Local Environment Fine Structure in the 29Si NMR Spectra of

J. Phys. Chem. 1995, 99, 6128-6144

6128

Local Environment Fine Structure in the 29SiNMR Spectra of Faujasite Zeolites M. T. Melchior,” D. E. W. Vaughan, and C. F. Pictroski Exxon Research and Engineering Company, Annandale, New Jersey 08801 Received: November 3, 1994@

The 29SiNMR spectra of FAU framework (X and Y) zeolites exhibit a well-resolved splitting into five major bands Si(nAl), where n is the number of first shell aluminum neighbors about silicon. It is well-established that the intensities Si(nA1) reflect the local order resulting from “Al-A1 avoidance” in the placement of first-shell (Loewenstein’s rule) and second-shell (“Dempsey’s rule”) aluminum neighbors. Study of framework metals ordering in FAU materials has been limited by the information content of the intensities Si(nA1) and by the range of SUA1 compositions available by direct synthesis. Recent synthetic advances have greatly increased the composition range of available materials. In this paper we report 29Si NMR spectra of 15 directly synthesized FAU zeolites ranging in SQA1ratios from -1.3 to -5.3. Careful study of the 29SiNMR spectra reveals considerable information beyond the intensities Si(nAl), manifested in the complex compositional dependence of the band positions and heterogeneous band shapes. The basic premise of this paper is that the 29Si NMR spectra of FAU zeolites are superpositions of many components arising from the multiple local environments for a silicon atom, these local environments differing in the number and types of first- and second-shell A1 substituents. Compositional dependence arises because the relative populations of these local environments are afunction of composition. This paper discusses the process by which this additional information has been retrieved and its implications concerning the building units involved in FAU crystallization. The major conclusion is that the immediate precursor to the FAU lattice is the hexagonal prism tertiary building unit and that the secondary unit is the single 4-ring.

Introduction Order in the distribution of silicon and aluminum atoms in the tetrahedral framework of zeolites in general, and faujasite zeolites in particular, has been the subject of often vigorous debate for nearly a quarter of a century. The only direct information on the Si,A1 distribution comes from 29Si NMR. Since the pioneering 1981 experiment~l-~ on the application of 29Simagic angle spinning (MAS) NMR to faujasite zeolites it has been widely recognized that these spectra provide a direct measurement of the average population of the five possible silicon environments with respect to first-shell tetrahedral neighbors Si(nAl), n = 0-4. It was shown3that this information could be used to c o n f i i the absence of A1-0-A1 linkages (Loewenstein’s rule4) and that structural units which minimize A1,Al next nearest neighbors AI-0-Si-0-A1 are favored, as envisioned by D e m p ~ e y . ~ The intensities Si(nA1) represented new information which stimulated vigorous research activity during 1982- 1986 aimed at relating this information to various descriptions of the Si,A1 distribution. This body of work has been reviewed by Englehardt and MicheL6 The approaches taken to model Si,A1 distributions in FAU zeolites have ranged from the assumption of full long range ordered structures with translational periodicity in the framework metals distribution’s7 to completely random distributions, subject only to Loewenstein’s r ~ l e . ~The , ~ observed 29SiNMR results show clearly that some degree of local Si,Al order exists in X and Y zeolites. It was first shown by VegaIo that the observed Si(nA1) distributions provide a direct measure of the density of Al-0-Si-0-Al (second-shell A1,Al pairs) in the FAU framework as a function of framework composition. This quantity, closely related to the second moment of the distribution Si(nAl),” provides a model inde* Corresponding author, permanent address:

P.O. Box 447, Quakertown,

NJ 08868. @

Abstract published in Advance ACS Abstracts, April 1, 1995.

0022-365419512099-6128$09.0010

pendent measure of the degree of local order in the Si,Al distribution. The concentration of second-shell ALA1 pairs in directly synthesized FAU zeolites is intermediate between random (constrained only by Loewenstein’srule and framework connectivity) and the minimum possible at a given framework composition, these limiting cases having been simulated by Monte Carlo methods.I0 The results of the present work show this intermediate degree of local order exists over the entire composition range 1 < SUA1 < -5. Understanding the observed intermediacy of the second-shell A1,Al pair density in FAU zeolites is an important goal which has motivated much of our research in this area. Two quite different points of view can be taken. The first is that the observed local order is a manifestation of the energetics of Al,Al repulsive interactions in the FAU framework, moderated by entropic effects. Under this set of circumstances, the Si,Al distribution should lend itself to calculation by Monte Carlo methods. The early Monte Carlo simulations of Si(nA1) distributions did not provide quantitative tests of this approach, in one case because entropic effects were not included,I0in the other because the calculation employed a diamond lattice as a simple model for the zeolite lattice.I2 Calculations using sophisticated simulated annealing techniques and the correct framework connectivitieshave been reported more r e ~ e n t l y . ’ ~ . ’ ~ None of these Monte Carlo simulations gives a fully satisfactory result for Si(nA1),I4 especially at SUA1 < 2. A second point of is that the intermediacy of the second-shell Al,Al pair avoidance is more a characteristic of the way in which a basic ordered subunit crystallizes than it is a manifestation of A1,Al interactions in the FAU framework. The concept is as follows. An ordered subunit has a Si,Al distribution which minimizes A1,Al painvise interactions, but irreversible coupling (crystallization) of these units may result in a framework Si,Al distribution which does not minimize second-shell A1,Al pairs. If this is the case, the observed local 0 1995 American Chemical Society

J. Phys. Chem., Vol. 99, No. 16, 1995 6129

Fine Structure of Faujasite Zeolites

SomDle

SiA

15

5.31

14

4.60

11

2.97

I

I

I

I

1

I

I

80

85

90

95

100

105

110

PPm

Figure 1. The 29SiNMR spectra of six directly synthesized FAU zeolites spanning the composition range. Spectra were obtained at 39.5

MHz. order may carry important mechanistic information. The ordered subunit approach to simulating the local order in FAU zeolites can provide very satisfactory agreement with experimental Si(nAl). This agreement is sufficient to demonstrate the power of this approach but not sufficient for a unique definition of a crystallization pathway.16 The results of these studies of framework metals ordering in faujasite have been controversial and only partially conclusive. New synthetic techniques have provided a greatly expanded range of directly synthesized FAU materials. Improved NMR procedures have significantly improved our ability to test models which describe the local Si,Al order. These improvements in the range and quality of the measured Si(nAl) distributions cannot alter the basic fact that the overall first-shell distributions do not contain sufficient information to fully characterize the Si,Al order. In particular it has not been possible to separate the effects of incomplete AI-0-Si-0-Al avoidance from the effects of macroscopic inhomogeneity in composition.6 This situation is altered by the work described in this paper. Previous studies of Si,Al ordering in FAU zeolites have concerned the compositional dependence of the intensities of the five observed bands Si(nAl). In the following we show that analysis of the complex compositional dependence of the position and shape of the five Si(nAl) bands provides information sufficient to determine the local Si,A1 order in directly synthesized FAU zeolites without recourse to models and independently from compositional heterogeneity.

Compositional Dependence of Faujasite 29SiNMR Spectra The 29Si NMR spectra of FAU framework zeolites are deceptively simple, the obvious resolution into five Si(nA1) bands masking a complex evolution of the band shapes with composition. This is evident from Figure 1 which shows the spectra of six directly synthesized FAU zeolites covering a composition range 1 < Si/Al < 6. The positions and shapes of the five major bands Si(nA1) show a significant systematic variation with composition, especially the Si( 1Al)and Si(0Al) bands. (Compare the positions of the small Si(1Al) and Si(0Al) bands at -99 and -103 ppm for sample 1 with the strong bands at -101 and -106.5 ppm for sample 15.) A basic assertion of

Figure 2. Part of the FAU structure with Si/N = 1 showing two sodalite units @ cage) connected through a double 6-ring unit and the arrangement of atoms around the supercage (acage). Oxygens are

omitted, solid circles are Al, open circles Si. The insert shows the local environment of a silicon atom according to our definition.

this work is that this compositional dependence is a manifestation of chemical shift dispersion arising from the superposition of many unresolved components with different local environments within each Si(n4Z). These differences are in the local geometry of the n first-shell Al substituents or in the number and types of second-shell Al neighbors. (The compositional dependence of the Si(0Al) band must arise from influences beyond the first shell.) NMR transverse relaxation measurements support the assertion of heterogeneous broadening. Measurements on selected FAU materials have shown that the homogeneous lineshapes are a mixture of Lorentzian and Gaussian with widths of -10 Hz for Si(0Al) to -25 Hz for Si(4Al), i.e., from 0.25 to 0.65 ppm for 29Siat 39.5 MHz, to be compared with observed bandwidths of 2-5 ppm. These results are consistent with our observation that the 29Si NMR of X zeolites at 99.3 MHz show only a very slight improvement in resolution (about 10% for Si(4Al)) and Y zeolites exhibit virtually no improvement. A partial view of the FAU framework is shown in Figure 2. Although the framework has a high degree of symmetry, such that all sites are crystallographically equivalent, none of the symmetry elements passes through the atoms. As a consequence, local symmetry is absent and a silicon atom in the FAU framework has four distinct first-shell tetrahedral neighbors (illustrated by the insert in Figure 2) and nine distinct secondshell tetrahedral neighbors. Of the nine second-shell neighbors, three are doubly connected (across 4-rings (4R's)) to the central silicon atom and six are situated across 6-rings (6R's) and 12rings. The point of view we have taken in this work is that the chemical shift position of a silicon atom in the FAU lattice is influenced by relatively short range interactions so that the chemical shift of a particular local environment is, to first order at least, independent of sample average composition. Compositional dependence of the observed 29SiNMR spectra arises because, while the chemical shifi of a particular environment is constant, each Si(n.41) band Cfor n .c 4 ) comprises many such environments, the relative populations of which are a function of composition. Prior to the present work a careful study of the compositional dependence of the average chemical shift positions (centroids) of the five Si(nAl) bands was based on the concept of local

6130 J. Phys. Chem., Vol. 99, No. 16, 1995

Melchior et al.

