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Zeolite structure determination using electron crystallography
Zeolites and Related Materials: Trends, Targets and Challenges Proceedings of 4th International FEZA Conference A. Gédéon, P. Massiani and F. Babonneau (Editors) © 2008 Elsevier B.V. All rights reserved.
799
Zeolite structure determination using electron crystallography Junliang Sun1,2, Daliang Zhang1,2, Zhanbing He1, Sven Hovmöller1, Xiaodong Zou1,2*, Fabian Gramm3, Christian Baerlocher3, Lynne B. McCusker3, Avelino Corma4, Manuel Moliner4 and María J. Díaz-Cabañas4 1
Structural Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden Berzelii Centre EXSELENT on Porous Materials, Stockholm University, SE-106 91 Stockholm, Sweden 3 Laboratory of Crystallography, ETH Zurich, CH-8093 Zurich, Switzerland 4 Instituto de Tecnología Química, UPV-CSIC, Universidad Politécnica de Valencia, Avda. de los Naranjos s/n, 46022 Valencia, Spain *E-mail: [email protected], Fax: +46 8 15 21 87 2
Abstract The structures of zeolite beta polymorph B and of IM-5 have been determined by combining selected area electron diffraction (SAED) patterns and high resolution transmission electron microscopy (HRTEM) images. The zeolite beta polymorph B structure could be solved using just a single HRTEM image while that of IM-5 required three images taken along the main crystallographic directions. The average deviations of the IM-5 model from that refined using X-ray powder diffraction data are about 0.16 Å for Si and 0. 31Å for O. Keywords: zeolite beta, IM-5, SAED, electron diffraction, HRTEM, image processing
1. Introduction Zeolite structures sometimes remain unsolved for a long time, because of either their complexity, the minute size of the crystallites or the presence of defects or impurities. One extreme example of stacking disorder is provided by zeolite beta [1,2]. Different stacking sequences give rise to two polymorphs (A and B) in zeolite beta that always coexist in very small domains in the same crystal. Not only do the small domains make the peaks in the powder X-ray diffraction pattern broad and thereby exacerbate the reflection overlap problem, but the presence of stacking faults also gives rise to other features in the diffraction pattern that further complicate structure solution. Electron crystallography offers an alternative approach in such cases, and here we describe a complete structure determination of the structure of polymorph B of zeolite beta [3] using this technique. The clear advantage of electron microscopy over X-ray powder diffraction for elucidating zeolite structures when they only occur in small domains is demonstrated. In order to test the limit of the structural complexity that can be addressed by electron crystallography, we decided to re-determine the structure of IM-5 using electron crystallography alone. IM-5 was selected for this purpose, because it has one of the most complex framework structures known. Its crystal structure was solved only recently after nine years of unsuccessful attempts [4]. Given the fact that structure determination by electron crystallography is general, success with these two zeolite structures also has implications for other materials, where
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the crystals are too small or contain too many defects and/or the structures are too complicated to be solved from X-ray powder diffraction data alone.
2. Experimental Both samples were prepared as reported in the literature [3,5]. A small amount of each sample was ground to a fine powder and dispersed in acetone. A drop of this suspension was transferred onto a holey carbon film supported by a copper grid. Tilt series of SAED patterns were collected on Philips CM-30 and JEOL JEM-2000FX transmission electron microscopes. Other SAED patterns and the HRTEM images were taken on a JEOL JEM-3010 transmission electron microscope at 300kV, having a point resolution of 1.7 Å. The SAED patterns and HRTEM images were recorded by Gatan multiscan A40 or Keenview CCD cameras. To minimize the dynamic effects, only the thinnest edges of the crystals were selected for HRTEM images and SAED patterns. All SAED patterns were analyzed by the program ELD [6]. Tilt series were combined to determine the unit cell parameters using the program Trice [7]. HRTEM images were processed by the program CRISP from Calidris to yield reflection amplitudes and phases [8]. Three-dimensional electrostatic potential maps were calculated using the program eMap [9]. The final structure model was refined using the distance least squares refinement program DLS-76 [10].
