TY - JOUR
AU - Terasaki, Osamu
AB - Abstract This paper reviews diverse capabilities offered by modern electron microscopy techniques in studying fine structures of nanoporous crystals such as zeolites, silica mesoporous crystals, metal organic frameworks and yolk-shell materials. For the case of silica mesoporous crystals, new approaches that have been developed recently to determine the three-dimensionally periodic average structure, e.g., through self-consistent analysis of electron microscope images or through consideration of accidental extinctions, are presented. Various structural deviations in nanoporous materials from their average structures including intergrowth, surface termination, incommensurate modulation, quasicrystal and defects are demonstrated. Ibidem observations of the scanning electron microscope and atomic force microscope give information about the zeolite-crystal-growth mechanism, and an energy for unstitching a building-unit from a crystal surface is directly observed by an anatomic force microscope. It is argued how these observations lead to a deeper understanding of the materials. electron microscopy, AFM, structure modulation, zeolite, silica mesoporous crystal, MOF Introduction Many efforts have been made to synthesize new nanoporous materials in order to explore novel properties and functions. Their properties and functions are primarily governed by the periodic arrangement of material within the bulk of the crystal, but surface and defect fine structures of crystalline materials also play important roles. Porous materials are classified by IUPAC based on their pore diameter, d. Microporous for d < 20 Å, mesoporous for 20 Å < d < 500 Å, and macroporousfor d > 500 Å. Four typical nanoporous materials described in this review are as follows: Zeolites: Microporous zeolites are the most typical crystalline nanoporous crystals. They are composed of aluminosilicate with Mx/m[AlxSi1−xO2]nH2O, where M is a cation of valence m. Their frameworks are built from TO4 tetrahedra (T stands for Si, Al, P, G, Ge, etc.) to produce spaces (channels or cavities) within crystals by corner sharing of O of TO4. More than 200 different types of framework structures have been approved by the structure commission of international zeolite association (IZA), and the number is still increasing. Silica mesoporous crystals (SMCs): Self-assembled surfactant or block copolymer micelles are used as templates for subsequent and/or simultaneous condensation of inorganic precursors soluble in water. Depending upon conditions and reagents, structures of SMCs changes from cage-type, 2D-cylindrical, bicontinuous cubic or tricontinuous hexagonal and lamellar by increase of the packing parameter from 1/3 to 1. Metal organic frameworks (MOFs): MOFs (including ZIFs and MOFs) are composed of two major building blocks: metal ion clusters, and organic linker molecules that connect via a coordination bond, forming 1D-, 2D-, or 3D periodic networks, frequently forming micro- or mesopores within the frameworks. One may potentially exploit the use of discrete molecular units in the assembly of extended networks with a design. It is of particular importance to observe defects in MOFs for the validity and enhancement of this concept. Yolk-shell materials (core-shell systems): Catalytically active metal nanoparticles, such as Au, Pt, Ru and Pd, are encapsulated in hollow spheres formed by metal oxide nanocrystals or carbon. Nanoparticles are prevented from agglomeration at high temperature and hollow spheres are to some extent porous. Most nanoporous materials are synthesized only in powder form. Often the yield is small and not completely crystalline. Powder X-ray diffraction (XRD) is routinely used in solving the structures of unknown nanocrystalline materials. Powder XRD provides preciseness in intensity measurements but significant overlap of reflections even in high-resolution data using synchrotron X-ray sources. Nanocrystals with large unit-cell size and low symmetry exacerbate this problem. The interaction of electrons with atoms is 103 ∼ 104 times stronger than that of X-rays, which thereby make it possible to obtain enough diffraction or imaging information from nanomaterials. As well as being electrical insulators, many nanoporous materials are known to be electron beam sensitive [1]. The extent and type of damage (e.g. ionization, displacement) is dependent upon the bonding nature of the material. A more systematic study is required to overcome this problem. Accumulated knowledge of radiation-damage in organic or biological science [2] and in physical science [3,4] will help the study. Despite this weakness, the high-resolving power of electrons makes them very useful for the microscopist. Electron diffraction (ED) patterns, high resolution transmission electron microscopy (HRTEM) and scanning electron microscopy (SEM) images can give invaluable structural information about not only average periodic structure, but also structural defects and surface selective information that cannot be obtainable by other techniques. If pore-openings of nanoporous materials are blocked, i.e. a surface barrier (See the work of J Körger et al. [5]), the barrier may be observed by SEM but neither by TEM nor scanning TEM (STEM). Conversely, the existence of pores beneath the barrier can be observed by TEM and STEM but not by SEM. Quantitative lateral and vertical information on surface topography, along with frictional and chemical information, can be accurately obtained by atomic force microscopy (AFM) [6]. Meanwhile, nuclear magnetic resonance (NMR) can be useful in deriving local structural information [7]. The task of the microscopist here is to develop appropriate methodologies for the structural characterization of the above material for a better understanding of their functions and properties. Special attention is placed on the crystal defect, since it is a letter from nature for understanding the crystal growth mechanism. This review article provides an overview, with examples of materials and methodologies, firstly of average structures and then of structural deviations from perfect infinite crystal, such as defects, incommensurate structures, and a special type of incommensurate structure called quasicrystals, before reviewing crystal surfaces (the interface between a crystal and vacuum due to finite size). Solving the crystal structure Kinematical approach Elastic scattering of incident electrons (charge –e, mass m, accelerating voltage E plane wave along z axis) with an atom (atomic number Z) can be described by the Schrödinger equation for static state as an electron wave function scattered by an electrostatic potential (Vatom(r)). Using the wave number and the corresponding wave number vector k:   (1) where interaction constant σ and A are defined by . Using definitions that incident plane wave and scattered spherical outward wave have wave vectors k0, k, and scattering wave vector is defined as , is given as the Born series:   (2) where:   (3) and:   (4) Terms of the series for n = 1, 2, … are considered to represent the contribution from single, double, and multiple scattering of the incident electron plane wave. If the assumption of sufficiently weak interaction of incident electrons with the potential Vatom is applicable, then the 1st Born approximation terminating the series at the second term is adequate:   (5) where fel(K) is expressed using Poisson's equation as [8]:   (6) This approximation may correspond to kinematical scattering in electron microscopy (EM). The last equation, known as the Mott formula, gives relation between the atomic scattering (form) factor for electrons and that for X-ray, fel and fX(K), respectively. For a crystalline material, this factor will be a crystal structure factor for electrons Fel(K) by replacing atomic potential Vatom(r) by crystal periodic potential Vcryst(r). Therefore, for the case when kinematical scattering is applicable, the electrostatic potential Vcryst(r) can be directly obtained from Fourier Transform (FT) or Fourier sum of Fel(K). From the crystal potential map, one can identify atomic positions; therefore we have to make efforts to obtain data which are either kinematic, or as close as possible to kinematic [9]. To identify atomic species from Vcryst(r), it is often not straightforward as is the case with XRD, where atomic number directly correlates with charge density. This will be discussed shortly. It is known that fel is very sensitive to electron charge distribution of valence/conduction electrons [10,11]. If the dynamical scattering effect plays an important role [corresponding to higher Born series (eq. 2)] then intensity profiles give not only amplitude but also the phase information of crystal structure factors (CSFs), which is both a drawback and an advantage [12]. The listed values in International Tables were obtained assuming the spherical potential distribution of an isolated atom [13]. Deviation from spherical electron distribution of Vanadium was discussed by XRD based on atom [14,15] and by Compton scattering [16]. Therefore, for the study of bonding charge distribution special attention has to be paid [17,18]. fel of ionized atoms behaves in a different manner than expected for neutral atoms in a low scattering angle range, as drastic increases (or decreases) of fel can be seen depending on the ionization degree [19]. A double refraction effect gives fine structures of diffraction spots called multiplets. If a specimen is a parallel-sided slab then a reflection should be a single sharp spot. The observed effect comes from refraction through mainly mean inner potential, V0, 0-th Fourier component of crystal potential Vcryst(r) and through g-th Fourier components. MgO has a cubic structure with the space group Fm-3m, and Debye-Scherrer rings should be formed with sharp rings for unmixed hkl reflections from many small crystals. However, cubic morphology of MgO crystal clearly gives a double reflection effect as shown in Figure 1. One should therefore be careful to collect electron diffraction data sets from a parallel-sided slab. Fig. 1. View largeDownload slide Double refraction multiplets observed in Debye-Scherrer rings of MgO smokes. Fig. 1. View largeDownload slide Double refraction multiplets observed in Debye-Scherrer rings of MgO smokes. Since structure analysis by electron crystallography (EC) is increasingly considered an important method and structural refinement is becoming more quantitative, one must highlight the differences and similarities between atomic scattering factor for X-ray and electron. A naïve idea that fel(K) increases with Z at any wave number K (or scattering angle ), is not correct, as seen by plotting values of fel listed in Table 4.3.1.1 in International tables for Crystallography, volume C. Figure 2 shows the atomic number Z dependence of fel for different values of sinθ/λ = (1/2▪d). fel does not increase with atomic number Z (some neighbouring 3d-elements from Z = 21 to 30 are collected) as expected but decreases, showing a wavy nature. The elastic scattering cross section as a function of atomic number is also discussed by John Spence [20,21]. Specific care must therefore be taken if structural determination and refinement by electron diffraction data utilize the atomic scattering factor information. Fig. 2. View largeDownload slide (a) The atomic scattering factors (fel) for electrons at various scattering angles are plotted according to the neighboring atom species (chosen from transition metals, Z = 21–30). In the range of the values do not increase simply with the increase of Z as expected normally. Fig. 2. View largeDownload slide (a) The atomic scattering factors (fel) for electrons at various scattering angles are plotted according to the neighboring atom species (chosen from transition metals, Z = 21–30). In the range of the values do not increase simply with the increase of Z as expected normally. Periodic systems Self-consistent solution of SMCs by EC combined with the curvature assessment Three-dimensional (3D) reconstruction by electron crystallography (EC) based on TEM image data is a powerful method for solving a structure without adopting any geometrical assumptions. We have previously developed an EC reconstruction technique to give 3D electrostatic crystal potential p(r), which clearly illustrates the geometry, arrangement and connectivity of periodic mesopores [22,23]. An isopotential surface (IS) with a potential level c (p(r) = c) partitions space into the wall and the non-wall regions (cages or channels). The structure of SMCs' walls fluctuates as they are a soft matter system. Coupled with large pore sizes, this causes a rapid decay of the Fourier component with respect to the scattering angle, and the reconstructed crystal potential p(r) normally shows a very blurred distribution of potential values in 3D space (see Figure 3). Redetermination of a clear-cut boundary surface discriminating the mesopore and the wall within the averaged structural scheme is desired in order to discuss further details of the underlying mesostructure, which substantially corresponds to the determination of the proper isopotential level (cT.). Fig. 3. View largeDownload slide One unit cell representation of reconstructed crystal potential distribution of MCM-48. The distribution is highly blurred, which makes it difficult to distinguish a clear boundary between the mesopore and wall architecture. Fig. 3. View largeDownload slide One unit cell representation of reconstructed crystal potential distribution of MCM-48. The distribution is highly blurred, which makes it difficult to distinguish a clear boundary between the mesopore and wall architecture. A plausible value of cT may be determined by combining the EC data and the pore volume information obtained from gas adsorption measurements (which provides the required information about the wall density–else it is assumed) [23]. Let us call it a ‘combined method’ for convenience. The combined method is geometrically reasonable, yet is restricted to highly crystalline materials only. While the information of the gas adsorption comes from the bulk amount (at least ∼0.01 g in sample weight for mesoporous silicas) of the sample, TEM data necessary for EC reconstruction can be collected from a few single nanocrystals. This difference produces uncertainty in determination of cT due to the possible presence of uncontrolled impurities, different mesophases, and structural defects. Calcination of the sample to let the gas molecules be accessible to the mesopores is required. Some structure solutions are shown in Figure 4 [23–29]. Fig. 4. View largeDownload slide Structure types solved with Electron Crystallography. Fig. 4. View largeDownload slide Structure types solved with Electron Crystallography. Attempts to obtain a plausible pore wall structure using EC data only was especially motivated by the recent progresses in SMCs: (i) structure of as-synthesized SMCs should be solved to observe structural change from as-synthesized SMC to a calcined one; (ii) new structure should be solved even from minor crystals in a mixture of different mesostructures; (iii) SMC is extended to non-silica materials whose true density might be different from that of bulk materials; and (iv) it is necessary to give structural data of pore volume and surface area for different types of pore structure to give an insight into gas adsorption science. To overcome the limitations of the combined method, we developed an approach to obtain a pore-wall architecture of SMCs in a self-consistent manner [30]. On the varying value of the potential level c, every IS defined as p(r) = c can be a candidate of an effective representation of the pore wall structure in a unit cell of the underlying MC. The question was then ‘Which EPS is the most stable?’ To evaluate the stability of each IS, we relied on the curvature elastic energy [31] as a criterion. The formation of SMCs is based on the co-operative self-assembly of amphiphilic molecules (or copolymers) and inorganic species in water. Polymerization of inorganic precursors takes place around the boundary between water and amphiphile sheet. One may therefore postulate that the boundary surface energy is predominant during the structural formation of MCs. When the amphiphile sheet is approximated as an elastic continuum, the curvature energy (F), as a function of the mean curvature (H) and the Gaussian curvature (note that K does not represent wave number in this section), plays a dominant role as introduced by Helfrich [31]. The minimization of F offers a simple yet reasonable way to optimize the structure [32]. To determine the proper potential level cT, we first assessed local curvatures of H and K on every IS with c, then evaluated the value of F given by the form of surface integral. The structural topology associated with the surface integral of K was assumed to be unchanged and the spontaneous mean curvature (H0) was adopted as the surface-average of H so that the most probable value is obtained. From a set of the assessment, we selected the value of cT as the best-determined IS representing the mean pore-wall position that gave the minimum of F/A (A = surface area) [30,33]. This is equivalent to choosing an IS closest to a constant mean curvature surface within the reconstructed crystal potential distribution. This approach was applied to various MCs with the cubic crystal system; an example is shown in Figure 5 using SMC MCM-48 (analogous to the minimal G-surface). By using EC data, one may evaluate the porosity of SMCs for which mesopores were fulfilled by surfactants, and thus it was possible to show the structural change from as-synthesized to calcined crystal forming a more homogeneous surface. (Figure 6). Fig. 5. View largeDownload slide (a) The curvature energy density plotted with respect to the potential level c. The best-determined ISs are depicted on the bottom of the plot. (b) The simulated TEM images from the best-determined IS was compared with the observed TEM image for cal-MCM-48. Fig. 5. View largeDownload slide (a) The curvature energy density plotted with respect to the potential level c. The best-determined ISs are depicted on the bottom of the plot. (b) The simulated TEM images from the best-determined IS was compared with the observed TEM image for cal-MCM-48. Fig. 6. View largeDownload slide Curvature distribution on the best-determined ISs of one unit cell: (a) as-syn-MCM-48 and (b) cal-MCM-48. Fig. 6. View largeDownload slide Curvature distribution on the best-determined ISs of one unit cell: (a) as-syn-MCM-48 and (b) cal-MCM-48. The constant mean curvature regime alone may not be sufficient to describe formation of the SMC interface (boundary from silica wall to void/surfactant) morphology quantitatively. Using electron tomography analysis, Jinnai et al. reported that the interface of a G-morphology formed by triblock copolymer deviates from the perfect constant mean curvature surface due to the ‘packing frustration’ from the entropic cost for polymer configuration [34]. A similar but more complicated system of SMCs should also be subjected to analogic consideration for future studies in attempt to elucidate a true view of mesostructures. Accidental extinction – layered nanosheets and 3D-cubic SMCs with spherical pores A perfect crystal C(x) can be described by functions of basis B(x), lattice L(x) and size(shape) S(x) as,   (7) where x represents a positional vector in real space, S(x) is a crystal function and equal to 1 when x is inside the crystal, and equal to 0 when x is outside the crystal. A symbol * gives an operation of convolution. The Crystal structure factor (CSF) for g-th reflection is defined by Fourier g-component of the crystal as:   (8) where C(x) is the density distribution of scattering matter over the whole crystal, and the symbol represents FT, and g is a wave vector in reciprocal space. The crystal structure C(x) is obtained through inverse FT from a set of CSFs for many reflections. If the kinematical scattering approach, based on which X-ray and neutron crystallography has been developed, is applicable, then the ED intensity I(g) is given as:   (9) The crystal structure C(x) can then be solved straightforwardly using various algorithms developed for finding phase of F(x) from a set of I(g) data as discussed before. An accidental extinction comes not from the symmetry of lattice through but from zero-cross of in a one-dimensional (1D-) crystal of layered zeolite-nanosheets separated periodically by surfactants and 3D- cubic SMCs with spherical pores. In both cases B(x) does not bring extra symmetry to the lattices such as a plate with uniform density perpendicular to the z-axis (1D) and spherical pores, respectively. Graphical presentations are given in Figure 7a and b for 1D- and 3D- cases, respectively. Fig. 7. View largeDownload slide Graphical presentation of the crystal and symbolic expression of the crystal structure factor for one-dimensional system (a), and three-dimensional system of BCC (b), where an infinite plane with thickness Z and a cube of size L are assumed as their crystal shapes respectively. Fig. 7. View largeDownload slide Graphical presentation of the crystal and symbolic expression of the crystal structure factor for one-dimensional system (a), and three-dimensional system of BCC (b), where an infinite plane with thickness Z and a cube of size L are assumed as their crystal shapes respectively. For 1D-crystals, C(x) is reduced to:   (10) where B(z) is the basis(slab) with unit thickness corresponding to the lattice periodicity along z, L(z) the infinite 1D-lattice function along z, and H(x, y), S(z) the crystal-size functions in x–y plane (2D) and along z axis (1D). For the case, the size of the crystal slab in x and y directions and n, number of nano sheets along z, are large enough, then F(k) will have a non-zero value only when wave vector k is equal to lc* (l = integer), then:   (11) where A and B are scattering factors for slabs A and B, respectively. Figure 8a [35] shows normalized intensities of reflections for k = lc* obtained from equations above with l = 2, 3, 4 and 5 reflections to that of l = 1 for the case of B/A = 0.5, as . The intensity of nth order reflection (l = n) extinguishes when the rational layer thickness a reaches to 1/n. Fig. 8. View largeDownload slide (a) Relative XRD intensities (F(k)2) of l-th order reflections relative to that of the 1st reflection in the one-dimensional system. (b) Relative XRD intensities of 200, 211, 220 and 310 reflections relative to that of the 1st reflection (110). Fig. 8. View largeDownload slide (a) Relative XRD intensities (F(k)2) of l-th order reflections relative to that of the 1st reflection in the one-dimensional system. (b) Relative XRD intensities of 200, 211, 220 and 310 reflections relative to that of the 1st reflection (110). In the case of a three-dimensional structure, a similar situation may happen. The F(g) is non-zero only at specific reciprocal indices depending on the space group of the structure. For BCC, whose space group is , the non-zero intensities are observed for reciprocal lattice vectors hn corresponding to 110, 200, 211, 220, 310 … reflections in order of increasing d* in reciprocal space. The form factor B(g) is dependent on the shape of basis. For sphere of radius R, B(g) takes the form:   (12) and the diffraction intensity:   (13) shown graphically in Figure 8(b), where the intensity is normalized with respective to that of the 110 reflection. From equation 12 extinction occurs when gR equals 4.49, 7.72, 10.9, 14.0, 17.2, etc., meaning extinction occurs for different reflections at R = 0.226, 0.253, 0.292, 0.358, 0.389. (The R value cannot exceed in the case of BCC.) Ryong Ryoo et al. [36] succeeded in synthesizing hydrothermally ultrathin MFI zeolite nano sheets, which corresponded to only a single- unit-cell thickness (2.0 nm along the b-axis, which is along the straight channel) confirmed by an HRTEM image (after surfactant extraction) as shown in Figure 9a. Pillaring was carried out with tetraethoxysilane (TEOS) prior to a removal of the structure directing agent (SDA) to make mesopores within the interlamellar spaces. The mesopore diameters were uniform and precisely controlled according to the surfactant tail-lengths. Up to the fourth-order reflections corresponding to the interlayer distance were observed in powder XRD pattern at small scattering angle range due to the interlamellar structural coherence. This is the first material exhibiting two kinds of structural orders simultaneously in both mesoporous and microporous regimes among zeolites with 3D structure. An HRTEM image of the sheets synthesized by use of CnH2n+1 (n = 22) with pillars shows a = 0.5 in Figure 9b in this case, and we can observe the accidental extinction clearly for the second order reflection [2] in the powder XRD patterns from the sheets synthesized with CnH2n+1 only for n = 22 but not for n = 18 (Figure 9c). Fig. 9. View largeDownload slide MFI zeolite nanosheets synthesized using C22H45 (n = 22) (d) observed by HRTEM (a) and (b). Diffractograms (c) show that when n = 22, the second order reflection is missing due to accidental extinction. Fig. 9. View largeDownload slide MFI zeolite nanosheets synthesized using C22H45 (n = 22) (d) observed by HRTEM (a) and (b). Diffractograms (c) show that when n = 22, the second order reflection is missing due to accidental extinction. 3D-structural solutions of zeolites by various TEM approaches Solving a crystal structure using TEM requires simultaneous unit-cell parameters and possible reflection conditions. The dynamical effect sometimes makes it hard to confirm extinction conditions. Qualitative structure analysis of nanomaterials was performed by Dorset in 1995 [37] using direct methods for determining phases of CSFs from the observed ED amplitudes. Nicolopoulos et al. [38] independently showed the possibility of solving structure of zeolites by ED intensity measurement combined with direct method (three-phase invariants) taking MCM-22 as an example. We also solved the 3D-structure of unknown SFE (SSZ-48) using this approach [39]. In order to reduce the dynamical effect in electrons, precession electron diffraction (PED), electron diffraction tomography (EDT), and automated electron diffraction (AED) have attracted a lot of attention, especially in the inorganic chemistry community. The typical technique is PED, which was first introduced by Vincent and Midgley [40]. A PED pattern is recorded as the integration of a series of diffraction patterns during impact electron beam onto the specimen is tilted by with respect to the optic axis and rotated at the fixed precession angle on the same specimen position along the axis. Tilting the beam excites fewer strong reflections with a Laue circle of reflections than if the beam were exactly parallel to the zone axis. The number of strong multi-beam conditions excited by the tilted beam is reduced compared with the on-axis pattern. Some structures have been solved by this approach when diffraction intensities are collected down to the resolution limit ∼1.0 Å, where the diffraction intensities of all reflections are separately observed. Groups in Cambridge (Midgley) and North Western (Marks) have taken the method further, and the method has also been extended elsewhere to obtain structures of inorganic materials, especially by rotation electron diffraction (RED) by the Stockholm University group [41] and automated diffraction tomography (ADT) by the University of Mainz group [42,43]. A possibility of atomic resolution with 3D electron diffraction microscopy for nanoporous and nanocrystals was also shown by J. Miao et al. [44]. Diffraction/scattering techniques can give structural information very precisely; however, information is averaged over the volume. Imaging techniques are superior for obtaining local structural information to diffraction/scattering, although information is averaged along the beam path either coherently (TEM) or incoherently (STEM). There will be great progress in this field as a result of recent instrumental developments that allow small electron beam sizes on a specimen down to the Ångstrom range. TEM combined with XRD The combined approach of powder XRD with high resolution transmission electron microscopy (HRTEM) has shown success in determining complex zeolite structures such as: TNU-9 [45], IM-5 [46], SSZ-74 [47], and ITQ-37 [48]. Ohsuna et al. developed a new approach by combining analyses of HRTEM images with ED patterns to obtain a structural solution from particularly small and thin parts of crystal. Three dimensional electrostatic potential maps obtained from a set of HRTEM images are too blurred to locate atoms. However, without losing the uniqueness of structural solution, Patterson pairs from ED analysis is used and produce satisfactory Si atom positions. The structural solution is zeolite polymorph C of zeolite *BET (BEC) hypothetically proposed by J. Newsam and M. Treacey [49] and is shown in Figure 10, together with a schematic diagram of the analytical process. A study surface fine structure is also possible [50] (Figure 12). Fig. 10. View largeDownload slide Capturing a set of HRTEM images will produce a resultant three dimensional electron potential map; however, it is too blurred to locate atoms. Ohsuna et al. developed a new approach combining the potential maps with electron diffraction patterns. The resultant enhancement of the Patterson map through the use of a computer produced a framework. Fig. 10. View largeDownload slide Capturing a set of HRTEM images will produce a resultant three dimensional electron potential map; however, it is too blurred to locate atoms. Ohsuna et al. developed a new approach combining the potential maps with electron diffraction patterns. The resultant enhancement of the Patterson map through the use of a computer produced a framework. Fig. 11. View largeDownload slide Low magnification TEM image (a), corresponding ED pattern (b), HRTEM image from one of thin crystal (c). (d) Framework of three polymorphs. JEM-4000EX operated at 400 kV. High magnification HRTEM image of the overgrowth are marked by ‘New’, polymorphs A and B are marked by A and B. Fig. 11. View largeDownload slide Low magnification TEM image (a), corresponding ED pattern (b), HRTEM image from one of thin crystal (c). (d) Framework of three polymorphs. JEM-4000EX operated at 400 kV. High magnification HRTEM image of the overgrowth are marked by ‘New’, polymorphs A and B are marked by A and B. Intergrowths and surface terminations, incommensurate structure, quasi-crystals and other structural deviations The definition of a crystal has recently been extended to any material that has an essentially discrete diffraction diagram [51]. Structures that lack three-dimensional periodicity but are periodic in higher dimensions, such as incommensurate structures and quasicrystals, are now categorized as crystals. Many trials have been reported to produce quasicrystals with meso- or macroscale order. Whilst structural details are given by interference among reflections with high q-values, the topology and an arrangement of pores can be obtained from a rather small number of main reflections. Consideration of the structures of basic building units permits a structural solution of their arrangements even from low resolution diffraction/image data. Observation of the microscopic structural details of defects by TEM not only offers the possibility of gaining new insights into the structure, but also raises deeper questions regarding the underlying physics. The full potential of the technique is enhanced by not limiting arguments to microscopic images obtained but by exploring an intuitive theoretical model. The following SSZ-24 and quasicrystal sections show two kinds of materials exhibiting evidence of an aperiodic order under an EM. In an attempt to understand the physical origin of the aperiodicity in each case, a theoretical model that mimics the real system is introduced and the physical process that is essential in forming the structure is shown. Intergrowths and surface termination in Zeolite BEC Miguel Camblor et al. synthesized an interesting pure silica zeolite crystal, ITQ-14 [52] where extra small signals in powder XRD pattern and NMR spectrum were observed. Figure 11 shows tiny crystals overgrown on major *BET crystals composed of A and B polymorphs. Planar faults and defects were also observed. The volume of this new structural part was estimated at less than 5% of the total volume. ED pattern Figure 11b shows extra spots forming a rectangular net in addition to strong diffuse streaks corresponding to existence of many stacking faults (both in solid and thin overgrown regions) and a small amount of new phase from thin overgrown plates. Projected framework structures of polymorphs A, B and C suggested by JM Newsam and M Treacy et al., are also shown [49]. Fig. 12. View largeDownload slide This image is taken with [100] electron incidences by JEM-4000EX at 400 kV. Both (001) and (010) surfaces are clearly observed on the left and the above edges. Three different (010) Surface terminations, I, II and III, can be modeled, and they are energetically almost the same. However, Type II was not observed and type III was most frequently observed. Surface structure of Beta C (001) resolved - termination is distinct from (010). Fig. 12. View largeDownload slide This image is taken with [100] electron incidences by JEM-4000EX at 400 kV. Both (001) and (010) surfaces are clearly