TABLE 2: Samde DescriDtion ~

~~

~

chemical analysis (ICP-AES) Si/AI SUA1 sample (NMR) (chem)

(wt%)

A1 (wt%)

Na (wt%) template" (wt%)

1.26 1.33 1.38 1.41 1.46 1.76 2.17 2.54 2.60 2.91 2.97 3.39 3.54 4.60 5.31

18.00 16.80 16.90 17.50 17.60 25.69 26.84 27.54 22.98 23.90 26.80 26.30 28.60 28.10 29.10

13.65 12.00 11.90 11.70 11.70 13.57 11.53 10.50 8.54 7.86 8.28 6.96 7.23 5.66 5.99

10.28 10.10 9.98 9.95 9.90 10.43 11.53 7.82 4.59 5.88 5.82 4.22 4.32 3.15 N/A

1 2

3

b

a

Figure 3. Labeling of (a) first-shell and (b) second-shell positions in

the FAU framework.

TABLE 1: Local Environments in the FAU Framework NII first shell second shell reduced notation Nnr (1) Si(4A1) abcd abed (1) (4) Si(3A1) abc abc (4) abd abd acd

bcd (9)

Si(2Al)

ab

ac

acd bed ab ac *

(8)

ad bd bc*

be0 (12)

Si(lA1)

cd

cd

a

a*

(9)

a0

b C

b* bo c**

c *o co* coo

(8)

Si(OA1)

d

d

2

Z**

13 14 15

acO

ad bd bc

4 5 6 7 8 9 10 11 12

(4)

Z*O

ZO* ZOO

environment chemical shifts. This work showed that aluminum atoms in the six more remote second-shell positions have negligible effect on the central Si chemical shift." On the basis of this result we defined the local environment of a silicon atom in the FAU framework by specifying the identity of the tetrahedral atoms (Si or Al) in each of four first-shell sites (a, b, c, 6)and in the three doubly connected second-shell sites (i, ii, iii) as defined in Figure 3. We retain this definition of the local environment of a silicon atom in the FAU framework. The 34 possible local environments consistent with Loewenstein's rule are summarized in Table 1. The column at the left of Table 1 shows the number N,, of local environments associated with each Si(nAl) band.

Experimental Procedures Fifteen faujasites were synthesized in the SUAl range 1.274.76 using published techniques. Low SUAl ratio (< 1.5) X type materials were made from seededI8 sodium silicate-sodium aluminate gels (samples 1, 2, and 4) or cold aged sodium aluminate-colloidal silica (samples 3 and 5) gels having compositions in the range 2.3-5 Na20, A l 2 0 3 , 3-4 Si02, and 100-250 H20. Intermediate composition Y-type materials (1.5 < SUAl < 2.8) were made from seeded sodium silicate-sodium aluminate gels (samples 6, 7, 8, 9) in the composition range 3.2-3.7 Na20, Al203, 6.5-10 Si02, and 100-140 H20. In the X case, increasing Na20, SiO2, and H20 produced the higher Si/Al products, whereas lower Na20 and higher Si02 increased SgAl ratios in the Y faujasites. To obtain high silica faujasites with SUA1 > 2.8, alkylammonium templates are required in the

1.27 1.34 1.37 1.41 1.45 1.82 2.24 2.52 2.59 2.92 3.31 3.63 3.80 4.76 4.67

Si

none none none

none none none

none none none EMA EMA MTEA TEMA TPA TPA

(4.4) (4.7) (9.7) (7.3) (13.5) (N/A)

EMA = bis(2-hydroxyethy1)dimethylammonium. MTEA = methyltriethanolammonium. TEMA = triethylmethylammonium. TPA = tetrapropylammonium.

synthesis gels.I9 These are of the ECR-4 types,20synthesized in the presence of bis(2-hydroxyethy1)dimethylammonium (EMA, samples 10, 1l), methyltriethanolammonium (MTEA, sample 12), or triethylmethylammonium cations (TEMA, sample 13) and ECR-32 types,21made in the presence of tetrapropylammonium cations (TPA, samples 14, 15). All samples were characterized as highly crystalline faujasites (FAU) by X-ray diffraction (Siemens D500 diffractometer,Cu K a radiation) with no impurities present. Chemical compositions were determined on "as synthesized" materials using ICP-AES and these are tabulated in Table 2. Template contents were obtained from the characteristic high-temperature weight loss in thermogravimetric analyses run in air (DuPont TG 2100, 10 "C/min). For NMR chacterization these materials were first purged of template by heating in a forced air fumace at 600 "C for 3 h, followed by 1 h at 650 "C, at which time the samples were white. They were then cooled to room temperature and twice exchanged in a 2 N aqueous sodium chloride solution for 1 h. After chloride was washed free with distilled water, the NdA1 ratios were 1.0 2~ 0.02. High-resolution 29SiNMR spectra were obtained at 39.5 MHz on a JEOL FX200S spectrometer equipped with Chemagnetics high power rf amplifiers and probe, using the combined techniques of magic angle spinning and proton dipolar decoupling. Proton decoupling was found to have little or no effect on the spectra of these materials in which the only protons are due to hydration. The mobility of the water effectively removes any static 'H-29Si dipolar interaction. Direct Bloch decay FID detection was used throughout, employing 90" pulses with pulse repetition times of 60 s, demonstrated to allow spin-lattice equilibration and ensure quantitatively reliable intensities. All spectra were obtained as overnight accumulations (- 1000 transients) with a data point resolution of 0.2 Hz and Fouriertransformed with no exponential weighting of the FID. Chemical shifts were referenced to (4,4-dimethyl-4-silapentane)sulfonate (DSS), taken to have a 29SiNMR chemical shift of -1.30 ppm vs tetramethylsilane (TMS). Chemical shifts are reported in ppm vs TMS. All samples were equilibrated with water vapor before performing NMR experiments. The basic 29Si NMR data were supplemented by a limited number of spectra obtained at 99.3 MHz using a Chemagnetics CMX-500 spectrometer, also used for a brief study of transverse (T2) relaxation to determine the homogeneous line shape (taken to be the Fourier transform of the transverse relaxation curve).

J. Phys. Chem., Vol. 99, No. 16, 1995 6131

Fine Structure of Faujasite Zeolites Table 2 summarizes the compositional details of the 15 FAU framework materials used in this study. Included in this table are the SUA1 ratios determined from the 29SiNMR ~ p e c t r a . ~ . ~ In all cases except for sample 15 the agreement of NMR and chemical analysis is satisfactory. The chemical analysis was performed on “as synthesized” materials, while the NMR analysis for the high-silica materials was performed after template removal and back exchange with sodium. For five of the six high-silica materials there is no evidence of any postsynthetic modification of the framework. Evidently, some dealumination did occur in sample 15. Since this material is of questionable integrity we have used it only as a reference material, useful in the preliminary stages of the characterization because of its unusually high SUA1. The analytical and NMR data show that the sample pairs 8 and 9, 10 and 11, and 12 and 13 are virtual duplicates. In many of the figures the data for these pairs have been averaged and plotted as a single point for the sake of clarity. The data analysis programs used for maximum likelihood spectral reconstruction (SSRES) and spectral fitting (CURVEFIT) were part of the LABCALC package from Galactic Industries, Inc.

Methodology Our goal in this work is an accurate representation of the observed 29SiNMR spectra of FAU zeolites as linear combinations of a multicomponent basis set of simple line shapes and the assignment of the components of this basis set to the various local environments as defined above. From the outset we felt that the problem was vastly underdetermined unless the position, line shape, and line width of the basis set components were taken as composition-independent. Logically there are three steps to the solution of this problem: 1. generation of an empirical basis set of N components with fixed positions and line shapes, which provides excellent spectral fits to the entire range of FAU materials; 2. assignment of each basis set component to one or more specific local environments; 3. demonstration that the results satisfy fundamental constraints imposed by the symmetry and connectivity of the FAU framework and Loewenstein’s rule. In practice the process was lengthy, highly nonlinear, and necessarily iterative, with these steps strongly coupled. An obvious starting point was provided by the chemical shift study noted aboveI7 in which the observed compositional dependence of the centroids of the Si(nAl) bands was accounted for by a weighted linear combination of deshielding effects of Al atoms in the four first-neighbor sites and the three secondneighbor sites which are doubly connected to the central Si atom. The evolution of the average populations of these sites with composition was calculated using a variant of the local ordering model.” This study provided strong support for the basic concept of local environment chemical shift sensitivity as well as initial estimates for a trial basis set of about 15 components. Translation of these results to a local environment basis set proved less than straightforward, at least partly because the assumptions of linear additivity of deshielding effects and the local ordering model are only rough approximations, to be used primarily as assignment aids. This study did provide estimates for the high-silica limiting 29Si NMR chemical shifts of the Si(OA1) and Si( 1Al) bands, experimental results of crucial importance to the present work. A more fundamental shortcoming of a trial basis set derived from the average band positions is the failure to use all the information contained in the band shapes. To this end we have made extensive use of resolution enhancement techniques.

