Microscopy of Nanoporous Crystals

  • Yanhang Ma
  • Lu Han
  • Zheng Liu
  • Alvaro Mayoral
  • Isabel Díaz
  • Peter Oleynikov
  • Tetsu Ohsuna
  • Yu Han
  • Ming Pan
  • Yihan Zhu
  • Yasuhiro Sakamoto
  • Shunai Che
  • Osamu TerasakiEmail author
Part of the Springer Handbooks book series (SHB)


Nanoporous crystals are widely studied and used for applications in \(\mathrm{H_{2}}\) storage, \(\mathrm{CO_{2}}\) capture, petrochemical catalysis and many other applications, yet the imaging of their atomic structure has proven difficult because of their radiation sensitivity and the small size of these microcrystals. This chapter describes the development of the new modes of electron microscopy needed to study them, and compares these with traditional methods such as x-ray diffraction. This class of materials has traditionally been dominated by the zeolites and zeotype materials, but has recently been expanded to include meso-/macroporous crystals and other new framework structures (MOFs, ZIFs COFs, etc.). Using different building blocks or units, versatile crystal structures have been synthesized for various applications. Their properties and functions are governed primarily by periodic arrangements of pores and/or cavities and their surroundings with various atomic moieties inside crystals. In this chapter, electron microscopy studies of nanoporous materials are discussed from different perspectives. Special attention is paid to the observation of fine defect structures, through careful analysis of electron diffraction, high-resolution images and spectroscopy data. The experimental conditions for imaging beam-sensitive materials, such as MOFs, are described. The contents have been divided into sections based on the types of materials and their geometric features. Examples of structure analysis of various nanoporous materials are given and discussed. New technical developments and existing challenges are described.

electron microscopy structure modulation zeolite silica mesoporous crystal MOF 

Nanoporous crystal are studied for applications in \(\mathrm{H_{2}}\) storage, \(\mathrm{CO_{2}}\) capture, petrochemistry catalysis and other uses, by taking advantages of their well-defined pore systems on the nanometer or subnanometer scale. To understand the growth mechanisms and properties of the wide variety of nanoporous materials, it is necessary to determine their crystal structure, including the existence of defects. In this way, the design of improved functional porous materials may be facilitated. We will see that, because of their radiation sensitivity and small crystal size, conventional methods often cannot be used to determine their structure. This chapter focuses on the use of high-resolution electron microscopy methods for structure analysis of radiation-sensitive nanocrystals, and provides a comparison with x-ray diffraction methods.

A crystal is defined as a material which gives a sharp diffraction pattern, according to the International Union of Crystallography (IUCr) definition. In particular, nanoporous crystals are crystals where channels/cavities are arranged periodically. According to this notion, many mesoporous silicas [29.1] and recently discovered silica mesoporous quasicrystals [29.2] are also nanoporous crystals.

Based on the geometric aspect International Union of Pure and Applied Chemistry (IUPAC), porous materials are classified into three types based on their pore diameter \(d\), microporous, mesoporous and macroporous for \(d<{\mathrm{20}}\,{\mathrm{\AA{}}}\), \({\mathrm{20}}\,{\mathrm{\AA{}}}<d<{\mathrm{500}}\,{\mathrm{\AA{}}}\), and \(d> {\mathrm{500}}\,{\mathrm{\AA{}}}\), respectively. Nanoporous materials can also be categorized based on their bonding features into:
  1. 1.

    Alumino- or transition metal silicates

  2. 2.

    New frameworks such as metal organic frameworks ( s), zeolitic imidazolate frameworks ( s), and covalent organic frameworks ( s)

  3. 3.

    A composite of nanocrystals.


Many efforts have been made to synthesize new nanoporous crystals in order to explore novel properties and functions. Their properties and functions are primarily governed by periodic arrangement of pores and/or cavities and their surroundings with various atomic moieties inside crystals. It has also been well recognized that the detailed atomic structure of surfaces and defects within crystals play important roles in their properties. Therefore, it is import to reveal this fine structure through microscopy studies.

In this chapter, the content is organized by the material and its geometric features rather than by electron microscopy ( ) techniques.

29.1 Classification of Nanoporous Crystals

29.1.1 Microporous Crystals

Zeolites are typical microporous crystals. They are crystalline aluminosilicate crystals with chemical formula \(\mathrm{M_{\mathit{x}/\mathit{m}}}\)[\(\mathrm{Al_{\mathit{x}}Si_{1-{\mathit{x}}}O_{2}]\cdot{}\mathit{n}H_{2}O}\), where M is a cation of valence \(m\) and \(\mathrm{\mathit{n}H_{2}O}\) is zeolitic water. Their frameworks are built from \(\mathrm{TO_{4}}\) tetrahedra (T stands for Si, Al, P, Ga, Ge, etc.). Through corner-sharing of O atoms and spaces, channels or cavities are produced within the crystals. Zeolites are classified into different framework types using a three-letter code defined by the Structure Commission of the International Zeolite Association (IZA ). More than \(\mathrm{230}\) different framework types have been approved (up to 2017) [29.3], and the number is still growing.

Transition metal silicates, titanium silicates such as ETS-10 [29.4] and ETS-4 [29.5], vanadium silicate AM-6 [29.6], Cu silicate SGU-29 [29.7], and recently reported framework structures of transition metal oxides [29.8] are derivatives of zeolites. New properties are found by incorporating transition metal atoms into the frameworks.

29.1.2 Mesoporous Crystals

Silica mesoporous crystal (SMC ) is the most typical mesoporous crystal. SMCs are normally formed through self-assembled surfactants or by using block copolymer micelles as templates for subsequent and/or simultaneous condensation of inorganic silica, soluble in water [29.10, 29.11, 29.9]. The synthesis field diagram for SMCs is more complex and diverse compared to that for the lyotropic liquid crystals (LLC s) formed by amphiphilic molecules in the presence of water such as bilayer, cylindrical and spherical. LLCs are generally described by either a surfactant packing parameter \(g\) (\(g=V/a_{0}l\), where \(V\) is the surfactant chain volume, \(a_{0}\) is the effective hydrophobic/hydrophilic interfacial area, and \(l\) is chain length) or the curvature of the interface between water and amphiphilic molecules [29.12]. Structures of SMCs change from cage type, two-dimensional ()-cylindrical, bicontinuous cubic or tricontinuous hexagonal and one-dimensional ( )-lamellar by increase of the packing parameter from \(1/3\) to 1. Many other mesoporous crystals have been prepared by either using SMCs as hard templates or post-chemical treatments such as preferential dissolution of certain elements, crystal growth-controlling processes or crystal growth prohibition in certain regions.

29.1.3 New Frameworks

Metal organic frameworks (MOFs), zeolitic imidazolate frameworks (ZIFs) and covalent organic frameworks (COFs) belong to this category [29.13, 29.14, 29.15]. MOFs and ZIFs are composed of two major building blocks, clusters of metal ions and organic linker molecules that are connected via coordination bonds, while most COFs are built from organic molecules through covalent bonds. These extended connections form 1-D, 2-D or three-dimensional () periodic networks and also frequently form micro- or mesopores within the frameworks. They are now of great interest due to the advantages of using discrete and well-defined molecular units in the assembly of extended networks with a design. Unfortunately, at present, the crystallinity of COFs is much lower than that of MOFs and ZIFs. It is of particular importance to observe defects or surface terminations in these new frameworks.

29.1.4 Composites

Composites may be formed with more than one basic structural unit. Catalytically active metal nanoparticles, such as Au, Pt, Ru and Pd, are encapsulated in hollow spheres formed by metal oxide nanocrystals or carbon (yolk-shell materials or core-shell systems) to prevent agglomeration at high temperature [29.16, 29.17]. Many interesting systems, for example, metals or other materials, are synthesized within mesopores such as Pt@MCM-48 [29.18] and carbons in micropores such as carbon@zeolites [29.19, 29.20]. These have become interesting and challenging targets for study and characterization by EM.

29.2 History of Transmission Electron Microscopy (TEM) Study of Nanoporous Materials

29.2.1 Zeolites

Menter observed lattice fringes by EM for the first time in 1956 using platinum phthalocyanine [29.21] and the natural mineral FAU [29.22], although both are quite electron-beam-sensitive materials. He succeeded because both have large lattice spacing, which were larger than the resolution limit at that time (ca. \({\mathrm{10}}\,{\mathrm{\AA{}}}\)). After Menter's pioneering work, EM was mostly applied to detect the presence of small amounts of impurities, and to study zeolite fine structures mostly through electron diffraction ( ) patterns.

In the early 1970s, Sanders and his colleague continued the development of methods to determine structure from lattice images in the study of the defect structure of zeolites [29.23, 29.24]. In the late 1970s, Thomas and his group at Cambridge developed various techniques useful for high-resolution transmission electron microscopy ( ) observation of zeolites, including dehydration, dealumination (to reduce the Al/Si ratio of the framework for improving e-beam stability) and ion exchange with heavy ions [29.25, 29.26, 29.27, 29.28, 29.29, 29.30]. Eight-, six- and five-membered rings (8MR s, 6MR s and 5MR s) and their shapes and arrangements were successfully observed in addition to 12MRs. Terasaki planned to make arranged-cluster crystals within the periodic spaces of zeolites; however, this was not successful, since zeolites contain various defects. It became necessary to characterize the defects and to solve new zeolite structures. Therefore, planar defects, stacking faults and intergrowths were characterized in various zeolites in which pores and channels show characteristic geometries such as LTL, MAZ [29.31], ABC-6 family [29.32], FAU and EMT [29.33], MFI and MEL [29.34]. Similar studies of inorganic clusters confined within the cavities of zeolites were carried out, for examples, Se in MOR [29.35], Pt in FAU [29.36], \(\mathrm{PbI_{2}}\) in LTA [29.37], FeOx in FAU [29.38] and \(\mathrm{MoS_{2}}\) in FAU [29.39].

Three important studies have been reported on the structure solution of microporous crystals describing an approach and methodological developments—these will be discussed later in more detail:
  1. 1.

    The very complex titanosilcate structure of ETS-10 was solved by combining electron microscopy with nuclear magnetic resonance (NMR) [29.4]

  2. 2.

    For the first time, an unknown complex zeolite structure SFE was solved solely from a set of electron diffraction ( ) patterns, like an ordinary single-crystal x-ray structure analysis  [29.40]

  3. 3.

    The structure of BEC was determined uniquely, not as a most probable solution, using HRTEM images with the help of Patterson functions from ED patterns [29.41, 29.42].


The dealumination process in FAU and EMT by acid treatment (selective dissolution of Al from framework structure) has also been studied [29.43].

29.2.2 Mesoporous Silica Crystals

Kresge et al cleverly combined electron microscopy observations with powder XRD experiments in order to solve the structure of MCM-41 in their paper [29.9]. The essential structural features of 2-D mesoporous crystals can be observed by TEM images taken along the channel direction, if there is no structural order inside the silica wall, such as inorganic–organic hybrid mesoporous crystal [29.44]. Two cases will be discussed later. For 3-D mesoporous crystals, as it is a 3-D crystal, requiring crystallography instead of tomography, we can dramatically (i) reduce the number of images required to only a few depending on crystal symmetry (the higher the crystal symmetry, the fewer images are required) and (ii) enhance signal-to-noise ratio, because all structural information concentrates on reciprocal points. Then, periodically averaged structural information is collected through the Fourier diffractogram ( ) from the HRTEM image of the thin region.

The 3-D crystal structure solution method that we have developed, based on Fourier analysis of a set of HRTEM images (electron crystallography ( )), remains the most powerful approach currently available for obtaining structure solution of mesoporous silica crystals. The result shows electrostatic potential maps giving channel/cage size and connectivity, and therefore giving fundamental information on pore volume/shape and surface area without the need for assumed structural models [29.45, 29.46, 29.47, 29.48].

29.2.3 New Frameworks

Electron microscopy is a powerful tool for determining crystalline structures and observing local details. However, it is conventionally unsuitable for MOFs, ZIFs or COFs, because they are easily destroyed by electron beams. Therefore, necessary attention must be paid during observation of these materials [29.49, 29.50]. Within the current scope, there have been different methodologies, with the intention of imaging the pore distribution of these materials. In every case, low-dose conditions are imperative with the intention of minimizing the damage and extending the lifetime of the MOFs under the irradiation. To date, several MOF structures [29.51, 29.52, 29.53, 29.54] have been solved by electron diffraction. HRTEM imaging has also been applied to several typical MOFs, including MIL-101 [29.55], MOF-5 [29.56], UiO-66 [29.57] and ZIF-8 [29.58].

On the other hand, simple control of the beam current has been attempted as an alternative method for imaging the framework of beam-sensitive materials [29.59, 29.60, 29.61]. In these studies, a spherical aberration-corrected (\(C_{\mathrm{s}}\)-corrected) column was used for the analysis with the electron beam set in the probe mode. The beam was focused and corrected prior to interaction with the sample, and then scanned over the material for observation. The electrons passing through the sample are collected with an annular detector. This approach is beneficial in terms of image interpretation, as artifacts are minimized and the contrast is not altered by focus variations. In this mode, the contrast is strongly related to the atomic number of the elements in the material (Z-contrast) allowing a clearer visualization of the heavier elements, particularly if an annular dark-field detector (ADF) is used. The disadvantage of this type of observation is that the strongly focused electron spot would result in damage to the structure while creating a hole in the area of study. As an alternative, careful control of the electron dose to a minimum in order to reduce the beam damage may yield data with unprecedented resolution. While this technique has been more frequently applied to zeolites and loaded zeolites [29.59, 29.62, 29.63], the possibility of exporting this methodology to metal organic frameworks has also been tested. With the aim of minimizing the radiolytic mechanism, 300 kV was chosen as the accelerating voltage.