observed on the left and the above edges. Three different (010) Surface terminations, I, II and III, can be modeled, and they are energetically almost the same. However, Type II was not observed and type III was most frequently observed. Surface structure of Beta C (001) resolved - termination is distinct from (010). Atomistic modeling of surface structure can be a useful tool; an alternative nanoscope that provides Angstrom level resolution [53,54]. Advances in HRTEM revealed the surface structure of zeolite Y prompting tests of whether observed terminating structures could be explained by modeling [55]. Whitmore et al. found that three distinct terminations of the (111) facet had the same surface energy and therefore, from thermodynamic considerations, all three terminations should be observed. Only two were observed via HRTEM [56] prompting study about the growth mechanism. Whitmore et al.'s study was one of the first to report the barrier to adsorption from the external surface to the internal surface, noting the barrier at the external surface was less than that in the interior. Similar findings have been reported in zeolite A more recently [57]. Initial studies by Slater et al. [58] found that the surface structure of BEC (010) could be explained only by considering the mechanism of formation. In Figure 12, two terminations of BEC are found. Type I shows a crenellated surface decorated with double 4 rings (D4Rs) and type III displays a regular, flat surface. Three terminations could be expected upon examination of the cross section of the (010) BEC surface in Figure 12, since each of the three terminations has the same number of dangling bonds and the same density of silanol groups, and it was expected that the stability of each termination would be very similar in energy. Brent et al. have confirmed this premise directly [59], affirming earlier computational work [60–64]. Slater et al. [58] (later revisited in Slater et al. [65]) show the addition of the S4R to the type III surface to generate type II is a mildly endothermic process. Addition of a S4R to type II to yield type I is an exothermic process. Addition of a D4R to the type III surface to give the type I surface is exothermic according to density functional approaches. D4R is known to be a very stable species in solution and is present in the reaction media, unlike the S4R species. The two-step S4R mechanism suggests that type III to type II is likely to be slow, and dissolution of the S4R to yield the starting type III surface is thermodynamically favoured. However, if type II is formed by addition of S4R, attachment of another S4R is thermodynamically favourable, hence assuming a small barrier and a high concentration of S4R; type II is kinetically and thermodynamically unstable with respect to type I. However, it is tempting to consider that a more plausible mechanism, given the surfeit of D4Rs under crystallization conditions, is the direct addition of D4Rs. Both two-step S4R addition and one-step D4R addition can provide explanations for the absence of the type II surface. Figure 12 also shows the (001) surface of BEC at the top of the crystal showing possible terminating structures. In the [100] projection shown, three possible terminating structures are displayed. The type I termination on the right of the figure shows a clear D4R structure and in type III the D4R is absent. By analogy with the (010) surface, type II appears to present a S4R termination. The HRTEM image show types I and III terminations, implying a possible D4R mediated growth mechanism, which is discussed in detail in Slater et al. [65]. Figure 11 highlights the crystal morphology, which is needle-like, akin to many zeolites. In Slater et al. [65] the surface energies were calculated for the (010) and (001) faces and found to be 0.53 and 0.83 J/m2 respectively for the lowest energy terminations studied. A low surface energy implies a large morphological importance and conversely, surfaces that have higher surface energies are intrinsically less stable and hence become overgrown with more stable crystal planes. Hence, the computed surfaces energies suggest a smaller morphological importance for (001) in comparison with (010), as is evident from the aspect ratio of the BEC crystal in Figure 12. Incommensurate structure and phase transition in zeolite SSZ-24 Silica zeolite, SSZ-24, is a structure originally reported [66] to be a hexagonal open framework (space group, P6/mcc) composed of SiO4 tetrahedral units interconnected by sharing O atoms (Figure 13). The structure posed a controversy because the space group enforced the Si-O-Si angles parallel to the c-axis [located at the connecting corners of adjacent tetrahedra that are aligned vertically in Figure 13(a)] to be 180°, which was physically implausible. The original report [66], based on the X-ray crystallography, proposed that a possible displacement of the O atom from its highest symmetric position to a few lower symmetric positions, each of which has a fractional occupancy, should reduce the Si-O-Si angles to within 140–150°, although this entails the reduction of the space group to Pcc2, P6 or lower. Our preliminary powder X-ray diffraction data showed that the material exhibits a set of weak reflections that cannot be indexed with P6/mcc [67]. All these incongruous hypotheses from the various sets of data prompted us to carry out a thorough investigation of the structure in nanometre scales using HRTEM. Fig. 13. View largeDownload slide A perspective view of the unit cell (a) and a view along the c-axis (b) for SSZ-24. Each tetrahedron represents the SiO4 unit. Fig. 13. View largeDownload slide A perspective view of the unit cell (a) and a view along the c-axis (b) for SSZ-24. Each tetrahedron represents the SiO4 unit. The unusual feature of SSZ-24 is immediately identified as an incommensurate modulation along the c-axis by TEM. A set of sharp satellite reflections along the [1–10] axis was observed in the ED patterns, and was successfully indexed using the 4th reciprocal basis vector with a magnitude of q ∼ 0.38c* (Figure 14a and b). Linear bright contrasts (or wrinkles) were observed in HRTEM images taken with [1–10] incidence (Figure 14e); their intervals did not show periodicity. The intensities of the satellite reflections are relatively weak as compared to those of the main reflections, and cannot be maintained if temperature is raised to 100°C. The modulation is therefore most likely to be of the displacive type. Although these findings may well be taken as a victory of electron microscopy, the physical origin of this phenomenon can be fully understood only with a proper theoretical analysis. Fig. 14. View largeDownload slide Electron diffraction patterns of SSZ-24 taken with (a) [1–10] incidences and (b) the corresponding schematic drawing. (c) Electron diffraction pattern of SSZ-24 at 100°C. High resolution TEM image of SSZ-24 taken with (d) [001] and (e) [1–10] incidences. (f) The distribution of the soft phonon modes in the ΓMLA-plane is shown. The shadowed points have at least one phonon mode with a frequency of less than 0.01 THz. Fig. 14. View largeDownload slide Electron diffraction patterns of SSZ-24 taken with (a) [1–10] incidences and (b) the corresponding schematic drawing. (c) Electron diffraction pattern of SSZ-24 at 100°C. High resolution TEM image of SSZ-24 taken with (d) [001] and (e) [1–10] incidences. (f) The distribution of the soft phonon modes in the ΓMLA-plane is shown. The shadowed points have at least one phonon mode with a frequency of less than 0.01 THz. It is postulated that the displacive modulation was caused by the inherent instability of the silica framework as framework minerals often have various soft-mode instabilities against displacive structural transformations depending on the framework topology. A dedicated approach was developed to enumerate all the possible soft-modes; this is called the rigid-unit mode (RUM) model. The structure of SSZ-24 was modeled based on the original report [66] as a network of tetrahedra interconnected by sharing their vertices, where each tetrahedron is identified as the SiO4 unit (Figure 13) to apply the theory to the present case. Each SiO4 unit is rather rigid against deformations, whereas two connected SiO4 units resemble a hinge around which the two units can tilt or rotate easily with respect to each other. The elastic property of each SiO4 unit is taken into account with the split-atom method, which allows two vertices at one hinge to separate and assumes a harmonic potential U(r) = kr2/2 between the two split vertices where r stands for the distance between the vertices and k the effective elastic constant. If a structural distortion involved little deformations of individual SiO4 units, the energy cost associated with the distortion would be very little and the restoring forces would be very small. The corresponding phonon mode would have very small frequencies. The RUM approach allows us to analyse phonon frequency spectra for various frame work structures numerically and to enumerate all the soft modes. We have found from a numerical investigation of the RUM for SSZ-24 that the phonon dispersion curves along the c* included a quadruple set of dispersionless phonon branches with zero-frequency. There are also several discrete RUMs at the Γ point as well as at fractional wave vectors kz = 0.304 c* and 0.392 c*, accompanied by sharp drops of phonon branches. It appears that the incommensurate RUM at 0.392 c* is in reasonable agreement with the modulation wave vector q ∼ 0.38 c*. As all the soft modes indicate possible flexible distortions of the idealized structure, their distribution in the reciprocal space was calculated. In the ΓMLA-plane (h0l plane) of the reciprocal space, the soft modes are distributed along the shadowed regions shown in Figure 14(f), where black dots present the positions for fundamental reflections. The distribution shows good agreement to the diffuse streaks that are observed in an ED pattern for the higher-temperature phase (Figure 14c). Mesoscale quasicrystal, its approximants and growth form We have recently reported that mesoporous silica forms a quasicrystalline structure. The synthesis details can be found in the original paper [68]. It was previously reported that two different crystal structures are obtained just by varying the ionization degree of surfactant with different additional amounts of NaOH. These structures are isostructural to the A15-type structure (at low pH) and the σ phase structure (at high pH) included in the Frank-Kasper family of alloy phases; the space groups are Pm-3n and P42/mnm, respectively. Recall that they involve three kinds of Voronoi polyhedron: [512], [51262] and [51263], where [5i6j] stands for a polyhedron having i pentagonal and j hexagonal faces. The boundaries of the Voronoi polyhedra represent the silica walls in the mesoporous silica system. Both these structures reveal a tiling composed of squares and/or equilateral triangles when they are orthogonally projected down to the (001) plane. TEM images taken along the [001] axis are shown in Figure 15a and b for the Pm-3n and P42/mnm structures, respectively. The three-dimensional Voronoi packing associated with the square and triangle columns are depicted in Figure 15d and e. Fig. 15. View largeDownload slide The three basic crystal structures and their packing geometries. a–c, TEM images taken along the [001] axis for the (a) (b) P42/mnm and (c) Cmmm structures. The yellow lines in each TEM image show the corresponding tiling. (d) Three-dimensional packings for squares and triangles. The three kinds of Voronoi polyhedra, that is, [51262], [51263] and [512] are shown blue, red and yellow, respectively. (e) Projections of the polyhedral frames, demonstrating the two-dimensional/three-dimensional relationship of squares and triangles, where the centre of each polyhedron is indicated by a dot symbol (see key, where z stands for the fractional coordinate in the normal direction to the plane). Fig. 15. View largeDownload slide The three basic crystal structures and their packing geometries. a–c, TEM images taken along the [001] axis for the (a) (b) P42/mnm and (c) Cmmm structures. The yellow lines in each TEM image show the corresponding tiling. (d) Three-dimensional packings for squares and triangles. The three kinds of Voronoi polyhedra, that is, [51262], [51263] and [512] are shown blue, red and yellow, respectively. (e) Projections of the polyhedral frames, demonstrating the two-dimensional/three-dimensional relationship of squares and triangles, where the centre of each polyhedron is indicated by a dot symbol (see key, where z stands for the fractional coordinate in the normal direction to the plane). Quasicrystalline order has been realized when the ionization degree (i.e., the NaOH molar ratio) is slightly reduced from that for obtaining the P42/mnm structure. A remarkable feature of this particular sample is in the morphology of individual particles; the majority of the particles exhibit an outward appearance of dodecagonal prisms with a diameter of a few micrometers (Figure 16a). This strongly indicates an inherent aperiodicity of the structure, because periodicity is incompatible with dodecagonal symmetry. A question then arises about whether the material involves dodecagonal quasicrystallinity or just multiple twinning. Cross sectional images of a few of the particles have been taken using HRTEM, revealing that the structure can be represented as a tiling composed of squares and equilateral triangles. A quasicrystalline order was realized in the central region of the tiling, confirmed with electron diffraction patterns showing a perfect dodecagonal symmetry (Figure 16b). A quantitative higher-dimensional analysis of the central tiling in some of the particles has demonstrated a close proximity to ideal quasicrystallinity (Figure 16d). The central region is usually surrounded by 12 fans of crystalline domains, each of which is composed of a periodic structure that is isostructural to the H-phase (space group, Cmmm) in the Frank-Kasper family (Figure 16c). All these observations are presented in Ref [68]. Fig. 16. View largeDownload slide (a) SEM images taken from the sample; the particles are dodecagonal prisms. (b) Electron diffraction pattern taken from a sample using selected area aperture size, as indicated by the white circle in the inset. (c) A TEM image taken from the peripheral part of the sample. Bottom right inset, the box in the low magnification TEM image indicates from which part of the sample the tiling is observed. Irregular polygons (yellow lines) are observed in the boundary area between two fans. Linear rows of vertices within each fan are marked with broken lines: pink, 33.42 vertices; light blue, 44 vertices. A defect row bounding two parallel domains is marked by white lines. (d) TEM image taken from crushed quasicrystalline sample. Fig. 16. View largeDownload slide (a) SEM images taken from the sample; the particles are dodecagonal prisms. (b) Electron diffraction pattern taken from a sample using selected area aperture size, as indicated by the white circle in the inset. (c) A TEM image taken from the peripheral part of the sample. Bottom right inset, the box in the low magnification TEM image indicates from which part of the sample the tiling is observed. Irregular polygons (yellow lines) are observed in the boundary area between two fans. Linear rows of vertices within each fan are marked with broken lines: pink, 33.42 vertices; light blue, 44 vertices. A defect row bounding two parallel domains is marked by white lines. (d) TEM image taken from crushed quasicrystalline sample. The striking features of our new material, as they have been revealed through TEM observations, make us wonder how they formed during the synthesis. The dodecagonal shaped particles can be seen as composites consisting of a quasicrystalline center and a twin-like arrangement in the peripheral region. Such particles are likely to have formed under a strongly non-equilibrium environment, where the primary building units are the micelles, stacked locally into columnar arrangements represented as squares and triangles in the planer representation. These secondary building units seem to maintain a certain degree of rigidity; hence, we may set aside the behavior of individual micelles while focusing on how squares and triangles are arranged during the growth process. Motivated by the above consideration, we have proposed a stochastic growth model in order to simulate the formation of the present material. The structure is represented as a patch of square-triangle tiling in the plane, whereas a simplified energetics for the tiling is introduced to take into account effectively the interactions between