80

85

95

90

100

105

ppm

Figure 4. Resolution enhancement by maximum likelihood restoration (MLR). a. Observed 29SiNMR spectrum of sample 4 (Si/AI = 1.40). b. Reference line shape which represents the best fit to the Si(4Al) band. c. The resolution-enhanced spectrum obtained using this

reference line shape. Resolution enhancement by maximum likelihood reconstruction (MLR) has proven to be especially powerful in this regard. This t e c h n i q ~ eis~ designed ~ , ~ ~ to treat spectra in which all the lines are subject to a common broadening function, which may be instrumental or, in the present case, a line shape assumed to be the same for all components. MLR uses an assumed line shape and an estimated noise level to produce apparently noise-free spectra of greatly improved resolution. The apparent increase in “signal-to-noise” is not real, however, since any peak which is below the estimated noise level does not appear in the enhanced spectrum. Extensive study of synthetic data (always with random noise added) has provided a good feel for the reliability of MLR. We have concluded that as long as the choice of reference line width is within about a factor of 2 of the “correct” value, the number and positions of major features in the resolved spectrum are not affected, even by the choice of line shape (Gaussian vs Lorentzian). Intensities in the resolved spectra are treated as semiquantitative. a. Generation of a Multicomponent Basis Set for Spectral Fitting. It is not our purpose here to discuss the merits of MLR but to show how this technique may be used to generate a basis set for spectral fitting. Figure 4 illustrates the use of MLR resolution enhancement of the 29Si NMR spectrum of a NaX material (sample 4). The observed spectrum is shown in Figure 4a. According to our basic definitions (Table 1) the peak assigned to Si(4Al) at -84.7 ppm represents a single local environment. The best fit to this nearly baseline-resolved peak is a 75/25 mixed GaussiadLorentzian line shape of full width half height -2.2 ppm, shown as Figure 4b. Figure 4c shows the result of using this simple line shape as the reference line shape for MLR resolution enhancement. Figure 4c shows 10 major peaks and represents the smoothest (most likely)24curve which upon convolution with the reference line shape reproduces the experimental spectrum (Figure 4a) within the specified uncertainty (noise level). The enhanced spectrum in Figure 4c can be thought of as providing an answer to the question: “Given that the reference line shape represents the 29Si NMR signal from a single local environment in the FAU framework, what is the minimum number of spectrally distinct environments contributing to the observed spectrum of this particular sample and what are the associated chemical shifts?’ The answer to this question for the material shown in Figure 4 is a minimum

Melchior et al.

6132 J. Phys. Chem., Vol. 99, No. 16, 1995

a.

N

b.

80

06

w

06

1W

106

110

ppm

Figure 5. The MLR resolution enhanced 29SiNMR spectra for three directly synthesized FAU materials. a. High-silica FAU, SUA1 = 5.31 (sample 15). b. Conventional Y zeolite, SUA1 = 2.17 (sample 7). c. X zeolite, SUA1 = 1.41 (sample 1). The 20 resolved peaks used to generate a trial basis set for spectral fitting are indicated.

of 10 environments. What makes the MLS method so powerful for our purposes is that it provides an objective and systematic method of answering this question for a sample set covering the entire composition range of directly synthesized FAU framework materials. The observed 29SiNMR spectra for NaX materials such as that shown in Figure 4 have little overlap with the high-silica FAU members of our sample set. The process of building a basis set begins with these extreme compositions and works toward the middle, or Y, composition range. Figure 5 shows the MLR resolution-enhanced 29SiNMR spectra for three FAU framework materials ranging in composition from a NaX (sample 4,SUA1 = 1.4) through a conventional NaY (sample 7, SUA1 = 2.2) to a high silica ECR-32 material (sample 15, SUA1 = 5.3). These resolution enhanced spectra show a systematic evolution of 20 major peaks, as indicated in Figure 5. Of these, the component at -102.8 ppm (peak 15 in Figure 5) represents the Si(OA1) peak in Figure 5c and one Si(lA1) peak in Figure 5a. A 20-component trial basis set with chemical shifts taken from Figure 5 (75% Gaussian line shape, width 2.0 ppm) gives excellent spectral fits to the observed 29SiNMR spectra for the three materials from which this basis set was derived, as shown by Figure 6 . The trial basis set of 20 components (one for Si(4A1), three for Si(3Al), five for Si(2A1), five for Si(OAl), and one shared between Si(lA1) and Si(0Al)) generated by the process just described, after minor iterative adjustments of positions and line shape, provides excellent fits to the observed 29SiNMR spectra over the entire data set 1.3 < SUA1 < 6. These fits are generally as good as, or better than, those shown in Figure 6. We feel that this number of spectral components is the minimum number consistent with our basic hypothesis conceming local environments, i.e., that a silicon atom in a given local environment should be represented by a fixed position and line shape, independent of composition, and that the line shape is the same for all environments. (The only deviation from this hypothesis is our use of a slightly greater line width (2.2 ppm) for Si(4Al) and a slightly modified line shape (15% Lorentzian rather than 25%) for Si(OA1) components 17-20.) b. Assignment of Basis Set Components to SpeciRc Local Environments. The observed intensities of the six basis set

C. I

I

I

1

I

I

I

80

a5

90

95

100

105

110

PPm

Figure 6. Spectral fits superimposed on the observed 29SiNMR spectra for samples 4, 7, and 15 (shown as c, b, and a) obtained using a 20component trial basis set with chemical shifts suggested by the MLR results in Figure 5 .

13

14

15

16

17

18

19

20

21

Silicons per Sodalite Unit

Figure 7. Intensities of Si(lA1) components vs composition, both expressed as the number of Si atoms per sodalite unit (24 T atoms). Basis set components are identified by the bracketed numbers at the right.

components associated with the Si(lA1) band are shown in Figure 7. The intensities are expressed as the number of silicon atoms in a particular component plotted vs the total number of silicon atoms, both axes on a per sodalite unit or 24 T sites basis. Assignment of these six spectral components to specific local environments can be accomplished by analysis of the evolution of the six intensities with composition, with particular emphasis on the composition extremes. At the composition extremes, Ns, < 15 and Nsi > 19, predictably fewer local environments predominate. The high-silica limit can be described by “isolated” A1 atoms in a mostly silica FAU lattice, i.e., Al atoms that have no second-shell A1 neighbors. In this limit there are four possible Si( 1Al) local environments a(O,O,O), b(O,O,O), c(O,O,O), and d(O,O,O) which must be equally populated. Although none of the directly synthesized FAU materials in this study falls into this composition range, published data for

Fine Structure of Faujasite Zeolites

J. Phys. Chem., Vol. 99, No. 16,1995 6133

0.3

0.2

I

13

14

15

16

17

18

19

20

21

Silicons per Sodalite Unit

Figure 8. Intensities of the three high-silica limiting basis set components 13 (A), 14 (O), and 15 (0)at -100.4, -101.6, and -102.8 ppm expressed as fractions of the total Si(lA1) band intensity. These are assigned to local environments d(O,O,O), a(O,O,O) b(O,O,O), and

+

Figure 9. Structural units which may contain the high-silica limiting Si(lA1) environments at SUA1 = 3.0 (18 Si per sodalite unit). Note that these local environments a(O,O,O),b(O,O,O), and d(O,O,O) correspond to silicons having no second-shell A1 atoms in positions i, ii, and iii.

c(O,O,O), respectively.

materials prepared by postsynthesis dealumination were included in the chemical shift study noted above.I7 This study provided two important results: the limiting chemical shift 60 for a hypothetical totally dealuminated FAU framework (corresponding to the local environment z(O,O,O)) and the average chemical shift for the four limiting Si(lA1) local environments A

6, = -107.8 & 0.2 ppm

(1)

(d(lAl)), = -101.4 f 0.2 ppm

(2)

At the highest composition shown in Figure 7, the three strongest components of Si(lA1) are components 13, 14, and 15 at -100.4, -101.6, and -102.8 ppm with intensities 25%, 35%, and 20% of the total Si(lA1) band. The weighted average chemical shift of these three major components is - 101.5 ppm, consistent with their representing the four limiting environments, with the -101.6 component representing two of the four. Other assignments, such as including the component at -99.3 ppm as one of the four limiting local environments, cannot account for the observed (d(1Al))o. Figure 8 shows the intensities of the -100.4, -101.6, and - 102.8 ppm components with intensities expressed as fractions of the total Si(lA1) band intensity. These three component intensities show very different compositional dependences. The - 100.4 ppm component represents a significant fraction of Si(lA1) over the entire range (note the appearance of peak 13 in parts a and c of Figure 5 ) , the - 101.6 component is relatively minor for Nsi 16 (especially in view of the assertion that this component represents the superposition of two limiting environments), and the -102.8 ppm component is not apparent at all below Nsi % 18, becoming a major component only at the highest compositions. The data in Figure 8 provide the necessary connection with structure allowing tentative assignment of these three limiting components. The assignments of the four limiting Si(lA1) environments can be made on the basis of the general principle of second-shell A1,Al pair avoidance, i.e., that Si,Al distributions in FAU tend to favor those structural units which minimize second-shell A1-0-Si-0-AI pairs and that the local environments which can exist in these favored structural units are correspondingly favored at a given composition. The discussion is simplest in terms of D6R structural units (hexagonal prisms), but the conclusions do not depend on this choice. We designate a particular D6R unit by Dn@,q)where n denotes the number of A1 atoms, p the number of second

Figure 10. Structural units which may contain the local environments a(O,O,O), b(O,O,O), and d(O,O,O) at SUA1 = 2.0 (16 Si per sodalite unit).

shell A1,AI pairs doubly connected across 4R’s, and q is the number of AI-0-Si-0-AI pairs across 6R’s. This is a very efficient notation, being essentially a condensation of the notation used by Peters.I5 There are 19 distinct D6R types ranging from n = 6 to n = 0, and, except for Dz(O,O), corresponding to which there are three different D6R arrangements, this notation provides an unambiguous designation. Figure 9 shows four D6R subunits D3(p,q) each of which contains one of the four limiting Si(1AI) local environments. Of the four subunits one is clearly disfavored. This unit, &(2,1), which contains three AI-0-Si-0-AI pairs, is the one which may include the local environment c(O,O,O). On the basis of this we assert that the c(O,O,O) local environment is disfavored at this composition (SUAI = 3). The other three structural units each contain only one A1,Al pair, the minimum possible at this composition. This essentially qualitative argument supports the assignment of basis set component 15 at -102.8 ppm to c(O,O,O) and the assignment of the basis set components 13 and 14 at -100.4 ppm and -101.6 ppm, which predominate at SUA1 % 3 (Nsi 18 in Figure 8), to the other three local environments. The line of reasoning used in the foregoing can be extended to lower SUA. Figure 10 shows the D&,q) subunits (SUA1 = 2) containing a(O,O,O), b(O,O,O), and d(O,O,O) local environments. The a(O,O,O) and b(O,O,O) environments require a D6R subunit Dd3,2), withfive AI-0-Si-0-AI pairs, whereas d(O,O,O) can exist in Dd2,1), with only three AI-0-Si-0-AI pairs. Thus, at Ns, 16 the local environment d(O,O,O) is favored over a(O,O,O) or b(O,O,O). Inspection of Figure 8 indicates we should

6134 J. Phys. Chem., Vol. 99, No. 16, 1995

Melchior et al.

