.132 A T(1)A1 X x

-0.05034

DLS Model C, Al in Para Positions, F4i22 (Origin at 222), a = 2A.808 A T(l)Si (7)

X

0.17879

X T(2)Si x

0.03763 0.12330 (0.021) 0.03679

y z

T(2)A1 (12)

X

-0.00025 0.09147 (0.089) 0.17518

&

y z

-0.05033 0.12471 (0.021)

X

0.08957 0.00201 (0.058) 0.08667

y z

T(4)Si (10)

X

0.18192 -0.00025 (0.133) -0.00161

6

T(5)A1 X (9)

0.18402 0.08688 (0.190) 0.00542

y z

T(6)Si (8)

X

0.08827 0.17140 (0.176) 0.08986

6

X y z

0(12)

T(2)A1 (ll)

X y z

T(3)Si (12)

X

0.08724 -0.00118 (0.058) 0.08795

y z

T(4)Si (7)

X

0.17759 0.00092 (0.027) -0.00286

y z

T(5)Si (8)

X

0.18178 0.08807 (0.121) 0.00460

y z

T(6)A1 X (9)

0.08876 0.16747 (0.281) 0.08867

6

y z

0(11)

-0.00718 0.08948 (0.309) 0.17950

6

&

0.00092 -0.09854 0.10310 (0.084)

y z

6

y z

y z

0.18795

6

6

X

X

6

y z

T(3)Si (H)

0(1)

T(l)Si (10)

6

6

y z

DLS Model D, Al in Meta Positions, Fddd (Origin at 222), a = 24-808 A

X y z

0.00443 0.17289 (0.134) 0.23047 0.01953 0.12500 (0.014) 0.22914 0.13100 0.02174 (0.157)

y z

0(11)

X y z

0(12)

X y z


0.00532 0.17241 (0.189) 0.23684 0.01871 0.12315 (0.215) 0.22708 0.13048 0.02863 (0.232)

3.

MEIER

Table V . DLS Model B, Al Alternating with Si, Fd3 (Origin at 3), a = 25.132 A

X y

z

0(14)

X y


z X y

z

-0.00079 -0.00460 0.14868 (0.068)

0(21)

X y

z

0(22)

X y

z

0(23)

X y

z 0(3)

X y

z

-0.02539 0.07701 0.07121 (0.103)

0(31)

X y

z

0(32)

X y

z 0(33)

X y

z

0(4)

X y

z

-0.07265 0.07971 0.17444 (0.074)

Continued

DLS Model C, Al in Para Positions, Fh22 {Origin at 222), a = 84.808 A 0(13)

0(2)

49

Zeolite Frameworks

0(41)

X y

z

0(42)

X y

z

0(43)

X y

z

0.12716 0.22863 0.01888 (0.069) 0.01721 0.23279 0.12500 (0.095) 0.13329 -0.02123 0.13241 (0.142) 0.12068 0.12994 -0.01836 (0.210) -0.01985 0.13392 0.12353 (0.182) 0.15547 0.04903 0.05664 (0.138) 0.04751 0.16610 0.04877 (0.324) 0.06369 0.05709 0.14590 (0.357) 0.19582 -0.04845 0.05182 (0.117) -0.05137 0.20310 0.05017 (0.241) 0.04347 -0.03893 0.18513 (0.331)

DLS Model D, Al in Meta Positions, Fddd (Origin at 222), a = 2A.808 A 0(13)

0.13112 0.22323 0.01723 (0.228)

X y

z

0(21)

X y

z

0(22)

X y

z

0(23)

X y

z

0(31)

X y

z 0(32)

X y

z 0(33)

X y

z

0(41)

X y

z

0(42)

X y

z

0(43)

X y

z

0.13886 -0.02033 0.12957 (0.284) 0.11964 0.12300 -0.01383 (0.256) -0.01948 0.13108 0.12485 (0.116) 0.16745 0.03385 0.04382 (0.451) 0.04806 0.16651 0.05089 (0.210) 0.05613 0.05986 0.14106 (0.541) 0.20706 -0.06235 0.06150 (0.438) -0.05319 0.19754 0.05017 (0.066) 0.04038 -0.04520 0.18369 (0.458)

° Displacements in parentheses. Equivalent T position in hexagonal prism (Figure 4). 6


50

MOLECULAR SIEVES

distances i n t h e s y m m e t r i z e d m o d e l s t r u c t u r e s . T h e i n t e r a t o m i c distances i n s y m m e t r i z e d D L S m o d e l C a r e l i s t e d i n T a b l e V I I . T h i s is a n o t h e r e x a m p l e d e m o n s t r a t i n g t h e s h o r t e n i n g of b o n d distances o n s y m m e t r i z a t i o n . T h e m e a n T - 0 distance of 1.647 A i n t h e s y m m e t r i z e d s t r u c t u r e w o u l d i n d i c a t e 53 A l ' s p e r u n i t c e l l i n s t e a d of 64. T h i s shows c l e a r l y t h a t S i / A l Table IV.