3. Results and discussion 3.1. Polymorph B of zeolite beta For normal zeolite beta samples, the domains of polymorphs A and B are only a few nanometers in size and heavily intergrown. This is not large enough for a full structure determination by electron microscopy. However, in a polymorph B enriched zeolite beta sample [2], we could find areas of sufficient size. The unit cell parameters of polymorph B were determined from a tilt series of SAED patterns to be a = 17.97 Å, b = 17.97 Å, c = 14.82 Å, α = 90º, = 113.7º and γ = 90º with the Laue class 2/m. Based on the reflection conditions observed in the SAED patterns (hkl: h + k = 2n; h0l: h = 2n, l = 2n; 0k0: k = 2n), there are only two possible space groups: Cc and C2/c. HRTEM images of polymorph B taken along the [1-1 0] direction clearly showed 12ring channels with an ABCABC… stacking sequence and well resolved 4-, 5-, and 6rings, which are characteristic of the polymorph B structure (Figure 1a). The lattice averaged projection derived from the HRTEM images shows 2-fold symmetry, and is consistent with the monoclinic space group C2/c. From HRTEM images of the thinnest area of the polymorph B crystals oriented along [1-1 0], amplitudes and phases of 39 independent reflections were extracted. Because of the C2/c symmetry, HRTEM images taken along the [1-1 0] direction are equivalent to those taken along the [1 1 0] direction. Thus, 39 independent hk0 reflections from a single projection generate a 3D hkl list with 152 reflections (hk0, h-k0,-hk0 and –h-k0). This is sufficient to solve the 3D structure of polymorph B of zeolite beta. A 3D potential map (Figure 1b) was calculated from these 152 reflections by inverse Fourier transformation. All nine unique Si atoms could be resolved from this map. Each Si atom was clearly connected to four other Si atoms, resulting in a 3D framework (Figure 1b). Oxygen atoms could not be resolved at this resolution of the HRTEM images, but were inserted geometrically halfway between the neighboring Si atoms. The positions of the nine Si and sixteen O atoms were then refined using a distance least-squares procedure. The unit cell parameters were also refined with DLS-76 to give a = 17.70(15) Å, b =
Zeolite structure determination using electron crystallography
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Figure 1. a) HRTEM image of polymorph B of zeolite beta along the [1-10] direction. Insets are (from left to right) Fourier transform and averaged images with p1 and p2 symmetries applied. b) The 3D potential map reconstructed from this HRTEM image. All nine unique Si atoms were obtained from this 3D map, and are shown superimposed on the potential map.
17.70(15) Å, c = 14.33(11) Å and = 114.89(1)º. The final structural model of polymorph B agrees with that described in the literature [1-2]. 3.2. IM-5 The 3D structure of polymorph B of zeolite beta could be solved from a single HRTEM image taken along the diagonal [1 -1 0] direction. For more complicated structures such as that of IM-5, it is not possible to determine the full 3D structure from only one projection, so a more general approach involving several projections is needed. Here we show such a general structure determination for IM-5 using electron crystallographic techniques and no prior knowledge about the structure. The first step was to establish the unit cell dimensions and the space group, and the second to determine the atomic positions. 3.2.1. The unit cell and space group The unit cell and the Bravais lattice type for IM-5 were obtained from tilt series of SAED patterns such as that shown in Figure 2 (a = 14.3 Å, b = 57.4 Å, c = 20.1 Å with
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C-centering). Its Laue class was determined to be mmm since the SAED patterns show mmm symmetry. Thus, the IM-5 structure is C-centered orthorhombic. From the SAED patterns, the reflection rules were determined to be hkl: h+k = 2n; 0kl: k = 2n; h0l: h = 2n, l = 2n; hk0: h+k = 2n; h00: h = 2n; 0k0: k = 2n; 00l: l = 2n, so there are only three possible space groups: Cmc21, C2cm and Cmcm.
Figure 2. A tilt series of SAED patterns of IM-5. The crystal was determined to be C-centred orthorhombic with a = 14.3 Å, b = 57.4 Å, c = 20.1 Å.
Figure 3. HRTEM images along three main crystallographic axes. The inserts (from left to right) show their corresponding Fourier transforms and images with P1 and Cmcm symmetry imposed, respectively.