Figure 11. The lowest Si/AI structural units which may contain Si( 1Al) environments c( l,l,O), b( 1,O,l), a(0,1,0), and d(0,0,1).

0.7

T

0.6

i "\

Oe5 0.4

1'\

13

14

15 16 17 18 19 Silicons per Sodalite Unit

20

21

Figure 12. Intensities of the four basis set components which comprise Si(lA1) at low SUAl, expressed as fractions of the total Si(lA1) band intensity. Component 11 ( x ) at -98.8 is assigned to c(l,l,O), component 10 (0)at -98.1 is assigned to b(l,O,l), and component 12 (W) at -99.3 is assigned to a(0,1,0). Component 13 (A) at -100.4 has already been assigned to d(O,O,O) at high SUAl.

assign the -100.4 ppm component to d(O,O,O) and the -101.6 component to the sum of a(O,O,O) and b(O,O,O). The assignment of the Si( 1Al) basis set components proceeds by focusing on the other end of the composition scale, at the low SUA1 limit, where there are four possible Si(lA1) local environments: a(0,1,0), b(l,O,l), c(l,l,O), and d(0,0,1). Figure 11 shows the lowest SUA1 subunits which contain these local environments. The lowest composition D6R subunit which may contain a Si(1Al) local environment is D5(4,4) with SUA1 = 1.4, which may contain c( 1,1,0) but not the other three limiting local environments. The basis set component which dominates the Si(lA1) band at the lowest SUA1 is assigned to local environment c(l,l,O). According to Figure 12 which shows the intensity of components 10, 11, 12 and 13 expressed as a fraction of the total Si(nAl) band intensity, the component which appears at lowest SUA1 is component 11 at -98.8. It is important to note, however, that the c( 1,1,0) environment can only exist if there are adjacent D6R units which contain para Al-substituted D6R units such as D&O) or D 4 2 J ) . This fact is a consequence of Loewenstein's rule and the connectivity of the FAU lattice. Thus, the occurrence of Si( 1Al) at S i / A l 5 1.4 is direct evidence for a distribution of D6R subunits including, at least, Da(6,6), D5(4,4),and D42,O). Excellent fits to the experimental Si(nAl) intensities for SUA1 5 2 are obtained using a binomial distribution of these three D6R units randomly assembled subject only to Loewenstein's rule.I6 The unit D4(2,0) may contain

the local environments a(0,1,0) and b( 1,O,l). The details of the calculation for random assembly of this unit with the other D6R units indicate that b(l,O,l) is favored at lower Si/A1. Local environment d(O,O,1) requires D4(2,I), assumed to be less favored, but not necessarily excluded, on the basis of Al,Al pair avoidance. On the basis of this analysis we anticipate that the local environment populations should evolve with increasing SUA1 in the order c(l,l,O) > b(l,O,l) 1 a(0,1,0) > d(0,0,1). Reference to Figure 12 shows that component 10 at -98.2 ppm should be assigned to b(l,O,l) and component 12 at -99.3 ppm should be assigned to a(0,l ,O). The foregoing analysis has allowed the assignment of the six basis set components associated with the Si(1Al) band to the local environments which must exist at the composition extremes. Three of the basis set components (10, 12, and 13) have significant intensities over the entire composition range. One local environment expected to exist over the entire composition range is a(0,1,0). Basis set component 13 at -100.4 ppm has already been assigned to d(O,O,O) at high Si/ A1 while component 10 has been assigned to b(l,O,l) at low Si/Al. A consistent picture emerges if we assign component 10 at high SUA1 to b(1,0,0) and component 13 to d(0,0,1) at low compositions, suggesting that the presence of a secondshell AI neighbor in site iii (cf.Figure 3) has negligible effect on the chemical shift of the central Si atom. This is precisely the conclusion we reached previ~usly'~ based on different evidence-the compositional dependence of the Si(OA1) band. On the basis of the immediately foregoing we can drop the designation of second-shellsubstituent iii and simplify notation:

b(l,O,l) z b(1,0,0)

b(1,O)

(3)

d(0,0,1)= d(O,O,O)

d(0,O)

(4)

etc. Of greater significance is the fact that the number of distinguishable local environments in Si( 1Al) is reduced from 12 to 9. Seven have been identified (a(O,l), b(1,0), c ( l , l ) , d(O,O), a(O,O),b(O,O), c(O,O)),these seven environments being those which should exist at the compositional extremes. The remaining two local environments are c(1,O) and c(O,I),expected to be of significant intensity only in the middle of the composition range. Presumably it is the population of these environments which complicates the Si(lA1) region in the Y composition range as shown in Figure 5. Since we have obtained excellent spectral fits throughout the entire composition range, additional basis set components are not justified. We hypothesize that c(I,O) and c(O,I) fall between a(0,I)and d(0,O) and partition the intensity of components 12 and 13 according to the dictates of the fundamental framework constraints to be applied during the next step, described in the following section. The assignment of the Si( 1Al) components has been deduced from essentially qualitative considerations based on the generally accepted criterion of second-shell A1,Al pair avoidance. It is interesting to use the assigned chemical shift positions for a(O,O), b(O,O),c(O,O), and d(0,O) with that for z(O,O,O) to calculate the 29SiNMR shielding effect of an Al substituent in each of the four first-shell positions. These results (60 = -107.8 for no A1 substituent, 6.2 ppm for an Q or b substituent, 5.0 ppm for a c substituent, and 7.3 ppm for a d substituent) are remarkably similar to the set of first-shell shielding parameters deduced from study of Si(nAl) average band position^.'^ Recall that the previous treatment was based on an assumption of linear additivity of shielding effects. This encourages testing such an assumption as a tool for assignment of the Si(3Al) and Si(2Al) local environments. For Si(3Al), linear additivity of first-shell shielding predicts -88.1 ppm for d(abd), -89.3 ppm

Fine Structure of Faujasite Zeolites

a

4

J. Phys. Chem., Vol. 99, No. 16, 1995 6135

C

Figure 13. Three bonding situations which give rise to fundamental constraints on the local environment populations in the FAU framework.

for G(acd) or G(bcd), and -90.4 ppm for G(abc). These estimates coincide almost exactly with the average positions of basis set components 2, 3, and 4 at -88.2, -89.3, and -90.4 ppm, which are assigned accordingly. The reduced definition of local environments represented by eqs 3 and 4 implies that the five basis set components in Si(2Al) represent eight local environments. Starting (trial) assignments were based on chemical shift positions estimated by assuming linear additivity of first-shell shielding. Basis set component 5 at -92.8 ppm is assigned to bc(l,O), component 6 at -93.8 ppm to ad(0,O) and bd(O,O),component 7 at -94.8 ppm to ac(O,I),component 8 at -95.6 ppm to ab(0,O)and cd(O,O), and component 9 at -96.7 ppm to ac(0,O) and bc(0,O). The assignment of the Si(OA1) local environments is less straightforward. Six basis set components have been used (including component 15, which represents z(l,l,l) at low Si/ Al), two more than anticipated for the reduced definition of local environments, in which an A1 substituent in position iii (Figure 3) does not influence the 29Sichemical shift. Components 16-20 have been assigned to environments z(l,l,O), z(1,0,1) + z(1,0,0), z(O,l,1), z(O,l,O) + z(O,O,1), and z(O,O,O), respectively. c. Fundamental Constraints on Local Environment Populations; Constrained Spectral Fitting. The assignment of basis set components to specific local environments invokes a number of constraints based on fundamental considerations of the FAU framework symmetry and connectivity, and Loewenstein's rule, which is taken as absolute. These considerations impose fundamental relationships between the local environment populations which must hold over the entire composition range. The most obvious of these relationships can be seen very simply by noting that each of the Si(nA1) bands is a superposition of local environments involving the four first-shell positions a, b, c , d in various combinations. Since these four positions are crystallographically equivalent in the FAU framework, the aluminum occupancy of each site, summed over all Si(nAl), must be equal to the total aluminum content. This provides three independent expressions which we specify as A = B = C = D where, for example, A = Ckfk A@), f k being the population of the kth local environment and A(u) is unity if site u is occupied in the kth local environment and zero if it is not. Additional constraint equations can be derived in a number of ways. The most systematic approach is to note that a constraint relationship is imposed whenever two Si atoms share multiple first- and/or second-shell neighbors. There are two relevent situations in the FAU lattice, shown in Figure 13, in which a Si-Si' pair lies along one of the edges of a D6R unit, common to two 4R units. By Loewenstein's rule the four sites adjacent to the Si-Si' pair in each case (i.e., the four corners of the shaded rectangles in parts a and b of Figure 13) can be occupied by 0, 1, and 2 AI atoms. For each case (13a or 13b) there are five possible distinct arrangements. A constraint equation arises from any arrangement in which Si and Si' have different environments with respect to the four shared sites. There are three such bonding situations in 13a and four in 13b. From each of these seven arrangements the corresponding constraint is obtained by summing over all local environments

having the central arrangement in common. This process is illustrated in the Appendix, in which the seven constraint equations are derived. The seven relationships derived from parts a and b of Figure 13 along with the three site occupancy relationships already noted form a set of 10 linearly independent constraint equations. It turns out that all other constraint equations we have been able to discover are linear combinations of these 10. It is advantageous to seek the simplest set of constraint equations (those which involve the fewest local environments). There is one more bonding situation (illustrated in Figure 13c) which provides a particularly useful simplification. The "most orthogonal" set of 10 constraint equations AlA10 is given in the appendix. The 10 constraint equations derived in the Appendix involve all 34 local environments based on specification of four firstshell neighbors and all three second-shell neighbors surrounding the central silicon atom. On the basis of the discussion in the foregoing section it is appropriate to adopt the simpler representation of local environments, based on specification of only two second-shell substituents, as implied by eqs 3 and 4. On this basis there are just 26 distinct local environments, and the number of constraint equations is reduced to seven. A simpler notation for these 26 reduced local environments is useful, in which, for example, b(l,O,l) 2 b(1,0,0) 2 b(1,O) b*O 2 b(O,O,O) 2 b(0,O)E

b(0,0,1)

00-

b*

(5)

0

b =b

(6)

etc. The 26 reduced local environments are listed in Table 1. In terms of these local environments the 10 constraint equations derived in the Appendix translate to the following seven expressions.