29.3 Comparison with X-Ray Diffraction

An incident plane wave \(\exp(\mathrm{i}\boldsymbol{k}_{0}\boldsymbol{r})\) is elastically scattered into a spherical outward wave \({\mathrm{e}^{\mathrm{i}\boldsymbol{k}\boldsymbol{r}}}/{r}\) with wave vectors \(\boldsymbol{k}_{0}\), \(\boldsymbol{k}(k=|\boldsymbol{k}_{0}|=|\boldsymbol{k}|=2\uppi/\lambda)\), and the scattering wave vector is defined as \(\boldsymbol{K}=\boldsymbol{k}-\boldsymbol{k}_{0}\) (\(|\boldsymbol{K}|={4\boldsymbol{\uppi}{\sin}\theta}/\lambda\), \(\theta\) is the scattering angle). The atomic scattering powers of x-rays and electrons, \(f^{\mathrm{x}}(\boldsymbol{K})\) and \(f^{\text{el}}(\boldsymbol{K})\), are represented by
$$\begin{aligned}\displaystyle f^{\mathrm{x}}(\boldsymbol{K})&\displaystyle=\int\rho_{\text{atom}}(\boldsymbol{r})\exp(-\mathrm{i}\boldsymbol{K}\boldsymbol{r})\equiv\mathfrak{F}(\rho_{\text{atom}}(\boldsymbol{r}))\;,\,\text{and}\\ \displaystyle f^{\text{el}}(\boldsymbol{K})&\displaystyle=\int V_{\text{atom}}(\boldsymbol{r})\exp(-\mathrm{i}\boldsymbol{K}\boldsymbol{r})\equiv\mathfrak{F}(V_{\text{atom}}(\boldsymbol{r}))\;,\end{aligned}$$
respectively, where the symbol \(\mathfrak{F}\) represents Fourier transformation, and \(\rho_{\text{atom}}(\boldsymbol{r})\) and \(V_{\text{atom}}(\boldsymbol{r})\) are the electron charge distribution and the electrostatic potential distribution of an atom, respectively. Characteristic features of the scattering power of an electron are as follows:
  1. 1.

    Approximately \(\mathrm{10^{4}}\) times greater than that of an x-ray (e. g., for Fe, \(f^{\text{el}}(K=0)={\mathrm{7.4\times 10^{-8}}}\,{\mathrm{cm}}\) and \(f^{\mathrm{x}}(K=0)={\mathrm{7.3\times 10^{-12}}}\,{\mathrm{cm}}\))

  2. 2.

    Not so strongly dependent on atomic number \(Z\) as for x-ray

  3. 3.

    Strongly dependent on electronic state (ionicity) in the small \(K\) region.

In the case of periodic systems, i. e., crystals, the scattering powers are represented by a crystal structure factor ( ) (\(\boldsymbol{K}_{hkl}\)) and sometimes by a scattering mean-free path ( ) (\(\boldsymbol{K}_{hkl}\)) for a reflection \(\boldsymbol{K}\) specified with Miller indices \(h\), \(k\) and \(l\). Both have dimension of length, and when scattering is strong, the CSF is large and MFP is small.

The advantage of the x-ray diffraction ( ) method lies in the fact that the diffraction intensities may be accurately quantified, so that measurement and analysis can be done simply by assuming kinematic scattering. Most of the nanoporous materials are synthesized only in powder form, which are too small for single-crystal XRD experiments, and furthermore they are sometime neither single-phase nor well crystallized. Therefore, we need to use the powder XRD method, which is well established as the most powerful technique for solving the structures of unknown nanocrystalline materials.

The main difficulty in powder XRD arises from the two types of reflection overlap found even in high-resolution experiments using a synchrotron x-ray source: (i) inherent degeneracies, for reflections with the same magnitude of \(\boldsymbol{K}\), such as the 333 and 511 reflections in the cubic system (which therefore fall on the same powder ring, but may have different structure factors); and (ii) many reflections can coexist within \(\boldsymbol{K}\pm\Updelta\boldsymbol{K}\), where \(\Updelta\boldsymbol{K}\) is the experimental resolution of detection, for nanocrystals with a large unit cell and low crystal symmetry. It is easy to understand the first case; however, the importance of the second case can be understood through the example of SMC AMS-9 (Fig. 29.1a-d). The powder XRD profile (Fig. 29.1a-da) shows only two very broad peaks. However, the HRTEM image of AMS-9 shows a beautiful ordered arrangement of squares and equilateral triangles (Fig. 29.1a-db). Therefore, a beautiful Fourier diffractogram (FD) with well-defined spots can be obtained from the image, and we can observe extinction rules (Fig. 29.1a-dc). Rotationally integrated intensity profiles obtained from FD of the image (Fig. 29.1a-dd) shows a well-resolved profile in contrast to the powder XRD.

Fig. 29.1a-d

Powder XRD pattern of mesoporous silica crystal AMS-9 with space group \(P_{2}/mnm\), \(a=b={\mathrm{19.7}}\,{\mathrm{nm}}\), \(c={\mathrm{10.2}}\,{\mathrm{nm}}\) (a), HRTEM image taken along \(c\)-axis (b), Fourier diffractogram (FD) of the image with indices based on the crystal structure (c), and intensity profile of the FD after rotational integration to make the 2-D spot intensity distribution into a 1-D profile (d). Adapted from [29.64]. Copyright 2005 John Wiley & Sons, Ltd.

During our studies of the structures of nanoporous crystals, we encountered a few new problems. It is therefore important to formulate the basic crystallography needed to clarify these points, arising from new problems in the next section.

29.4 Crystal and Crystal Structure Factors

In a space of n-dimension (\(n\)-D), a periodic lattice \(L(\boldsymbol{r})\) is given by an infinite array of points in space using the Dirac delta function,
where any lattice point \(\boldsymbol{r}_{n}\) has a center of symmetry and is given by a linear combination of primitive translational vectors, \(\{\boldsymbol{a}_{i}\}\), \(1\leq i\leq n\) (\(n\leq 3\)), as
where \(n_{i}\) (\(1\leq i\leq n\)) are arbitrary integers.
For simplicity, let us discuss here the 3-D case. Any position \(\boldsymbol{r}\) in the crystal is given by the origin of the \(m\)-th unit cell, \(\boldsymbol{r}_{m}\), and its coordinates (\(x\), \(y\), \(z\)) within the cell as
where \(0\leq x\), \(y\), \(z\leq 1\).
Each reciprocal lattice point \(hkl\) represents a set of lattice planes in real space and corresponds to the reciprocal lattice vector,
The interplanar spacing \(d_{hkl}\) is given by
A crystal structure \(C(\boldsymbol{r})\) is given by an atomic distribution within a basis \(B(\boldsymbol{r})\) and underlying the periodic lattice \(L(\boldsymbol{r})\) of infinite size.
$$C(\boldsymbol{r})=B(\boldsymbol{r})\otimes L(\boldsymbol{r})\;.$$
A finite crystal can take any size and shape, given by \(Z(\boldsymbol{r})=1\) when \(\boldsymbol{r}\) is inside the crystal and \(Z(\boldsymbol{r})=0\) otherwise. Then the crystal \(C(\boldsymbol{r})\) and crystal structure factor (CSF) \(F(\boldsymbol{K}_{hkl})\) are defined by the following general equations
$$C(\boldsymbol{r})=B(\boldsymbol{r})\otimes[L(\boldsymbol{r})\cdot Z(\boldsymbol{r})]\;,$$
\(\mathfrak{F}[Z(\boldsymbol{r})]\) is a more general function than the so-called Laue function or (geometric) shape function.

Crystallographic point-group ( ) symmetries require one, four (oblique, rectangular, square and hexagonal) and seven (triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal and cubic) crystal systems for 1-D, 2-D and 3-D systems, respectively. A Bravais lattice is defined as a distinct lattice type; there are one, five and 14 Bravais lattices for 1-D, 2-D and 3-D systems, respectively. The combination of \(\mathrm{32}\) crystallographic PGs, \(\mathrm{14}\) Bravais lattices together with the screw axis and glide plane symmetry operations results in a total of \(\mathrm{230}\) different space groups ( s), describing all possible crystal symmetries in 3-D, and quasicrystals are described in higher dimensions. Extinction of certain reflections occurs either through symmetry of the lattice \(\mathfrak{F}[L(\boldsymbol{r})]\) or through the zero-crossing of the form factor of basis \(\mathfrak{F}[B(\boldsymbol{r})]\), which will be discussed in detail, and they are classified here as systematic and accidental extinction, respectively.

29.5 Accidental Extinction

As an example of accidental extinction, we consider 1-D crystals of MFI nanosheets, which have been synthesized by Ryoo et al It grows in the \(a\)\(c\) plane with just a single unit cell's thickness (\({\mathrm{2.0}}\,{\mathrm{nm}}\)) along the \(b\)-axis [29.65]. The layered lamellar structure is very uniform and the interlayer distance could be precisely controlled according to the hydrophobic chain length of surfactants. Pillaring was carried out with tetraethoxysilane (TEOS ) prior to the removal of the template in order to make mesopores within the interlamellar spaces. An HRTEM image of the layered MFI sheets synthesized by use of \(\mathrm{C_{\mathit{n}}H_{2\mathit{n}+1}}\) (\(n={\mathrm{22}}\)) with pillars is shown in Fig. 29.2a-c; the thickness of both the MFI layer and the mesopore layer is \(\approx{\mathrm{3}}\,{\mathrm{nm}}\) [29.66]. Up to fourth-order reflections corresponding to the interlayer distance were observed in the powder XRD pattern (\(\lambda\): Cu \(K_{\alpha}\)) at small scattering angles, due to the interlamellar structural coherence; interestingly, the accidental extinction of the second-order reflections can be clearly observed in the powder XRD patterns from the sheets synthesized with \(n={\mathrm{22}}\) but not with \(n={\mathrm{18}}\).

Fig. 29.2a-c

MFI zeolite nanosheets synthesised using a surfactant with a tail of \(\mathrm{C_{\mathit{n}}H_{2\mathit{n}+1}}\). (a) HRTEM image of the sheets synthesised with \(n=22\) molecules. Reprinted with permission from [29.65] Copyright © 2009, Springer Nature. (b) Powder XRD patterns (\(\lambda\): Cu \(K_{\alpha}\)) showing that when \(n=22\), the second-order reflection is missing due to accidental extinction. (c) Graphic representation of the crystal and symbolic expression of the crystal structure factor for the 1-D system. Adapted with permission from [29.65]

As discussed in (29.7) and (29.8), the accidental extinction comes not from the symmetry of the lattice through \(\mathfrak{F}[L(\boldsymbol{r})]\), but from the zero-crossing of \(\mathfrak{F}[B(\boldsymbol{r})]\) in the 1-D crystal. \(B(\boldsymbol{r})\) does not bring extra symmetry to the lattices. A graphical representation is given in Fig. 29.2a-cc.

For 1-D crystals, \(C(\boldsymbol{r})\) is reduced to
$$C(\boldsymbol{r})=\{B(\boldsymbol{z})\cdot H(x,y)\}\otimes\{L(\boldsymbol{z})\cdot S(\boldsymbol{z})\}\;,$$
where \(B(\boldsymbol{z})\) is the basis (slab) with unit thickness corresponding to the lattice periodicity along \(z\), \(L(\boldsymbol{z})\) is the infinite 1-D lattice function along \(z\) and \(H(x,y)\) and \(S(\boldsymbol{z})\) are the crystal size functions along the \(x\)\(y\) plane (2-D) and \(z\)-axis (1-D), respectively.
If the size of the crystal slab in the \(x\) and \(y\) directions and the number \(n\) of nanosheets along \(z\) are large enough, then \(F(\boldsymbol{k})\) will have a nonzero value only when the wave vector \(\boldsymbol{k}\) is equal to \(l\boldsymbol{c}^{*}\) (\(l=\) integer). Then
where \(A\) and \(B\) are scattering factors for slabs \(A\) and \(B\), respectively.

Figure 29.3a,b shows the intensities of reflections for \(k=l\boldsymbol{c}^{*}\), obtained from the equations above, with \(l={\mathrm{2}}\), 3, 4 and 5 reflections normalized to the intensity of \(l={\mathrm{1}}\) for both \(B/A={\mathrm{0}}\) and \(B/A={\mathrm{0.5}}\) cases, since \(F(\boldsymbol{k}=\boldsymbol{c}^{*})\neq 0\). It is clear from the figure that the intensity of \(n\)-th-order reflection (\(l=n\)) is extinguished when the rational layer thickness reaches \(1/n\). The intensity of the second-order reflection of MFI nanosheets will disappear at \(B/A={\mathrm{0.5}}\).

These accidental reflections have also been observed in two-dimensional (2-D) systems, and an example of a 2-D system can be found in the paper by K. Lund et al [29.66].

Fig. 29.3a,b

Relative XRD intensities \(|F(\boldsymbol{k})|^{2}\) of \(l\)-th-order reflections relative to the first-order reflection for (a) \(B/A={\mathrm{0.0}}\) and (b\(B/A={\mathrm{0.5}}\). Reprinted from [29.66], with permission from Elsevier

This can be explained using Babinet's principle , which is used to understand contrast scattering in porous nanocrystals. Babinet's principle states that, apart from a small region around the center, the diffraction pattern from an aperture \(a(x)\) is the same as the pattern from an opaque object of the same shape, \(b(x)\equiv 1-a(x)\), illuminated in the same manner.