The three space groups Cmc21, C2cm and Cmcm have the same systematic absences and cannot be distinguished from diffraction data. However, their projection symmetries are different (see Table 1). Since HRTEM images maintain the phase information, it is
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Zeolite structure determination using electron crystallography
possible to determine the projection symmetries from HRTEM images. The projection symmetries were determined from CRISP[8] to be close to pmg, pmm and cmm for the three main zone projections, respectively (Figure 3), so the most probable space group was considered to be Cmcm. Table 1. Projection symmetries for three possible space groups Space group
[1 0 0]
[0 1 0]
[0 0 1]
Cmc21
pg
pm (m⊥a)
cmm
C2cm
pmg
pm (m⊥c)
cm(m⊥b)
Cmcm
pmg
pmm
cmm
3.2.2. Atomic positions Unlike polymorph B of zeolite beta, where a single HRTEM image was sufficient for structure determination, three HRTEM images along different directions were needed for the more complex IM-5 structure. High quality HRTEM images were taken along the [100], [010] and [001] directions. From these, amplitudes and phases of 144 independent reflections were obtained and merged into one set of 3D reflections. A 3D potential map was calculated from the 144 independent reflections by inverse Fourier transformation (Figure 4)[9]. All 24 unique Si positions but no oxygens could be determined directly from the peaks in this 3D potential map.
Figure 4. The 3D potential map reconstructed from 144 reflections using the program eMap The Si net is superimposed. Green is outside and blue inside the walls.
Table 2. Fractional atomic coordinates of Si in IM-5 after DLS refinement Atom Si1 Si2 Si3 Si4 Si5 Si6 Si7 Si8 Si9 Si10 Si11 Si12
x 0 0 0 0 0 0 0.196(2) 0.203(2) 0.195(2) 0.203(1) 0.204(1) 0.187(2)
y 0.0819(9) 0.1189(12) 0.2083(11) 0.2454(8) 0.3992(9) 0.4559(8) 0.0605(6) 0.1379(7) 0.1895(7) 0.2639(4) 0.3912(8) 0.4801(6)
z 0.058(2) 0.176(2) 0.174(2) 0.058(2) 0.126(3) 0.126(3) 0.030(2) 0.173(1) 0.129(2) 0.060(1) 0.174(1) 0.173(1)
Atom Si13 Si14 Si15 Si16 Si17 Si18 Si19 Si20 Si21 Si22 Si23 Si24
x 0.318(3) 0.295(1) 0.299(2) 0.304(2) 0.295(1) 0.305(2) 0.5 0.5 0.5 0.5 0.5 0.5
y 0.0180(3) 0.1069(3) 0.2351(8) 0.3106(5) 0.3638(5) 0.4375(8) 0.0443(7) 0.1008(8) 0.2529(12) 0.2914(8) 0.3810(9) 0.4174(11)
z 0.061(1) 0.064(2) 0.173(1) 0.028(2) 0.056(2) 0.128(2) 0.025(3) 0.025(3) 0.172(2) 0.062(2) 0.061(2) 0.173(1)
[9]
.
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Since the intensity data from electron microscopy are not as accurate as those from Xray diffraction, a direct structure refinement was not very stable. Therefore a geometry optimization was performed using the distance least-squares program DLS-76[10]. Before the optimization, oxygen atoms were added half-way between each Si-Si pair. In addition to the Si-Si distances (3.0824 Å), we also specified the distances of adjacent Si-O (1.616 Å) and O-O (2.639Å). In total, 261 equations (47 for Si-Si distances, 94 for Si-O distances and 120 for O-O distances) were used to refine 174 positional coordinates and 3 unit cell parameters. After the geometry optimization, the shift of the Si positions from those obtained directly from the 3D potential map was about 0.5(2) Å. The atomic positions in this final structural model deviate on average from those refined by X-ray powder diffraction[4] by 0.16 Å for Si and 0.31 Å for O. All Si atom positions are listed in Table 2.