A=B

0

C=D

(C2)

+ + c"* bo + bco = z*O + c*O ab + abc = z** + c** ad + ucd = bd + bcd ao uco = zo*

b*

+ bc* +z**

+ c * * +Z*O

+

C*O

= bd

)

(C3) (C4)

(C5) (C6)

+ bcd + d + cd (C7)

These seven constraint equations apply over the entire composition range. Constraints C3 through C6 are direct translations of the corresponding expressions A3 through A6 derived in the appendix from parts a and c of Figure 13. The last constraint C7 is obtained from the sum of A8, A9, and A10, derived in the appendix using Figure 13b. It is important to note that in the limit of low SiLAl,constraint C7 is the sum of two constraints, obtained from A9 and A10.

+ z** + z*O e cd + bcd c*O + c** + bc* d + bd

b*

GZ

(xC7') (xC7")

which can be assumed to apply for the X composition range (Si/Al 5 1.5). In principle, at least, the constraints C1 -C7 could be made an integral part of the spectral fitting process. None of the spectral fitting routines available to us supports a constrained fit of this type, in which a simultaneous fit to the spectral data

Melchior et al.

6136 J. Phys. Chem., Vol. 99, No. 16, 1995 and the constraint equations (suitably weighted) would be sought. We have employed a less elegant approach which we feel has approximated this process. The trial basis set developed and partially assigned in the foregoing provides excellent fits to the spectral data, as illustrated in Figure 6. This basis set consists of 20 components (one for Si(4A1), three for Si(3Al), five for Si(2A1), five for Si(lAl), five for Si(OAl), plus one component representing an Si(0Al) environment at low SUA1 and a Si( 1Al) environment at high Si/Al). Tentative assignment of these components has been in terms of the reduced set of 26 local environments listed in Table 1. As noted in Table 1 these local environments number one for Si((4Al), four for Si(3Al), er :ht for Si(2Al), nine for Si(lAl), andfour for Si(OA1). The 01 servation that six basis set components are required to fit Si ,OAl) shows that the reduced definition of local environments is inadequate for this band. In order to apply the constraint equations, the six Si(0Al) basis set components must be combined to four local environment populations:

z** = Z(L1,l) + z(1,1,0)

+ Z(l,O,O) zO*= z(O,l,l) + z(O,l,O) zoo= z(O,O,l) + z(O,O,O) Z*O

= z(l,O,l)

On the other hand, the 15 remaining basis set components must be apportioned among 22 local environments, requiring seven parameters. The fact that we have seven constraint equations suggests the information content of the data is adequate. The iterative procedure used initially was as follows. The starting basis set intensities were used in a spreadsheet containing the parameters necessary to convert these intensities to the 26 local environment populations. The seven main parameters were varied to give an "acceptable" fit to the seven constraint equations. This process included the assignment of the Si(OA1) components. Since this process only apportions the basis set intensities among local environments, the spectral fitting result is unaffected. The next step is to introduce several additional (interim) parameters which adjust the relative local environment populations {fko}, to improve the fit to the constraint equations. The modified set {fk'} was then used as the initial point for spectral fitting, first with fixed intensities allowing the positions to vary, then fixing the positions and allowing the intensities to vary. This new set of intensities {fk2} was the input to a second fine tuning to the constraint equations. This iterative process was continued until the result of the spectral fitting no longer required the additional parameters to fit the constraint equations to within 1-2%. This process was carried out with spectral data sets which had been interpolated to 4 times the actual spectral resolution (0.2 ppm). During this process we expanded the basis set to 22 components by splitting component 3 (acd bcd) and component 6 (ad bd). The resulting local environment populations {fk} provide spectral fits at least as good as those obtained initially. The procedure described in the foregoing gave excellent simultaneous least-squares fits to the spectral data and the seven constraint equations. The uniqueness of these fits is difficult to assess because of the complexity of the fitting process. A possible simplification suggests itself. Constraint C 1 can be expressed (using eq C6) as

+

+

a*

+ uc* + a0 + ucO= b* + bc* + bo + bcO

The fits obtained by the above procedure are characterized by the approximate relationships

TABLE 3: Local Environment Basis Set component 1 2 3A 3B 4 5 6A 6B 7 8 9 10 11 12 13 14 15 16 17 18 19 20

avg shift"

assignment

-84.67 -88.29 -89.13 -89.79 -90.41 -92.75 -93.42 -94.07 -94.81 -95.59 -96.75 -98.12 -98.91 C** -99.31 a* c*o d co* -100.47 -101.56 ao bo -102.82 cW ( I l l ) - 104.05 (110) (101) -105.20 (100) (011) -105.88 (001) (010) -106.71 -107.79 (000)

abcd abd acd bcd abc bc* ad bd ac* ab ab cd abo bco b*

+ + +

+ + + +

+ +

std devb

avg Xc

avg Y'

0.15 0.16 0.04 0.06 0.07 0.15 0.07 0.10 0.06 0.05 0.03 0.08 0.07 0.07 0.06 0.15 0.14 0.08 0.07 0.12 0.25 0.02

-84.62 -88.47 -89.11 -89.80 -90.35 -92.91 -93.37 -93.97 -94.82 -95.63 -96.13 -98.18 -98.90 -99.31 -100.45 -101.42 -102.91 -104.07 -105.26 -105.81 -106.57 -107.79

-84.70 -88.17 -89.14 -89.79 -90.45 -92.64 -93.45 -94.14 -94.81 -95.57 -96.76 -98.09 -98.91 -99.32 -100.48 -101.66 -102.76 - 104.03 -105.13 -105.92 -106.81 -107.79

Average chemical shift for best constrained fits over the sample set. Standard deviation of the chemical shift over the sample set. Average chemical shifts for the low (samples 1-6) and high (samples 7-14) composition ranges.

+ ac* x b* + bc* a0 + ucOM bo + bcO

a*

the first of these must hold at the low SUA1 limit and the second of which must hold at the high SUA1 limit. We have explored the consequences of assuming that these approximate expressions hold as equalities over the entire composition range. We replace the constraint C3 by the pseudoconstraint a0

+ ucO= bo + bcO

P3)

noting that any set of local environment populations satisfying the modified constraints satisfies the true constraints C1 -C7. It can be shown that eq P3 holds except for structures involving certain asymmetric D6R subunits which may be connected in the FAU framework in two alternative modes, in which the identities of the first-shell substituents designated as a and b are interchanged. Asserting that eq P3 holds is tantamount to asserting that these alternatives are equally populated. We view the constraint P3 as a hypothesis to be tested. The analysis is simplified because eq P3 leads to several algebraic relationships between the seven parameters and the basis set components and, in most cases, better fits to the constraint equations. We conclude that the spectral data and the assignment of local environment fine structure are, at the very least, consistent with the pseudoconstraint P3.

Results and Discussion The final basis set is listed in Table 3, including the averages over the sample set of the chemical shifts and the standard deviation of each peak position across the data set. These standard deviations range from 0.04 to 0.25 ppm, consistent with the spectral resolution of 0.2 ppm and with the inherent uncertainties of referencing solid state NMR spectra. For a few components a mild composition dependence was indicated. To show this, we have included the average shifts used in the low range of compositions (SUA1 5 2) and in the high range (Si/Al > 2 ) . A mixed GaussiadLorentzian line shape of width 2.0

J. Phys. Chem., Vol. 99, No. 16, 1995 6137

Fine Structure of Faujasite Zeolites

TABLE 4: Local Environment Populatioe sample

1

abed abd acd bcd abc bc* ad bd ac* cd ab aco+ beo b*

6.55 1.43 1.28 0.56 0.77 0.39 0.00 0.65 0.67 0.00

5.39 1.60 1.58 0.56 0.70 0.68 0.10 1.07 0.67 0.00

4.99 1.56 1.71 0.61 0.68 0.70 0.03 1.14 0.76

4.43 1.63 1.81 0.51 0.83 0.72 0.18 1.46 0.83

0.00

0.00

0.00

0.00 0.08

C**

0.12 0.16 0.29

a*

0.00

c*o co* d

0.14 0.16 0.43 0.18 0.07 0.07 0.00 0.00 0.00 0.28 0.02 0.02

0.06 0.12 0.21 0.49 0.15 0.02 0.07 0.08 0.12 0.00 0.27 0.09 0.02

+ bo

0.02 0.02 0.05 0.00

CW

0.00

Z** Z*O

totalSi

0.35 0.02 0.03 0.01 13.37

ao

'?* zoo a

2

3

4

0.00

0.00

13.72

13.89

0.04 0.26 0.69 0.11 0.07 0.07 0.00 0.00

0.00 0.27 0.02 0.02 0.00 14.03

5 3.63 1.90 2.07 0.45 0.86 0.88 0.10 1.65 0.92 0.00 0.03 0.08 0.23 0.67 0.22 0.09 0.09 0.00 0.04 0.00 0.27 0.02 0.02

0.00 14.23

6

7

8

1.47 1.49 1.70 0.63 0.92 1.03 0.90 1.98 1.17 0.33 0.43 0.22 0.46 0.90 0.31 0.17 0.17 0.15 0.34 0.00 0.40 0.06 0.06 0.02 15.32