Fig. 29.4a,b

Schematic drawing of Babinet's principle for the diffraction pattern from (a) an aperture and (b) a periodic comb function. Adapted from [29.67]. Copyright © 2014 John Wiley & Sons, Ltd

Let us take a rectangular function, \(f(x)=1\), for \(-L/2\leq x\leq L/2\), and \(f(\boldsymbol{x})=0\) otherwise (Fig. 29.4a,ba). Using \(\operatorname{sinc}(x)\equiv\sin(x)/x\) (shown in the inset of Fig. 29.4a,b)
$$\begin{aligned}\displaystyle\mathfrak{F}[f(\boldsymbol{r})]&\displaystyle=F(q)\\ \displaystyle&\displaystyle=\left(\frac{1}{\sqrt{2\uppi}}\right)\int^{L/2}_{-L/2}\mathrm{e}^{-\mathrm{i}qx}\mathrm{d}x\\ \displaystyle&\displaystyle=\left(\frac{L}{\sqrt{2\uppi}}\right)\cdot\operatorname{sinc}\left(\frac{qL}{2}\right).\end{aligned}$$
It is worth noting that integral representation for a \(\delta\) function is expressed as
$$\begin{aligned}\displaystyle&\displaystyle\delta(x)=\frac{1}{\sqrt{2\uppi}}\int^{\infty}_{-\infty}\frac{1}{\sqrt{2\uppi}}\mathrm{e}^{-\mathrm{i}qx}\mathrm{d}q,\,\,\text{therefore}\\ \displaystyle&\displaystyle\mathfrak{F}[\delta(x)]\equiv\Delta(q)=\frac{1}{\sqrt{2\uppi}}\mathrm{e}^{-\mathrm{i}qx}\;.\end{aligned}$$
$$\mathfrak{F}[a(x)+b(x)]=\Updelta(q)\;, $$
$$\mathfrak{F}[a(x)]\equiv A(q)=\Updelta(q)-\mathfrak{F}[b(x)]\equiv\Updelta(q)-B(q)\;.$$

Except for the origin of reciprocal space, the Fourier transforms of arbitrary shapes of an aperture \(a(x)\) and of the conjugate of the same aperture \(b(x)\) are the same in magnitude but opposite in sign.

Taking periodic comb functions \(a(x)\) and \(b^{\prime}(x)\) with \(a(x)+(1/c)b^{\prime}(x)=1\), the same argument is valid (Fig. 29.4a,bb).

29.6 Double Refraction

A double refraction effect produces fine structures on diffraction spots, called multiplets, which are due to the geometric relationship between the sample entrance and exit surfaces for an e-beam. If a transmission specimen is a parallel-sided slab, then a Bragg reflection should be a single sharp spot—an incident plane wave is focused to a point at the detector provided that the slab of crystal is free of defects. The double refraction effect comes from refraction effects due mainly to the mean inner potential \(V_{0}\), the 0-th Fourier component of the crystal potential \(V_{\text{cryst}}(r)\) and through the \(g\)-th Fourier components [29.68, p. 104].

MgO has a cubic structure with space group \(Fm\bar{3}m\) and cubic crystal morphology. Debye–Scherrer rings should be formed with spotty rings for unmixed \(hkl\) (\(h\), \(k\), \(l\) are all odd or even integers) reflections from many small crystals. However, the cubic morphology of the MgO crystal clearly gives a double refraction effect not for 200, but for 111, 220 and 311, as can be seen in Fig. 29.5a-c (experimental value, \(V_{0}\approx{\mathrm{13.6}}\,{\mathrm{eV}}\) for MgO). A simple schematic drawing for the case of 200 and 220 explains the multiplets (Fig. 29.6). The key point of the equations is given by the boundary condition for e-beam continuity; the tangential components of the wave vectors should be equal at both the incident boundary and exit boundary separately, that is, vacuum-to-MgO and MgO-to-vacuum. The relation of wave vectors in vacuum (\(\chi\)) and inside the crystal (\(\boldsymbol{K}\)) is given by the following
For the 200 reflection, wave vectors incident to, and exiting from, a crystal are parallel to \({\chi}_{0}\), and the amount of shift is negligible (since the size of the crystal is much smaller than one detector pixel). However, the (220) reflection behaves differently from the (200) reflection, as the entrance and exit surfaces for electrons are not parallel to each other. Neglecting the Bragg angle, as it is very small, the deviation angles of electrons \(\theta_{1}\) and \(\theta_{2}\) at the entrance and exit surfaces, and the total deviation \(\theta\), are given from the following boundary conditions,
$$\begin{aligned}\displaystyle\chi_{0}\cos\left(\frac{\uppi}{4}\right)&\displaystyle=\boldsymbol{K}\cos\left(\theta_{1}+\frac{\uppi}{4}\right),\\ \displaystyle\boldsymbol{K}\cos\left(\theta_{1}-\frac{\uppi}{4}\right)&\displaystyle=\chi_{1}\cos\left(\frac{\uppi}{4}-\theta_{1}-\theta_{2}\right),\\ \displaystyle\theta&\displaystyle=\theta_{1}+\theta_{2}\;.\end{aligned}$$
One should be aware that refraction effects may produce reflections as multiplets when collecting an electron diffraction data set from a large crystal (larger than the selected area diffraction aperture) with a clear crystal habit. For small crystals, we need to take into account the crystal shape effect from the Fourier transformation \(\mathfrak{F}[Z(\boldsymbol{r})]\), known as a relrod.
Fig. 29.5a-c

Debye ring pattern (electron diffraction pattern) of MgO nanoparticles taken at \({\mathrm{50}}\,{\mathrm{kV}}\). Rectangles marked by green lines in (a) and (b) are enlarged to (b) and (c), respectively, with indices

Fig. 29.6

Schematic illustration of double refraction of 200 and 220 reflections for a crystal with cube morphology

29.7 New Problems Give Exciting Challenges

It is known that the atomic scattering factor for electrons \(f^{\text{el}}\) is very sensitive to the electron charge distribution of valence/conduction electrons [29.69, 29.70]. The listed values in the IUCr International Tables for Crystallography were obtained assuming the spherical potential distribution of an isolated atom [29.71]. Precisely determined values of atomic scattering factor of \(f^{\text{el}}\) for fcc, bcc and hcp metals and \(\mathrm{TiO_{\mathit{x}}}\) (\({\mathrm{0.8}}\leq x\leq{\mathrm{1.25}}\)) crystals by the critical voltage (vanishing Kikuchi line) method indicated clearly an existence of bonding effect [29.70, 29.73, 29.74]. Furthermore, deviation from spherical electron distribution was discovered for vanadium (V) and chromium (Cr) by Compton scattering  [29.75, 29.76]. Therefore, special attention must be paid to the study of bonding charge distribution [29.77, 29.78].

The dependence of \(f^{\text{el}}\) (at \((\sin\theta)/\lambda=0\)) does not increase monotonically with atomic number Z as expected from that for x-rays, \(f^{\mathrm{x}}\) (Fig. 29.7a,ba). \(f^{\text{el}}\) of ionized atoms behaves in a different manner from that expected for neutral atoms in the low scattering angle range. Drastic increases (or decreases) of \(f^{\text{el}}\) can be seen depending on the ionic states [29.79]. This is typically shown in Fig. 29.7a,bb for different ionic states by taking the example of NaCl. So if we can observe diffraction intensity at small \(q\)-values, we are able to discuss more precisely electronic states. We can observe reflection intensities only at certain discrete \(q(q=4\uppi\sin\theta/\lambda=2\uppi/d)\) values corresponding to the reciprocal lattice points, which are determined by the size of the unit cell. Therefore, if we can prepare crystals inside the pores of a periodic system with a large unit cell like SMC, then we can measure the reflection intensities at many small \(q\)-values corresponding to the reciprocal lattice points of the large system. A typical candidate is shown in Fig. 29.8, where Pt nanowires synthesized in the mesopores of silica MCM-48 give many reflection spots, and their positions are given by a convolution with the Fourier transform ( ) of MCM-48.

Fig. 29.7a,b

Electron scattering power of (a) different atoms, (b) neutron/ionic atoms and crystals. Adapted from [29.72], by permission of Oxford University Press

Fig. 29.8

(a) Schematic diagram explaining complicated electron diffraction obtained from Pt nanowires prepared within pores of mesoporous silica crystal, MCM-48 (b). Powder x-ray diffraction pattern obtained from the Pt nanowires using a synchrotron x-ray (\(\lambda={\mathrm{1.0803}}\,{\mathrm{\AA{}}}\)) (c). Electron diffraction pattern of the Pt nanowires

Since structure analysis by electron crystallography (EC) is becoming an important practical method for structural refinement, which can give quantitative information, even hydrogen atoms have been detected [29.80]. For further refinement, we should handle properly both \(f^{\text{el}}(\boldsymbol{K})\) for small \(\boldsymbol{K}\) and the dynamical scattering treatment, including refraction effects from the crystal morphology.

We also need to understand the differences and similarities between atomic scattering factors for x-rays and electrons. The naive notion that \(f^{\text{el}}(\boldsymbol{K})\) increases with \(Z\) at any wave number \(K\) (or scattering angle \(\theta\)) is not correct, as seen by plotting values of \(f^{\text{el}}\) listed in Table of the IUCr International Tables for Crystallography, volume C [29.72]. Specific care must therefore be taken when utilizing atomic scattering factor information for structural determination and refinement by electron diffraction data.

29.8 Recent Technical Developments Important for the Structural Study of Nanoporous Crystals

29.8.1 3-D Electron Diffraction Tomography

Nowadays, synchrotrons and transmission electron microscopy ( ) are used for the investigation of very small crystals, both in imaging and diffraction modes. However, the TEM approach offers a major advantage. Electrons strongly interact with matter, which makes it possible to work with crystals only a few nanometers in linear size. Unfortunately, the traditional TEM technique (collecting electron diffraction patterns along some zone axes from one or several crystals) is quite tedious, time-consuming and demanding for a skillful operator. These drawbacks become clear when a high-quality 3-D data set needs to be acquired, which can easily take weeks.

In the mid-2000s, an obvious need arose for fast and automated 3-D ED data collection and processing methods. Initially, the precession electron diffraction method with conical electron beam rocking [29.81] gained some attention in the electron crystallography community. However, this technique is only able to collect data using a certain limited geometry and cannot be considered as a 3-D data collection method. The real 3-D data can only be recorded using methods such as electron diffraction tomography [29.82, 29.83, 29.84, 29.85]. All modern 3-D ED approaches were developed from the x-ray single-crystal diffraction technique, where the Bragg condition (monochromatic radiation) for each reflection is satisfied by rotating the crystal. Lattice planes come into the diffraction condition for a certain time during the crystal rotation (Fig. 29.9a-d). The following setup is equivalent: the reciprocal lattice points pass through the Ewald sphere during the lattice rotation.

Fig. 29.9a-d

Diffraction experiment geometry. Reciprocal space side views: (a) the exact zone axis orientation and (b) during the Ewald sphere sweeping. The schematic front view: the difference between (c) the static and (d) the rotating crystals (the reflections will be recorded in the areas marked with brown color). After [29.86]

The wavelength of the electrons is \(\approx{\mathrm{50}}\) times smaller than the wavelength of the x-ray photons (\(\approx 0.02{-}0.03\,{\mathrm{\AA{}}}\) vs. \(\approx 1{-}2\,{\mathrm{\AA{}}}\) for x-rays). This introduces a significant difference between x-rays and electrons because the radius of the Ewald sphere becomes very large in the case of electron diffraction. This eliminates the influence of geometric limits on resolution.

29.8.2 Data Collection

There are two main approaches that can be distinguished for 3-D electron diffraction. Both techniques and their derivatives will be discussed in this section.

The first approach ( , automated diffraction tomography) combines the crystal tilting (usually with \(1^{\circ}\) steps around the principal sample holder axis) followed by the acquisition of a hardware precession electron diffraction pattern [29.82]. The diffraction patterns are collected in the nanobeam diffraction mode, where, in contrast to selected area electron diffraction ( ), only a desired area of the sample is illuminated during the acquisition, thereby leaving the adjacent areas unexposed. This beam geometry has similarities to the scanning transmission electron microscopy ( ) imaging mode; therefore, for crystal tracking, the STEM mode (with reduced beam convergence, \(\upmu\)-probe STEM for an FEI TECNAI instrument) is used. A TEM control module was developed in cooperation with the FEI company, which loops a STEM imagenanodiffractiongoniometer tilt sequence in an automated fashion; thus the method was named automated diffraction tomography (ADT). Practical data collection using a conventional TEM equipped with a STEM detector in many cases cannot be performed automatically for the following reasons:
  1. 1.

    Many instruments have a STEM detector with a manual insertion/retraction system.

  2. 2.

    Some TEM manufacturers do not provide software access to the STEM images.

  3. 3.

    Precession-assisted ADT requires expensive third-party hardware, which together makes it very difficult to adopt the ADT technique for most TEMs.