4. Conclusion The power of electron crystallography has been demonstrated with the determination of the structure of polymorph B of zeolite beta from a single HRTEM image. Using a similar but more general approach, the complicated structure of IM-5 structure could be established from HRTEM images taken along three main zone axes. This shows that structure determination by electron crystallography can be applied successfully, even for the most complicated zeolites. For both structures, all final Si positions were obtained with reasonable accuracy (0.1 0.2 Å) by a 3D reconstruction of HRTEM images followed by a distance least-squares refinement. This kind of accuracy is sufficient for normal property analysis, such as catalysis, adsorption and separation, and as a starting point for structure refinement with X-ray powder diffraction data. The technique demonstrated here is general and can be applied not only to zeolites, but also to other complicated crystal structures.
Acknowledgements Junliang Sun and Zhanbing He are supported by post doctoral grants from the CarlTryggers Foundation. This project is supported by the Swedish Research Council (VR) and the Swedish Governmental Agency for Innovation Systems (VINNOVA) through the Berzelii Center EXSELENT.
References [1] Higgins, J.B., LaPierre, R.B., Schlenker, J.L., Rohrman, A.C., Wood, J.D. Kerr, G.T., Rohrbaugh, W.J. Zeolites, 8 (1988) 446. [2] Newsam, J.M., Treacy, M.M.J., Koetsler, W.T. and de Gruyter, C.B. Proc. R. Soc. Lond. A, 420, (1988) 375. [3] Corma, A., Moliner, M., Cantín, A., Díaz-Cabañas, M.J., Jordá, J.L., Zhang, D.L., Sun, J.L., Jansson, K., Hovmöller, S., Zou, X.D. Chem. Mater. (2008) in press. [4] Baerlocher, Ch., Gramm, F., Massüger, L., McCusker, L.B., He, Z.B., Hovmöller, S., Zou, X.D. Science, 315 (2007) 1113. [5] Benazzi, E., Guth, J.L., Rouleau, L., PCT WO 98(1998) 17581. [6] Zou, X. D.; Sukharev, Yu.; Hovmöller, S. Ultramicroscopy 49 (1993) 147. [7] Zou, X.D., Hovmöller A., Hovmöller S. Ultramicroscopy 98 (2004) 187. [8] Hovmöller, S. Ultramicroscopy 41 (1992) 121. [9] Oleynikov, P. http://www.analitex.com/. [10] Baerlocher, Ch., Hepp, A., Meier, W.M. DLS-76, ETH Zurich, Switzerland, 1976.
799
Zeolite structure determination using electron crystallography Junliang Sun1,2, Daliang Zhang1,2, Zhanbing He1, Sven Hovmöller1, Xiaodong Zou1,2*, Fabian Gramm3, Christian Baerlocher3, Lynne B. McCusker3, Avelino Corma4, Manuel Moliner4 and María J. Díaz-Cabañas4 1
Structural Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden Berzelii Centre EXSELENT on Porous Materials, Stockholm University, SE-106 91 Stockholm, Sweden 3 Laboratory of Crystallography, ETH Zurich, CH-8093 Zurich, Switzerland 4 Instituto de Tecnología Química, UPV-CSIC, Universidad Politécnica de Valencia, Avda. de los Naranjos s/n, 46022 Valencia, Spain *E-mail: [email protected], Fax: +46 8 15 21 87 2
Abstract The structures of zeolite beta polymorph B and of IM-5 have been determined by combining selected area electron diffraction (SAED) patterns and high resolution transmission electron microscopy (HRTEM) images. The zeolite beta polymorph B structure could be solved using just a single HRTEM image while that of IM-5 required three images taken along the main crystallographic directions. The average deviations of the IM-5 model from that refined using X-ray powder diffraction data are about 0.16 Å for Si and 0. 31Å for O. Keywords: zeolite beta, IM-5, SAED, electron diffraction, HRTEM, image processing
1. Introduction Zeolite structures sometimes remain unsolved for a long time, because of either their complexity, the minute size of the crystallites or the presence of defects or impurities. One extreme example of stacking disorder is provided by zeolite beta [1,2]. Different stacking sequences give rise to two polymorphs (A and B) in zeolite beta that always coexist in very small domains in the same crystal. Not only do the small domains make the peaks in the powder X-ray diffraction pattern broad and thereby exacerbate the reflection overlap problem, but the presence of stacking faults also gives rise to other features in the diffraction pattern that further complicate structure solution. Electron crystallography offers an alternative approach in such cases, and here we describe a complete structure determination of the structure of polymorph B of zeolite beta [3] using this technique. The clear advantage of electron microscopy over X-ray powder diffraction for elucidating zeolite structures when they only occur in small domains is demonstrated. In order to test the limit of the structural complexity that can be addressed by electron crystallography, we decided to re-determine the structure of IM-5 using electron crystallography alone. IM-5 was selected for this purpose, because it has one of the most complex framework structures known. Its crystal structure was solved only recently after nine years of unsuccessful attempts [4]. Given the fact that structure determination by electron crystallography is general, success with these two zeolite structures also has implications for other materials, where
800
J.L. Sun et al.