the micelles. Note that the vertices of a square-triangle tiling can be mutually connected through edges represented by the unit vectors, ej = (cos(πj/6), sin(πj/6)) with j = 1, … ,12. It follows that a possible new vertex (or a ‘candidate’) must be given at a point that lies outside the outer boundary of the patch and that is connected to a vertex on the boundary through one of the unit vectors ej. The total free energy, F, of the patch is defined as comprising the effective chemical potential, μ, associated with every vertex, the effective interaction potential, V, between vertices and/or tiles, and the surface energy, σ, associated with every edge on the boundary; hence, F = μN + V + σM, where N is the total number of vertices in the patch and M the total number of edges comprising the outer boundary of the patch. The simulation details can be found in the original paper [68]. There exists a range of possibilities in the definition of the interaction potential V. The simplest choice is to introduce a central-force field (or pair-potential) v(r) between an arbitrary pair of vertices in the patch, where r stands for the distance between the vertices. (A more realistic potential based on multi-body interactions between vertices and tiles is adopted in Ref [68].) Then the total interaction energy is calculated as V = Σ<〈i,j〉>v(rij), in which <〈i, j〉> runs over all the pairs of occupied vertices in the patch. We have surveyed different types of v(r) in search of the best potential that reproduces the structural characteristics of the present material. When a Lennard-Jones potential having a minimum at the distance 1 (the edge length of the tiling) was used for v(r), we could only obtain domains of triangular tilings separated by defects. It then turned out that if v(r) takes only negative values, an aggregation of triangles cannot be avoided because the attractive interactions between adjacent vertices will enforce the coordination number of vertices to be maximized. In an attempt to prevent triangles from been aggregated, we manipulated v(r) so that it had a positive barrier at , which corresponds to the long diagonal of a rhombus composed of two equilateral triangles. Figure 17 shows two examples of v(r) that produced a tiling with similar characteristics to our materials. Note that they have double minima, at around r = r1:= 1 and r = r4:= √(2 + √3). The second minimum is necessary to promote the pairing of a square and a triangle. A systematic change was observed in the simulated structures when the height of the barrier as well as the depth of the second well was slightly changed. The σ phase structure is obtained when the barrier height and the depth of the second well are sufficiently large, while a reduction of them turns the structure into what we have observed in the cross sectional images of our dodecagonal particles with a randomized center and multiply-twinned like peripheries. Fig. 17. View largeDownload slide (a) The pair-wise potential of the interactive energy between vertices of the tilings. The simulated patterns from the potential b and c are shown in (b) and (c) respectively. Fig. 17. View largeDownload slide (a) The pair-wise potential of the interactive energy between vertices of the tilings. The simulated patterns from the potential b and c are shown in (b) and (c) respectively. Note that in the above case study, a slight change in the pair-potential has abruptly changed the structure produced. This is consistent with the experimental finding that a slight decrease of the alkalinity transforms the σ phase structure into the composite structure having a dodecagonal morphology. The growth of each fan in Figure 17c is initiated once a particular configuration at the tip of the fan is formed. This occurs when the candidate B in Figure 18 is chosen through a competition between two different candidates A and B. Note that when v(r4) and v(r5) are comparable these two candidates are chosen with similar probabilities, but if the ratio v(r4)/v(r5) becomes larger the candidate A is much more likely to be chosen, in favor of the σ phase structure. After the tip of the fan is formed, geometrical constraints will enforce a stable growth of a fan; observe that in Figure 18 the candidate D is much more likely to be chosen than the candidate C because v(r3) − v(r4) + v(r5) takes a significantly large positive value primarily due to the potential barrier at r = r3. When the barrier is significantly suppressed, the competition between configurations similar to C and D can be greatly enhanced, so that the growth of a fan will no longer be stable. Similar arguments apply also to the case when a different type of potential energy is used as in Ref. [68]. It is important to note that the potential barrier represents an effective repulsion between adjacent triangles. It was argued in Ref. [68] that the repulsion is associated with the interfacial force between the micelles and that it is suppressed when the alkalinity is reduced. In this sense, the physical picture of the structural transformation provided by the model reasonably agrees with the behavior of the real materials observed experimentally. Fig. 18. View largeDownload slide Left: The patch that could initialize a fan-like configuration. Right: Graphic illustration of the environments for different candidate vertices. Fig. 18. View largeDownload slide Left: The patch that could initialize a fan-like configuration. Right: Graphic illustration of the environments for different candidate vertices. Defect structure – cage-type SMC We are focusing on defect structures in cage- and bicontinuous-type SMCs. Cage-type SMCs are formed by the ordered arrangement of the spherical (or ellipsoidal) micelles with the smallest surfactant packing parameter g value of 1/3, having the highest organic/inorganic interface curvature. In particular, compared with the traditional atomistic crystals, the intergrowth and defects of SMCs are more diverse because the silica framework wall is so flexible before completion of silica polymerization that the structures still sensitively respond to changes in a synthesis condition. Planar defects, such as intergrowth, twinning and stacking faults, are typical examples observed in SMCs, especially the synthesis system with co-structure directing agent (CSDA). A distinguishable benefit of the CSDA method developed by Che et al. [69] is that the mesostructure can be easily controlled to show a variety of mesostructures and morphologies. Several cage-type structures have been synthesized, for instance, body centred cubic (bcc) (SG: Im-3m, SBA-16 etc), face centered cubic (fcc) (SG: Fm-3m, SBA-12 etc), cubic A-15 type (SG: Pm-3n, SBA-1 etc), cubic Fd-3m (FDU-2, AMS-8), hexagonal closest pack (hcp) (SG: P63/mmc, SBA-2 etc), tetragonal (SG: P42/mnm, AMS-9) and body centred cubic (bcc) (SG: Im-3m, SBA-16) [70]. Both the ccp and hcp structures have the highest packing density ca. 0.74 of unimodal spheres and form octahedral and tetrahedral interstitial spaces among the spheres. While SBA–1 and SBA–6 (space group Pm–3n), AMS–8 (space group Fd–3m) and AMS–9 (space group P42/mnm) have multimodal cages, and the interstices of the spheres are only tetrahedrally cordinated. These structures may correspond to the tetrahedrally close–packed (tcp) structures governed by area–minimizing effect rather than total packing entropy of ccp/hcp structure. It has been assessed that there is a distinct difference between unimodal and multimodal mesostructures, in that the unimodal structures possess mostly concave surfaces (Gaussian curvature K > 0), while the multimodal structures have a saddle shape surface (Gaussian curvature K < 0) [32]. In this case, the soft micelles make interfaces with the adjoint micelles and become polyhedra instead of the spherical cages. Figure 19 shows four types of polyhedra introduced for intermetallic compounds by Frank and Kasper [71] 512, 51262, 51263, and 51264, which construct tcp structures. Thus, the Pm-3n structure (SBA-1), Fd-3m structure (AMS-8) and P42/mnm (AMS-9) structures can be described by the polyhedra packing model as ‘MEP’, ‘MTN’ and ‘SIG’ structures, respectively, according to the system of symbols for nets (Figure 19) [72]. Fig. 19. View largeDownload slide Schematic drawings of four types of polyhedra and the structural description of the tcp mesostructures with a polyhedra packing model. Fig. 19. View largeDownload slide Schematic drawings of four types of polyhedra and the structural description of the tcp mesostructures with a polyhedra packing model. The Pm-3n structure consists of four 512 polyhedra arranged in bcc (Wyckoff 2a site), and six 51264polyhedra form three sets of perpendicularly interlocking columns (6c site). The Fd-3m structure consists of eight 51264 are arranged in the diamond structure (8b site) and sixteen 512 located between 16-hedra (16c site). The 51264polyhedra connect to four 51264polyhedra and twelve 512polyhedra, and the 512polyhedra connect to six 51264polyhedra and six 512polyhedra. The Fd-3m structure can be also described as a stacking of two kinds of layers made of these two polyhedra along the [111]cub direction. One of the layers has only 512 arranged in the Kagomé net, termed layer A (or B or C). The other has 512 and 51264, termed layer α (or β or γ), and their mirrors are denoted by α′ (or β′ or γ′). The structure follows the stacking sequence of AαBβCγ; however, if the layer α (or β or γ) goes to its mirror structure α′ (or β′ or γ′), e.g. AαBβCβ′Bα′A, a twin is formed. Meanwhile, the P42/mnm structure is more complicated, following a tetragonal symmetry and have 512, 51262 and 51263. The structure has five different crystallographic sites, three different cages and thirty cages in one unit cell. It can be concluded that three-dimensional packings for squares and triangles can be achieved by employing different types of the polyhedra. By controlling the chemical composition and the synthesis parameter well, diverse cage-type mesostructures can be formed according to the packing behavior of the micelles. The structural change from the Fm-3m to Fd-3m was observed by changing synthesis condition [70]. In the intermediate region, the intergrowth of these two structures has been directly observed using HRTEM. Figure 20a and b shows the HRTEM images of the intergrowth with two successive tilt series along the vertical axis of these images (along the [111]) by 30°. It is clear from the HRTEM images and FDs of both domains that the [-110] direction of the Fm-3m structure (top and bottom) corresponds with the [-211] of the Fd-3m structure (middle) with common [111] axis in Figure 20a and the [-211] of the Fm-3m structure corresponds with the [-101] of the Fd-3m structure in Figure 20b as well. Thus, the Fm-3m structure and the Fd-3m structure can grow epitaxially with 30° rotation along the common [111] axis. They have a relationship of a(Fd-3m)/a(Fm-3m) = √3 ≈ 1.73. Based on the HRTEM images, the intergrowth can be described by introducing an intermediate layer (termed layer λ) between the Fd-3m structure and the Fm-3m structure (Figure 20c). The layer λ consists of two kinds of hard spheres, where a small sphere occupies the lattice point of the triangular net as shown in orange colour, and a large sphere sits on the centre of the hexagon of the Kagomé net as shown in blue. The layer λ results in the base layer (e.g., layer a) for the successive Fm-3m structure. Then the hard spheres layer can be placed on layer λ for both the ccp or hcp. According to this model, a good agreement between observed and simulated HRTEM images is observed, as shown in Figure 20a and b. Fig. 20. View largeDownload slide HRTEM images of the intergrowth of the Fm-3m and Fd-3m structures. Each domain is taken along (a) [-211] Fd-3m and [-110] Fm-3m directions and (b) [-101] Fd-3m and [-211] Fm-3m axis. (c) Schematic drawings of the boundary layer (layer λ) on layer A. Fig. 20. View largeDownload slide HRTEM images of the intergrowth of the Fm-3m and Fd-3m structures. Each domain is taken along (a) [-211] Fd-3m and [-110] Fm-3m directions and (b) [-101] Fd-3m and [-211] Fm-3m axis. (c) Schematic drawings of the boundary layer (layer λ) on layer A. Besides, in the Fd-3m structure, several twin structures and different kinds of defect are observed. Figure 21e and f show the HRTEM images taken from the [-110]cub and [-12-1]cub directions respectively, including one type of defect, which consists of an ABBA stacking sequence of 512 hedron layers. The new layer is termed layer z, which has the space group of P6/mmm and can be explained well by introducing two types of polyhedra. One is a 51263 polyhedron arranged in the triangular net, the other is a 51262 polyhedron, which occupies the center of the triangular net, forming a ‘zra-d’ net. Thus, the defect layer has the AαBzBα′A stacking sequence. The schematic figures of the layers and simulated TEM images of layer z are inserted in observed HRTEM images. They agree with each other very well. Fig. 21. View largeDownload slide (a–d) Schematic drawing and the HRTEM images taken from (e) [-110]cub and (f) [-12-1]cub directions with the simulated TEM images of the defect layer z. Copyright 2009 Wiley-VCH Verlag GmbH & Co. KGaA. Fig. 21. View largeDownload slide (a–d) Schematic drawing and the HRTEM images taken from (e) [-110]cub and (f) [-12-1]cub directions with the simulated TEM images of the defect layer z. Copyright 2009 Wiley-VCH Verlag GmbH & Co. KGaA. Interestingly, another type of defect has been discovered, which does not keep the original threefold symmetry along the [111]cub axes and has not been reported. From the cage positions and the contrast from the HRTEM images, a polyhedra model was built to interpret the defect structure. However, the defect cannot be built by using only the four types of polyhedra, while three new polyhedra, 4151062, 425865, and 4151064, were employed (Figure 22a). All of the polyhedra were discovered in Matzke's experiment on random foam structure [73,74]. Fig. 22. View largeDownload slide (a) Three new polyhedra for building the defect structure (b–e) Schematic drawing and the HRTEM images taken from (f) [1-10]cub, (g) [1-21]cub, (h) [0-11]cub and [-1-12]cub directions with the simulated TEM images of the defect. Copyright 2009, Wiley–VCH Verlag GmbH & Co. KGaA. Fig. 22. View largeDownload slide (a) Three new polyhedra for building the defect structure (b–e) Schematic drawing and the HRTEM images taken from (f) [1-10]cub, (g) [1-21]cub, (h) [0-11]cub and [-1-12]cub directions with the simulated TEM images of the defect. Copyright 2009, Wiley–VCH Verlag GmbH & Co. KGaA. The defect layer has a monoclinic unit cell with space group of C2/m. As shown in the figure, simulated TEM images and the structure models have a good agreement with the observed HRTEM images (Figure 22(f–i)), which support the faithfulness of the structure model and brings the new possibility of constructing new cage-type structures by stacking the micelles with various types and sizes. It has been found that the defect is formed as a result of a mismatch of the stacking sequence of the Fd-3m structure, which has been also observed in the ETS-10 structure [75]. A full-scaled synthesis-field diagram, where micellar cubic Fm-3m, Pm-3n, Fd-3m, micellar tetragonal P42/mnm, 2D-hexagonal p6mm and bicontinuous cubic Pn-3m (D-surface) appeared, have been obtained [76]. It has been found that the formation of the mesostrucutres is governed by the organic/inorganic interface curvature and the mesocage–mesocage electrostatic interaction, and that weaker mesocage–mesocage repulsion stabilizes soft sphere packing of cubic Pm-3n, Fd-3m and tetragonal P42/mnm structures, while hard sphere packing Fm-3m mesostructure was obtained with strong mesocage–mesocage repulsion. Pore minimal surfaces – AMS series The lamellar, bicontinuous cubic D- and G-surface structures (Pn-3m and Ia-3d) and 2D–cylindrical structure (p6mm) have increased organic/inorganic interface curvatures with the g values of 1, 2/3 and 1/2, respectively. The structural transformation from lamellar to bicontinuous and to cylindrical has been followed with interest. Hyde indicated that at a given chain packing parameter, small variations in the chain volume fraction (defined as the total apolar fraction of the amphiphilic molecule, including apolar solvents) may cause phase transformations between the different cubic bicontinuous phases. Transitions with increasing chain volume fraction may occur in the sequence lamellar and D- and G-surface structures [77]. However, the details of the microscopic dynamics of the structural transitions and their intergrowth have not been observed directly because of limited resolution of the scattering experiments, and the difficulties of direct observation