Electron Diffraction Structure Solution of a Nanocrystalline Zeolite at

California 94802, and Institute for Materials Research (IMR), Tohoku UniVersity, Sendai 980-8577, Japan. ReceiVed: April 28, 1999; In Final Form: July...
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J. Phys. Chem. B 1999, 103, 8245-8250

8245

Electron Diffraction Structure Solution of a Nanocrystalline Zeolite at Atomic Resolution Paul Wagner,† Osamu Terasaki,*,‡,§ Stephan Ritsch,§,| Jose Geraldo Nery,† Stacey I. Zones,⊥ Mark E. Davis,† and Kenji Hiraga| DiVision of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, Department of Physics, Graduate School of Science and Center for Interdisciplinary Research (CIR), Tohoku UniVersity, Sendai 980-8578, Japan, CREST, Japan Science and Technology Corporation (JST), Kawaguchi 332-0012, Japan, CheVron Research and Technology, Richmond, California 94802, and Institute for Materials Research (IMR), Tohoku UniVersity, Sendai 980-8577, Japan ReceiVed: April 28, 1999; In Final Form: July 8, 1999

Electron diffraction data are used to obtain the structure solution of a large-pore, high-silica zeolite, SSZ-48 that contains an occluded organic structure directing agent. The structure is determined by electron diffraction refinement and is confirmed by high-resolution transmission electron microscopy and Rietveld refinement of powder synchrotron X-ray data. The structure is found to contain a one-dimensional pore system circumscribed by 12 tetrahedral atoms (12 MR). SSZ-48 is the most complex three-dimensional material to be solved at atomic resolution using electron diffraction methods and illustrates the power of electron diffraction data for resolving the structures of materials that form crystals too small for standard single-crystal X-ray analysis.

Introduction Microporous materials (including zeolites) that contain molecular-sized pores and cavities have found widespread use in industry as molecular sieves for chemical separations, as ion exchangers for detergents, and as heterogeneous, shape-selective catalysts.1 Knowledge of the crystal structure of these microporous materials can provide important insights into their properties and can lead to the design of desirable materials. The structure solution of microporous materials can be challenging, however, because these materials tend to form as micron- or submicron-sized crystals that are too small for singlecrystal X-ray analysis.2 In the absence of single-crystal data, the structure solution and refinement has typically required the use of powder X-ray data.3,4 The difficulty in solving crystal structures from powder X-ray data is that the three dimensions of information available in a single-crystal data set are collapsed into one dimension (d spacing) in a powder X-ray data set. If the reflections in the powder X-ray data significantly overlap, then solving the crystal structure from these data can be extremely difficult. While the techniques for solving complicated crystal structures using powder X-ray data continue to advance,5-7 they are still far from routine, particularly for zeolites that may contain several hundred atoms in a unit cell. Alternatively, electron microscopy may be utilized for solving the crystal structures of materials that form crystals too small for single-crystal X-ray analysis. In particular, image reconstruction from high-resolution transmission electron micrographs has been applied for solving structures from micro- and nanocrystals.8-10 However, materials that tend to be highly electronbeam sensitive, e.g., organic crystals11,12 and crystalline microporous materials, may be easily destroyed by the highly * Corresponding author. † California Institute of Technology. ‡ Department of Physics, Tohoku University. § CREST, Japan Science and Technology Corp. | Institute for Materials Research (IMR), Tohoku University. ⊥ Chevron Research and Technology.