the crystals are too small or contain too many defects and/or the structures are too complicated to be solved from X-ray powder diffraction data alone.
2. Experimental Both samples were prepared as reported in the literature [3,5]. A small amount of each sample was ground to a fine powder and dispersed in acetone. A drop of this suspension was transferred onto a holey carbon film supported by a copper grid. Tilt series of SAED patterns were collected on Philips CM-30 and JEOL JEM-2000FX transmission electron microscopes. Other SAED patterns and the HRTEM images were taken on a JEOL JEM-3010 transmission electron microscope at 300kV, having a point resolution of 1.7 Å. The SAED patterns and HRTEM images were recorded by Gatan multiscan A40 or Keenview CCD cameras. To minimize the dynamic effects, only the thinnest edges of the crystals were selected for HRTEM images and SAED patterns. All SAED patterns were analyzed by the program ELD [6]. Tilt series were combined to determine the unit cell parameters using the program Trice [7]. HRTEM images were processed by the program CRISP from Calidris to yield reflection amplitudes and phases [8]. Three-dimensional electrostatic potential maps were calculated using the program eMap [9]. The final structure model was refined using the distance least squares refinement program DLS-76 [10].
3. Results and discussion 3.1. Polymorph B of zeolite beta For normal zeolite beta samples, the domains of polymorphs A and B are only a few nanometers in size and heavily intergrown. This is not large enough for a full structure determination by electron microscopy. However, in a polymorph B enriched zeolite beta sample [2], we could find areas of sufficient size. The unit cell parameters of polymorph B were determined from a tilt series of SAED patterns to be a = 17.97 Å, b = 17.97 Å, c = 14.82 Å, α = 90º, = 113.7º and γ = 90º with the Laue class 2/m. Based on the reflection conditions observed in the SAED patterns (hkl: h + k = 2n; h0l: h = 2n, l = 2n; 0k0: k = 2n), there are only two possible space groups: Cc and C2/c. HRTEM images of polymorph B taken along the [1-1 0] direction clearly showed 12ring channels with an ABCABC… stacking sequence and well resolved 4-, 5-, and 6rings, which are characteristic of the polymorph B structure (Figure 1a). The lattice averaged projection derived from the HRTEM images shows 2-fold symmetry, and is consistent with the monoclinic space group C2/c. From HRTEM images of the thinnest area of the polymorph B crystals oriented along [1-1 0], amplitudes and phases of 39 independent reflections were extracted. Because of the C2/c symmetry, HRTEM images taken along the [1-1 0] direction are equivalent to those taken along the [1 1 0] direction. Thus, 39 independent hk0 reflections from a single projection generate a 3D hkl list with 152 reflections (hk0, h-k0,-hk0 and –h-k0). This is sufficient to solve the 3D structure of polymorph B of zeolite beta. A 3D potential map (Figure 1b) was calculated from these 152 reflections by inverse Fourier transformation. All nine unique Si atoms could be resolved from this map. Each Si atom was clearly connected to four other Si atoms, resulting in a 3D framework (Figure 1b). Oxygen atoms could not be resolved at this resolution of the HRTEM images, but were inserted geometrically halfway between the neighboring Si atoms. The positions of the nine Si and sixteen O atoms were then refined using a distance least-squares procedure. The unit cell parameters were also refined with DLS-76 to give a = 17.70(15) Å, b =
Zeolite structure determination using electron crystallography
801
Figure 1. a) HRTEM image of polymorph B of zeolite beta along the [1-10] direction. Insets are (from left to right) Fourier transform and averaged images with p1 and p2 symmetries applied. b) The 3D potential map reconstructed from this HRTEM image. All nine unique Si atoms were obtained from this 3D map, and are shown superimposed on the potential map.