of these structures. Very recently, a series of AMS materials have been obtained with an unusual structural change of cage–type → 2D cylindrical p6mm → epitaxial intergrowth of p6mm and D–surface → epitaxial intergrowth of p6mm and G–surface → D–surface → G–surface → lamellar [78]. The observed epitaxial relationship between p6mm and D-surface by the HRTEM image is that the cylinders of p6mm are parallel to the <110> of D–surface with a {11}p6mm ↔ {221} D (Figure 23a). Meanwhile, for the G-surface, two kinds of connection were observed. It can be clearly observed from the HRTEM image that the cylinders of p6mm are parallel to the <111> of G side by side with both {10} p6mm↔{211}G and {10} p6mm↔{220}G relationships (Figure 23b and c). For the {10} p6mm↔{220}G intergrowth, the cylinders of p6mm domain cannot fit well the G domain perfectly, creating numerous defects with elliptical channels at the boundary (marked by the red arrows in Figure 23c). Fig. 23. View largeDownload slide TEM images of the samples synthesized with C18GluA and Brij–56. (a) intergrowth of p6mm and D-surface structure, taken along [110]cub axis, (b–c), intergrowth of p6mm and G-surface, taken along [111]cub axis, (d) D-surface sphere with icosahedron hollow and (e) 3D reconstruction and experimental g value distribution of the D-surface and G-surface structures. Reproduced from ref. 78 and 83. Copyright 2011, American Chemical Society. Fig. 23. View largeDownload slide TEM images of the samples synthesized with C18GluA and Brij–56. (a) intergrowth of p6mm and D-surface structure, taken along [110]cub axis, (b–c), intergrowth of p6mm and G-surface, taken along [111]cub axis, (d) D-surface sphere with icosahedron hollow and (e) 3D reconstruction and experimental g value distribution of the D-surface and G-surface structures. Reproduced from ref. 78 and 83. Copyright 2011, American Chemical Society. It is worth noting that the phase transition of the G-surface structure and the hexagonally packed cylinder structure have been discovered in the corresponding liquid-crystalline phases, the block copolymer melts and the SMCs. Most of the existing experiments and theories support the correlation that the two phases align side by side with the {10} p6mm↔{211}G [56,79–82]. In the previous studies, the details of the microscopic dynamics of this epitaxial transition were not observed directly because of limitation of the scattering experiments. However, the formation of SMCs enables detailed study of these intergrowth and defects by the HRTEM technique. Interestingly, the sample with D–surface showed spherical morphology with inner polyhedron hollows (icosahedral, such as those observed for proteins of virus capsids, decahedral, Wulff polyhedral, etc.) formed by the reverse multiply twinned D–surface structure (Figure 23d) [83]. It has been found that vesicles with low-curvature lamellar structures were firstly obtained, then a structural transformation to D–surface structure occurred, which induced the formation of the reversely multiply twinned icosahedral/decahedral hollows. In addition, the local g parameter of both D– and G–surface has been calculated from electron crystallography reconstruction by the mean curvatures and Gaussian curvatures of the equielectrostatic potential surface. Defects in MOFs Metal catecholates (CATs) synthesized by solvothermal reactions of 2,3,6,7,10,11-hexahydroxytriphenylene (HHTP) with metal [II] ions (Co and Ni) to form extended metal-organic framework (MOF) structures. (Synthesis details were described in [84].) Synthesized crystals of Ni-CAT-1 were not of suitable size for single crystal X-ray analysis. Nevertheless, a Rietveld refinement of Ni-CAT-1 was performed against the powder diffraction pattern collected with synchrotron radiation, employing the atomic coordinates obtained from the single crystal data of Co-CAT-1. The refinement converged with excellent residual values (Rwp = 8.54%, Rp = 6.33), demonstrating that Co-CAT-1 and Ni-CAT-1 have the same structure. In this study, the structure and the size and arrangement of the pores of Ni-CAT-1 were further visualized by HRTEM. A JEM-2010F field emission transmission electron microscope equipped with a CEOS post-specimen spherical aberration corrector (Cs corrector) was operated at 120 kV for HRTEM imaging. And a JEOL 2100F with a cold field-emission gun equipped with a newly designed aberration corrector (the DELTA-corrector) was operated at 60 kV for scanning transmission electron microscopy (STEM). A Gatan GIF Quantum equipped on the above JEM-2100F was used for performing electron energy loss spectroscopy (EELS) analysis in STEM mode at 60 kV. MOF materials tend to be electron beam sensitive; in order to reduce the electron beam damage, the beam density during the observations was from 50 to 150 electrons/(nm2 s). A single HRTEM image with an exposure time of 2 s or a sequence of 10 frames was recorded with a 0.5 s exposure time for each and after drift compensation some frames were superimposed to increase the signal-to-noise (SN) ratio for display. Image simulation for HRTEM was performed by using Mactempas software. The inner and outer collection angles for the annular dark field (ADF) image were 58 and 130 mrad, respectively. The beam current was 10 pA for the ADF imaging and the EELS chemical analysis. Figure 24 shows a low magnification HRTEM image of the activated Ni-CAT-1 taken at 120 kV. Both channel direction in lattice fringes (incident electron beam perpendicular to the channels) and hexagonal channel arrangement in a uniform honeycomb structure (incident electron beam parallel to the channels) can be clearly observed. Some defects can be identified as indicated by the arrow. Although HRTEM is a powerful method for determining surface structures in inorganic porous materials [50,85–88], this is the first example where the terminal structure of a crystalline MOF is observed. This terminal structure of activated Ni-CAT-1 can be clearly observed in Figure 25a as indicated by the arrows. The simulated image and the proposed layered 2D model being geometrically optimized by using molecular mechanics with the MM + force field method are inserted Figure 25b. However, this model is slightly different from the structure of the as-synthesized single crystal deduced by synchrotron radiation XRD analysis. The main differences are in the area assigned to the position of the metal atoms of the interlayer complexes. This fact suggests small changes might happen probably in the orientation of the complexes after the activation process and under the acquisition conditions (high vacuum) for the HRTEM image. Fig. 24. View largeDownload slide HRTEM image of the activated Ni-CAT-1 taken at 120 kV. Fig. 24. View largeDownload slide HRTEM image of the activated Ni-CAT-1 taken at 120 kV. Fig. 25. View largeDownload slide (a) High-magnification HRTEM image showing the terminal structure of activated Ni-CAT-1 as indicated by arrows. (b) Simulated TEM image and (c) 2D model of the structure. Fig. 25. View largeDownload slide (a) High-magnification HRTEM image showing the terminal structure of activated Ni-CAT-1 as indicated by arrows. (b) Simulated TEM image and (c) 2D model of the structure. The HRTEM images are accompanied with fast Fourier transform (FFT) diagrams of the corresponding areas indicated by arrows (Figure 26). It corresponds to the projection of the pores along the <001> direction, which allowed the determination of the unit cell lattice parameter of a = 2.02 nm. This finding is in agreement with the value obtained from the single crystal data analysis of Co-CAT-1 (a = 2.21 nm) and the one obtained from the X-ray powder diffraction study of Ni-CAT-1 (a = 2.19 nm). Fringes perpendicular to the pore walls can be clearly seen in the region enclosed right square of Figure 26. The arc line reflection labeled by the 001 reflection shown in the FFT pattern in the inset of top right of Figure 26 demonstrates the wavy feature of the fringes perpendicular to the pore walls, which can be clearly identified in Figure 27a, indicating the fluctuation of the Ni atoms. It can be roughly deduced that the curvatures of the lattice fringes along c directions were ±15° through the analysis of the half maximum full-width of the intensity of 001 arc line reflection. The average spacing between these wavy fringes, calculated from the FFT patterns, is about 0.32 nm, which corresponds to the inter-layers distance (0.33 nm according to the X-ray data). The comparison between the HRTEM and simulated images looking through the [001] direction is shown in Figure 27b. The characteristic six black dots and the small circle inside, which are labeled by the white circles in both HRTEM and simulated images, match well, further verifying the proposed changing of the structure (Figure 25b). Fig. 26. View largeDownload slide High-magnification HR-TEM image of Ni-CAT-1 taken at 120 kV, the inset images are the fast Fourier transform (FFT) analysis of the corresponding areas indicated by arrows. Fig. 26. View largeDownload slide High-magnification HR-TEM image of Ni-CAT-1 taken at 120 kV, the inset images are the fast Fourier transform (FFT) analysis of the corresponding areas indicated by arrows. Fig. 27. View largeDownload slide FFT image demonstrating the wavy characterization of the edges perpendicular to the pore walls and the comparison between the HRTEM and simulated images looking through the [001] direction is shown on the right. Fig. 27. View largeDownload slide FFT image demonstrating the wavy characterization of the edges perpendicular to the pore walls and the comparison between the HRTEM and simulated images looking through the [001] direction is shown on the right. It is also a challenge to observe MOFs by using STEM due to a focused beam that has a higher beam density than in transmission electron microscopy (TEM) mode. Typically, zeolites and mesoporous silicas are damaged much faster in STEM mode than in conventional TEM mode. Remarkably, for the first time we were able to overcome this challenge and observe a crystalline MOF material by using STEM at 60 kV. The honeycomb structure of Ni-CAT-1 is clearly observed in the STEM image (Figure 28a), albeit at the expense of structural electron beam stability, which collapsed after the whole scan was complete. Electron energy loss spectrum shows existences of Ni (L-edge) and O (K-edge) (Figure 28b). Fig. 28. View largeDownload slide Electron energy loss spectroscopy (EELS) spectrum with the annular dark-field scanning transmission electron microscopy (ADF-STEM) image taken under 60 kV shown in the inset. Fig. 28. View largeDownload slide Electron energy loss spectroscopy (EELS) spectrum with the annular dark-field scanning transmission electron microscopy (ADF-STEM) image taken under 60 kV shown in the inset. Another example is the observation of several members of a series of compounds whose structures are expanded versions of MOF-74 [89–91], M2(2,5-DOT) (M = Zn2+, Mg2+; DOT = dioxidoterephthalate). These MOF structures are extended from the original DOT link of one phenylene ring (I) to two (II), three (III), four (IV), five (V), six (VI), seven (VII), nine (IX) and eleven (XI) to give an isoreticular (having the same topology) series of MOF-74 structures (termed IRMOF-74-I to XI) with the dimension of the pore apertures ranging from 1.4 to 9.8 nm. Figure 29 shows the HRTEM images of IRMOF-74-VII (Figure 29a) and IRMOF-74-IX (Figure 29b) taken from the incident electron beam parallel to the channel directions. Ordered pores of 6 ‘member-ring’ (surrounded by 6 channels) arranged in a hexagonal structure are clearly resolved. The inserted images in the left topside of Figure 29a and b are the FFTs of the corresponding square areas. Six reflection spots corresponding to the 110 reflections can be clearly identified from the FFT patterns, from which the d-spacings were measured (3.95 and 5.57 nm for IRMOF-74-VII and IX, respectively). These values are in good agreement with the d-spacing values derived from the x-ray crystal structure analysis (4.59 and 5.69 nm for IRMOF-74-VII and IX, respectively). Defects formed in 4 ‘member-ring’ (surrounded by 4 channels) and 8 ‘member-ring’, (surrounded by 8 channels) can seldom be found but are observed here as shown in Figure 29c. Fig. 29. View largeDownload slide HRTEM images of (a) IRMOF-74-VII and (b) -IX, respectively. The corresponding FFT diffraction patterns of the dashed square area in the original images. (c) Defects formed in 4 ‘member-ring’ (surrounded by 4 channels) and 8 “member-ring”. Fig. 29. View largeDownload slide HRTEM images of (a) IRMOF-74-VII and (b) -IX, respectively. The corresponding FFT diffraction patterns of the dashed square area in the original images. (c) Defects formed in 4 ‘member-ring’ (surrounded by 4 channels) and 8 “member-ring”. Understanding the surface structure of MOFs is becoming increasingly important as MOFs start to find market-place applications. Fischer and Schmid [92] recently reviewed the importance of MOF interfaces and highlighted the need to better understand and characterize the nature of the sites found on the external surface, and Bradshaw et al. [93] focused on composite MOFs. Both reviews emphasized the need for input from computer modeling, which is the focus of some current work [B. Slater, unpublished results]. Chizallet et al. [94,95] have demonstrated through computational studies complemented by experimental data, especially IR, that the external surface of MOFs could act as a potent catalyst. There is still a debate about the structure of MOF surfaces, but work by Anderson and Attfield and co-workers [96–100] has provided clear evidence of the structure of, for example, ZIF-8. In Ref. [100], by performing time-resolved in situ AFM, it was shown that by comparing height differences measured from AFM for the ZIF-8 structure, the structure which persisted for longest under activated conditions must be terminated by low coordinate metal sites–this is a very important result. Knowing the terminating structure at surface is essential if, for example, post synthetic functionalization of the surface is to be achieved. Of course, the terminating structure may well depend on the solvent, the reagents and the physical conditions under which the MOF is synthesized. Similarly, substrates can be used to select which face of a MOF grows in order to create oriented self-assembled mono or multilayers of MOF films. Since MOFs are notionally two-component materials, i.e. containing metal and some organic based links, at the simplest level, the terminating structure could contain under-coordinated metals of low coordination and/or under-coordinated organic linker functionalities. However, the organic link itself may contain bonding of very varied strengths, suggesting that it could expose different terminating structure. As already discussed, Attfield et al. showed that ZIF-8 terminates with low coordinate zinc ions. In reality, those zinc ions are likely passivized by solvent ligand, neutral HMeIm (where MeIm is methyl imidazolate) units or negatively charged MeIm units, but there is no experimental evidence to indicate whether one or all of these units are present at the surface. By inference from Attfield's AFM work, it seems likely that solvent or neutral HMeIm units decorate the surface since the negatively charged MeIm units would form a strong bond with the zinc which would provide strong resistance to the AFM tip. It is interesting now to examine the first example of imaging a MOF surface, CAT-1 shown in Figure 25. From this image, the surface structure is deduced to contain both low coordinate metal and under-coordinated oxygen but no uncoordinated functionality of the organic ligand. The particle itself is, in the absence of point defects, likely to be charge neutral. If one imagines tearing apart a MOF material into two pieces, the weakest bonds will break first and these are likely to be the bonds from the metal to the organic linker. Three possible structural outcomes are possible from physically cleaving the MOF crystal to yield two pieces of MOF: One piece is entirely terminated by low-coordinate metal ions whilst the other piece is terminated by links of under-coordinated functionalities. Equal numbers of low-coordinated metal and under-coordinated functionalities are present on both pieces. Unequal numbers of both of these are present on both pieces. 