converged electron beam under imaging conditions (resolution J2 Å). In contrast, under optimal diffraction conditions, we can reduce electron density 10-2 times lower than that for the imaging by parallel illumination and can obtain a resolution better than 1 Å. Therefore, the use of electron diffraction analysis rather than image analysis for crystal structure elucidation can allow for higher resolution and higher dimensional information to be collected from a single-crystal of an electron-beam sensitive material. Electron diffraction data, obtained from a transmission electron microscope (TEM), also have inherent advantages over X-ray data for analyzing small crystals due to the stronger interaction between the electron beam and matter compared to X-rays.13 This stronger interaction allows a single-crystal diffraction data set to be obtained from much smaller crystals. Provided that the interaction of the incident electron beam with the crystal is nearly kinematical; i.e., the diffraction intensity is proportional to the square of the structure factor, indicating that there are few dynamical scatterings of the electrons within the crystal, direct methods can be used as a powerful tool for obtaining the phase information required to solve the crystal structure. High-silica microporous materials are particularly well suited to electron diffraction analysis14,15 due to the low density of porous materials and the absence of heavy atoms. To illustrate the feasibility of structure solution of complex crystal structures via electron diffraction data, we report here the structure solution of the new high-silica molecular sieve, SSZ-48, containing an organic structure directing agent.16 The atomic resolution structure solution and refinement highlights the power of electron crystallography for resolving structures from micro- and nanocrystals that are too small for single-crystal X-ray analysis. Experimental Section Synthesis. N,N-Diethyldecahydroquinolinium cation, used as a structure directing agent (SDA) in the synthesis of the high silica zeolite SSZ-48, is synthesized by dissolving 24.8 g of

10.1021/jp991389j CCC: $18.00 © 1999 American Chemical Society Published on Web 09/11/1999

8246 J. Phys. Chem. B, Vol. 103, No. 39, 1999 decahydroquinoline (Aldrich, mixture of isomers) and 26 g of potassium bicarbonate in 170 mL of methanol. A 67.4 g sampole of iodoethane is added dropwise to the solution over a 10-15 min period. The solution is refluxed for 48 h. The reaction mixture is cooled to room temperature, the methanol is evaporated, and the remaining solids are treated with 250 mL of chloroform; the precipitated solids are filtered out. The chloroform fraction is evaporated and the solids are recrystallized from a minimum of hot isopropyl alcohol. The dried solids are then ion-exchanged to the hydroxide form by treatment with BioRad AG 1-X8 OH resin, and the molarity is determined by titration. The borosilicate zeolite SSZ-48 is synthesized by mixing 3 mmol of the N,N-diethyldecahydroquinolinium structure directing agent solution (5.33 g, 0.562 mmol of OH-/L) with 1.2 g of 1.0 N NaOH and 5.4 g of water. Sodium borate decahydrate (0.057 g) is added to this solution and stirred until all of the solids have dissolved. Cabosil M-5 fumed silica (0.92 g) is then added to the solution, and the resulting mixture is heated at 160 °C and rotated at 43 rpm for 49 days. The precipitated product is filtered out, washed, and air-dried. The SiO2/B2O3 ratio was found by ICP methods to be 63. The presence of the intact organo-cation was found via 13C MAS NMR studies.17 Analytical Details. TEM. The as-synthesized SSZ-48 crystals were prepared for microscopy by embedding them in epoxy followed by ultramicrotomy. The resulting thinly sliced crystalembedded epoxy was then transferred onto a holey carbon foil supported by a Cu grid. Electron diffraction data were collected on a JEM-4000EX operating at 400 kV equipped with a slowscan CCD detector (Gatan 694). HRTEM images were also collected on a JEM-4000EX operating at 400 kV (point resolution 1.7 Å) and were recorded on high-sensitivity photographic film. Image contrast calculations were performed according to the multislice algorithm with Mac Tempas software. All Fourier image filtering of the HRTEMs were performed with the Gatan DigitalMicrograph 2.5 software. SEMs of the as-made SSZ-48 crystals were collected on a Hitachi S-3200 scanning electron microscope operating at 5 kV. Synchrotron Powder X-ray Diffraction. Synchrotron powder X-ray diffraction (SPXRD) data were collected on the X7A synchrotron beam line at Brookhaven National Laboratory. The SSZ-48 sample was prepared for data collection by first calcining the material at 923 K (heating from room temperature at 5 K/min). The calcined sample was then packed into a 1 mm glass capillary and the synchrotron data were collected at ambient conditions with a step size of 0.01° from 4 to 55° 2θ at a wavelength of 1.19963(6) Å. Results and Discussion Crystal Size Determination. Low-resolution transmission electron micrographs and scanning electron micrographs are shown in Figure 1. These micrographs reveal that the typical crystal dimensions of SSZ-48 (synthesized as discussed previously) are 0.05 µm × 0.25 µm × 10 µm. While single-crystal X-ray analyses have been carried out on high silica molecular sieves that are greater than 1 µm in size, the SSZ-48 crystals are well below the size restriction for standard single-crystal X-ray analysis, as seen from Figure 1. Electron Diffraction Structure Solution of SSZ-48. The integrated intensities for 600 reflections (326 unique reflections) were extracted from 11 zones of selected area electron diffraction data that were collected to a resolution of 0.99 Å (-8 < h < 8, -4 < k < 4, -10 < l < 13) and merged by normalizing the diffraction data between zones containing common reflec-