17.70(15) Å, c = 14.33(11) Å and = 114.89(1)º. The final structural model of polymorph B agrees with that described in the literature [1-2]. 3.2. IM-5 The 3D structure of polymorph B of zeolite beta could be solved from a single HRTEM image taken along the diagonal [1 -1 0] direction. For more complicated structures such as that of IM-5, it is not possible to determine the full 3D structure from only one projection, so a more general approach involving several projections is needed. Here we show such a general structure determination for IM-5 using electron crystallographic techniques and no prior knowledge about the structure. The first step was to establish the unit cell dimensions and the space group, and the second to determine the atomic positions. 3.2.1. The unit cell and space group The unit cell and the Bravais lattice type for IM-5 were obtained from tilt series of SAED patterns such as that shown in Figure 2 (a = 14.3 Å, b = 57.4 Å, c = 20.1 Å with
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J.L. Sun et al.
C-centering). Its Laue class was determined to be mmm since the SAED patterns show mmm symmetry. Thus, the IM-5 structure is C-centered orthorhombic. From the SAED patterns, the reflection rules were determined to be hkl: h+k = 2n; 0kl: k = 2n; h0l: h = 2n, l = 2n; hk0: h+k = 2n; h00: h = 2n; 0k0: k = 2n; 00l: l = 2n, so there are only three possible space groups: Cmc21, C2cm and Cmcm.
Figure 2. A tilt series of SAED patterns of IM-5. The crystal was determined to be C-centred orthorhombic with a = 14.3 Å, b = 57.4 Å, c = 20.1 Å.
Figure 3. HRTEM images along three main crystallographic axes. The inserts (from left to right) show their corresponding Fourier transforms and images with P1 and Cmcm symmetry imposed, respectively.
The three space groups Cmc21, C2cm and Cmcm have the same systematic absences and cannot be distinguished from diffraction data. However, their projection symmetries are different (see Table 1). Since HRTEM images maintain the phase information, it is
803
Zeolite structure determination using electron crystallography
possible to determine the projection symmetries from HRTEM images. The projection symmetries were determined from CRISP[8] to be close to pmg, pmm and cmm for the three main zone projections, respectively (Figure 3), so the most probable space group was considered to be Cmcm. Table 1. Projection symmetries for three possible space groups Space group
[1 0 0]
[0 1 0]
[0 0 1]
Cmc21
pg
pm (m⊥a)
cmm
C2cm
pmg
pm (m⊥c)
cm(m⊥b)
Cmcm
pmg
pmm
cmm
3.2.2. Atomic positions Unlike polymorph B of zeolite beta, where a single HRTEM image was sufficient for structure determination, three HRTEM images along different directions were needed for the more complex IM-5 structure. High quality HRTEM images were taken along the [100], [010] and [001] directions. From these, amplitudes and phases of 144 independent reflections were obtained and merged into one set of 3D reflections. A 3D potential map was calculated from the 144 independent reflections by inverse Fourier transformation (Figure 4)[9]. All 24 unique Si positions but no oxygens could be determined directly from the peaks in this 3D potential map.
Figure 4. The 3D potential map reconstructed from 144 reflections using the program eMap The Si net is superimposed. Green is outside and blue inside the walls.
Table 2. Fractional atomic coordinates of Si in IM-5 after DLS refinement Atom Si1 Si2 Si3 Si4 Si5 Si6 Si7 Si8 Si9 Si10 Si11 Si12
x 0 0 0 0 0 0 0.196(2) 0.203(2) 0.195(2) 0.203(1) 0.204(1) 0.187(2)
y 0.0819(9) 0.1189(12) 0.2083(11) 0.2454(8) 0.3992(9) 0.4559(8) 0.0605(6) 0.1379(7) 0.1895(7) 0.2639(4) 0.3912(8) 0.4801(6)
z 0.058(2) 0.176(2) 0.174(2) 0.058(2) 0.126(3) 0.126(3) 0.030(2) 0.173(1) 0.129(2) 0.060(1) 0.174(1) 0.173(1)
Atom Si13 Si14 Si15 Si16 Si17 Si18 Si19 Si20 Si21 Si22 Si23 Si24
x 0.318(3) 0.295(1) 0.299(2) 0.304(2) 0.295(1) 0.305(2) 0.5 0.5 0.5 0.5 0.5 0.5
y 0.0180(3) 0.1069(3) 0.2351(8) 0.3106(5) 0.3638(5) 0.4375(8) 0.0443(7) 0.1008(8) 0.2529(12) 0.2914(8) 0.3810(9) 0.4174(11)
z 0.061(1) 0.064(2) 0.173(1) 0.028(2) 0.056(2) 0.128(2) 0.025(3) 0.025(3) 0.172(2) 0.062(2) 0.061(2) 0.173(1)
[9]
.