0.30 1.08 1.03 0.31 0.70 1.08 1.37 2.05 1.35 0.86 0.34 0.46 1.12 0.61 0.84 0.43 0.42 0.57 0.70 0.00 0.43 0.17 0.18 0.02 16.43

0.09 0.49 0.80 0.06 0.56 0.90 1.15 1.91 1.06 1.32 0.36 0.72 1.44 0.04 1.27 0.56 0.67 0.93 1.20 0.00 0.82 0.39 0.28 0.19 17.23

9 0.10 0.40 0.86 0.00 0.44 0.86 1.12 1.93 1.07 1.25 0.37 0.76 1.50 0.03 1.28 0.68 0.60 1.01 1.30

0.00 0.87 0.34 0.44 0.11 17.34

10

11

12

13

14

0.00

0.00

0.00

0.00

0.25 0.36 0.00 0.29 0.80 1.10 1.45 1.23 1.20 0.27 0.72 1.61 0.02 1.17 0.87 0.61 1.74 2.14 0.02 0.54 0.56 0.81 0.13 17.89

0.25 0.40 0.12 0.15 0.58 1.15 1.43 1.06 1.20 0.50 0.60 1.51 0.14 1.01 0.93 0.82 1.50 2.36 0.04 0.52 0.56 0.67 0.44 17.95

0.19 0.10 0.15 0.11 0.58 0.96 0.91 0.68 1.00 0.39 0.60 1.47 0.24 1.37 0.87 0.75 2.19 2.68 0.41 0.26 0.84 0.95 0.85 18.53

0.06

0.00 0.03

0.16 0.06 0.01 0.44 0.84 0.94 0.77 0.88 0.43 0.64 1.55 0.08 1.22 1.16 0.55 2.35 2.96 0.54 0.37 0.64 1.24 0.83 18.71

0.03 0.03 0.21 0.48 0.45 0.48 0.73 0.14 0.50 1.19 0.04 0.92 1.29 0.33 2.57 3.88 0.65 0.14 0.91 1.87 2.85 19.71

0.00

Populations expressed as numbers of silicon atoms per sodalite unit (24 T atoms).

ppm was used, except for Si(4Al) (component 1) which was 2.2 ppm. The line shape used for components 1- 16 was 25% Lorentzian, while for Si(0Al) components 17-20 a 15% Lorentzian gave somewhat better fits. Table 4 contains the local environment populations resulting from the iterative process described above. These populations produced excellent simultaneous fit to the spectral data and the fundamental framework constraints C1-C7. The results in Table 4 are consistent with the pseudoconstraint P3. As a consequence, only the sums (aco bco) and (ao bo) can be determined. The seven contraints are those imposed by Loewenstein's rule and the short range connectivity of the FAU framework. These short range constraints arise from the special configuration and double connectivity of the intersecting 4-rings and 6-rings of the D6R units. It is important to note that there are additional, longer range constraints associated with the connectivity of the sodalite cages and supercages. These additional constraints have not been imposed on the results. One of the facts which gives us a great deal of confidence in the essential correctness of our results is that we find evidence of these longer range constraints therein. Moreover, aside from the qualitative arguments used to assign some of the basis set components, nothing has been assumed conceming A1,Al avoidance beyond Loewenstein's rule. Nor have we made any assumptions conceming compositional homogeneity. Thus, the results are model-independent and contain information sufficient to determine A1,Al avoidance and, independently, to test the effects of compositional homogeneity on local Si,Al order. a. Calculation of Average Si(nA1) Properties. An immediate dividend of the results in Table 4 is a significant improvement in our ability to calculate properties averaged over first neighbors. Table 5 summarizes the first-neighbor Al distributions Si(nA1) derived from the local environment populations in Table 4. The aggregate distributions are only weakly dependent on the details of the assignment of local environments. Inspection of the chemical shifts assigned to local environments in Table 3 shows that there is some overlap of the Si(nA1) bands. For this reason and because the spectral data were obtained under equilibrium (quantitative) conditions, these Si(nAl) distributions are somewhat different from previ-

+

+

TABLE 5: Aggregate First-Shell A1 Neighbor Distributions Si(nA1) sample SUAP Ns? Si(4A1) Si(3A1) Si(2AI) Si(lA1) Si(OA1) 1 2 3 4 5

6 7 8 9 10 11 12 13 14

1.26 1.33 1.38 1.41 1.46 1.76 2.17 2.54 2.60 2.91 2.97 3.39 3.54 4.60

13.37 13.72 13.89 14.03 14.23 15.32 16.43 17.23 17.34 17.89 17.95 18.53 18.71 19.71

6.55 5.39 4.99 4.43 3.63 1.47 0.30 0.09 0.10 0.00 0.00

0.00 0.00 0.00

4.04 4.44 4.57 4.78 5.28 4.74 3.12 1.92 1.70 0.90 0.93 0.56 0.29 0.09

1.83 2.67 2.81 3.31 3.66 6.06 7.53 7.42 7.37 6.78 6.51 5.11 4.94 2.98

0.55 0.91 1.14 1.21 1.35 2.52 4.68 6.12 6.40 8.18 8.31 9.97 10.41 10.88

0.41 0.31 0.39 0.31 0.31 0.54 0.80 1.68 1.76 2.04 2.19 2.90 3.07 5.76

a Determined from 29SiNMR data. Number of silicon atoms per sodalite unit calculated from SUAl.

ously published results" on some of the same samples. The present data cover a broader range of compositions because of the inclusion of high silica ECR-4 and ECR-32 materials. The improved integration of band areas provided by the full profile spectral fit increases the accuracy and precision of the Si(nA1) intensities. For all these reasons the results in Table 5 represent the best available data on overall Si(nA1) distributions in FAU framework materials. Another application of these results is the calculation of the average density of Al-0-Si-0-A1 nonbonded pairs as a function of compositionlo

Pavg= (61,

+ 31, + IJ(SUA1)

(7)

where I,, is the fraction of total Si with n fist-shell Al neighbors. The average A1-0-Si-0-A1 pair densities Pavgcalculated from Table 5 are shown in Figure 14, plotted vs composition. Figure 14 shows the line representing the average density of Al,Al pairs predicted for the case in which the siting of Al atoms in the FAU framework obeys Loewenstein's rule but is otherwise random. Also shown in Figure 14 is the minimum density of Al-0-Si-0-A1 pairs possible in the FAU frame-

Melchior et al.

6138 J. Phys. Chem., Vol. 99, No. 16, 1995 1

l

k

0.9

E 0.8 U J E o)

0.7

.$

0.6

0

;

0.5

0.5

0 0.4

0.4

? 0 a

0.3

0.3

0.2

0.2 -

0.1

0.1 -

-

\

\

0

12

13

14

15

16

17

18

19

20

Silicons per Sodalite Unit

line, Loewenstein rule only) and the FAU-framework-allowed minimum (lower line) pair density.

work. These results confirm the conclusion first reached by Vega'O that nonbonded Al,AI pairs are avoided in these materials but that this avoidance is significantly less than that allowed within the framework connectivity. It is clear from Figure 14 that intermediate local order in the Si,AI distributions in directly synthesized FAU framework materials exists over the entire composition range 1 5 SUA1 I5. As applied to the calculation of properties averaged over firstshell A1 neighbors, the spectral data summarized in Table 5 provide the best available data set for the properties of Si,AI distributions at the level of detail achieved in previous work. That which follows illustrates the significant increase in the information content achieved by the present work. The results in Table 4 provide a detailed description of the Si,AI distribution in synthetic faujasites. We first develop this description in very general terms, focusing on the density of specific nonbonded A1-0-Si-0-AI pairs, followed by a description in terms of specific structural subunits. The D6R representation is shown to be a very useful way of looking at the results. b. Nonbonded A I 4 1 Pairs and the Nature of Local Order in Faujasites. The FAU framework may contain six structurally distinct types of Al-O-Si-O- Al nonbonded pairs. Previously only the average density of these pairs could be determined from the observed Si(nAl) intensities without recourse to some model. We can now determine the resolved pair densities Pxy,where x, y are a, b, c, or d, obtained by summing over all local environments which have both x and y sites occupied by aluminum,

where fk is the fraction of the total Si in the kth local environment and A(x)A(y) is unity if the kth local environment has both x and y sites occupied by aluminum and is otherwise zero. Thus, for example, the pair density P a b is given by

+ UbC + Ubd + ab)(Si/Al)

13

14

15

16

17

18

19

20

Silicons per Sodallte Unit

Figure 14. Average A1-0-Si-0-A1 pair density calculated from Table 2 and eq 7. Broken lines show limiting cases of random (upper

Pa, = (UbCd

12

(9)

Reference to Figure 2 shows that three of these pairs (ac, ad, and bd) correspond to doubly connected nonbonded pairs across 4-rings. The ac pair is across a 4-ring (4R) in the sodalite cage while ad and bd are in D6R units. The pairs ab and bc are

Figure 15. 4R A1,Al pair densities Pd P b d (0)and P,, (+) for the case uco = bco, with the possible extremes for P,, shown as dashed lines (- - -), Figure also shows Loewenstein random (- -) and FAU framework minimum (-

*

-) pair densities.

nonbonded A1,Al pairs across 6-rings (6R), ab being within the D6R, and bc being across the single 6R in the sodalite cage. The remaining pair cd is situated across the 12-ring (12R) window of the supercage. There is a limitation to the resolution of A1-0-Si-0-AI pairs inherent in the inability to resolve the populations ucOand bco, as indicated in Tables 3 and 4. This has little effect at low SUA1 where these populations are small but is a major limitation at high SUA1 where Pbc and Pa, have significant contributions from bcOand ucO. First consider the 4R pair densities pad, Pbd, and pac. Constraint C6 used with eq 8 shows that Pad must be equal to Pbd over the entire composition range. Moreover, the FAU framework and Loewenstein's Rule restrict the density of 4R pairs to minimum values:

where Nsi is the composition expressed as the number of Si atoms per sodalite unit (24 T atoms). Equation 10 expresses the minimum possible number of doubly occupied (by Al) 4R units at a given composition. Figure 15 shows the 4R pair densities calculated from Table 4. The Values of Pad and Pbd are virtually identical over the entire composition range, as required by the constraint equations. The values of Pa, are essentially the same as the other two pair types over the X composition range (Si/AlI 2.0, Nsi I16), the range over which the ambiguity between ucoand bco has little effect. This result is not required by the constraints. Finally, note that the 4R pair densities are very close to the minimum allowed values over the X composition range but deviate significantly for the Y composition range. This deviation is most apparent for compositions near Nsi w 18, where the framework minimum given by eq 10 goes to zero. The observed values of Pad and Pbd are equivalent to just less than one 4R occupied by two A1 atoms per D6R unit. Figure 15 shows the range of values calculated for Pacassuming, alternatively, ucO= 0 or bco = 0, as well as the average of these extremes. Even the lower limiting values are significantly greater than the framework constraint and are very similar to the values observed for P a d

J. Phys. Chem., Vol. 99,No. 16, 1995 6139

Fine Structure of Faujasite Zeolites

Oe6 0.5

i

0 ‘ 12

‘. ‘.