The second technique, so-called electron diffraction tomography or  [29.84, 29.85], which has the same purpose of scanning 3-D reciprocal space, utilizes a software-induced electron beam tilt (typically \(0.1^{\circ}\) beam-tilt steps) along a line instead of a hardware conical precession, combined with manual crystal tracking. It was initially developed for JEOL electron microscopes that are not equipped with third-party hardware tools and only have computer control over the beam tilt, two image shift coils and the stage. The method works identically in both nanobeam and conventional SAED modes. However, it should be noted that the method described in reference [29.84] is not optimal, due to the use of two image shift coils in an electron microscope that participate in the de-scan of the tilted beam. This leads to a complicated iterative alignment procedure and can only be used on JEOL TEMs which allow software access to both image shift coils. This drawback is absent in the EDT method described in [29.85] because it utilizes an optimal way of performing compensation of the ED pattern shift induced by the beam tilt and has been successfully implemented on all computer-controlled TEMs from JEOL, FEI and Zeiss. Soon after the EDT technique was introduced [29.84], the ADT method was also extended to the SAED mode with manual crystal tracking, as described in [29.87].

The 3-D EDT data collection module is available for computer-controlled TEMs from most manufacturers [29.88]. The hardware line-scan implementation of the 3-D EDT technique has been incorporated into the commercial precession units available from various manufacturers (NanoMEGAS [29.89], TVIPS [29.90]). At the time of writing, there is no free or commercial software available to the electron crystallography community for data collection using the described ADT method. For the precession-assisted ADT data collection, either a third-party hardware unit [29.89, 29.90] or a slower software implementation [29.88] can be used.

The main advantages of both the ADT and EDT methods are that (i) the crystal does not need to be oriented throughout the data collection process, which results in (ii) reduced dynamical scattering, producing less dynamical intensities. The practical data collection and analysis shows that dynamical scattering effects strongly influence the intensities of zone axis-oriented ED patterns, so it is generally better to avoid these orientations during data collection. Because of the integration effect, the diffuse scattering intensities have a higher amplitude on ED patterns. This simplifies the measurements and the quantification of diffraction frames from nanosized, disordered or modulated samples.

The main problem that arises with electron diffraction tomography is the so-called missing cone. Some part of reciprocal space cannot be reached by the sample holder (\(\approx 20{-}55\%\) of total reciprocal space depending on the holder used). In this case, low-symmetry crystals (monoclinic and triclinic crystal systems) will have lower data completeness. This problem can be partially or fully eliminated by merging two or more data sets collected from different crystals.

There are variations of the electron diffraction tomography data acquisition method. The first technique allows ultrafast data collection, as described elsewhere [29.91]. The principle remains the same; however, the experimental setup is quite different from both ADT and EDT and relies on a single sweep of the specimen holder within the accessible tilting angles, with simultaneous diffraction pattern recording in frame-by-frame or video acquisition camera modes. The second approach, called microED [29.92], is in fact a standard ADT/EDT technique that can utilize the precession hardware, with the difference being the electron dose used during data acquisition (reduction by the factor of \(\mathrm{200}\) [29.92]) and use of a single-electron counting area detector. The overall small dose and short data collection times allow sampling of reciprocal space from small protein crystals acceptable for solving high-resolution structures.

29.8.3 Data Processing

A typical ADT data collection experiment generally produces \(\approx 100{-}120\) individual precession frames, while the EDT method features much higher throughput, resulting in \(800{-}2000\) individual electron diffraction patterns over a similar data collection period. The EDT method has much finer reciprocal space sampling that allows for quantification of diffuse scattering (Fig. 29.10a,b) and analysis of the reciprocal shape of reflections (rocking curves) in 3-D.

Fig. 29.10a,b

Titanosilicate zeolite ETS-10. (a) A 3-D reciprocal space reconstruction from the 3-D EDT data set covering \(\approx 150^{\circ}\). (b) The sum of \(\mathrm{30}\) individual electron diffraction frames with a step of \(0.15^{\circ}\). The diffuse streaks between main spots can be clearly observed

The collected data sets have some similarities to data obtained in single-crystal x-ray experiments. However, the electron diffraction frames have certain peculiarities, so that new processing strategies have been developed, and dedicated software packages have been produced (ADT3-D: [29.83, 29.89, 29.93] and 3-D-EDT: [29.85, 29.88]).

The structures solved by the ADT and EDT methods come from different areas of science: organic and inorganic materials chemistry, pharmacology, mineralogy, biology, etc. Many scientific articles have been published describing 3-D electron diffraction techniques and here we name only some of them.

Complex electron-beam-sensitive organic materials could be solved ab initio from ADT data [29.94]. The structures of two minerals, charoite [29.95] and vaterite [29.96] whose structures were debated for many years, have been published. Later, structural studies based on ADT data covered a large spectrum of materials—a large cage zeolite [29.97], metal organic framework [29.52], hybrid organic–inorganic composite [29.98], a new sodium titanate phase [29.99], etc.

The EDT technique has been applied to the study the structure of a complex intergrowth zeolite [29.100], energy-related materials [29.101], gadolinium phosphate nanorods [29.102], nanowires [29.103, 29.104], small-angle 3-D EDT for nanoparticle superlattices [29.105], molecular sieves [29.106], covalent organic frameworks [29.107], handedness of chiral zeolites [29.108], etc.

29.8.4 Direct Detection and Electron Counting

Successful imaging of the pristine structures of nanoporous materials at high resolution is critically dependent on the image detector performance under low electron beam conditions. To acquire images with good signal-to-noise ratio () under the low-dose conditions, it is essential to minimize or eliminate noise in the detector.

Detective quantum efficiency ( ) is a measure of the detector's ability to render SNR at a given electron dose. DQE is defined as the ratio of the squared SNR of the captured image (output) and that of the input signal [29.109].
where \(N\) is the dose in primary electrons per pixel and \(s\) is the spatial frequency in reciprocal space of the captured image. Detectors with high DQE means high image quality for a given electron dose.

When the electron beam intensity is high, the total noise in the captured image is dominated by the shot noise in the electron beam (Poisson noise) that is proportional to \(\sqrt{N}\). Under low-dose conditions, the noise in the detector becomes dominant, which limits the image quality. Therefore, to design optimal detectors for low-dose imaging, it is critical to minimize noise levels in the detector.

The noise in conventional scintillator-based cameras (left in Fig. 29.11) mainly comes from:
  1. 1.

    Electron–photon conversion

  2. 2.

    Electron backscatter noise

  3. 3.

    Electronic readout.

Fig. 29.11

(a) Conventional scintillator-based camera; (b) direct-detection camera. Courtesy of Gatan, Inc.

Typical DQE is limited to \(\approx{\mathrm{10}}\%\) at \(1/2\) Nyquist (dashed-dotted curve in Fig. 29.12).

Fig. 29.12

Detective quantum efficiency () measurement at \({\mathrm{300}}\,{\mathrm{kV}}\) for K2 direct-detection cameras in electron counting (dashed line) and direct-detection linear (solid line) mode, and scintillator/fiber-coupled camera (dashed-dotted line). Reproduced with permission from [29.110]. Copyright © John Wiley & Sons, Ltd.

Direct-detection cameras (Fig. 29.11b) improve DQE (solid curve in Fig. 29.12) by eliminating the noise associated with electron–photon conversion and electron backscatter.

Furthermore, significant improvement in DQE (dashed curve in Fig. 29.12) can be achieved by counting electrons directly, which drastically reduces the noise of electron scattering and electronic readout (Fig. 29.13b). In Fig. 29.13a is a \({\mathrm{2.5}}\,{\mathrm{ms}}\) single frame of \({\mathrm{300}}\,{\mathrm{kV}}\) electrons recorded using the intensity readout (linear mode) in a direct-detection camera under electron dose rate of \(\approx{\mathrm{10}}\,{\mathrm{{e}^{-}/(pixel{\,}s)}}\). The bright dots in the image correspond to individual electrons striking the sensor. The intensity variation is due to multiple scattering of the electrons in the image sensor during detection. It is noted that the left image also contains a weak background—electronic readout noise. The right image is the same image frame after electron counting. It is obvious that electron counting drastically removes the noise associated with electron scattering and electronic readout. This reduction in detector noise is responsible for the significant improvement in DQE. With electron counting, it is also possible to determine the electron striking position in the image detector to an accuracy of \(1/2\) pixel (super-resolution).

Fig. 29.13

(a) Single \({\mathrm{2.5}}\,{\mathrm{ms}}\) image frame of \({\mathrm{300}}\,{\mathrm{kV}}\) electrons using intensity readout (corresponding to the solid curve in Fig. 29.12). (b) Same frame after counting (corresponding to the dashed curve in Fig. 29.12). Courtesy of Gatan, Inc.

Coincidence loss can occur during electron counting. This refers to two or more electrons striking the same pixel during readout that results in a single count in the captured image. To avoid coincidence loss, the image detector must operate at a minimum readout speed for a given electron dose rate. It was found that when the image readout speed is at \({\mathrm{400}}\,{\mathrm{fps}}\) (frame per second), coincidence loss is \(\approx{\mathrm{10}}\%\) for a given electron dose rate of \({\mathrm{10}}\,{\mathrm{e^{-}/(pixel{\,}s)}}\) [29.110].

In electron counting mode, for any given exposure time, images are captured and saved as a 3-D stack. The individual frames in the 3-D stack allow accurate image drift measurement and correction during the exposure. This is extremely important for imaging nanoporous materials at atomic scale under low-dose conditions.

Figure 29.14a-d below is an example of image drift correction for zeolite beta under an electron dose rate of \({\mathrm{4}}\,{\mathrm{e^{-}/(pixel{\,}s)}}\). Figure 29.14a-da and b is an uncorrected image and its FFT. Figure 29.14a-dc and d is an image after drift correction and the corresponding FFT. Image drift correction is essential to achieving high resolution.

Fig. 29.14a-d

Example of image drift correction of zeolite beta. Electron dose rate was \({\mathrm{4}}\,{\mathrm{e^{-}/(pixel{\,}s)}}\), total exposure \({\mathrm{2}}\,{\mathrm{s}}\), TEM magnification \({\mathrm{180}}\,{\mathrm{k}}\times\) and \({\mathrm{200}}\,{\mathrm{kV}}\). Images were saved at \({\mathrm{8}}\,{\mathrm{fps}}\). (a) sum of images in the stack as captured (no drift correction); (b) FFT of (a); (c) sum of images with drift correction; (d) FFT of (c). Courtesy of Gatan, Inc.

Direct detection and electron counting represent a quantum leap in image detector technology that greatly benefits high-resolution imaging of nanoporous materials [29.111]. These super-sensitive cameras have shown success in imaging pristine structures at atomic resolution.

It is worth briefly mentioning another type of direct electron detection and electron counting detectors—pixelated electron detectors that have recently emerged with promising potential for enabling new EM applications [29.112, 29.113]. Pixelated detectors are designed and optimized for STEM diffraction applications. These detectors have fewer pixels (e. g., \({\mathrm{128}}\times{\mathrm{128}}\) or \({\mathrm{264}}\times{\mathrm{264}}\)), but larger pixel size (e. g., \(\approx{\mathrm{50}}\,{\mathrm{\upmu{}m}}\)) and much thicker sensor layer (e. g., \(\approx{\mathrm{500}}\,{\mathrm{\upmu{}m}}\)). The pixelated STEM detectors typically operate at a speed \(\approx{\mathrm{1000}}\,{\mathrm{fps}}\) without binning.

For the purpose of high-resolution imaging of nanoporous materials, the requirement will be larger sensor size with more pixel counts, and higher image readout speed for better electron counting efficiency and DQE.

29.8.5 In Situ (S)TEM Studies

In situ transmission electron microscopy is also attracting great interest and gaining importance, as it allows live visualization of phenomena in material science [29.114, 29.115], biological samples [29.116], semiconductor devices [29.117] and, more recently, nucleation reactions in liquid environments [29.118, 29.119, 29.120, 29.121, 29.122]. Liquid cell transmission electron microscopy ( ) can provide direct images of solutions/processes in real time with great spatial resolution coupled even with chemical information. This recently emerging methodology can be translated into MOF chemistry with the expectations of giving precise information on particle growth, morphology, nucleation, internal rearrangement or growth rates. Furthermore, the combination of electron microscopy, diffraction and EDS/EELS analyses gives the possibility of acquiring a direct image and chemical information [29.123] of a material.

29.9 Structural Characterization and Solutions

29.9.1 Average Structures

Average structures of crystals are normally obtained using powder XRD profiles; however, electron microscopy can provide similar information even from nanocrystals. There are two main approaches, through ED patterns or HRTEM images, to obtain a structural solution (Fig. 29.15). The biggest difference comes from treatment of the phase problem: the former approach assumes phases of crystal structure factor and finds the best possible solution, while the latter measures the phases and obtains a unique solution, although resolution is limited. Both approaches can be applicable in principle for micro- and mesoporous crystals. However, no structure solutions have been reported solely from an analysis of ED patterns for mesoporous crystals, while from HRTEM image analysis (together with ED patterns), many structure reports can be found for both zeolites and mesoporous crystals.

Fig. 29.15

Diagram of structure solution of crystals using electron crystallography approaches. Adapted from [29.67]. Copyright © 2014 John Wiley & Sons, Ltd

There is a long history of using electron diffraction (ED) for structure analysis of inorganic crystals. For example, the structures of long-period antiphase domain structures were intensively studied by electron diffraction as an order–disorder transformation problem in Ogawa's group in Tohoku University for a long time [29.124, 29.125]. Thin evaporated single-crystal A1 structure films (fcc disordered alloys such as an Au-Cu system) were prepared on an NaCl cleaved surface and subsequently properly heat-treated.