2 and 3 are expected to be more plausible than outcome 1, since that results in two charged and hence unstable pieces that would require passivation by a solvent or some other chemisorbed species. Outcome 3 results in partially charged pieces that again require passivation. Outcome 2 results in charge neutral pieces and is expected to be most thermodynamically stable in the absence of solvent effects. In the first direct imaging of a MOF surface, CAT-1, it appears outcome 2 arises. However, Attfield's results suggest outcome 1. In the case of ZIF-8, this leaves open the question of what happens to the positive charge on the zinc terminated structure–presumably it has chemisorbed solvent or mother-liquor species bound to it to help stabilize the cationic surface. Another possibility is that the residual positive charge may partially delocalize within the structure. Calculations to investigate the atomic structure and electronic structure of the surface will help to shed light on the complex nature of the MOF surface. We speculate here that solvent and solvent polarity may play a role in stabilizing a particular MOF surface structure. Surface selective structural details by SEM and AFM Achieving nanometre resolution of insulating, fragile materials employing low voltage SEM Usually, magnetic lenses are used in modern SEM. The typical trajectory of an electron (ray path) is illustrated in Figure 30a. Here, a magnetic lens changes the electron trajectory, and forms small electron probes on a sample. When a bias voltage is applied to the specimen substrate, an electrostatic field is produced between the magnetic lens and substrate. This electrostatic field constitutes a bi potential lens, which is a convex lens for electrons. This lens works for both impact electrons to the sample and outgoing electrons from the specimen. Furthermore, this lens decelerates impact electrons to the specimen and accelerates outgoing electrons from the specimen. A typical ray path with the substrate bias is illustrated in Figure 30b. As shown here, by the electrostatic field, focal length can be significantly shorter with substrate bias than without it. Generally, shorter focal length makes chromatic and spherical aberrations smaller. A lens using both electrostatic field and magnetic field is known as an electromagnetic lens, which was first introduced by Rau [101]. Several others also realized electromagnetic lenses using various methods [102–105]. In addition, the substrate bias also improves efficiency in collecting BSEs and SEs. Without strong electrostatic field between a magnetic lens and a substrate generated by substrate bias, trajectory of BSE is rather straight, which makes most BSEs not going into SEM column (Figure 30c). Thus, a conventional high efficiency BSE detector should be placed between a substrate and a magnetic lens (Figure 30c), making both the working distance and the focal length long, and degrading the diameter of primary beam. In addition, the detection efficiency of the conventional BSE detector significantly decreases at low acceleration voltage, which makes detection of low energy BSEs difficult. The substrate bias change trajectory of BSE: trajectory is almost parabolic near the substrate, and directions of BSEs are modified to upwards, making them go into the SEM column (Figure 30d). In addition, these BSEs are accelerated by the electric field, which makes detection of these BSEs easy. These enable detection of BSE inside the column with a shorter working distance and a small diameter of primary beam even at low landing energy of impact electrons. Thus we have overcome traditional problems in BSE. Fig. 30. View largeDownload slide Trajectories of primary electrons (ray paths) and trajectories of signal electrons. Ray paths of primary electrons without substrate bias (a) and with substrate bias (b). Focal length of primary electrons is significantly shorter for (b) than for (a). Trajectories of backscattered electrons (BSEs) without substrate bias (c) and with substrate bias (d). Trajectories of secondary electrons (SEs) and BSEs with substrate bias and grid bias (e). The grid separates electrons to UED or USD depending on their kinetic energies larger or smaller than the Grid-bias voltage, respectively. Fig. 30. View largeDownload slide Trajectories of primary electrons (ray paths) and trajectories of signal electrons. Ray paths of primary electrons without substrate bias (a) and with substrate bias (b). Focal length of primary electrons is significantly shorter for (b) than for (a). Trajectories of backscattered electrons (BSEs) without substrate bias (c) and with substrate bias (d). Trajectories of secondary electrons (SEs) and BSEs with substrate bias and grid bias (e). The grid separates electrons to UED or USD depending on their kinetic energies larger or smaller than the Grid-bias voltage, respectively. Furthermore, some of the equipment has an energy filter (Grid) inside the column. Instruments we used are JSM-7800F and JSM-7100F TTL (JEOL Ltd.) which have an upper electron detector (UED) and an upper secondary electron detector (USD) inside a SEM column as well as a lower electron detector (LED) outside of the column (Figure 30e). Between UED and USD, a grid is placed, which allows simultaneous detection of energy selected electrons at low landing energy of primary electron, as well as traditional SE detection using LED: the grid works as a high pass filter for UED so that mainly BSEs with high energy can be selectively detected with UED, and SEs with low energy can be reflected by the grid so that USD can mainly detect SEs. These supply not only endurance for charging but also various kinds of information. One example of utilizing such a detecting system is shown in Figure 31, where the two micrographs are taken with the same landing and primary electron energy. The detection system allows simultaneous detection of SE using USD, producing topographic contrast, and BSEs producing Z (atomic number) contrast using UED. Grid bias voltage and substrate bias voltage select the energies and angles of electrons, which can be detected by UED and USD. This allows further tuning of the contrasts. The yolk-shell materials imaged contain hemispherical shells made of carbon and catalyst particles made of gold (Au@Carbon). This structure allows efficient stabilization of the metallic cores at high temperature conditions, while maintaining high catalytic activity. The high structural and compositional definition of yolk-shell particles make these kinds of material ideally suited for studies in heterogeneous catalysis [106–109]. Fig. 31. View largeDownload slide Electron energy selected images of Au@Carbon with different grid bias. (a) grid bias = −0.6 kV and (b) grid bias = −1.49 give information obtained close to that of SE and BE. Therefore (a) and (b) give topographic and elemental (Z-contrast) information, respectively. The gold particle is highlighted by bright contrast in (b). Conditions: JSM-7800F (JEOL Ltd.) primary electron energy = 1.0 keV; specimen bias = 500 V; electron beam current: 63 pA. Fig. 31. View largeDownload slide Electron energy selected images of Au@Carbon with different grid bias. (a) grid bias = −0.6 kV and (b) grid bias = −1.49 give information obtained close to that of SE and BE. Therefore (a) and (b) give topographic and elemental (Z-contrast) information, respectively. The gold particle is highlighted by bright contrast in (b). Conditions: JSM-7800F (JEOL Ltd.) primary electron energy = 1.0 keV; specimen bias = 500 V; electron beam current: 63 pA. It is possible to obtain clear images at high magnification with substrate bias as shown in Figure 32. The landing energy is so low that the detected information only comes from the very surface of the material, and thus the topographic feature is highly enhanced. Together with the enhanced the topography is the weakened Z contrast, which can be seen by the similar brightness from the gold particle and the carbon shell. In principle some contrast should be observed due to the different energy-dependency of the secondary electron yield for different elements. However the unavoidable contamination inside the SEM would cover the surface with a layer whose thickness becomes non-negligible at low landing energies. Fig. 32. View largeDownload slide High-resolution image of the Au@Carbon, with the Au particle marked by arrow. Conditions: Landing energy = 0.3 keV; Specimen bias = 5.0 kV. Fig. 32. View largeDownload slide High-resolution image of the Au@Carbon, with the Au particle marked by arrow. Conditions: Landing energy = 0.3 keV; Specimen bias = 5.0 kV. Crystal growth from surface structure by AFM and HRSEM Studies on the growth of crystals have been carried out for a quite long time. Knowing the nanoscopic structural detail is vital to understand not only how crystals grow perfectly, but also, more importantly for today's applications, (i) how crystal growth goes wrong and defects are incorporated, or (ii) how crystals switch growth mode at the unit cell scale forming crystal intergrowths that could ultimately be controlled at this scale thereby fashioning crystals with multiple functionality. In the last 10 years crystal growth studies have been transformed with the development of scanning probe microscopies that, for the first time, permit in situ observation of molecular details in solution under growth conditions. Scanning tunnelling microscopy (STM) readily achieves atomic resolution but usually under high vacuum conditions and requires conducting samples. In order to observe processes under solution conditions, on any crystal type, AFM is the technique of choice. This technique readily achieves Ångstrom vertical resolution and nanometer lateral resolution that is ideal for observing terrace growth at crystal surfaces as the terraces reflect a similar aspect ratio. However, it is also possible to achieve true atomic resolution, and indeed sub-atomic resolution, by careful choice of cantilever and operation of the microscope. Ultimately AFM has superior lateral resolution to STM, although achieving this under solution conditions is at the forefront of current technology and needs considerable development. As a consequence of these and other breakthroughs in technology (for example HRSEM), it is now possible to map precisely how crystals develop with the prospect of creating designer crystals honed precisely to end user requirements. M. Anderson et al. reported the first use of AFM to study the growth mechanism in a zeolite [110]. Since that first publication we have been developing a methodology that uses a variety of techniques in order to probe the rather complex train of events during the crystallization of a nanoporous material. The approach combines both experimental and theoretical methods. Experimentally it is crucial to follow both solution speciation as well as the development of the solid-state phase. The solution speciation has been targeted by a combination of mass spectrometry (MS) and NMR [111–113]. These techniques are complementary with MS, delivering fast temporal identification of solution species with limited speciation resolution, and with NMR, providing accurate speciation identification at the expense of a longer spectral collection time. Together these techniques can disentangle the rather complex solution chemistry of oxide precursors. Development of the solid, crystalline phase can then be studied by a combination of HRTEM, HRSEM and AFM. HRTEM is used to identify the termination structure at the crystal surface and the type and number of internal defect structures [57]. Understanding the incorporation of defects is critical for the understanding of crystal growth as any model developed must be able to account not only for the regular crystal structure but also for the inclusion of well-defined defects. In framework structures the defect signatures are particularly varied and unique to different crystal systems and consequently act as very important guides to the growth process. We have also been developing HRSEM such that we are the first team to demonstrate that it is possible to observe sub-nanometer growth features at the surface of non-conducting framework materials without having to coat the surface with a conducting film [6,114–116]. We have demonstrated by using a combination of HRSEM and AFM on the same crystals that any electron beam damage is confined to sub-surface layers and therefore does not interfere with delicate surface structures [116]. Figure 33b shows both HRSEM and AFM measurements taken on the same crystal (zeolite A, LTA) and in the same place on the crystal, grey image is the HRSEM and orange image AFM (quite a technical achievement). This allows us to rapidly screen complex crystal surfaces that may be twinned or highly inter grown and rather difficult to tackle by AFM. Another advantage of this technique over AFM is the enhanced lateral resolution achieved at terrace edges, which is superior using HRSEM. This technique is, therefore, a key input for the modeling studies that simulate details of surface structure. We have also demonstrated, for the first time, that by slicing micron-sized crystals with an Ar ion beam that it is then possible using HRSEM to observe internal faulting structures that hold clues to the crystal growth history [117,118]. Fig. 33. View largeDownload slide AFM images of: (a) interlaced spiral on aluminophosphate STA-7; (b) zeolite A, LTA, recorded by both AFM and HRSEM; (c) Monte Carlo simulation of LTL; (d) in-situ ZnPO4 growth FAU structure; (e) exothermic nano-chemistry highlighted by lateral force microscopy on ZnPO4 with SOD structure; (f and g) in situ dissolution zeolite LTL. Fig. 33. View largeDownload slide AFM images of: (a) interlaced spiral on aluminophosphate STA-7; (b) zeolite A, LTA, recorded by both AFM and HRSEM; (c) Monte Carlo simulation of LTL; (d) in-situ ZnPO4 growth FAU structure; (e) exothermic nano-chemistry highlighted by lateral force microscopy on ZnPO4 with SOD structure; (f and g) in situ dissolution zeolite LTL. However, AFM is the most versatile and powerful technique for exploring crystal growth from a solution environment and we have been at the forefront developing the full potential of this tool [59,99,110,119,120]. Nanoporous materials grow in environments from quite mild and benign to extremely aggressive. In the extreme this ranges from near room temperature in an aqueous pH 7 or simple organic solvent environment at one atmosphere pressure to in excess of pH 13, 220°C and tens of atmospheres pressure. In order to cover this complete range of conditions for AFM measurement we have developed a dual strategy. For conditions of temperature and pressure inaccessible to the AFM crystals are prepared offline but carefully quenched in order to preserve surface structure. The AFM is then performed on crystals in an ex situ manner. This strategy gives the greatest flexibility in terms of structure and conditions; however, some very rapid and crucial steps can be lost during the quenching step. Therefore, where possible, in situ studies are preferred. We have shown that some systems are particularly amenable to in situ study, including most metal-organic framework (MOF) systems, zinc phosphate analogues of aluminosilicate framework structures, and dissolution rather than growth studies of aluminosilicates [59,97,98,121–123]. Figure 33 illustrates some of the power of AFM to tackle crystal growth problems and all these illustrate firsts within the field: a movie of a Frank-Reed Dislocation Loop on ZIF-8; a movie of a Spiral and Birth-and-Spread Growth on ZIF-8; a movie of interlaced spiral growth on zincophosphate (SOD) [101]; a movie of multiple interlaced spiral growth on zincophosphate (SOD) [101]; a movie of spiral birth-and-spread growth on zincophosphate (SOD) [112]; a movie of zeolite A dissolution; a movie of zeolite L dissolution with lateral deflection highlighting chemistry; a movie of birth-and-spread growth on zincophosphate (FAU) [112]; and a movie of anisotropic friction and growth highlighted in lateral force (ZnPO-SOD). A particularly important recent publication [59] has further demonstrated that the nanoscopic region where chemical activity is taking place can be directly targeted and highlighted by monitoring the energy imparted from the crystal surface to the AFM tip during a local exothermic or endothermic process (see Figure 33e). This is a tremendous breakthrough and is a general phenomenon that we have now observed across many crystal systems. This offers tremendous potential to delineate the different energetics at different growth sites discerned at the nanoscale. The same paper also shows, for the first time, extraction of accurate activation energies for specific nanoscopic processes during the chemical transformation of a zeolite surface. Until now it has only been possible to determine activation energies for bulk (average) crystal growth phenomena experimentally. Having access to activation energies for specific processes gives the possibility to turn some processes off or on selectively. Such control is exactly what is required in order