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Figure 1. Scanning electron micrographs (a) and low-resolution transmission electron micrograph (b) of as-made SSZ-48 crystals.

tions. The indexation of these reflections revealed a monoclinic crystal class having unit cell parameters of a ) 11.19 Å, b ) 4.99 Å, c ) 13.65 Å, and β ) 100.7° (V ) 748.6 Å3). The analysis of the reflections for systematic absences indicated a space group consistent with P21 (No. 4). The unit cell parameters and space group assignment are in agreement with the synchrotron powder X-ray data. The experimental electron diffraction data for the three principal zones axes are presented in Figure 2. Electron atomic scattering factors,18 were used in the direct methods structure solution19 and subsequent refinement.20 The integrated intensities were not corrected for dynamical diffraction effects or curvature of the Ewald sphere (the inverse of the wavelength for 400 kV electrons, λ ) 0.0164 Å, is 60.98 Å-1, and therefore the Ewald sphere can reasonably be approximated as a plane). The primary effect of neglecting the curvature of the Ewald sphere will be to increase the temperature factors: however, the value obtained for the isotropic temperature factors from the Wilson21 plot (Biso ) 1.94 Å2) is consistent with the isotropic temperature factors obtained for zeolites refined from synchrotron powder X-ray data (typical range: 0.2 Å2 < Biso < 4.0 Å2).22 The temperature factor obtained from the Wilson plot also provides additional support that the electron diffraction data are not seriously perturbed by dynamical diffraction effects, as the temperature factor tends to 0 as the electron diffraction data become more convoluted by dynamical diffraction effects.23 Reflections with normalized structure factors between 0.65 and 10.0 were used in the direct methods structure solution, resulting in 157 reflections that were employed to calculate 2588 unique triple product relations. The phases obtained from the direct methods structure solution were used to generate a 3-dimensional potential map that easily revealed the 7 silicon atoms in the basis set of the framework structure for the high-

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Figure 2. Experimental electron diffraction data from three principal zone axes of SSZ-48.

TABLE 1: Atomic Positions (Fractional Coordinates) from the 3-Dimensional Model Obtained from Electron Diffraction Structure Solution (Space Group P21, a ) 11.19 Å, b ) 4.99 Å, c ) 13.65 Å, and β ) 100.7°)

Figure 3. Model of SSZ-48 crystal structure obtained from electron diffraction structure solution.

silica molecular sieve, SSZ-48. The 3-dimensional potential map also contained the positions of 5 of the 14 oxygen atoms. Additional scattering material in the potential map was located within the channel system of the model and is attributed to the occluded organic structure directing agent (SDA), N,N -diethyldecahydroquinolinium. The 3-dimensional model obtained from the direct methods structure solution is shown in Figure 3 and the atomic coordinates of the asymmetric unit are presented in Table 1. The remaining oxygen atoms in the framework were located using distance least squares refinement (DLS24) to optimize Si-O bond distances and O-Si-O bond angles. The DLS refined model (DLS R value ) 0.0028) contains 7 silicon and 14 oxygen atoms in the asymmetric unit. Refinement of SSZ-48 Structure from Electron Diffraction Data. The silicon and oxygen atoms from the DLS refined structure, together with 3 carbon atoms (placed at the coordinates of the largest potential peaks inside the channel system) were input as the starting model for the least squares refinement. The structural refinement was carried out in space group P21 (No. 4) with the unit cell parameters determined from the indexing of the electron diffraction data. The model was refined against Fo2 with 600 experimentally measured reflections (326 unique reflections). The Fourier difference map revealed the positions of 4 additional scattering centers located within the channel system that were attributed to the carbon atoms of the organic

atom type

a

b

c

Si Si Si Si Si Si Si O O O O O C C C C C C C C C

0.26370 0.38860 0.44340 0.58230 0.32030 0.76410 0.96020 0.14770 0.25800 0.34500 0.63300 0.03650 0.01640 0.66940 0.95720 0.04880 0.08050 0.12720 0.87940 0.19950 0.84460