R.

13

14

15

16

‘.

17

18

19

20

Sillcons per Sodalite Unit Figure 16. 6R and 12R pair densities Pd (O), P b c

(+), and Pc,, (A). The points shown are for the case ucO= bco,with the possible extremes indicated by broken lines (- - -). The figure also shows the Loewenstein random case. It should be noted that the random curve is different from that in Figure 15.

and Pbd. These lower limiting values correspond to approximately one doubly occupied 4R per sodalite unit. That the three 4R pair densities are at the framework minimum allowed value for the X composition range is not surprising. This observation falls into the category of results which are predictable from previous results not dependent on the resolution of local environments. As such this observation provides an essential connection between basis set components and specific local environments and contributes to our confidence in the essential correctness of the assignment. On the other hand, the results for Ns, > 16 represent new ordering information. The nature of this information will be made more explicit in the following section, in which we recast the local environment populations in terms of specific subunits. Now consider the other three resolved pair densities Pab, Pbc, and Ped. Recall that P a b is the density of meta placed Al,Al pairs in the D6R units, P b c is the density of meta placements in the single 6R’s within the sodalite units, and P c d is the density of Al,Al nonbonded pairs across the 12R windows of the supercage. The observed values are shown in Figure 16. These three pair densities have remarkably similar values for Nsi I 16. Only for Ns, > 17 is there significant dispersion, with P a b approaching zero and the 12R pair density P e d approaching the values calculated for random siting.24 In this range of composition the 6R pair density Pbc has significant uncertainty arising from the ambiguity with respect to w 0and bco. Figure 16 shows the extremes as well as the mean values for Pbc, calculated for aco = bco. The lower and upper extremes for Pbc correspond closely to the observed Values of P a b and Ped, it.,

the limits shown in Figures 15 and 16, assuming the lower limit for one implies the upper limit for the other. c. The Subunit (D6R) Representation. In this section we show how the data in Table 4 can be recast to describe the FAU lattice in terms of its composite subunits, such as D6R or sodalite units. We stress that such a description asserts nothing having to do with actual building units or crystallization pathways, representing just another way of summarizing the results, this time in terms of easily visualizable structural units. This approach will be illustrated for D6R subunits. This tums out to be a particularly convenient representation. The FAU framework can be viewed as a tetrahedral array of D6R subunits. Expressing the local environment populations in terms of specific D6R subunits and the manner in which they are interconnected provides a useful description of the local Si,Al order. This description can be used to measure the compositional homogeneity of the D6R population. The representation of the local environments in terms of D6R subunits is particularly convenient in view of the reduced local environment set in Table 1. As can be seen by reference to Figure 3, the first-shell sites a, b, d and the second-shell sites i, ii are part of the D6R containing the central Si atom. The remaining first-shell site c is part of a different D6R. One-half of the 26 reduced environments shown in Table 1 have site c occupied by an Al atom. Thus, we can specify 13 pairwise sums of local environment populations in which the members of each pair differ only in the presence or absence of an A1 atom in site c. These pairwise sums represent 13 possible D6R environments. For example, we sum the environments abcd and abd to calculate a D6R environment ABD, reserving the use of upper case letters for subunit environments. The D6R representation of the data is completed by calculating 13 “connective probabilities” /3(XYZ), where for example

/3(ABD) = abcd/ABD; B(AD) = acd/AD

(12)

That is to say, /3(XYZ) is viewed as the probability that the environment XYZ in a given D6R is connected to its adjacent D6R through an aluminum atom. We emphasize that going to this representation of the data in terms of a specific subunit is a purely formal step with no mechanistic implications. The convenience of this representation is apparent when it is noted that six of the seven constraint equations (C2 through C7) transform directly into constraints on the D6R environments. Thus, for example, eq C7 is equivalent to

B*

+ Z** + Zo* = BD + D

(C7’)

Although it is clear that the D6R environment populations are constrained by eqs C2-C7, there are also important constraints on the connective probabilities. Equation C1 can be rewritten to provide the constraint on the weighted average for the 13 D6R environments

pbc

W(XYZ)) = AlJSi

Of all the pair densities shown in Figures 14 and 15, P a b deviates most from random placementz4 in the high silica range of compositions. Here, framework constraints are weak or absent, and the indicated para placement of Al atoms within the D6R population can be safely attributed to A1,Al avoidance. On the other hand, the data for P c d in Figure 15 ‘showthat there is little or no Al-0-Si-0-Al pair avoidance within the 12-membered rings of the supercages. The average values of the pair densities Ph and Pacindicated in Figures 15 and 16 show that aluminum pair avoidance within the sodalite cages is, at most, intermediate. These pair densities (Pbc and Pat) can only be specified within

A less obvious constraint on the /3’s applies to the five D6R environments in eq C7’. These D6R environments form an important subset, in that these connective probabilities are subject to an additional framework constraint at low SUAl. Recall that eq C7 was obtained as the sum of the expressions given as eqs xC7’ and xC7” which can be assumed to apply for the X composition range (SUA1 I 2). These limiting constraints, transformed to the D6R representation, provide the following expression for the limiting weighted average connective probability for the five D6R environments B*, Z**, Z*O, BD, and D.

(13)

6140 J. Phys. Chem., Vol. 99, No. 16, 1995

3/,

Gg(B*,Z**,Z*',BD,D)) =

SUA1 is given by the ratio Al/Si = '/3. Note that the values of /?k in Table 6 range from zero to about 3/5. We have shown that topological constraints are virtually absent for SUAI 1 3. The dispersion in& in Table 6 can be amibuted to AI,AI avoidance not inherent in the FAU framework topology. Table 6 shows the average probability (P(nA1)) that a silicon site having n Al substituents within a D6R subunit is connected to the adjacent D6R unit through an A1 atom. As might be expected for general A1,Al avoidance this probability is a strong function of n, with @(nAl)) decreasing with increasing n. Note, however, that the dispersion within the different environments corresponding to the same n is as large as that between those with different n. We are optimistic that this very detailed structural information is key to the understanding of the crystallization pathways in FAU synthesis.

Summary and Conclusions In this paper our primary concern is the description of the process whereby the information contained in the band positions and band shapes of 29SiNMR spectra of FAU zeolites has been retrieved. We have shown how this information, which is well beyond what is contained in the five intensities Si(nAl), can be reduced to a determination of the Si,Al distribution, expressed in terms of 27 local environment populations. These environments are defined by a specification of the four first-shell neighbors and two of the three doubly connected second-shell neighbors. Here, we have dealt with directly synthesized FAU zeolites, but the approach has obvious application to any FAU framework material, including the various postsynthesis dealuminated or "ultrastabilized" high-silica Y materials. The results described above have a high degree of internal consistency, deriving smoothly from a relatively simple hypothesis: a single local environment can be represented by a single NMR line, fixed in line shape and chemical shift. These results (i.e. Table 4)contain a wealth of information, previously unavailable, concerning the local order in the placement of framework metals in directly synthesized FAU zeolites. We cannot prove uniqueness, but we have been impressed by the congruence of these results with previous work. Here we refer

J. Phys. Chem., Vol. 99, No. 16, 1995 6143

Fine Structure of Faujasite Zeolites to the results in Figure 18, for example, which shows the compositional dependence of certain connective probabilities, behavior which is in part a previously recognized consequence of long range connectivity &**)‘I and in part a consequence of AI,A1 avoidance (BB* vs /&D) in the X range of composition.I6 In both cases this behavior can be verified by explicit calculation; in neither case is this behavior inherent in our procedures. From the above discussion it is clear that the topological constraints imposed by the FAU framework connectivity and Loewenstein’s Rule dominate the resolved AI-0-Si-0-AI pair densities in the X composition range, impose strong correlations between these measures of local order in the Y range, and can be safely ignored only for high-silica FAU materials. With this caveat in mind we assert that the highsilica behavior of the resolved AI-0-Si-0-AI pair densities shown in Figures 15 and 16 provides important mechanistic information. What these results show is that the three A1-0Si-0-A1 pair types within the D6R subunits (densities Pab, Pad, Pbd) are more strongly avoided than are those pairs involving substituents in different D6R units (densities Pa,, Pbc, Ped). This observation implicates the D6R as the tertiary building unit in FAU crystallization. A second notable result is the populations of the D6R subunits { g,,} shown in Figure 21 and the standard deviation of n within {G,,} shown in Figure 22. The strong maximum for C&, corresponding to the “notch” in a,,evident in Figure 22, has important implications with regard to the secondary unit which is the precursor to the D6R tertiary unit. The dependence of the set on composition shown in Figures 21 and 22 can be shown to be essentially that predicted for D6R’s comprising a set of single 4R’s with the minimum A1-0-Si-0-AI pairs. Such a set of 4R’s is constructed simply by minimizing at each composition the number of 4R’s with two A1 atoms. Note that a set of 4R’s with one A1 each, an infinitely narrow distribution, has SiIA1 = 3 and corresponds to Ns, = 18, in agreement with observation. A substantial portion of the local order observed in FAU materials can be ascribed to the compositional narrowness of the 4R ensemble which is an evident precursor to the D6R tertiary building unit. The observed behavior is in contrast to what is predicted were a 6R ensemble” the precursor. In the latter case the narrowest distribution would be expected for Ns, = 16, or SUA1 = 2, with a corresponding strong maximum at %, contrary to observation. Thus, the results in Table 4 support the conclusion that FAU syntheses follow the crystallization pathway