Faujasite.

Atomic Coordinates of Symmetrized D L S Models


(Origin at 3m) Symmetrized DLS Model

DLS Model A FdSm

B FdS-Fd3m

x y z x y z x y z x y z x y z

0.96234 0.87438 0.05079 0 0.90057 0.09943 0.00176 0.85169 0.00176 0.92135 0.92135 0.02654 0.92616 0.82384 0.07551

0.96279 0.87599 0.05034 0 0.89918 0.10082 0.00270 0.85132 0.00270 0.92589 0.92589 0.02539 0.92236 0.82764 0.07265

Table VII.

Faujasite.

T

0(1)

0(2)

0(3)

0(4)

C F4i22-Fd3m 0.96379 0.87663 0.05237 0 0.89493 0.10507 0.00396 0.85519 0.00396 0.92879 0.92879 0.03082 0.92237 0.82763 0.06968

1.645(1.656) 1.649 1.647 1.649

0.96336 0.87494 0.05278 0 0.89624 0.10376 0.00283 0.85712 0.00283 0.92377 0.92377 0.03334 0.92713 0.82287 0.07110

Shortening of Interatomic Distances (A) on Symmetrization

T-O(l) T - 0 (2) T-0(3) T-C(4)

D Fddd-FdSm

0

0(l)-0(2) 0(l)-0(3) 0(l)-0(4) 0(2)-0(3) 0(2)-0(4) 0(3)-0(4)

2.697(2.704) 2.687 2.696 2.694 2.687 2.693

° DLS model C with 64 Al's and space group F4i22 symmetrized to FdSm (expected average values in parentheses). r a t i o s i n f a u j a s i t e - t y p e f r a m e w o r k s s h o u l d n o t b e d e t e r m i n e d o n t h e basis of o b s e r v e d T - 0 distances w h e n FdSm s y m m e t r y is a s s u m e d . Conclusions E x p e r i m e n t a l l y o b t a i n a b l e d a t a s u c h as c e l l constants, a t o m i c c o ordinates, a n d t h e r m a l parameters of s y m m e t r i z e d s t r u c t u r e s c a n i n fact



3. MEIER

Zeolite Frameworks

51

supply some information on Si, A l order in zeolite frameworks. In particular, it appears possible to detect and to distinguish specific short-range ordering schemes with the aid of computer-optimized model structures (DLS models) using a relatively simple approach which could be termed "framework mechanics." Bond distances are invariably shortened on symmetrization as can be generally proved. For this reason, it is dangerous to determine the amount of A l substitution in T sites of high-symmetry structures from T - 0 distances without exploring possible symmetrization effects. Symmetrized structures represent a special type of "average" structure. To prevent confusion it is suggested that the term "average" structure be avoided whenever the averaging is specifically caused by a pseudosymmetry operation. Acknowledgments I am grateful to K . F . Fischer, V. Gramlich, and T . P. Woodman for comments on the paper. Literature Cited 1. Meier, W. M., Villiger, H., Z. Kristallogr. (1969) 129, 411. 2. Villiger, H., "DLS Program and Manual," ETH, Zurich, 1969. 3. Gramlich, V., Meier, W. M., Z. Kristallogr. (1971) 133, 134. 4. Ribbe, P. H., Gibbs, G. V., Amer. Mineral. (1969) 54, 85. 5. Taylor, W. H., Z. Kristallogr. (1930) 74, 1. 6. Calleri, M., Ferraris, G., Atti Acad. Sci. Tor. (1964) 98, 1. 7. Knowles, C. R., Rinaldi, F. F., Smith, J. V., Indian Mineral. (1965) 6, 127. 8. Bartl, H., Fischer, K. F., Neues Jahrb. Mineral. Monatsh. (1967) 2/3, 33. 9. Schramm, V., Fischer, K . F., ADVAN. CHEM. SER. (1971) 101, 259. 10. Kucera, B., Novotna, B., Casopis Morav. Zernsk. Mus. (1927) 25, 214. 11. Breck, D. W., Flanigen, E. M., "Molecular Sieves," p. 47, Society of the Chemical Industry, London, 1968. 12. Dempsey, E., Kühl, G. H., Olson, D. H., J.Phys. Chem. (1969) 73, 387. 13.

Smith, J. V., ADVAN. CHEM. SER. (1971) 101, 171.

14. Olson, D. H., Dempsey, E., J. Catal. (1969) 13, 221. 15. Dempsey, E., "Molecular Sieves," p. 293, Society of the Chemical Industry, London, 1968. 16. Baur, W.H., Amer. Mineral. (1964) 49, 697. 17. Meier, W. M., Olson, D. H., ADVAN. CHEM. SER. (1971) 101, 155. RECEIVED November 24, 1972. This work is part of an investigation on zeolite structures supported by the Schweiz. Nationalfonds.


Symmetry Aspects of Zeolite Frameworks

Recommend Documents