Cowley [29.126] and Kuwabara [29.127] measured ED patterns in order to solve unknown structures of inorganic crystals. Dorset and Hauptman were the first to apply the direct method for ED intensity data showing a 3-D structure solution of organic macromolecules [29.128]. They obtained the phases of reflections through the phase correlations based on the fact that the scattering density must be a positive real number. Dorset has shown the power of electron crystallography (EC) for various crystals.

Carlsson et al [29.38] obtained a framework structure Na-Y (FAU) zeolite and localized the iron atomic position of Fe oxide incorporated in a cavity of the zeolite. Dorset and Gilmore further refined the crystal structure of Na-Y from \(\mathrm{87}\) unique reflections observed by Carlsson et al, using maximum entropy and maximum likelihood approaches [29.129].

29.9.2 Disorder Within Order: Distribution of Clusters with Different Sizes Within Uniform Zeolite Pores

Even though HRTEM images can give projected structure information along the e-beam, Ohnishi et al [29.130] succeeded in observing different amounts of \(\mathrm{MoS_{2}}\) molecules in thin parts of zeolite FAU (Figs. 29.16a-d and 29.17).

Fig. 29.16a-d

ED patterns of Na-FAU (a) and \(\mathrm{MoS_{2}}\)@Na-FAU (b), along [110] incidence. Corresponding HRTEM image of \(\mathrm{MoS_{2}}\)@Na-FAU (c) and a part of image (c) is enlarged (d). Experiments were done at \({\mathrm{400}}\,{\mathrm{kV}}\) using a JEM 4000EX. Reprinted from [29.130], with permission from Elsevier

Fig. 29.17

Observed and calculated HRTEM images of \(\mathrm{MoS_{2}}\)@FAU and the intensity profiles at different positions, revealing different loading amounts of \(\mathrm{MoS_{2}}\) in pores. Reprinted from [29.130], with permission from Elsevier

29.9.3 Zeolites

The direct (numerical) phasing method is the most powerful technique for determining the crystal structure from diffraction data alone for crystals with small unit cells. The method fails if the number of atoms per unit cell becomes too large. In general, direct methods do not seem to be applicable to ED intensity, because dynamical scattering effects are often not negligible. There are two typical ways to reduce dynamical scattering effects on the ED intensity: the first (and simplest) is to collect the intensity from very thin specimens, and the second is to use precession ED patterns which reduce this effect via the Vincent–Midgley approach [29.81].

For the first case, a successful example is a framework determination of borosilicate SSZ-48 (framework type: SFE) [29.3]. The typical crystal dimensions are \({\mathrm{0.05}}\,{\mathrm{\upmu{}m}}\times{\mathrm{0.25}}\,{\mathrm{\upmu{}m}}\times{\mathrm{10}}\,{\mathrm{\upmu{}m}}\) and are well below the size restriction for standard single-crystal x-ray analysis. Provided that the interaction of the incident electron beam with the crystal is nearly kinematic; i. e., the diffraction intensity is proportional to the square of the structure factor, indicating that there are few dynamical scatterings of the electrons within the crystal, we have found that direct methods can be a powerful tool for obtaining the phase information required to solve the crystal structure. Therefore, we collected data from thinly sliced crystal embedded in epoxy and thin parts of crushed crystals using a JEM-4000EX operating at \({\mathrm{400}}\,{\mathrm{kV}}\) equipped with slow-scan CCD (Gatan 694). The integrated intensities were quantitatively measured for \(\mathrm{326}\) unique reflections from the ED patterns taken at 11 crystal zones (resolution \({\mathrm{0.99}}\,{\mathrm{\AA{}}}\)). The phases obtained from the direct method structure solution were used to generate a 3-D potential map that easily revealed the seven silicon atoms and five (out of 14) oxygen atoms in the asymmetric unit. A space group of \(P2_{1}\) (monoclinic) was observed, with \(a={\mathrm{11.19}}\,{\mathrm{\AA{}}}\), \(b={\mathrm{4.99}}\,{\mathrm{\AA{}}}\), \(c={\mathrm{13.65}}\,{\mathrm{\AA{}}}\) and \(\beta=100.7^{\circ}\), containing a \(\mathrm{Si_{14}O_{28}}\)/unit cell and a \(\mathrm{Si_{7}O_{14}}\)/asymmetric unit. The remaining oxygen atoms in the framework were located using distance least-squares ( ) refinement [29.131] to optimize Si–O bond distances and O–Si–O bond angles (Fig. 29.18). Dynamical scattering effects are included for the analysis, as we know the crystal thickness.

For the second case, new structural solutions of zeolites with relatively simple structures, such as for MCM-68 and for ZSM-10 [29.132, 29.133], have been reported by Dorset et al using a  precession electron diffraction device, which is now commercially available, for ED intensity measurement.

Fig. 29.18

Ab initio structure solution of a zeolite SSZ-48 by direct method using electron diffraction data. Reprinted with permission from [29.40]. Copyright 1999 American Chemical Society

It is not easy to take several HRTEM images from a zeolite with different incident beam directions. At the same time, Fourier reconstruction of the images can produce a blurred 3-D electrostatic potential distribution from which atom positions in the framework are difficult to recover. Using the ED information, atom positions in the framework can be enhanced by using several ED patterns in the blurred distribution. Ohsuna et al solved uniquely the structure of zeolite BEC through analysis of HRTEM images with the help of a Patterson pair map obtained from the ED patterns [29.42].

After determining the space group as \(P4_{2}/mmc\), a reasonable framework topology with seven unique Si positions was retrieved in the Fourier reconstructed potential from two HRTEM images with framework enhancement from seven ED patterns (Fig. 29.19). Finally, after O atoms were put temporarily at the centers of two neighboring Si atoms, all atom positions were refined using a simple molecular mechanics calculation similar to DLS, which is a least-squares minimization of Si–O bond length and O–O distance in each \(\mathrm{SiO_{4}}\) tetrahedron for the given mean bond length, \(\mathrm{0.16}\) and \({\mathrm{0.26}}\,{\mathrm{nm}}\), respectively.

Fig. 29.19

Unique structure solution of zeolites by combining HRTEM images and ED patterns. Reprinted with permission from [29.42]. Copyright 2002 American Chemical Society

There are many interfaces and boundaries, and, among them, the surface is the most important as reactant molecules enter the crystals through the surface. Surface fine structure also gives information concerning the crystal growth process. After solving the structure of zeolite BEC by Ohsuna et al [29.42], a new type-C structure of zeolite beta was found. There was a report of a germanate with the same framework topology of BEC [29.134]; however, it is well known that the chemistry of germinates and silicates are quite different. Figure 29.20 shows an HRTEM image of BEC taken with [100] incidence and simulated images for different structure terminations are inserted. Two different surface terminations, double four-membered ring (D4R ) and D4R free, are observed on both (010), indicated by red and blue arrows, respectively, and (001), indicated by green and black arrows, respectively [29.41]. Intense discussion of these corresponding surface terminations was reported by Slater et al [29.135, 29.136], suggesting that two-step S4R addition (quickly reacts to give the D4R) and one-step D4R addition may happen.

Fig. 29.20

HRTEM image of zeolite BEC taken along [100] at \({\mathrm{400}}\,{\mathrm{kV}}\) using a JEM-4000EX. The surface termination indicated by arrows from two different surfaces of (001) and (010) are enlarged with the corresponding HRTEM simulation and the structural models. Reprinted with permission from [29.41]. Copyright 2001 American Chemical Society

Figure 29.21a-d shows another example of the HRTEM images of faujasite (FAU ) and EMT zeolites. Structures of both EMT and FAU zeolites are formed from the same layer structure called the FAU sheet, and successive sheets are stacked with mirrors or inversions, respectively, as shown schematically in Fig. 29.21a-da,b. Figure 29.21a-dc shows clearly the manner of the intergrowths of FAU and EMT from highly crystalline samples. Figure 29.21a-dd shows both surface terminations at the {111} surface without double six-rings (D6R s) and a twin plane of FAU. It is obvious from the image that the EMT framework is formed locally at the twin plane. It is rare to observe the framework so clearly at the boundaries, showing that the framework of the twin plane is well connected [29.138].

Fig. 29.21a-d

HRTEM image of FAU and EMT zeolites taken with a JEM-4000EX at \({\mathrm{400}}\,{\mathrm{kV}}\). Structures of faujasite (FAU) (a) and EMT (b) lattices, which are composites of FAU sheets by inversion and mirror symmetries, respectively. Si atoms correspond to vertices, double six-membered rings (D6Rs), sodalite (SOD ) cages and FAU sheets are indicated. HRTEM images of FAU and EMT intergrowth (c) and twinning in FAU (d) taken with a JEM-4000EX at \({\mathrm{400}}\,{\mathrm{kV}}\). Reproduced with permission from [29.137]. Copyright © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim


ETS-10 (Engelhard titanosilicate)
is a titanosilicate material with pore dimensions of \({\mathrm{4.9}}\,{\mathrm{\AA{}}}\times{\mathrm{7.6}}\,{\mathrm{\AA{}}}\). The structure is formed by –O–Ti–O–Ti–O– chains linked by \(\mathrm{TiO_{6}}\) octahedra surrounded by Si–O linkages connected by O bridges [29.139, 29.4, 29.60]; the membered rings that can be observed in this material are 12MR, 7MR and 3MR. Because of its particular structural features [29.60], the characterization of this material has been quite complex and the location of the cationic species has been far from easy; several studies have been dedicated to this effort [29.140, 29.141, 29.142, 29.143, 29.144, 29.145]. As expected, the properties of this material are directly related with the structural features of ETS-10. Among the different techniques, electron microscopy has been the most beneficial one to elucidate the structural units, connectivity and defects [29.146, 29.60]. Three-dimensional electron diffraction enabled the unit cell parameters to be determined as \(a=b={\mathrm{21}}\,{\mathrm{\AA{}}}\), \(c={\mathrm{14.5}}\,{\mathrm{\AA{}}}\), \(\alpha=90^{\circ}\), \(\beta=111.12^{\circ}\), and \(\gamma=90^{\circ}\), taking a space group of \(C_{2}/c\). Figure 29.22 shows the HRTEM image recorded at \({\mathrm{400}}\,{\mathrm{kV}}\) of the ETS-10 (polymorph B) with the corresponding SAED pattern and the 3-D EDT of the crystal, which provides the location of the atomic positions of Si, Ti and O atoms, except for three oxygen positions. Figure 29.22b depicts the schematic representation of the polymorphs A and B with the Ti shown in red. A closer observation of the framework is presented in Fig. 29.23a-c, with the data acquisition taken at \(\mathrm{400}\) and \({\mathrm{1250}}\,{\mathrm{kV}}\), as in Fig. 29.23a-ca and c, and the comparison with recent images that were acquired by spherical aberration-corrected (\(C_{\mathrm{s}}\)-corrected) scanning transmission electron microscopy ( ) using a high-angle annular dark-field detector ( ); where it is possible to unambiguously determine the Ti and Si atomic positions [29.4, 29.60]. Enormous work has been done regarding the structural solution and the study of the defects due to their intrinsic complexity. In addition, there are also various studies devoted to understanding its ion-exchange capability, since locating the cationic species has been complicated and experimental. A theoretical study has been devoted to understanding their interesting properties [29.140, 29.141, 29.142, 29.143, 29.144, 29.147, 29.148]. More recently, an electron microscopy study has focused on the analysis with atomic resolution of the elucidation of certain \(\mathrm{Na^{+}}\) sites and on the study of the ion-exchanged Europium ETS-10 [29.145]. Although the STEM-HAADF technique is highly sensitive to the atomic number, and is therefore the most appropriate method for observing heavier elements in light supports, a different configuration of the detectors that collect the electrons may lead to a complementary set of data that contains information on light elements. For this study, the synthesis route reported by Anderson et al [29.149] was reproduced. The \(\mathrm{Eu^{3+}}\) ion exchange was achieved using \({\mathrm{0.5}}\,{\mathrm{g}}\) of the as-synthesized ETS-10 with \({\mathrm{100}}\,{\mathrm{mL}}\) of a \({\mathrm{0.05}}\,{\mathrm{M}}\) solution of \(\mathrm{EuCl_{3}\cdot H_{2}O}\). The mixture was stirred for \({\mathrm{24}}\,{\mathrm{h}}\) at room temperature and then filtered, washed with deionized water and dried at room temperature. The electron microscopy observations were performed using an X-FEG FEI Titan \(60{-}300\), operated at \({\mathrm{300}}\,{\mathrm{kV}}\), with an annular dark-field configuration ( ) where the detector was set to have diameters of \(\mathrm{30}\) and \({\mathrm{160}}\,{\mathrm{mrad}}\). Figure 29.24a-da corresponds to the parent material with the \(\mathrm{Na^{+}}\) cations in the structure, with the schematic model superimposed; by simple image analysis, the perfect match between the theoretical framework and the experimental data can be observed. Interestingly, with such high-resolution data, it is possible to visualize the existence of a faint signal in the center of the 7MR, denoted by a white arrow. The intensity profile extracted along that arrow is plotted in Fig. 29.24a-db; the strongest signal's central peak corresponds to the Ti atomic column, while the other, less intense maxima are separated by approximately \({\mathrm{3}}\,{\mathrm{\AA{}}}\). This observation, together with previous reports [29.141, 29.144, 29.148], suggests that the cations may occupy the 7MR. The same observation was carried out in the ion-exchanged material (Fig. 29.24a-dc); by comparison with Fig. 29.24a-da, the significant difference between the two materials in those regions is evidenced. The intensity profile recorded in the equivalent position (Fig. 29.24a-dd), marked by a white arrow, shows the presence of three maxima that are much more intense than those in the initial ETS-10. The interatomic distances vary from 3 to \({\mathrm{2.59}}\,{\mathrm{\AA{}}}\), suggesting that \(\mathrm{Eu^{3+}}\) may only replace certain \(\mathrm{Na^{+}}\) sites. In addition to this direct comparison, the intensity coming from the Si columns surrounding the \(\mathrm{TiO_{6}^{2-}}\) octahedra in the corners of the butterfly units is different from the starting material in Fig. 29.25a,b. Figure 29.25a,ba corresponds to the parent ETS-10; in the model proposed by Anderson, \(\mathrm{Na^{+}}\) would also occupy the position outside the 7MR very close to the framework, and therefore the signal that we experimentally measure would correspond to the Si–Si columns, around \({\mathrm{1.44}}\,{\mathrm{\AA{}}}\). However, after the introduction of Eu cations, a much stronger signal appears (Fig. 29.25a,bb), enlarging the experimental distance measured to \({\mathrm{2.48}}\,{\mathrm{\AA{}}}\). This variation confirms that the first distance is in fact two Si columns, and when the \(\mathrm{Na^{+}}\) is replaced by \(\mathrm{Eu^{3+}}\), the latter would go into those positions outside the 7MR. As the scattering factor of Eu is much stronger than Na, the increased signal intensity detected is attributed to the presence of this metal.
Fig. 29.22