{an}

4R

- D6R

FAU

(18)

Further details of the steps in this pathway are to be found in the specific D6R units in { g,, and } in the connective probabilites which describe how these D6R units are coupled. (On the basis of our results the hexagonal prisms should perhaps be referred to as “triple 4-rings”.) The set of D6R units, which predominate according to the above analysis, is qualitatively very similar to the set deduced by Peters.I5 The D6R units favored at a given composition tend to be those having fewer A1-0-Si-0A1 pairs. In his work, Peters asserted that the Si(nAl) distributions of a set of FAU materials could be used to deduce the D6R populations by assuming that all D6R sites had equal probability of connecting into the FAU lattice through an aluminum substituent. This uniform connective probability (in the terminology of the present work) is just the sample average given by the M S i ratio. Although this assumption ignores the constraints arising from short range9 and longer connectivity of the FAU lattice, this approach apparently gives the correct qualitative results. The framework constraints can

a

b

d

C

e

Figure 25. Bonding arrangements which give rise to seven fundamental constraints on the local environment populations. These diagrams relate to Figure 13, the atoms (0 or 0) shown here being those included in the shaded areas in Figure 13. Diagrams a, b, and c refer to Figure 13a, diagrams d, e, f, and g refer to Figure 13b.

be safely ignored for materials in the high-silica FAU range of compositions (Ns, I 18). Assuming a uniform connective probability for compositions in the high-silica FAU range is tantamount to asserting that assembly of D6R subunits is random. Our results, typified by Table 6, show that there is a substantial dispersion in the connective probabilities for materials of composition well beyond the range subject to strong framework topological constraints. Future work will address these details and their implications vis-a-vis the processes represented by the arrows(-) in the pathway (17).

Appendix Fundamental FAU Framework Constraints on Local Environment Populations. The connectivity of the FAU framework, specifically with respect to the network of edgesharing four-membered rings, together with Loewenstein’s rule gives rise to certain fundamental constraints on the local environment populations listed in Table 1. For the 34 local environments based on specification of the aluminum occupation of the four distinct first-shell positions and three doubly connected second-shell positions we have identified 10 linearly independent constraint equations. These are as follows:

A=B

(AI)

C=D

(-42)

+ ac(O,O,O) = c(O,I,O) + z(O,l,l)+ z(O,I,O) b(O,O,l)+ b(O,O,O) + bc(O,O,O) = c(I,O,O) +

a(O,O,O)

(A3)

z(1,0,1) + z(l,l,O) (A41

ab(O,O,O)

+ abc(0,0,0) = c(l,l,O) + z ( l , l , l ) + z ( l , l , O ) 645)

6144 J. Phys. Chem., Vol. 99, No. 16, 1995

+

ad(O,O,O) acd(0,0,0)= bd(O,O,l)

Melchior et al.

+ bd(O,O,O)+

(nu,l,nc, 11o,o,s3). Summing over the unspecified occupations and equating the results for Si and Si’, after cancellation of like terms, gives eq A6.

bcd(0,0,0) b(O,O,I )

+ z(0,I , 1) + z(O,O, I ) = c(O,I,O) + c(O,O,O) +

References and Notes

bc(O,O,O)

+ z ( l , l , O ) + z(I,O,O) = d(O,O,O)+ bd(O,O,O)

(1) Englehardt, G.; Lohse, U.; Lippmaa, E.; Tarmak, M.; Magi, M. Z. Anorg. Allg. Chem. 1981, 482, 49. (2) Ramdas, S.; Thomas, J. M.; Klinowski, J.; Fyfe, C. A.; Hartman, J. S. Nature (London) 1981, 292, 228. (3) Melchior, M. T.; Vaughan, D. E. W.; Jacobson, A. J. J. Am. Chem. Soc. 1982, 104, 4859. (4) Loewenstein, W. Am. Mineral. 1954, 39, 92. c(I,O,O) c(l,l,O) bc(l,O,O)= d(O,O,l) bd(O,O,l) (5) Dempsey, E. J . Phys. Chem. 1969, 73, 3660. (6) Englehardt, G.; Michel, D. High Resolution Solid-state NMR of The first two of these express the requirement of equal Zeolites and Related Systems; John Wiley and Sons: London, 1987. aluminum occupation of the four first-shell neighboring sites, (7) Klinowski, J.; Thomas, J. M.; Fyfe, C. A,; Hartman, J. S. J . Chem. Soc., Faraday Trans. 2 1982, 78, 1025. as discussed above. The remaining expressions are derived fiom (8) Beagley, B.; Dwyer, J.; Fitch, F. R.; Mann, R.; Walters, J. J. Phys. the bonding situations shown in Figure 13. Equations A3, A4, Chem. 1984, 88, 1744. and A5 derive from Figure 13a. By Loewenstein’s rule the (9) A number of workers have used a simple binomial expansion in four adjacent sites common to the central Si-Si’ pair (Le., the the average probability of forming an Si-0-A1 bond under the constraint four comers of the shaded areas in Figure 13a) can be occupied of Loewenstein’s rule to represent Si,A1 distributions which are random, by 0, 1, or 2 A1 atoms. There are five distinct arrangements. A subject only to Loewenstein’s rule. This assumption is equivalent to assuming independent probabilities for all Si-0-A1 bonds and is incorrect constraint equation arises from any arrangement in which Si in the topology of the FAU lattice subject to Loewenstein’s rule, because and Si‘ have different environments with respect to the four es are strongly coupled. shared sites. There are three such arrangements which are (10) Vega, A. J. ACS Symp. Ser. 1983, No. 218, 217. shown as a, b, c in Figure 25. We designate the population of (11) Melchior, M. T. ACS Symp. Ser. 1983, No. 218, 243. a local environment identified by its four first-shell substituents (12) Soukoulis, C. M. J. Phys. Chem. 1984, 88, 4898. and three second-shell substituents as f(tza,nb,nc,nd(Sl,s2,s3),where (13) Herero, C. P. J . Phys. Chem. 1991, 95, 3282 nk or si is 1 if the corresponding site is occupied by A l and 0 if (14) Newsam, J. M. Proc. 9th. Int. Zeolite Conference: von Ballmoos, it is occupied by Si. Consider the arrangement shown as in R. A,, Higgins, J. B., Treacy, M. M. J., Ed.; Butterworth-Heinemann: Figure 25 in which Si‘ has any environment (1,0,n,,0(0,0,0) and Boston, 1993; pp 127-141. Si has ( 0 , 0 , ~ c , 0 ~ 0 , 1 , ~Summing 3). each over the unspecified (15) Peters, A. W. J . Phys. Chem. 1982, 86, 3489. occupations and equating the results for Si’ and Si gives the (16) Melchior, M. T.; Vaughan, D. E. W. Unpublished results. constraint equation (17) Melchior, M. T.; Newsam, J. M. Zeolites: Facts, Figures, Future. Proc. 8th lnt. Zeolite Conference; Jacobs, P. A,, van Santen, R. A,, Ed.; Elsevier: Amsterdam; pp 805-814. f(1,0,0,0~0,0,0) f(1,0,1,0~0,0,0)= f(0,0,1,010,1,0) (18) Vaughan, D. E. W.; Edwards, G. C.; Barrett, M. G. U.S.Patent f ( 0 , 0 , 0 , 0 l 0 , ~ , ~ )f~0,0,0,0l0,~,0)4,340,573, 1982. (19) Vaughan, D. E. W.; Strohmaier, K. G. Proc. 7th lnt. Zeolite which is equivalent to Conference Murakami, Y . , Iijima, A., Ward, J. W., Eds.; 1986; pp 207214. (20) Vaughan, D. E. W.; Strohmaier, K. G. U. S. Patent 4,714,601, 1987; a(O,O,O) ac(O,O,O)= c(O,l,O) z(O,l,l) z(O,l,O) 4,965,059, 1990. (21) Vaughan, D. E. W.; Strohmaier, K. G. US. Patent 4,931,267, 1989. i.e., to eq A3. In forming the summation on the right hand (22) Frieden, B. R. J. Opt. Soc. Am. 1972, 62, 51 1; J. Opt. Soc. Am. side, note that the term with both nc and s3 occupied by Al is 1983, 73, 927. disallowed by Loewenstein’s rule. Equations A7, A8, A9, and (23) Belton, P. S.; Wright, K. M. J. Magn. Reson. 1986, 68, 564. A10 derive from Figure 13b, which provides the arrangements (24) The curves shown in Figures 15 and 16 for random (Loewenstein) shown in Figure 25, using the same sort of argument. The placement were calculated using analytical expressions developed by Vega.25 remaining constraint eq A6 is derived from the arrangement Note that the A1,Al pair densities for random placement are different for Figures 15 and 16. shown in Figure 13c for the case in which the 4R containing (25) Vega, A. J. Unpublished results (1982), private communication Si’ and Si is doubly occupied by A1 atoms. The AI atoms are (1991). in sites a and d for Si but in sites b‘ and d’ for Si’. Thus Si has

b ( l ,O,l)

+

+

+

a

+

+

+

+

+

allowed local environments (l.nb,nc,l lO,O,O)

+

and Si’ has

JP94295 13