to tune defect structures and defect concentration, intergrowth structures and ultimately gross morphological change such as in the production of single crystal thin films. In a recent paper [59] we made an exciting discovery with enormous potential ramifications for crystal growth studies in general. The AFM works by tracking a sharp needle (tip) across a surface with atomic precision thereby tracking the surface topography–essentially creating a topographic map where the contours can be measured in nanometers. The force between this tip and the surface can be controlled to nano-Newtons and we were aware that, depending on the force, the tip could play a role in the crystal growth process. In usual operation we try to eliminate this contribution from the tip so that we reveal the underlying fundamental crystal growth process. However, we showed recently that it is possible to use the tip in a proactive manner to unstitch the crystal, nanoscopic-unit by nanoscopic-unit. As each unit is decoupled from the crystal there is an associated energy that is imparted to the AFM tip and can be measured. Further, the persistence of each unit before it is decoupled gives a measurement of the stability of the unit. It is somewhat akin to the use of AFM to unfold proteins via ‘nano-fishing’ and extracting the associated energies [124], which has revolutionized the study of protein folding. So now we have available a technique that can probe all the individual sub-steps in a crystal growth process and should be applicable across all crystal classes. The paper also describes in detail a coarse-grained Monte Carlo approach to the modeling of zeolite L growth that accurately predicts, for the first time, crystal habit, aspect ratio and surface structure in terms of energies of attachment and supersaturation (see 2D and 3D movies). This permits both the calculation of meta-stable local-equilibrium crystal shapes and surface structures as well as the effect of raised or lowered supersaturation. Consequently, we can now follow the course of a crystallization from high supersaturation, monitoring habit and surface topography by HRSEM and AFM, through to near equilibrium, and model the process in order to extract the relevant crystal attachment energies. At present the computer codes that have been developed in Manchester are hard-wired to specific crystal systems, such as zeolite A; however, we are now developing general algorithms for any crystal system. Concluding remarks Electron microscopy approaches have been developed not only for studying the three-dimensionally periodic average structures of crystals, but also for characterizing various structural modulations inside crystals from their average structures. In particular, the techniques offer a powerful means of identifying the microscopic details at the termination of the crystal surface. Theoretical models have been employed for studying the incommensurate modulation and the structure transformation in zeolite SSZ-24, and also for studying the formation of mesoporous silica with dodecagonal quasicrystalinity and morphology. Surface topological information, localization of metal nanoparticles in nanoporous materials and direct observation of pore-openings of MOF are successfully shown by developing low voltage HRSEM, which is especially powerful for observing surface features of non-conducting materials without coating surface with conducting particles. Direct observations of pore arrangements, defects and EELS have successfully shown for the first time from very electron beam sensitive MOFs, which will give invaluable information of designing novel MOFs. Crystal growth processes have been elucidated in a scale of building units of nanoporous crystals by combining AFM and HRSEM measurements on the same crystal and in the same place on the crystal. It has been shown that nanoscopic region where chemical activity is taking place is directly targeted and that an associated energy to unstitch a building unit of crystal (zeolite L) has been imparted to the AFM tip, which gives a measurement of the stability of the unit. As a whole, the power and importance of microscopy for the structural study of nanoporous materials have been exhibited. Abbreviations  AED: automated electron diffraction. AFM: atomic force microscope. bcc: body centered cubic. CAT: metal catecholate. COF: covalent organic framework. CSDA: co-structure directing agent. CSF: crystal structure factor. DOT: dioxidoterephthalate. D4R: double 4 ring. EC: electron Crystallography. ED: electron diffraction. EDT: electron diffraction tomography. EELS: electron energy loss spectroscopy. EM: electron microscopy. fcc: face centered cubic. FD: fourier diffraction. FFT: fast Fourier transformation. FT: fourier transformation. hcp: hexagonal closest pack. HHTP: hexahydroxytriphenylene. HRTEM: high resolution transmission electron microscopy. IS: isopotential surface. LLC: lyotropic liquid crystal. MOF: metal organic framework. MS: mass spectrometry. NMR: nuclear magnetic resonance. PES: precession electron diffraction. RUM: rigid-unit mode. SDA: structure directing agent. SEM: scanning electron microscope. SMC: silica mesoporous crystal. SN: signal-to-noise. STEM: scanning transmission electron microscope. S4R: single 4 ring. TEM: transmission electron microscope. TEOS: tetraethoxysilane. XRD: X-ray diffraction. ZIF: zeoliticimidazolate framework. 3D: three dimensional. Funding This work is supported by JST (Japan), VR, Knut and Alice Wallenberg Foundation, Berzelii EXSELENT (Sweden) and WCU (R-31-2008-000-10055-0, Korea). Acknowledgements We thank Professors Omar M. Yaghi, Ferdi Schüth, Shunai Che, Tetsu Ohsuna, Kazu Suenaga, Jaheon Kim and Dr Carolina Galeano for helpful discussions and supplying samples, and John C.H. Spence and Kenneth Harris for critical reading and comments. References 1 Ugurlu O,  Haus J,  Gunawan A A,  Thomas M G,  Maheshwari S,  Tsapatsis M,  Mkhoyan K A.  Radiolysis to knock-on damage transition in zeolites under electron beam irradiation,  Phys. Rev. B ,  2011, vol.  83 (pg.  113408- 113412) Google Scholar CrossRef Search ADS   2 Henderson R.  The potential and limitations of neutrons, electrons and X-rays for atomic resolution microscopy of unstained biological molecules,  Quarterly Reviews of Biophysics ,  1995, vol.  28 (pg.  171- 193) Google Scholar CrossRef Search ADS PubMed  3 Egerton R F.  Radiation damage in the TEM and SEM,  Micron ,  2004, vol.  35 (pg.  399- 409) Google Scholar CrossRef Search ADS PubMed  4 Jiang N,  Spence J. CH.  On the dose-rate threshold of beam damage in TEM,  Ultramicroscopy ,  2012, vol.  113 (pg.  77- 82) Google Scholar CrossRef Search ADS   5 Hibbe F,  Chmelik C,  Heinke L,  Pramanik S,  Li J.  Tzoulaki D,  Körgen J.  M, R. D. The Nature of Surface Barriers on Nanoporous Solids Explored by Microimaging of Transient Guest Distributions,  J. Am. Chem. Soc. ,  2011, vol.  133 pg.  2804  Google Scholar CrossRef Search ADS PubMed  6 Stevens S M,  Jansson K,  Xiao X,  Asahina S,  Klingstedt M,  Grüner D,  Sakamoto Y,  Miyasaka K,  Cubillas P,  Brent R,  Han L,  Che S,  Ryoo R,  Zhao D,  Anderson M W,  Schüth F,  Terasaki O.  An Appraisal of High Resolution Scanning Electron Microscopy Applied To Porous Materials,  JEOL News ,  2009, vol.  44 pg.  17  7 Tauelle F.  Fundamentals principles of NMR crystallography,  Encyclopedia of Magnetic Resonance ,  2009 8 Spence J. CH,  Carpenter R W.  Electron microdiffraction,  Principles of analytical electron microscopy ,  1992 New York Plenum Press 9 McKeown J T,  Spence J. CH.  The kinematic convergent-beam electron diffraction method for nanocrystal structure determination,  J. Appl. Phys. ,  2009, vol.  106 pg.  074309  Google Scholar CrossRef Search ADS   10 Watanabe D,  Uyeda R,  Fukuhara A.  Determination of the atom form factor by high-voltage electron diffraction,  Acta Crysta. A ,  1969, vol.  25 pg.  138  Google Scholar CrossRef Search ADS   11 Fujimoto M,  Terasaki O,  Watanabe D.  Determination of atomic scattering factors of vanadium and chromium by means of vanishing Kikuchi line method,  Phys. Lett. ,  1972, vol.  41A (pg.  159- 160) Google Scholar CrossRef Search ADS   12 Terasaki O,  Watanabe D,  Gjonnes J.  Determination of crystal structure factors of Si by the intersecting-Kikuchi-line method,  Acta Cryst. A ,  1979, vol.  A35 (pg.  895- 900) Google Scholar CrossRef Search ADS   13 Doyle P A,  Turner P S.  Relativistic Hartree-Fock X-ray and electron scattering factors,  Acta Crystallogr. Sect. A ,  1968, vol.  24 (pg.  390- 397) Google Scholar CrossRef Search ADS   14 Weiss R J,  J D. J.  X-Ray Determination of the 3d-Orbital Population in Vanadium Metal,  Phys. Rev. A ,  1965, vol.  140 (pg.  1223- 1225) Google Scholar CrossRef Search ADS   15 Azaroff L V. ,  X-ray diffraction ,  1974 McGraw; Hill 16 Terasaki O,  Fukamachi T,  Hosoya S.  Anisotropy of Compton profile on vanadium single crystal,  Phys. Lett. A ,  1973, vol.  43 (pg.  123- 124) Google Scholar CrossRef Search ADS   17 Zuo J M,  Kim M,  O'Keeffe M,  Spence J. CH.  Direct observation of d-orbital holes and Cu–Cu bonding in Cu2O,  Nature ,  1999, vol.  401 (pg.  49- 52) Google Scholar CrossRef Search ADS   18 Tsuda K,  Ogata Y,  Takagi K,  Hashimoto T,  Tanaka M.  Refinement of crystal structural parameters and charge density using convergent-beam electron diffraction - the rhombohedral phase of LaCrO3,  Acta Cryst. A ,  2002, vol.  A58 (pg.  514- 525) Google Scholar CrossRef Search ADS   19 Boris K V. ,  Modern Crystallography 1: Fundamentals of Crystals. Symmetry, and Methods of Structural Crystallography, ,  1994 New York Springer Verlag Heidelberg 20 Spence J. CH. ,  High-resolution Electron Microscopy, ,  2003 New York Oxford University Press Inc. 21 Vainshtein B K. ,  Structure Analysis by Electron Diffraction ,  1964 Pergamon Press 22 Carlsson A,  Kaneda M,  Sakamoto Y,  Terasaki O,  Ryoo R,  Joo S H.  The structure of MCM–48 determined by electron crystallography,  J. Electron Microsc. ,  1999, vol.  48 (pg.  795- 798) Google Scholar CrossRef Search ADS   23 Sakamoto Y,  Kaneda M,  Terasaki O,  Zhao D Y,  Kim J M,  Stucky G,  Shim H J,  Ryoo R.  Direct imaging of the pores and cages of three-dimensional mesoporous materials,  Nature ,  2000, vol.  408 (pg.  449- 453) Google Scholar CrossRef Search ADS PubMed  24 Garcia-Bennett A E,  Terasaki O,  Che S,  Tatsumi T.  Structural Investigations of AMS-n Mesoporous Materials by Transmission Electron Microscopy,  Chem. Mater. ,  2004, vol.  16 (pg.  813- 821) Google Scholar CrossRef Search ADS   25 Che S,  Liu Z,  Ohsuna T,  Sakamoto K,  Terasaki O,  Tatsumi T.  Synthesis and characterization of chiral mesoporous silica,  Nature ,  2004, vol.  429 (pg.  281- 284) Google Scholar CrossRef Search ADS PubMed  26 Garcia-Bennett A E,  Miyasaka K,  Terasaki O,  Che S.  Structural Solution of Mesocaged Material AMS-8,  Chem. Mater. ,  2004, vol.  16 (pg.  3597- 3605) Google Scholar CrossRef Search ADS   27 Gao C,  Sakamoto Y,  Sakamoto K,  Terasaki O,  Che S.  Synthesis and Characterization of Mesoporous Silica AMS-10 with Bicontinuous Cubic Pn-3m Symmetry,  Angew. Chem. Int. Ed. ,  2006, vol.  45 (pg.  4295- 4298) Google Scholar CrossRef Search ADS   28 Huo Q,  Leon R,  Petroff P M,  Stucky G D.  Mesostructure Design with Gemini Surfactants: Supercage Formation in a Three-Dimensional Hexagonal Array,  Science ,  1995, vol.  268 (pg.  1324- 1327) Google Scholar CrossRef Search ADS PubMed  29 Miyasaka K,  Han L,  Che S,  Terasaki O.  A Lesson from the Unusual Morphology of Silica Mesoporous Crystals: Growth and Close Packing of Spherical Micelles with Multiple Twinning,  Angew. Chem. ,  2006, vol.  118 (pg.  6666- 6669) Google Scholar CrossRef Search ADS   30 Miyasaka K,  Terasaki O.  Self-Consistent Structural Solution of Mesoporous Crystals by Combined Electron Crystallography and Curvature Assessment,  Angew. Chem. Int. Ed. ,  2010, vol.  49 (pg.  9051- 9055) Google Scholar CrossRef Search ADS   31 Helfrich W.  Elastic properties of lipid bilayers: theory and possible experiments,  Naturforsch ,  1973, vol.  C28 (pg.  693- 703) 32 Safran S A.  Curvature elasticity of thin films,  Advances in Physics ,  1999, vol.  48 (pg.  395- 448) Google Scholar CrossRef Search ADS   33 Miyasaka K,  Garcia-Bennett A E,  Han L,  Han Y,  Xiao C,  Fujita N,  Castle T,  Sakamoto Y,  Che S,  Terasaki O.  The role of curvature in silica mesoporous crystals,  Interface Focus ,  2012, vol.  2 (pg.  634- 644) Google Scholar CrossRef Search ADS PubMed  34 Jinnai H,  Nishikawa Y,  Spontak R J,  Smith S D,  Agard D A,  Hashimoto T.  Direct Measurement of Interfacial Cruvature Distributions in a Bicontinuous Block Copolymer Morphology,  Phys. Rev. Lett. ,  2000, vol.  84 (pg.  518- 521) Google Scholar CrossRef Search ADS PubMed  35 Lund K,  Muroyama N,  O T.  Accidentalextinction in powder XRD intensity of porous crystals: Mesoporous carbon crystal CMK-5 and layered zeolite-nanosheets,  Micro. Meso. Mater. ,  2010, vol.  128 (pg.  71- 77) Google Scholar CrossRef Search ADS   36 Choi M,  Na K,  Kim J,  Sakamoto Y,  Terasaki O,  R R.  Stable single-unit-cell nanosheets of zeolite MFI as active and long-lived catalysts,  Nature ,  September 2009, vol.  461 (pg.  246- 249) Google Scholar CrossRef Search ADS   37 Dorset L D. ,  Structure Electron Crystallography. ,  1995 NY Plenum Press 38 Nicolopoulos S,  Gonzalez-Calbet J M,  Vallet-Regi M,  Camblor M A,  Corell C,  Corma A,  Diaz-Cabanas M J.  Use of Electron Microscopy and Microdiffraction for Zeolite Framework Comparison,  J. Am. Chem. Soc. ,  1997, vol.  119 (pg.  11000- 11005) Google Scholar CrossRef Search ADS   39 Wagner P,  Terasaki O,  Ritsch S,  Nery J G,  Zones S I,  Davis M E,  Hiraga K.  Electron Diffraction Structure Solution of a Nanocrystalline Zeolite at Atomic Resolution,  J. Phys. Chem. ,  1999, vol.  B103 (pg.  8245- 8250) Google Scholar CrossRef Search ADS   40 Vincent R.  A, M. P Double conical beam-rocking system for measurement of integrated electron diffraction intensities,  Ultramicroscopy ,  1994, vol.  53 (pg.  271- 282) Google Scholar CrossRef Search ADS   41 Xiaodong Z,  Hovmöller S,  Oleynikov P. ,  Electron Crystallography, ,  2011 New York Oxford University Press Inc. 42 Kolb U,  Gorelik T,  Kubel C,  Otten M T,  Hubert D.  Towards automated diffraction tomography: Part I—Data acquisition,  Ultramicroscopy ,  2007, vol.  107 (pg.  507- 513) Google Scholar CrossRef Search ADS PubMed  43 Kolb U,  Gorelik T,  Otten M T.  Towards automated diffraction tomography. Part II—Cell parameter determination,  Ultramicroscopy ,  2008, vol.  108 (pg.  763- 772) Google Scholar CrossRef Search ADS PubMed  44 Miao J,  Ohsuna T,  Terasaki O,  O'Keefe M A.  Atomic Resolution Three-Dimensional Electron Diffraction Microscopy,  Phys. Rev. Letters ,  2002, vol.  89 pg.  155502  Google Scholar CrossRef Search ADS   45 Gramm F,  Baerlocher C,  McCusker L B,  Warrender S J,  Wright P A,  Han B,  Hong S B,  Liu Z,  Ohsuna T,  Terasaki O.  Complex zeolite structure solved by combining powder diffraction and electron microscopy,  Nature ,  2006, vol.  444 (pg.  79- 81) Google Scholar CrossRef Search ADS PubMed  46 Baerlocher C,  Gramm F,  Massüger L,  McCusker L B,  He Z B,  Hovmöller S,  Zou X D.  Structure of the polycrystalline zeolite catalyst IM-5 solved by enhanced charge flipping,  Science ,  2007, vol.  315 (pg.  1113- 1116) Google Scholar CrossRef Search ADS PubMed  47 Baerlocher C,  Xie D,  McCusker L B,  Hwang S J,  Chan I Y,  Ong K,  Burton A W,  Zones S I.  Ordered silicon vacancies in the framework structure of the zeolite catalyst SSZ-74,  Nature Mater. ,  2008, vol.  7 (pg.  631- 635) Google Scholar CrossRef Search ADS   48 Sun J L,  Bonneau C,  Cantín Á,  Corma A,  Díaz-Cabañas M J,  Moliner M,  Zhang D L,  Li M R,  Zou X D.  The ITQ-37 mesoporous chiral zeolite,  Nature ,  2009, vol.  458 (pg.  1154- 1157) Google Scholar CrossRef Search ADS PubMed  49 Newsam J M,  Treacy M.  Structural Characterization of Zeolite Beta,  Proc. R. Soc. London ,  1988, vol.  420 (pg.  375- 405) Google Scholar CrossRef Search ADS   50 Liu Z,  Ohsuna T,  Terasaki O,  Camblor M A,  Diaz-Cabañas M J.  K, H The first zeolite with three-dimensional intersecting straight-channel system of 12-membered rings,  J. Am. Chem. Soc. ,  2001, vol.  123 (pg.  5370- 5371) Google Scholar CrossRef Search ADS PubMed  51 International Union of Crystallography ‘Report of the Executive Committee for 1991’,  Acta Cryst. A ,  1992, vol.  A48 (pg.  922- 946) 52 Díaz-Cabañasa M J,  Camblor M A,  Liu Z,  Ohsuna T,  Terasaki O.  Zeolite syntheses using linear diquats of varying length in fluoride media. The synthesis of ITQ-8, ITQ-10, ITQ-14 and high silica Nu-87,  J. Mater. Chem. ,  2002, vol.  12 (pg.  249- 257) Google Scholar CrossRef Search ADS   53 Baram P S,  Parker S C.  