(a) HRTEM image of ETS-10 recorded along the [110] orientation with the ED pattern inset (bottom) and the 3-D EDT data for the crystal (inset upper right corner). (b) Schematic representation of the two extreme cases of stacking, polymorph A and B. Reproduced with permission from [29.137]. Copyright © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Fig. 29.23a-c

HRTEM images of ETS-10 taken at (a\({\mathrm{400}}\,{\mathrm{kV}}\) and (b\({\mathrm{1250}}\,{\mathrm{kV}}\), and (c\(C_{\mathrm{s}}\)-corrected STEM-HAADF image with the ball-and-stick model superimposed, all oriented along the [110] direction. Reproduced with permission from [29.137]. Copyright © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Fig. 29.24a-d

\(C_{\mathrm{s}}\)-corrected STEM image of (a) Na ETS-10 along the [110] orientation. (b) Intensity profile extracted from the white arrow. (c\(C_{\mathrm{s}}\)-corrected STEM image of Eu ETS-10, which enables observation of all atomic atoms. (d) Intensity profiles extracted from the white arrow in Fig. 29.24a-dc. Reproduced with permission from [29.145]. Copyright © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Fig. 29.25a,b

\(C_{\mathrm{s}}\)-corrected STEM analyses of (a) as-synthesized ETS-10 with the corresponding intensity profile extracted from the white rectangle and (b) same observation performed on Eu-ETS-10. Reproduced with permission from [29.145]. Copyright © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Intergrowth of CHA- and AEI-Type Frameworks in SAPO-34 Nanosheets

Zeolites have been widely used as solid acid catalysts in many industrial processes. One of the reactions is methanol to olefins (MTO ). To date, many zeolites have been used as MTO catalysts, among which the aluminosilicate ZSM-5 (MFI-type) and the silicoaluminophosphate SAPO-34 (CHA-type) are the best catalysts. Compared with ZSM-5, SAPO-34 gives higher selectivity for light olefins. However, the main problem with SAPO-34 is the rapid deactivation during the conversion. Previous studies have revealed that the deactivation of catalysts in MTO reactions arises largely from the restriction of mass transfer due to the coke deposition. Therefore, catalysts with small crystallite sizes have demonstrated advantages in improved mass transfer and reduced coke formation. In particular, the SAPO-34 nanosheets provide a long catalyst lifetime and low coking rate in MTO reactions.

One study examined a SAPO-34 nanosheet sample exhibiting a long catalyst lifetime and a low coking rate [29.106]. In order to understand the relation between crystal structure and catalytic performance of synthesized nanocrystals, a 3-D EDT technique was applied for data collection and further ab initio structure solution. As a result, two phases were found: CHA- and AEI-type frameworks. In addition, diffuse streaks were observed along one direction in the reconstructed data, indicating the existence of layer stacking faults or intergrowth of two phases (Fig. 29.26a-d).

Fig. 29.26a-d

Reconstructed 3-D reciprocal space of one crystal with CHA-type phase. (a) The whole set of the 3-D EDT data (inset: the image of the crystal), (b\(h0l\) plane, (c\(hk0\) plane, and (d\(0kl\) plane cut from 3-D reciprocal space. Reproduced from [29.106] with permission of The Royal Society of Chemistry

As shown in Fig. 29.27, HRTEM images reveal that domains of CHA and AEI coexisted in a single nanosized crystal. The two frameworks have the same double six-ring (D6R) layers, but different stacking sequences. CHA and AEI can form an intergrowth by sharing a common layer without destroying the whole structure. The formation of different domains in one crystal might be related to the amount of silica source in the reaction. We found that the amount of AEI phase in the final product decreases with the increasing of silica source. It is worth mentioning that all \(00l\) diffraction spots are sharp, which means that there is no density modulation along the \(c\) direction. This ensures the mass transformation of reagents and products during the reaction.

Fig. 29.27

(a) HRTEM image of one SAPO-34 nanosheet containing both CHA and AEI frameworks and (b) the corresponding structure model to illustrate the intergrowth

The formation mechanism of SAPO-34 nanosheets is also related to its specific structure. Figure 29.28a shows an HRTEM image taken along the \(c\)-axis. In the upper left corner, we can see that the edge can be indexed as a (110) plane. Based on TEM observations, the facets of nanosheets can be indexed as shown in Fig. 29.28b. Notably, the straight eight-ring channels run along three directions and open to six external surfaces, which might explain the high efficiency of this MTO catalyst. Moreover, the special morphology of this nanosheet further leads us to envision other possible intergrowth frameworks. A typical morphology for a zeolite with pure CHA is a pseudocube, while the intergrowth with AEI gives a nanosheet shape. This is because the growth of thw crystal along one direction is impeded by the layer stacking fault along this direction. Similarly, we expect that rod-like and nanosized cube crystals will be obtained if CHA has intergrowth with SAV and KFI, respectively (Fig. 29.29a-d).

Fig. 29.28

(a) HRTEM image of SAPO-34 along the [001] direction; (b) schematic representation of different facets of the SAPO-34 crystal; (c) three directions of straight eight-ring channels

Fig. 29.29a-d

Four similar zeolite frameworks and their corresponding ideal crystal morphologies. From (ad), planes of inversion centers transfer to mirror planes one by one

Chiral Zeolites

Chirality is commonly observed in organic and biological molecules, as well as in many inorganic compounds. Chiral zeolites are of particular interest for their potential applications in enantioselective separation and catalysis. Several chiral zeolite frameworks have been reported to date, including *BEA, CZP, GOO, -ITV, JRY, LTJ, OSO, SFS and STW (a three-letter code is designated to each particular zeolite framework). However, there has been no report on achievements of enantiopure or even enantioenriched zeolite materials. One of the reasons is the lack of efficient characterization methods for chiral nanocrystals.

Utilizing anomalous scattering, single-crystal x-ray diffraction has been proved effective for chirality determination, but it is only applicable to single crystals with a size larger than \({\mathrm{5}}\,{\mathrm{\upmu{}m}}\). Furthermore, the anomalous scattering effects are weak for materials only containing light elements, such as zeolites (most of zeolites are aluminosilicates).

Here we propose two practical and efficient approaches for determining the handedness of zeolite crystals using electron crystallography [29.108]. The first approach employs high-resolution transmission electron microscopy ( ) imaging. A set of two HRTEM images from the same crystal are taken along two different zone axes by tilting it around a certain axis. Although the handedness feature was lost in 2-D projections, the comparison of the two images reveals a clear difference between two enantiomorphic crystal structures. In particular, setting the screw axis of the crystal as the tilting axis will maximize the difference between the two structure projections, and this will also make it easy to find two zone axes for HRTEM imaging. The second approach is based on multiple-beam scattering in electron diffraction. The principle is same as that of convergent-beam electron diffraction (CBED)—that is, the comparison of intensities of Bijvoet pairs of reflections. Instead of CBED, we employed precession electron diffraction ( ) with parallel electron illumination to reduce electron beam damage.

An STW sample that contains a mixture of two enantiomers has been chosen as an example for experiments. The sample is a pure silica chiral zeolite using an achiral organic template. This chiral zeolite, displaying good thermal and hydrothermal stability, is a promising candidate for enantioselective applications. Crystals exhibit a pencil-like morphology with spiral features on the tip surface. A 3-D EDT data set has been collected from a single crystal. The Laue class of the reconstructed 3-D reciprocal lattice was determined to be \(6/mmm\), and the reflection conditions were summarized as \(000l:l=6n\), which indicate two possible space groups of \(P6_{1}22\) and \(P6_{5}22\). The pair of two enantiomorphic space groups cannot be distinguished using 3-D EDT data.

Prior to performing further experiments, HRTEM images of the STW with different handedness were simulated along two zone axes, [2\(\bar{1}\bar{1}\)0] and [1\(\bar{1}\)00]. The [1\(\bar{1}\)00] zone axis was reached from [2\(\bar{1}\bar{1}\)0] by tilting the crystal to the right by \(30^{\circ}\) around the spiral axis (counterclockwise with the rotation axis pointing up). Of note, depending on the direction of the \(c\)-axis, either [1\(\bar{1}\)00] or [10\(\bar{1}\)0] can be reached from [2\(\bar{1}\bar{1}\)0] by the same tilting. It is worth mentioning that the choice of \(c\)-axis will not affect the final hand determination. For convenience, here the \(c\)-axis of the crystal structure was chosen to be up. Layers with strong contrast in two images were used as features (marked as f1 and f2) to reveal the shifting along the \(c\)-axis between two images. The f2 is shifted downward by \((1/12)c\) with respect to f1 in the right-handed structure, while the shift is upwards by the same distance in case of the left-handed structure. Therefore, this difference can be used for hand determination. In the experiment, a single STW crystal was first aligned to the [2\(\bar{1}\bar{1}\)0] zone axis and an HRTEM image was taken. Then the crystal was continuously tilted by \(30^{\circ}\) around the spiral axis (here in the \(c\)-axis). As a result, the [1\(\bar{1}\)00] zone axis was reached and a corresponding HRTEM image was recorded. By choosing two obvious features (indicated by two arrows) as references, the comparison of two images revealed the handedness of a crystal. Gold nanoparticles were used as markers to align two images before comparison. During the tilting, gold nanoparticles will move only in the plane perpendicular to the rotation axis. Therefore, they can be used as an internal standard. An experimental example is shown in Fig. 29.30a-f. The two images were aligned along the vertical direction so that the markers would be at the same height. The comparison of two images shows that the shift is downward after tilting, which indicates a crystal with right-handedness.

Fig. 29.30a-f

Determination of the handedness for the HPM-1 from a set of HRTEM images. (a,b) Simulated HRTEM images of the zeolite with right- and left-handedness, respectively. The atomic structure models, where blue and red balls represent Si and O atoms, were overlaid on top of the simulated images. (c,d) Images of chiral zeolite coated with gold nanoparticles taken along [2\(\bar{1}\bar{1}0\)] (c) and [1\(\bar{1}0\)0] (d) zone axes. [1\(\bar{1}0\)0] was reached from [2\(\bar{1}\bar{1}0\)] through tilting the crystal by \(30^{\circ}\) to the left. (e,f) The processed images of (c) and (d) after filtering in Fourier space that only include spatial frequencies within a particular range to enhance the contrasts of gold nanoparticles 1, 2 and 3. From [29.108]

In the next step, PED patterns of two enantiomorphic structures along [0001] were simulated using the Bloch wave method under the following conditions: \({\mathrm{200}}\,{\mathrm{kV}}\), 162 ZOLZ and 345 FOLZ reflections (excitation effort \({\mathrm{0.054}}\,{\mathrm{nm^{-1}}}\)), beam tilt angle \(0.1^{\circ}\) and precession step \(0.1^{\circ}\). Clear intensity differences were observed between two reflection pairs: 18 \(\bar{3}\,\overline{15}\) 1 and 15 3 \(\overline{18}\) 1 and 16 1 \(\overline{17}\) 1 and 17 \(\bar{1}\,\overline{16}\) 1. The comparison of an experimental PED pattern with simulated patterns will lead to a final handedness determination (Fig. 29.31a,b). Of note, the PED patterns along [0001] and [000\(\bar{1}\)] are the same. The rotation of PED patterns by \(n\cdot 60^{\circ}\) (\(n\) is an integer) will not change the intensity differences between chosen reflection pairs. To perform this PED approach, a proper zone axis should be found, here \(\langle h\overline{h}0l\rangle\), \(\langle hh\overline{2}hl\rangle\) or \(\langle hki0\rangle\) for the point-group symmetry \(\mathrm{622}\). As the PED pattern is collected from an area with different thickness, it is important to mention that intensity asymmetries of chosen reflection pairs should be relatively insensitive to the changes in crystal thickness. Moreover, the precession angle is one key parameter in the PED method. The original introduction of PED by Vincent and Midgley was intended to reduce dynamical scattering effects in electron diffraction. For that purpose, the optimal precession angle should exceed the Bragg angle for the highest-order reflection used in the structure solution [29.150, 29.151]. However, in our case, the existence of dynamical scattering is necessary for handedness determination. The use of PED is to diminish the effect caused by a slight misorientation of the crystal in practice. Here, the precession angle is set to \(0.1^{\circ}\).