0.37680 0.36240 0.23520 0.34610 0.25080 0.16000 0.18460 0.44200 0.43960 0.12900 0.38690 0.44640 0.38520 0.26290 0.39190 0.30610 0.19480 0.39150 0.10870 0.26880 0.51030

0.18050 0.37170 0.62170 0.87400 0.77750 0.11450 0.03870 0.13960 0.87740 0.53840 0.15800 0.97450 0.65080 0.45710 0.54440 0.76070 0.84070 0.37460 0.61460 0.27480 0.68000

SDA. All atomic positions were refined, however, due to poor overdetermination (326 unique reflections and 94 variables); constraints were placed on the Si-O bond distances (d(Si-O) ) 1.61(01) Å) and on the O-Si-O bond angles (d(O-O) ) 2.61(01) Å; O-Si-O ) 109.45°). The isothermal temperature factors were refined and constrained to the same values for Si and for O atom types. The isothermal temperature factors for the 7 carbon atoms within the pores were not constrained. The final RF value (RF ) ∑|Fo - Fc|/∑|Fo|) was reduced to 0.3283, resulting in a refined model containing chemically reasonable Si-O bond distances (av ) 1.601 Å), O-Si-O bond angles (av ) 109.47°), and Si-O-Si bond angles (av ) 147.3°). While the RF value is high compared to single-crystal X-ray analyses, it is comparable to the RF values obtained in other electron diffraction studies.23 Table 2 contains the atomic positional parameters for the refined model. The connectivity of the T atoms in the SSZ-48 structure is similar to the connectivity of the T atoms in the TON25 structure that contains 10 MR pores (Figure 4A). Both structures are composed of columns of [5.461] units, as seen in Figure 4. Within these columns the connectivity is identical; however, in the SSZ-48 structure the columns are expanded by the insertion of rings of 4 T atoms diagonally across the pore. This expansion can occur at the joining of any of the [5.461] units; however, the SSZ-48 material is neither disordered or faulted and indicates

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Figure 4. Illustration of the relationship between the TON (a), SSZ48 (b), and the hypothetical 14 MR (c) structures through the four MR expansion of the [5.461] units.

TABLE 2: Electron Diffraction Refined Atomic Positions (Fractional Coordinates) for SSZ-48 (Space Group P21 (No. 4), a ) 11.19 Å, b ) 4.99 Å, c ) 13.65 Å, and β ) 100.7°; Standard Deviation in Parentheses) atom type

a

b

c

Uiso (Å2)

Si Si Si Si Si Si Si O O O O O O O O O O O O O O C C C C C C C

0.2610(16) 0.3974(14) 0.4462(15) 0.6300(15) 0.3584(14) 0.7469(15) 1.0029(12) 0.2840(19) 0.352(2) 0.1232(16) 0.285(2) 0.360(3) 0.4388(16) 0.5082(16) 0.372(3) 0.4907(15) 0.667(3) 0.285(3) 0.2845(17) 0.8883(16) 0.0196(17) 0.095(5) 0.628(5) 1.001(8) 1.069(5) 0.875(5) 0.214(16) 0.963(14)

0.384(4) 0.277(4) 0.277(4) 0.379(4) 0.432(3) 0.409(4) 0.475(5) 0.343(5) 0.608(7) 0.477(5) 0.108(7) 0.319(4) 0.972(4) 0.472(4) 0.341(3) 0.471(4) 0.330(5) 0.208(5) 0.708(5) 0.389(5) 0.269(7) 0.484(15) 0.274(15) 0.35(2) 0.484(14) 0.532(17) 0.23(5) 0.57(4)