Atomistic simulation of hydroxide ions in inorganic solids,  Philosophical Magazine B - Physics of Condensed Mattr Statistical Mechanics Electronic Optical and Magnetic Properties ,  1996, vol.  73 (pg.  49- 58) 54 Loades S,  Carr S,  Gay D,  Rohl A.  Calculations of the morphology of silica sodalite,  Chem. Commun ,  1994(pg.  1369- 1370) 55 Whitmore L,  Slater B,  Catlow C.  RA Adsorption of benzene at the hydroxylated (111) external surface of faujasite,  Phys. Chem. Chem. Phys. ,  2000, vol.  2 (pg.  5354- 5356) Google Scholar CrossRef Search ADS   56 Rançon Y,  Charvolin J.  Epitaxial Relatlonships during Phase Transformations in a Lyotropic Liquid Crystal,  J. Phys. Chem. ,  1988, vol.  92 (pg.  2646- 2651) Google Scholar CrossRef Search ADS   57 Combariza A F,  Sastre G.  Influence of zeolite surface in the sorption of methane from molecular dynamics,  J. Phys. Chem. C ,  2011, vol.  115 (pg.  13751- 13758) Google Scholar CrossRef Search ADS   58 Slater B,  Catlow C R A,  Liu Z,  Ohsuna T,  Terasaki O,  Camblor M A.  Surface structure and crystal growth of zeolite Beta C,  Angew. Chem. Int. Ed. ,  2002, vol.  41 (pg.  1235- 1237) Google Scholar CrossRef Search ADS   59 Brent R,  Cubillas P,  Stevens S M,  Jelfs K E,  Umemura A,  Gebbie J T,  Slater B,  Terasaki O,  Holden M A,  Anderson M W.  Unstitching the Nanoscopic Mystery of Zeolite Crystal Formation,  J. Am. Chem. Soc. ,  2010, vol.  132 (pg.  13858- 13868) Google Scholar CrossRef Search ADS PubMed  60 Chiu M E,  Slater B,  Gale J D.  Simulating the dissolution and growth of zeolite beta C,  Angew. Chem. Int. Ed. ,  2005, vol.  44 (pg.  1213- 1217) Google Scholar CrossRef Search ADS   61 Ojo S A,  Whitmore L,  Slater B,  Catlow C.  RA Understanding nucleation and growth using computer simulation,  Solid State Sciences ,  2001, vol.  3 (pg.  821- 826) Google Scholar CrossRef Search ADS   62 Ohsuna T,  Slater B,  Gao F,  Yu J,  Sakamoto Y,  Zhu G,  Terasaki O,  Vaughan D E,  Qiu S,  Catlow C R.  Fine structures of zeolite Linde-L (LTL): Surface structures, growth unit and defects,  Chemistry ,  2004, vol.  10 (pg.  5031- 5040) Google Scholar CrossRef Search ADS PubMed  63 Slater B,  Titiloye J O,  Higgins F M,  Parker S C.  Atomistic simulation of zeolite surfaces,  Current Opinion in Solid State & Materials Science ,  2001, vol.  5 (pg.  417- 424) Google Scholar CrossRef Search ADS   64 Slater B,  Gale J D,  Catlow C.  Ohsuna T,  Terasaki O.  RA Surface structure determination of zeolites,  Recent Advances in the Science and Technology of Zeolites and Related Materials Pts a-c ,  2004, vol.  154 (pg.  1197- 1203) 65 Slater B,  Ohsuna T,  Liu Z,  Terasaki O.  Insights into the crystal growth mechanisms of zeolites from combined experimental imaging and theoretical studies,  Faraday Discussions ,  2007, vol.  136 (pg.  125- 141) Google Scholar CrossRef Search ADS PubMed  66 Bialek R,  Meier W M,  Davis M,  J A M.  The synthesis and structure of SSZ-24, the silica analog of AIPO4-5,  Zeolites ,  1991(pg.  438- 442) 67 Liu Z,  Fujita N,  Terasaki O,  Ohsuna T,  Hiraga K,  Camblor M A,  Diaz-Cabanas MJ,  K C A.  Incommensurate Modulation in the Microporous Silica SSZ-24,  Chemistry - A European Journal ,  2002(pg.  4549- 4556) 68 Xiao C,  Fujita N,  Miyasaka K,  Sakamoto Y,  Terasaki O.  dodecagonal tiling in mesoporous silica,  Nature ,  2012, vol.  487 (pg.  349- 353) Google Scholar CrossRef Search ADS PubMed  69 Che S,  Garcia-Bennett A E,  Yokoi T,  Sakamoto K,  Kunieda H,  Terasaki O,  Tatsumi T.  A novel anionic surfactant templating route for synthesizing mesoporous silica with unique structure,  Nature Materials ,  2003, vol.  2  70 Sakamoto Y,  L H,  Che S,  Terasaki O.  Structural Analyses of Intergrowth and Stacking Fault in Cage-Type Mesoporous Crystals,  Chem. Mater. ,  2009, vol.  21 (pg.  223- 229) Google Scholar CrossRef Search ADS   71 Frank F C,  Kasper J S.  Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures,  Acta Crystallogr. ,  1959, vol.  12 pg.  483  Google Scholar CrossRef Search ADS   72 Friedrichs O D,  O'Keefe M,  Yaghi O M.  Three-periodic nets and tilings: regular and quasiregular nets,  Acta Crystallogr. Sec. A ,  2003, vol.  59 (pg.  22- 27) Google Scholar CrossRef Search ADS   73 Matzke E B.  The three-dimensional shape of bubbles in foam-an analysis of the rôle of surface forces in three-dimensional cell shape determination,  Am. J. Bot. ,  1946, vol.  33 pg.  58  Google Scholar CrossRef Search ADS PubMed  74 Kraynik A M,  Reinelt D A,  Swol F V.  Structure of random monodisperse foam,  Phys. Rev. E ,  2003, vol.  67 (pg.  031403- 031414) Google Scholar CrossRef Search ADS   75 Ohsuna T,  Terasaki O,  Watanabe D,  Anderson M W,  Lidin S.  Microporous Titanosilicate ETS-10: Electron Microscopy Study,  Stud. Surf. Sci. Catal. ,  1994, vol.  84 (pg.  413- 420) 76 Gao C,  Qiu H,  Zeng W,  Sakamoto Y,  Terasaki O,  Sakamoto K,  Chen Q,  Che S.  Formation Mechanism of Anionic Surfactant-Templated Mesoporous Silica,  Chem. Mater. ,  2006, vol.  18 (pg.  3904- 3914) Google Scholar CrossRef Search ADS   77 Hyde S.  Holmberg K. ,  Handbook of applied surfaces and colloid chemistry ,  2001 New York John Wiley & Sons 78 Han L,  Miyasaka K,  Terasaki O,  Che S.  Evolution of Packing Parameters in the Structural Changes of Silica Mesoporous Crystals: Cage-Type, 2D Cylindrical, Bicontinuous Diamond and Gyroid, and Lamellar,  J. Am. Chem. Soc. ,  2011, vol.  133 (pg.  11524- 11533) Google Scholar CrossRef Search ADS PubMed  79 Rançon Y,  Charvolin J.  Fluctuations and Phase Transformations in a Lyotropic Liquid Crystal,  J. Phys. Chem. ,  1988, vol.  92 (pg.  6339- 6344) Google Scholar CrossRef Search ADS   80 Matsen M.  Cylinder ↔ Gyroid Epitaxial Transitions in Complex Polymeric Liquids,  Phys. Rev. Lett. ,  1998, vol.  80 (pg.  4470- 4473) Google Scholar CrossRef Search ADS   81 Honda T,  Kawakatsu T.  Epitaxial Transition from Gyroid to Cylinder in a Diblock Copolymer Melt,  Macromolecules ,  2006, vol.  39 (pg.  2340- 2349) Google Scholar CrossRef Search ADS   82 Landry C,  Tolbert S,  Gallis K,  Monnier A,  Stucky G,  Norby F,  Hanson J.  Phase Transformations in Mesostructured Silica/Surfactant Composites. Mechanisms for Change and Applications to Materials Synthesis,  Chem. Mater. ,  2001, vol.  13 (pg.  1600- 1608) Google Scholar CrossRef Search ADS   83 Han L,  Xiong P,  Bai J,  S C.  Spontaneous Formation and Characterization of Silica Mesoporous Crystal Spheres with Reverse Multiply Twinned Polyhedral Hollows,  J. Am. Chem. Soc. ,  2011, vol.  133 (pg.  6106- 6109) Google Scholar CrossRef Search ADS PubMed  84 Hmadeh M,  Lu Z,  Liu Z,  Gándara F,  Furukawa H,  Wan S,  Augustyn V,  Chang R,  Liao L,  Zhou F,  Perre E,  Ozolins V,  Suenaga K,  Duan X,  Dunn B,  Yamamto Y,  Terasaki O,  Yaghi O M.  New Porous Crystals of Extended Metal-Catecholates,  Chem. Mater. ,  2012, vol.  24 (pg.  3511- 3513) Google Scholar CrossRef Search ADS   85 Alfredsson V,  Ohsuna T,  Terasaki O,  Bovin J O.  The surface structure of the zeolites FAU and EMT. An HRSEM study,  Angew. Chem. Int. Ed ,  1993, vol.  32 (pg.  1210- 1213) Google Scholar CrossRef Search ADS   86 Ohsuna T,  Horikawa Y,  Hiraga K,  Terasaki O.  Surface structure of zeolite LTL studied by high-resolution electron microscopy,  Chem. Mater. ,  1998, vol.  10 (pg.  688- 691) Google Scholar CrossRef Search ADS   87 Ohsuna T,  Zheng L,  Terasaki O,  Hiraga K,  Camblor M A.  Framework determination of a polytype of zeolite beta by using electron crystallography,  J. Phys. Chem. B ,  2002, vol.  106 (pg.  5673- 5678) Google Scholar CrossRef Search ADS   88 Varoon K.  Dispersible exfoliated zeolite nanosheets and their application as a selective membrane,  Science ,  2011, vol.  334 (pg.  72- 75) Google Scholar CrossRef Search ADS PubMed  89 Rosi N.  Eddaoudi M,  Chen B,  O'Keeffe M,  Yaghi O M.  LKJ Rod Packings and Metal–Organic Frameworks Constructed from Rod-Shaped Secondary Building Units,  J. Am. Chem. Soc. ,  2005, vol.  127 (pg.  1504- 1518) Google Scholar CrossRef Search ADS PubMed  90 Dietzel P.  Blom R,  Fjellvåg H.  DC Base-Induced Formation of Two Magnesium Metal-Organic Framework Compounds with a Bifunctional Tetratopic Ligand,  Eur. J. Inorg. Chem. ,  2008(pg.  3624- 3632) 91 Deng H,  Grunder S,  Cordova K E,  Valente C,  Furukawa H,  Hmadeh M,  Gandara F,  Whalley F C,  Liu Z,  Asahina S,  Kazumori H,  O'Keeffe M,  Terasaki O,  Stoddart J F,  Yaghi O M.  Large-Pore Apertures in a Series of Metal-Organic Frameworks,  Science ,  2012, vol.  336 (pg.  1018- 1023) Google Scholar CrossRef Search ADS PubMed  92 Zacher D,  Schmid R,  Woell C,  Fischer R A.  Surface Chemistry of Metal-Organic Frameworks at the Liquid-Solid Interface,  Angew. Chem. Int. Ed. ,  2011, vol.  50 (pg.  176- 199) Google Scholar CrossRef Search ADS   93 Bradshaw D,  Garai A,  Huo J.  Metal-organic framework growth at functional interfaces: thin films and composites for diverse applications,  Chem. Soc. Rev. ,  2012, vol.  41 (pg.  2344- 2381) Google Scholar CrossRef Search ADS PubMed  94 Chizallet C,  Bats N.  External Surface of Zeolite Imidazolate Frameworks Viewed Ab Initio: Multifunctionality at the Organic-Inorganic Interface,  J. Phys. Chem. Letters ,  2010, vol.  1 (pg.  349- 353) Google Scholar CrossRef Search ADS   95 Chizallet C,  Lazare S,  Bazer-Bachi D,  Bonnier F,  Lecocg V,  Sover E,  Quoineaud A A,  Bats N.  Catalysis of Transesterification by a Nonfunctionalized Metal-Organic Framework: Acidio-Basicity at the External Surface of ZIF-8 Probed by FTIR and ab initio Calculations,  J. Am. Chem. Soc. ,  2010, vol.  132 (pg.  12365- 12377) Google Scholar CrossRef Search ADS PubMed  96 Attfield M P,  Cubillas P.  (41) Crystal growth of nanoporous metal organic frameworks,  Dalton Transactions , vol.  2012 (pg.  3869- 3878) 97 John N S,  Scherb C,  Shöâeè M,  Anderson M W,  Attfield M P,  Bein T.  Single layer growth of sub-micron metal-organic framework crystals observed by in-situ atomic force microscopy,  Chem. Commun. ,  2009(pg.  6294- 6296) 98 Shoaee M,  Anderson M W,  Attfield M P.  Crystal Growth of the Nanoporous Metal–Organic Framework HKUST-1 Revealed by In Situ Atomic Force Microscopy,  Angew. Chem. Int. Ed. ,  2008, vol.  47 (pg.  8525- 8528) Google Scholar CrossRef Search ADS   99 Holden M A,  Cubillas P,  Attfield M P,  Gebbie J T,  Anderson M W.  Growth mechanism of Microporous Zincophosphate Sodalite Revealed In-Situ Atomic Force Microscopy,  J. Am. Chem. Soc. ,  2012, vol.  134 (pg.  13066- 13073) Google Scholar CrossRef Search ADS PubMed  100 Moh P Y,  Cubillas P,  Anderson M W,  Attfield M P.  Revelation of the Molecular Assembly of the Nanoporous Metal Organic Framework ZIF-8,  J. Am. Chem. Soc. ,  2011, vol.  133 (pg.  13304- 13307) Google Scholar CrossRef Search ADS PubMed  101 Yau Y W,  Pease R.  Iranmanesh A A,  Polasko K J.  FW Generation and applications of finely focused beams of low-energy electrons,  J. Vac. Sci. Technol. ,  1981, vol.  19 (pg.  1048- 1052) Google Scholar CrossRef Search ADS   102 Frosien J,  Plies E,  Anger K.  Compound Magnetic adn Electrostatic lenses for Low-Voltage Applications,  J. Vac. Sci. Technol. B ,  1989, vol.  7 (pg.  1874- 1877) Google Scholar CrossRef Search ADS   103 Mullerova I,  Lenc M.  Some approaches to low-voltage scanning electron microscopy,  Ultramicroscopy ,  1992, vol.  41 pg.  399  Google Scholar CrossRef Search ADS   104 Ose Y,  Ezumi M,  Todokoro H.  Improved CD-SEM optics with retarding and boosting electric field,  SPIE Proceedings ,  1999, vol.  3677 (pg.  930- 939) 105 Yonezawa A,  Maruo M,  Takeuchi T,  Morita S,  Noguchi A,  Takaoka O,  Sato M,  Wannberg B.  Single pole-piece objective lens with electrostatic bipotential lens for SEM,  Journal of Electron Microscopy ,  2002, vol.  51 (pg.  149- 156) Google Scholar CrossRef Search ADS PubMed  106 Arnal P M,  Comotti M,  Scüth F.  High-Temperature-Stable Catalysts by Hollow Sphere Encapsulation,  Angew. Chem. Int. Ed. ,  2006, vol.  45 (pg.  8224- 8227) Google Scholar CrossRef Search ADS   107 Galeano C,  Güttel R,  Paul M,  Arnal P,  Lu A,  Schüth F.  Yolk-Shell Gold Nanoparticles as Model Materials for Support-Effect Studies in Heterogeneous Catalysis: Au, @C and Au, @ZrO2 for CO Oxidation as an Example,  Chem. Eur. J. ,  2011, vol.  17 (pg.  8434- 8439) Google Scholar CrossRef Search ADS   108 Güttel R,  Paul M,  Galeano C,  Schüth F.  Au, @ZrO2 yolk–shell catalysts for CO oxidation: Study of particle size effect by ex-post size control of Au cores,  J. Catal. ,  2012, vol.  289 (pg.  100- 104) Google Scholar CrossRef Search ADS   109 Güttel R,  Paul M,  Schüth F.  Ex-post size control of high-temperature-stable yolk–shell Au,@ ZrO2 catalysts,  Chem. Commun. ,  2010, vol.  46 (pg.  895- 897) Google Scholar CrossRef Search ADS   110 Anderson M W,  Agger J R,  Thornton J T,  Forsyth N.  Crystal Growth in Zeolite Y Revealed by Atomic Force Microscopy,  Angew. Chem. Int. Ed. Engl. ,  1996, vol.  35 (pg.  1210- 1213) Google Scholar CrossRef Search ADS   111 Petry D P,  Wong S.  Haouas M,  Taulelle F,  Gaskell S J,  Anderson M W.  CC. Combined MS and NMR: attractive route to future understanding of the first stages of nucleation of nanoporous materials,  Stud. Surf. Sci. Catal. ,  2008, vol.  174 (pg.  941- 944) 112 Haouas M,  Petry D P,  Anderson M W,  Taulelle F.  29Si NMR Relaxation of Silicated Nanoparticles in Tetraethoxysilane–Tetrapropylammonium Hydroxide–Water System (TEOS–TPAOH–H2O),  J. Phys. Chem. C ,  2009, vol.  113 (pg.  10838- 10841) Google Scholar CrossRef Search ADS   113 Haouas M,  Petry D P,  Wong S.  Aerts A,  Kirschhock C.  Martens J A,  Gaskell S J,  Anderson M W,  Taulelle F.  CC. EA Connectivity Analysis of the Clear Sol Precursor of Silicalite: Are Nanoparticles Aggregated Oligomers or Silica Particles?,  J. Phys. Chem. C ,  2009, vol.  113 (pg.  20827- 20836) Google Scholar CrossRef Search ADS   114 Stevens S M,  Cubillas P,  Jansson K,  Terasaki O,  Anderson M W,  Wright P A,  Castro M.  Nanometre resolution using high-resolution scanning electron microscopy corroborated by atomic force microscopy,  Chem. Commun. ,  2008pg.  3894  115 Stevens S M,  Jansson K,  John N S,  Terasaki O,  Anderson M W,  Castro M,  Wright P A,  Cubillas P.  High-Resolution scanning electron and atomic force microscopies: observation of nanometer features on zeolite Surfaces,  Stud. Surf. Sci. Catal. ,  2008, vol.  174 (pg.  775- 780) 116 Stevens S M,  Cubillas P,  Jansson K,  Terasaki O,  Anderson M W.  Nanoscale Electron Beam Damage Studied by Atomic Force Microscopy,  J. Phys. Chem. C ,  2009, vol.  113 pg.  18441  Google Scholar CrossRef Search ADS   117 Brent R. ,  2010 University of Manchester  PhD Thesis 118 Brent R,  Stevens S M,  Terasaki O,  Anderson M W.  Coaxial Core Shell Overgrowth of Zeolite L – Dependence on Original Crystal Growth Mechanism,  Cryst. Growth Des. ,  2010, vol.  10 (pg.  5182- 5186) Google Scholar CrossRef Search ADS   119 Agger J R,  Pervaiz N,  Cheetham A K,  Anderson M W.  Crystallization in Zeolite A Studied by Atomic Force Microscopy,  J. Amer. Chem. Soc. ,  1998, vol.  120 (pg.  10754- 10759) Google Scholar CrossRef Search ADS   120 Cubillas P,  Castro M,  Jelfs K E,  Lobo A.  Slater B,  Lewis D W,  Wright P A,  Stevens S M,  Anderson M W.  JW. Spiral Growth on Nanoporous Silicoaluminophosphate STA-7 as Observed by Atomic Force Microscopy,  Cryst. Growth Des. ,  2009(pg.  4041- 4050) 121 Shöâeè M,  Agger J R,  Anderson M W,  Attfield M P.  Crystal form, defects and growth of the metal organic framework HKUST-1 revealed by atomic force microscopy,  Cryst. Eng. Comm. ,  2008, vol.  10 pg.  646  Google Scholar CrossRef Search ADS   122 Meza L I,  Anderson M W,  Slater B,  Agger J R.  In situ atomic force microscopy of zeolite A dissolution,  Phys. Chem. Chem. Phys. ,  2008, vol.  10 (pg.  5066- 5065) Google Scholar CrossRef Search ADS PubMed  123 Holden M A,  Cubillas P,  Anderson M W.  In situ crystal growth of nanoporous zincophosphate observed by atomic force microscopy,  Chem. Commun. ,  2010, vol.  46 (pg.  1047- 1049) Google Scholar CrossRef Search ADS   124 Best R B,  Brockwell D J,  Toca-Herrera J L,  Blake A W,  Smith D A,  Radford S E,  Clarke J.  Force mode atomic force microscopy as a tool for protein folding studies,  Anal. Chim. Acta ,  2003, vol.  479 (pg.  87- 105) Google Scholar CrossRef Search ADS   © The Author 2013. Published by Oxford University Press [on behalf of The Japanese Society of Microscopy]. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com
TI - A review of fine structures of nanoporous materials as evidenced by microscopic methods
JF - Microscopy
DO - 10.1093/jmicro/dfs098
DA - 2013-01-24
UR - https://www.deepdyve.com/lp/oxford-university-press/a-review-of-fine-structures-of-nanoporous-materials-as-evidenced-by-R0EcbcNn9x
SP - 109
EP - 146
VL - 62
IS - 1
DP - DeepDyve
ER -