Fig. 29.31a,b

Determination of hand in a chiral zeolite using a PED pattern. (a) Simulation of PED pattern of HPM-1 chiral zeolite with space group \(P6_{1}22\) along the [0001] direction (\({\mathrm{200}}\,{\mathrm{kV}}\), \(\mathrm{507}\) reflections, \(t={\mathrm{100}}\,{\mathrm{nm}}\), precession angle \(0.1^{\circ}\), precession step \(0.1^{\circ}\)). (b) An experimental PED pattern of a chiral zeolite along the same direction. The area marked by the white rectangle is amplified to display the intensity difference between two pairs of reflections: \(18\,\bar{3}\,\overline{15}\,1\) (1) and \(15\,3\,\overline{18}\,1\) (\(1^{\prime}\)) and \(17\,\bar{1}\,\overline{16}\,1\) (2) and \(16\,1\,\overline{17}\,1\) (\(2^{\prime}\)). From [29.108]

In summary, two new and efficient approaches have been found for the determination of handedness in nanocrystals. This will overcome the limitations of the single-crystal x-ray diffraction method. These two approaches have been successfully applied to an enantioenriched zeolite sample.

29.9.4 Mesoporous Silica Crystals

Considerable research has been focused on silica mesoporous crystals because of their controllable structures, tunable compositions, large surface area and confined nanospace. Therefore, they are expected to find a broad range of applications in catalysis, sorption, controlled drug release and nanotechnology [29.11, 29.152, 29.9]. Mesoporous crystals are synthesized by the cooperative assembly of surfactants and water-soluble species into meso-structured domains, and successive calcination of organic-inorganic composites to create ordered nanospaces in the silica framework. We will discuss mostly silica mesoporous crystals with cage-type and bi-continuous structures, then a brief descriptions on kanemite base KSW-\(n\) [29.153] and inorganic–organic hybrid mesoporous crystals [29.154, 29.44].

Unlike conventional crystals, the silica mesoporous crystals are amorphous on the atomic scales, while the pores (templates) are arranged periodically at the mesoscale and show beautiful crystal morphology, which is commensurate with their point-group symmetry. Compared to traditional x-ray crystallography, crystal structure factors ( s) with both phase and amplitude information can be obtained through Fourier diffractograms ( s) of the HRTEM images taken from a very thin area of the sample, and thus the 3-D electrostatic potential distribution map can be reconstructed to elucidate the characteristic structural features of the mesoporous silicas (Fig. 29.32).

Fig. 29.32

The structures of silica mesoporous crystals solved by electron crystallography

Defects in Cage-Type Mesostructures

The cage-type mesostructures are formed by the packing of the spherical or ellipsoidal micelles (cages) with the highest organic/inorganic interfacial curvature. The cage-type mesostructure is analogous to the traditional atomistic crystal formed by the packing of atoms. Up to now, different types of cage-type mesostructures have been fabricated, providing us the opportunity to look into the structural relationships of their packing behaviors. In particular, compared to the traditional atomistic crystals, the intergrowth and defects of mesoporous silicas are more diverse due to the flexibility of the silica wall before completion of silica condensation so that the structures are sensitive to the synthesis conditions. Up to now, several cage-type structures have been solved by electron microscopy, for instance, cubic \(Im\bar{3}m\) (SBA-16, FDU-1), cubic \(Fm\bar{3}m\) (SBA-12, KIT-5, FDU-12), cubic \(Pm\bar{3}n\) (SBA-1, SBA-6), cubic \(Fd\bar{3}m\) (FDU-2, AMS-8), hexagonal \(P6_{3}/mmc\) (SBA-2, SBA-11), orthorhombic \(Pmmm\) (FDU-13), tetragonal \(P_{4}/mmm\) (FDU-11), tetragonal \(P4_{2}/mnm\) (AMS-9), etc. [29.155].

The closest packing of unimodal perfect spheres on a plane forms a hexagonal arrangement with \(p6mm\) symmetry, which will hereafter be called a layer; the layer can be a or B or C depending on the origin of the spheres. Then the three-dimensional packing of these layers can form two famous cases according to their stacking sequence, the cubic close-packed ( ) [29.156, 29.157] and hexagonal close-packed ( ) [29.158] structures corresponding to the ABCABC… and ABABAB… stackings, respectively. These are often found in the mesoporous silicas as random packings of both structural domains sharing the [0001]\({}_{\text{hex}}\) and the [111]\({}_{\text{cub}}\) directions. They have the highest packing density of ca. \(\mathrm{0.74}\), and easily form an intergrowth with each other. Interestingly, the pure ccp structure shows the typically icosahedral shape (Fig. 29.33a,b), which can be explained by the formation of multiple twinned particles (as for Au nanoparticles) [29.156, 29.157], consisting of packing of tetrahedral domains sharing the {111} surface.

Fig. 29.33a,b

HRTEM images from the [110] axis of the multiply twinned ccp structure with a decahedron shape (a) and the SEM image (b) of the SMC with icosahedron morphology. Reproduced from [29.157] with permission of The Royal Society of Chemistry

There is a distinct difference between unimodal and bimodal mesopore walls; the isosurfaces of unimodal walls are mostly concave (Gaussian curvature \(K> 0\)), indicating that the cages are highly spherical, while the bimodal types tend to be saddle-shaped (\(K<0\)), and the cage forms an interface with the next cage and becomes a polyhedron instead of a sphere [29.159].

The polyhedron packing structures, such as SBA-1 and SBA-6 (\(Pm\bar{3}n\)), AMS-8 (\(Fd\bar{3}m\)) and AMS-9 (\(P4_{2}/mnm\)), show the tetrahedrally close-packed ( ) feature. The tcp structures can be realized as a Frank–Kasper phase, which is observed in intermetallic compounds (Fig. 29.34a-fa). These structures are governed by an area-minimizing effect rather than total packing entropy of a ccp/hcp structure. In this case, the cages form interfaces with the adjoint ones and become polyhedra instead of the perfect spheres. Four types of Frank–Kasper polyhedra have been introduced, i. e., the \(5^{12}\), \(5^{12}6^{2}\), \(5^{12}6^{3}\) and \(5^{12}6^{4}\). The structure of SBA-1 or SBA-6 (\(Pm\bar{3}n\)) can be explained by clathrate type I (\(\mathrm{A_{3}B}\)) with \(5^{12}\) and \(5^{12}6^{2}\) polyhedra. The AMS-8 (\(Fd\bar{3}m\)) type of structure is the structural analog of clathrate type II, consisting of 16 \(5^{12}\) polyhedra and 8 \(5^{12}6^{4}\) polyhedra in a unit cell. Nevertheless, the AMS-9 (SG \(P4_{2}/mnm\)) is more complicated with five crystallographic sites and \(\mathrm{30}\) cages in one unit cell, which can be built by \(5^{12}\), \(5^{12}6^{2}\) and \(5^{12}6^{3}\) polyhedra (Fig. 29.34a-f) [29.155, 29.160].

Fig. 29.34a-f

HRTEM images of the defects and intergrowth of the ccp (hcp) and \(Fd\bar{3}m\) structures taken at \({\mathrm{300}}\,{\mathrm{kV}}\) using a JEM-3010. (a) The polyhedra to construct the tcp structures and the defects. (b) Intergrowth of ccp and \(Fd\bar{3}m\) structure. (c) The twins in the \(Fd\bar{3}m\) structure. (d) The defect layer z of [110]\({}_{Fd\bar{3}m}\). (e) The defect layer \(\upchi\) of [110]\({}_{Fd\bar{3}m}\). (f) Intergrowth of three different tcp structures. Reproduced with permission from [29.137]. Copyright © 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

By precisely controlling the synthesis condition, the epitaxial intergrowth of the spherical packing ccp (with hcp intergrowth) and the polyhedral packing \(Fd\bar{3}m\) structure have been obtained in the transition area, and the intergrowth of these two structures has been directly observed by HRTEM (Fig. 29.34a-fb). The \([\bar{2}11]\) of the ccp structure corresponds to the \([\bar{1}01]\) of the \(Fd\bar{3}m\) structure sharing the (111) plane, suggesting that the ccp structure and the \(Fd\bar{3}m\) structure have a \(30^{\circ}\) rotational relationship along the common [111] axis. The intergrowth can be described by introducing an intermediate layer between the \(Fd\bar{3}m\) structure (polyhedra) and the ccp structure (spheres). The small spheres occupy the lattice point of the triangular net and the large spheres sit on the center of the hexagon of the Kagomé net. The defect layer results in the base layer for the successive ccp structure, and therefore the ccp/hcp layer can be placed on the top [29.155].

For the polyhedral packing, we have studied the crystal twinning and various types of defects in the AMS-8-type structure (SG \(Fd\bar{3}m\)) in detail. The structure can be described as a stacking of two kinds of layers made of these two polyhedra along the \(\langle 111\rangle\) directions. One layer is composed of only \(5^{12}\) polyhedra arranged in a Kagomé net (layer A, B or C). The other has \(5^{12}\) and \(5^{12}6^{4}\) polyhedron (layer \(\upalpha\), \(\upbeta\) or \(\upgamma\) and \(\upalpha^{\prime}\), \(\upbeta^{\prime}\) or \(\upgamma^{\prime}\) for their mirrors). The crystal twinning in \(Fd\bar{3}m\) can be easily built by replacing the \(\upalpha\), \(\upbeta\) or \(\upgamma\) layer by their mirror structure on the top of the \(5^{12}\) polyhedron layer; e. g., the packing sequence of \(\ldots\mathrm{A}\upalpha\mathrm{B}\upbeta\mathrm{C}\upbeta^{\prime}\mathrm{B}\upalpha^{\prime}\mathrm{A}\ldots\) and the center of layer \(\mathrm{C}\) is the mirror plane (Fig. 29.34a-fc) [29.155, 29.160].

There are several planar defects observed in the \(Fd\bar{3}m\) structure. Figure 29.34a-fd shows HRTEM images projected along the \([\bar{1}10]_{\text{cub}}\) direction showing a defect layer with \(P6/mmm\) symmetry. The stacking layer between the same two \(5^{12}\) polyhedron layers (layer B) is named layer \(\upsigma\), so the defect layer has the \(\mathrm{A}\upalpha\mathrm{B}\upsigma\mathrm{B}\upalpha^{\prime}\mathrm{A}\) stacking sequence, which can be well explained by introducing the \(5^{12}6^{2}\) and \(5^{12}6^{3}\) polyhedron suggested by Frank and Kasper, with the \(5^{12}6^{3}\) polyhedron arranged in a triangular net and the \(5^{12}6^{2}\) polyhedron lying in the center. The proposed model was verified by the schematic drawing of the layers and simulated HRTEM images inserted in the HRTEM image [29.155, 29.160]. However, the other planar defect cannot be built using only these four Frank–Kasper polyhedra. Three new unique polyhedra (\(4^{1}5^{10}6^{2}\), \(4^{2}5^{8}6^{5}\) and \(4^{1}5^{10}6^{4}\)) were introduced, as shown in Fig. 29.34a-fe. The defect layer has monoclinic symmetry (\({C}2/{m}\)) [29.160]. All of them were discovered in Matzke's experiment on a random foam structure [29.161]. By different packing features, other related structures with unique stacking sequences can also be observed (Fig. 29.34a-ff), that is, \(Fd\bar{3}m\), z-phase and \(\upmu\)-phase [29.162, 29.163]. All of these structures can be explained by three kinds of polyhedral layers with different stacking sequences. Specifically, the structure with the \(\upmu\)-phase has large repeating units with the stacking sequence \(|\text{AzA}\upalpha\text{BzB}\upbeta\text{CzC}\upgamma|\), and \(\mathrm{13}\) polyhedra in the rhombohedral unit cell.

The polyhedron packing model of tcp structure provides us with a wealth of information about the relationship between different structures and the mechanism of crystal growth. It also shows the possibility of identifying the structural type, and generates new defect structures by introducing different types of polyhedra based on HRTEM image simulations.

Mesoscale Quasicrystal

Quasicrystalline structures have been reported in metallic alloys, dendrimeric supramolecular liquid crystals, ABC-star and linear terpolymers [29.164], colloids and inorganic nanoparticles, showing the potential applications in several forms [29.165]. In the silica mesoporous crystal systems, although we observe the icosahedral morphology and ED patterns with tenfold symmetry (Fig. 29.33a,b), the material turned out not to be quasicrystalline, but multiply twinned particles of ccp (space group \(Fm\bar{3}m\)).

Nevertheless, the Frank–Kasper quasicrystalline phases can be generated by mesoporous silica with tcp structure from a dodecagonal quasiperiodic tiling. For this instance, the position of the cages can be defined to an underlying tiling template made of squares and/or triangles. Figure 29.35a-e shows the synthesis field diagram of the AMS system [29.166], in which a few tcp structures can be formed. The \(Pm\bar{3}n\) structure is formed by the stacking of both \(5^{12}\) and \(5^{12}6^{2}\), showing the \(4^{4}\) tiling. To fabricate the dodecagonal square-triangle tiling, the \(5^{12}6^{3}\) with threefold symmetry is necessary. Therefore, the \(Pm\bar{3}n\) can be changed into Cmmm (\(3^{3}4^{2}\)) and \(P4_{2}/mnm\) (\(3^{2}434\)). The structure finally changed into the quasiperiodic tiling with the increase in the triangle/square ratio to \(4/\sqrt{3}\approx{\mathrm{2.31}}\).