0.1890(13) 0.3936(14) 0.6064(13) 0.8961(13) 0.8028(12) 0.1201(12) 0.0667(10) 0.3073(11) 0.162(3) 0.1509(12) 0.136(3) 0.5001(9) 0.384(2) 0.384(2) 0.6930(14) 0.870(2) 0.0139(12) 0.8519(15) 0.7968(12) 0.1147(16) 0.9806(18) 0.690(4) 0.473(4) 0.517(8) 0.430(5) 0.619(4) 0.533(15) 0.706(11)

0.111(13) 0.111(13) 0.111(13) 0.111(13) 0.111(13) 0.111(13) 0.111(13) 0.110(13) 0.110(13) 0.110(13) 0.110(13) 0.110(13) 0.110(13) 0.110(13) 0.110(13) 0.110(13) 0.110(13) 0.110(13) 0.110(13) 0.110(13) 0.110(13) 0.00(2) 0.003(19) 0.08(3) 0.000(19) 0.00(2) 0.24(9) 0.16(6)

a strong specificity of the N,N -diethyldecahydroquinolinium SDA for the SSZ-48 structure. If the 4 T atom rings are inserted at the joining of every [5.461] unit, a new extra-large pore framework structure is generated that contains 14 T atom pore openings and has a maximum internal pore diameter of 14.4 Å × 12.8 Å (Figure 4C). The detailed SSZ-48 crystal structure presented here, of the organic SDA within the pores of the SSZ48 framework, provides valuable insights into the organic/ inorganic interactions. Such information opens the possibility for rational zeolite design by modifying the SSZ-48 SDA to optimize the organic/inorganic interactions for the formation of the proposed extra-large pore 14 MR structure. Dynamical Scattering Refinement. To improve the match between the calculated and observed structure factors, dynamical diffraction effects were taken into account. The model used for the dynamical diffraction simulations was obtained by molecular modeling of the SDA in the high-silica framework. The organic SDA, N,N-diethyldecahydroquinolinium, was adjusted within the pores of the refined framework model to minimize the energy of the system using the open force field module of Cerius2 (Burchart 1.01-Universal 1.02 force field).26 The positions of the Si and O atoms in the framework and the unit cell parameters were fixed and the orientation and position of the organic SDA was allowed to vary in order to minimize the energy of the system. The modeling was carried out using one

Figure 5. Fourier-filtered experimental high-resolution transmission electron micrographs of SSZ-48 parallel to the pore direction, [010] (a), and perpendicular to the pore direction, [001] (b). Upper left corners are the simulated images.

TABLE 3: Dynamical Scattering Refinement of Reflections from Three principal Zone Axes no. of unique reflns

sample thickness (nm) for minimized R value

RF

[001] [100] [010]

14 14 105

55 67 25

0.224 0.199 0.241

3 zone RF

133

zone

0.232

SDA per two unit cells and is consistent with the thermal gravimetric analysis (TGA) results that indicate 0.8 SDAs per two unit cells. The energy-minimized model of the SDA occluded within the pores of the framework structure (atomic positional parameters located in Supporting Information, Table 3S) was then used for simulations of electron diffraction intensities27 for different crystal thicknesses that resulted in varying degrees of dynamical diffraction. Simulated diffraction intensities were obtained for the principal zone axes, [001], [010], and [100], and were quantitatively compared to the experimental data to determine the degree of dynamical diffraction by minimizing RF as a function of crystal thickness. As Table 3 indicates, the RF value for the 14 unique reflections of the [001] zone minimized to 0.224 at a thickness of 55 nm, the RF value for the 14 unique reflections of the [100] zone minimized to 0.199 at 67 nm, and the RF value for the 105 unique reflections of the [010] zone minimized to 0.241 at 25 nm. The overall RF calculated for all three zones, containing 133 reflections (structure factors located in Supporting Information, Table 4S), is 0.232. As a reference, an R value below 0.25 is an indication that the atomic positions of the structure are correct to within approximately 0.1 Å.28 The comparison between the Fourier-filtered experimental high-resolution transmission electron micrographs and the simulated TEM images viewed parallel to the pore direction, [010], and perpendicular to the pore direction, [001], shown in Figure 5, provide additional confirmation of the structure. The simulated images are calculated using the model obtained from the electron diffraction structure solution and refinement (Insets at left top in Figure 5). The differences between the experimental and the simulated images are hardly seen.