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Since the intensity data from electron microscopy are not as accurate as those from Xray diffraction, a direct structure refinement was not very stable. Therefore a geometry optimization was performed using the distance least-squares program DLS-76[10]. Before the optimization, oxygen atoms were added half-way between each Si-Si pair. In addition to the Si-Si distances (3.0824 Å), we also specified the distances of adjacent Si-O (1.616 Å) and O-O (2.639Å). In total, 261 equations (47 for Si-Si distances, 94 for Si-O distances and 120 for O-O distances) were used to refine 174 positional coordinates and 3 unit cell parameters. After the geometry optimization, the shift of the Si positions from those obtained directly from the 3D potential map was about 0.5(2) Å. The atomic positions in this final structural model deviate on average from those refined by X-ray powder diffraction[4] by 0.16 Å for Si and 0.31 Å for O. All Si atom positions are listed in Table 2.
4. Conclusion The power of electron crystallography has been demonstrated with the determination of the structure of polymorph B of zeolite beta from a single HRTEM image. Using a similar but more general approach, the complicated structure of IM-5 structure could be established from HRTEM images taken along three main zone axes. This shows that structure determination by electron crystallography can be applied successfully, even for the most complicated zeolites. For both structures, all final Si positions were obtained with reasonable accuracy (0.1 0.2 Å) by a 3D reconstruction of HRTEM images followed by a distance least-squares refinement. This kind of accuracy is sufficient for normal property analysis, such as catalysis, adsorption and separation, and as a starting point for structure refinement with X-ray powder diffraction data. The technique demonstrated here is general and can be applied not only to zeolites, but also to other complicated crystal structures.
Acknowledgements Junliang Sun and Zhanbing He are supported by post doctoral grants from the CarlTryggers Foundation. This project is supported by the Swedish Research Council (VR) and the Swedish Governmental Agency for Innovation Systems (VINNOVA) through the Berzelii Center EXSELENT.
References [1] Higgins, J.B., LaPierre, R.B., Schlenker, J.L., Rohrman, A.C., Wood, J.D. Kerr, G.T., Rohrbaugh, W.J. Zeolites, 8 (1988) 446. [2] Newsam, J.M., Treacy, M.M.J., Koetsler, W.T. and de Gruyter, C.B. Proc. R. Soc. Lond. A, 420, (1988) 375. [3] Corma, A., Moliner, M., Cantín, A., Díaz-Cabañas, M.J., Jordá, J.L., Zhang, D.L., Sun, J.L., Jansson, K., Hovmöller, S., Zou, X.D. Chem. Mater. (2008) in press. [4] Baerlocher, Ch., Gramm, F., Massüger, L., McCusker, L.B., He, Z.B., Hovmöller, S., Zou, X.D. Science, 315 (2007) 1113. [5] Benazzi, E., Guth, J.L., Rouleau, L., PCT WO 98(1998) 17581. [6] Zou, X. D.; Sukharev, Yu.; Hovmöller, S. Ultramicroscopy 49 (1993) 147. [7] Zou, X.D., Hovmöller A., Hovmöller S. Ultramicroscopy 98 (2004) 187. [8] Hovmöller, S. Ultramicroscopy 41 (1992) 121. [9] Oleynikov, P. http://www.analitex.com/. [10] Baerlocher, Ch., Hepp, A., Meier, W.M. DLS-76, ETH Zurich, Switzerland, 1976.