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Figure 7. SSZ-48 framework structure obtained from Rietveld refinement (oxygen atoms omitted for clarity): (a) viewed down pores ([010] direction); (b) cross section view perpendicular to the sinusoidal channel system ([001] direction), where arrows indicate side pockets in the channel that result in the sinusoidal oscillation of the pores.

Figure 6. Comparison of experimental synchrotron X-ray data (a), calculated data (b), and the difference profile (c) for the Rietveld refinement of SSZ-48 (λ ) 1.19963(6) Å). The 30-55° range is expanded by 5×.

TABLE 4: Crystallographic and Refinement Data for SSZ-48 from Synchrotron Powder X-ray Rietveld Refinement space group a (Å) b (Å) c (Å) β (deg) wavelength (Å) data collecn temp (K) profile range (deg) no. of observables step scan increments (deg) no. of variables

P21 (No. 4) 11.15272(69) 5.00214(21) 13.66726(76) 100.6331(9) 1.19963(6) 298 4.0-55.0 5100 0.01

wRp (%) Rp (%) av d(Si-O) (Å) min max av ∠Si-O-Si (deg) min max av ∠O-Si-O (deg) min max

9.78 8.89 1.592(3) 1.555(0) 1.621(1) 148.6(5) 132.4(4) 171.1(0) 109.4(5) 104.6(1) 113.8(2)

138

Rietveld Refinement from Synchrotron Powder X-ray Data. Synchrotron powder X-ray data (SPXRD) were collected from a sample of calcined borosilicate SSZ-48. Indexation of the SPXRD29 revealed a monoclinic crystal class for the SSZ-48 sample with refined unit cell parameters of a ) 11.15272(69) Å, b ) 5.00214(21) Å, c ) 13.66726(76) Å, and β ) 100.6331(9)°. The systematic absences in the SPXRD data are consistent with the space group assignment of P21 (No. 4). The initial atomic positions for the Rietveld refinement of SSZ-4830 were obtained from the electron diffraction leastsquares refinement. The scale factor, zero shift, and a 15 parameter shifted Chebyshev30 function for background subtraction were initially refined. The lattice parameters and the peak

shape function parameters31 were then refined until convergence of the R values was obtained. Soft geometric constraints for the Si-O bond distance (d(Si-O) ) 1.610(10) Å) and interatomic O-O distances (d(O-O) ) 2.610(10) Å) were employed for the initial stages of the atomic position refinement. The weighting factor for the soft geometric constraints was gradually reduced and eventually eliminated. Table 4 provides a summary of the refinement details. All structural parameters are within reasonable ranges for silicate materials.32 The average bond distance, d(Si-O), is 1.592(3) Å with a maximum of 1.621(1) Å and a minimum of 1.555(0) Å. The average O-Si-O bond angle is 109.4(5)° with a range of 104.6(1)-113.8(2)°, and the average Si-O-Si bond angle is 148.6(5)° with a maximum of 171.1(0)° and a minimum of 132.4(4)°. The residual values for the match between the experimental powder data and the simulated data (Figure 6) are: wRp ) 9.71% and Rp ) 8.87%. The structure of SSZ-48 viewed down the pores ([010] direction) is shown in Figure 7A (oxygen atoms have been omitted for clarity). The SSZ-48 framework structure contains a 1-dimensional, sinusoidal, pore system circumscribed by 12 tetrahedrally coordinated silicon atoms (12-membered rings, 12 MR). The pores are elliptical in shape with projected dimensions of 7.91 Å × 10.05 Å (center of oxygen to center of oxygen) and a maximum internal pore diameter of 11.19 Å × 13.65 Å (center of oxygen to center of oxygen). The asymmetric unit contains 7 tetrahedrally coordinated silicon atoms (T atoms) and 14 oxygens, resulting in a unit cell content of [Si14O28]. The framework density (FD) of the material is 18.7 T atoms/1000 Å3. The 12 MR one-dimensional sinusoidal channel system of SSZ-48 viewed along the [001] direction is presented in Figure 7B. Table 5 presents the final atomic positional parameters and isotropic temperature factors obtained from the Rietveld refinement. Conclusions The atomic resolution, 3-dimensional structure that is elucidated here is the most complicated solved via electron diffraction methods. These results demonstrate the feasibility of singlecrystal electron diffraction analysis for elucidating complex crystal structures of electron-beam sensitive materials that tend

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TABLE 5: Atomic Positional Parameters (Fractional Coordinates) and Isothermal Temperature Factors for SSZ-48 Refined from Synchrotron Powder X-ray Data (Space Groups P21 (No. 4), a ) 11.15272(69) Å, b ) 5.00214(21) Å, c ) 13.66726(76) Å, β ) 100.6331(9)°, Standard Deviations in Parentheses) atom

a

b

c

Uiso (Å2)

Si1 Si2 Si3 Si4 Si5 Si6 Si7 O1 O2 O3 O4 O5 O6 O7 O8 O9 O10 O11 O12 O13 O14

0.2558(8) 0.3963(8) 0.4323(10) 0.6337(8) 0.3516(9) 0.7451(8) 0.9952(8) 0.2820(9) 0.3294(16) 0.1138(8) 0.2936(16) 0.3565(12) 0.4574(13) 0.5020(11) 0.3430(12) 0.4891(7) 0.6629(12) 0.2652(13) 0.3071(14) 0.8812(8) 0.0061(14)

0.3385(22) 0.3355(31) 0.3363(30) 0.3380(21) 0.4094(20) 0.4067(20) 0.3947(33) 0.3816(30) 0.5403(24) 0.3692(46) 0.0386(24) 0.3572(32) 1.0463(36) 0.5462(36) 0.3596(29) 0.3747(41) 0.3845(36) 0.2098(20) 0.7112(19) 0.3410(29) 0.1947(37)

0.1869(7) 0.3874(7) 0.6058(8) 0.8955(6) 0.7996(7) 0.1181(7) 0.0657(6) 0.3036(6) 0.1315(12) 0.1504(7) 0.1620(13) 0.4942(05) 0.3752(11) 0.3807(11) 0.6825(7) 0.8557(11) 0.0099(6) 0.8435(11) 0.8097(11) 0.1139(9) 0.9774(9)

0.019(7) 0.064(8) 0.095(9) 0.004(5) 0.004(7) 0.003(5) 0.014(6) 0.002(4) 0.045(7) 0.001(4) 0.024(1) 0.012(1) 0.126(12) 0.073(4) 0.044(2) 0.002(4) 0.002(4) 0.073(7) 0.054(9) 0.002(4) 0.082(4)

to form as crystals too small for X-ray single-crystal analysis. It is clearly demonstrated that electron diffraction structure solution can be successfully applied to obtain the atomic level details of very complex materials with large unit cells, and the results are corroborated with both high-resolution transmission electron micrographs and Rietveld refinement from synchrotron powder X-ray data. Acknowledgment. The authors gratefully acknowledge CREST, JST, Japan, for financial support. O.T. also thanks the Grant-in-Aid for Scientific Research in Priority Areas, the Ministry of Education, Science, Sports, and Culture of Japan for support. We thank Drs. N. Ohnishi and T. Ohsuna (IMR) for their contributions. G. Karlsson (Lund University) is thanked for ultramicrotomy. R. Medrud is thanked for the collection of the synchrotron powder X-ray data. P.W. thanks Air Products and Chemicals Inc. and the Dow Chemical Co. Foundation for financial support. J.G.N. thanks FAPESP for a postdoctoral fellowship (proc. 98/11619-0). Supporting Information Available: The following information is available free of charge via the Internet at http:// pubs.acs.org: crystallographic information file for SSZ-48 electron diffraction refinement; hkl, observed and calculated structure factors from SHELX refinement, atomic positional parameters and unit cell information for the energy-minimized

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