Fig. 29.35a-e

The structural change of the tcp structure into quasicrystal form. (a) The synthesis field diagram of the mesoporous silica in an AMS synthesis system. (bd) TEM images and corresponding indexed FDs (top right insets) taken along the [001] axis for the \(Pm\bar{3}n\) (b), \(Cmmm\) (c) and \(P4_{2}/mnm\) (d) structures. The square and triangle tilings of the \(Cmmm\) structure are enlarged, showing the positions of the mesocages, in which the \(5^{12}6^{3}\) plays an important role in the triangle formation. (e) The Stampfli tiling with corresponding ED pattern

A quasicrystalline mesoporous silica with dodecagonal symmetry was successfully formed by the combination of \(5^{12}\), \(5^{12}6^{2}\) and \(5^{12}6^{3}\) with the correct triangle/square ratio and investigated by HRTEM, as shown in Fig. 29.36a-d [29.2]. The particles exhibit an extraordinary dodecagonal morphology with a diameter of a few micrometers, which strongly indicates an inherent aperiodicity of the structure, as the dodecagonal symmetry is incompatible with periodicity. The cross-sectional images of the particle were investigated by HRTEM, revealing that the structure can be represented as the square-triangle tiling. A quasicrystalline order was realized in the central region of the tiling, confirmed with ED patterns showing a perfect dodecagonal symmetry. A quantitative higher-dimensional analysis of the central tiling in some of the particles has demonstrated a close proximity to ideal quasicrystallinity. The central region is usually surrounded by \(\mathrm{12}\) fans of crystalline domains, each of which is composed of a periodic structure that is isostructural to the Cmmm structure. The distribution can be understood by SAD with different SA apertures. When the peripheral fans are included in the selected area, as shown in the right figure, a continuum of weak spots as well as diffuse components is observed along with strong and sharp spots. These additional reflections are dramatically reduced or disappear when the selected area is contracted in the center. One notable extra peak can be attributed to \(\mathrm{400}\) of Cmmm structure. As described by Sadoc et al [29.167], the dodecagonal square-triangle tiling has the slightly higher surface area compared to the Weaire–Phelan phase, which is a relaxed form of the \(Pm\bar{3}n\) structure and has the by far lowest surface area of all the known tcp structures.

Fig. 29.36a-d

Mesoporous particles with dodecagonal morphology and associated electron microscopy. (a) SEM images taken from the sample, showing the dodecagonal shape. (b) HRTEM image taken from the center part of the particle. (c) Electron diffraction pattern taken from the central part of a particle, as indicated by the white circle in the inset. (d) Electron diffraction pattern taken from the whole part of a particle. From [29.2]

Chiral Mesoporous Silica

Che et al succeeded in synthesizing chiral mesoporous materials using the chiral anionic surfactant sodium \(N\)-acyl-l-alanate with an aminosilane or a quaternized aminosilane as a co-structure-directing agent [29.168, 29.169]. The crystals showed characteristic morphologies of either twisted hexagonal rod-like morphology, with a diameter of \(130{-}180\,{\mathrm{nm}}\) and a length of \(1{-}6\,{\mathrm{\upmu{}m}}\), or spiral tubes as shown in Fig. 29.37a-f. They exhibit a 2-D hexagonal lattice with one-dimensional (1-D) channels with a diameter of \({\mathrm{2.2}}\,{\mathrm{nm}}\) and unit cell parameter of \({\mathrm{4.4}}\,{\mathrm{nm}}\). From these observations, these crystals appear to be chiral; however, in order to use chiral materials for various applications, it is essential to fully study the chirality they exhibit, that is, knowledge of the existence of chiral channels and their chiral direction (i. e., left- or right-handedness) by TEM.

If we can place a chiral crystal horizontally and align the channel direction on a tilting axis, then it is easy to determine the hand through the shift of (10) fringes upward or downward by tilting the crystal.

The method was developed for the general case in which the channel direction is not on the crystal-tilting axis. After tilting, one side of the crystal moves upward and the other side moves downward.

Fig. 29.37a-f

Twisted tube: SEM image of left-handed chiral crystals (a), schematic drawing of side view along \(\langle 10\rangle\) (b), a cross section (c) and schematic drawing of chiral channels in the tube (d). Spiral tube: SEM image of right-handed chiral crystals (e) and its side view (f). Reproduced with permission from [29.168]. Copyright © 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Some fringes corresponding to the (10) plane with a spacing of \(d_{10}={\mathrm{0.866}}\,{\mathrm{\AA{}}}\) are observed intermittently along the tube direction in the TEM image, as indicated by arrows in Fig. 29.38a,ba and b, showing the tilting effect on the {10} fringes in TEM images: TEM image of the tube (Fig. 29.38a,ba) and the same tube viewed after being tilted through \(\approx 20^{\circ}\) (Fig. 29.38a,bb).

Fig. 29.38a,b

Observed tilting effect on the {10} fringes in TEM images: TEM image of the tube (a) and the same tube viewed after being tilted through \(\approx 20^{\circ}\) (b). All intermittent {10} fringes curve to the same direction toward the right. The chiral direction (hand) can be determined by tilting. Reproduced with permission from [29.168]. Copyright © 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Fig. 29.39

HRTEM image simulation of twisted tube showing effect of crystal tilt on the \(\langle 10\rangle\) fringes through the projected potential maps and simulated images. Simulation conditions are as follows: weak phase object approximation, acc. voltage \(={\mathrm{300}}\,{\mathrm{kV}}\), \(C_{\mathrm{s}}={\mathrm{1.0}}\,{\mathrm{mm}}\), \(C_{\mathrm{c}}={\mathrm{1.0}}\,{\mathrm{mm}}\), defocus \(={\mathrm{203}}\,{\mathrm{nm}}\), OL aperture \(={\mathrm{2}}\,{\mathrm{nm}}\). Reproduced with permission from [29.168]. Copyright © 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

From the focus condition, we can judge that part A is upper or lower. Let us assume that part A is upper after tilting the crystal by \(\theta=15^{\circ}\). Simulations of projected potential maps and simulated images (Fig. 29.39) clearly indicate that the vertical (10) fringes (Fig. 29.39a) will change toward right-curled fringes (Fig. 29.39b) if the chiral direction is left-handed.

In the same way, we can determine the directions of the chiral channel and spiral direction of a crystal. Comparing the observations with simulated ones, we have only observed spiral tubes with the same direction as chiral channels.

Triply Periodic Minimal and Constant Mean Curvature Surface Mesostructures

In mathematics, a minimal surface is defined as a surface having zero mean curvature \(H\) everywhere; a surface with \(H\) constant is called a constant mean curvature ( ) surface; For a fixed lattice and space group, there is a family of the corresponding CMC surfaces [29.170]. The triply periodic minimal surface ( ) and CMC surface structures have been widely discovered in the biological and artificial self-organized systems, from butterfly wing scales to lyotropic liquid crystals and block copolymer melts. These structures are of great interest because of their complex and highly symmetrical structures with extraordinary material properties. The best-known examples include three basic categories:
  1. 1.

    The Schoen gyroid (G ) surface

  2. 2.

    The Schwarz diamond (D ) surface

  3. 3.

    The Schwarz primitive (P) surface [29.171].

In these structures, a single balanced continuous matrix with the CMC interfaces on both sides separate two intertwined labyrinths, which are well known as bicontinuous phases or interpenetrating networks. These structures can thus be called double-gyroid (DG ), double-diamond (DD ) and double-primitive (DP ) structures.

In the phase diagram of the mesoporous crystals, the TPMS and CMC structures appear between the lamellar and cylindrical phases with low organic/inorganic interfacial curvature. The structural transformation from lamellar to TPMS and/or CMC structures and to cylindrical has been followed with interest to understand the structural formation in both biological and artificial systems. 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-surface and G-surface structures [29.174]. 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.

We show an unexpected mesostructural change of cage-type \(\rightarrow\) 2-D cylindrical \(p6mm\) \(\rightarrow\) epitaxial intergrowth of \(p6mm\), and D-surface \(\rightarrow\) epitaxial intergrowth of \(p6mm\) and G-surface \(\rightarrow\) D-surface \(\rightarrow\) G-surface \(\rightarrow\) lamellar [29.172]. The HRTEM image showed that the cylinders of \(p6mm\) are parallel to the \(\langle 110\rangle\) of the D-surface with a {11}2-D-hex \(\leftrightarrow\) {221}D relationship (Fig. 29.40a-da). While for the G-surface, two kinds of connection were found. It can be clearly observed from the HRTEM image that the cylinders of \(p6mm\) parallel to the \(\langle 111\rangle\) of the G side by side with both {10}2-D-hex \(\leftrightarrow\) {211}G and {10}2-D-hex \(\leftrightarrow\) {220}G relationship (Fig. 29.40a-db–c). For the {10}2-D-hex \(\leftrightarrow\) {220}G intergrowth, the cylinders of the \(p6mm\) domain cannot fit well with the G domain perfectly, creating numerous defects with elliptical channels at the boundary (marked by the red arrows in Fig. 29.40a-dc). Interestingly, the sample with the D-surface showed spherical morphology with inner polyhedron hollows (icosahedra, such as those observed for proteins of virus capsids, decahedra and Wulff polyhedra) formed by the reversed multiply twinned D-surface structure (Fig. 29.40a-dd) [29.173]. In addition, the local \(g\) parameter of both D- and G-surface have been calculated from electron crystallography reconstruction by the mean curvatures and Gaussian curvatures of the equi-electrostatic potential surface.

Fig. 29.40a-d

TEM images of the samples synthesized with \(\mathrm{C_{18}GluA}\) and Brij-56. (a) Intergrowth of \(p6mm\) and D-surface structure, taken along the [110] cubic axis (b,c) intergrowth of \(p6mm\) and G-surface, taken along the [111] cubic axis, (d) D-surface sphere with a hollow icosahedron. Reprinted with permission from [29.172] and [29.173]. Copyright 2011 American Chemical Society

The reversed multiply twinned polyhedron hollow spheres are further investigated. The HRTEM image (Fig. 29.41a) taken from the common \([\bar{1}10]\) axes shows that the twin plane is (111). All of the domains are interconnected via a shared (111) surface and form an icosahedral shape, and the inner surface consists of twenty {111} facets. The FD pattern and the simulated ED pattern are shown in Fig. 29.41b and c, respectively. Interestingly, it has been realized that the twin boundary cannot be built by the stick model; however, the EC-reconstructed 3-D model shows a quite smooth boundary surface of the real silicate wall. This twinning structure shows a new concept of crystal twinning, and the formation mechanism is still under investigations.

Fig. 29.41

(a) HRTEM image with simulated HRTEM image of the twin, (b) corresponding FD, (c) simulated ED pattern, (d) the stick model and (e) the EC-reconstructed 3-D model of the twin. Reprinted with permission from [29.173]. Copyright 2011 American Chemical Society

To drive the self-assembly process into an advanced length scale, microphases formed via the self-assembly of block copolymers have attracted increasing attention for the synthesis of various supermolecular structures. By the core-shell bicontinuous microphase separation and the subsequent silica mineralization, we reported a macroporous silica with D-surface structure (Fig. 29.42) [29.175]. The material consists of a porous system separated by two sets of hollow D-surface frameworks shifted \(0.25c\) along \(\langle 001\rangle\) and adhered to each other crystallographically due to the loss of the mutual support in the unique synthesis, forming a tetragonal structure (space group \(I4_{1}/amd\)). The unit cell parameter was changed from \(a=168\) to \(\approx{\mathrm{240}}\,{\mathrm{nm}}\) with \(c=\sqrt{2}a\) by tuning the synthesis condition, and the wide edge of the macropore size was \(\approx{\mathrm{100}}\) to \(\approx{\mathrm{140}}\,{\mathrm{nm}}\). Electron crystallography is the only way to solve the complex structure in such length scale. In addition, this structure exhibited structural color that ranged from violet to blue from different directions, with the bandgap in the visible wavelength range, which is attributed to the structural feature of the adhered frameworks that have lower symmetry. Calculations demonstrate that this is a new type of photonic structure.

Fig. 29.42

(a,b) SEM images of the macroporous silica. (cf) TEM images recorded from [010], [001], [101] and [111] directions, respectively. The insets show simulated TEM images and the stick models are overlaid on both the TEM images and the simulation. (g,h) Representation of the 3-D reconstruction with the stick model superimposed in the hollow channels (\({\mathrm{1.5}}\times{\mathrm{1.5}}\times{\mathrm{1.5}}\) unit cells). Reprinted with permission from [29.175]. Copyright 2014 American Chemical Society

By tuning the synthesis condition, we found that a single-gyroid-structured mesoporous silica was evolved in the synthesis system of the double diamond (Fig. 29.43) [29.176]. The structure of the single-gyroid scaffold was solved by electron crystallographic 3-D reconstruction. The intergrowth between the cubic double-diamond and single-gyroid scaffolds was directly observed and investigated by electron microscopy. It was found that the transformation of the original unshifted double diamond and the single gyroid had taken place with an epitaxial relationship in which the \(\langle 110\rangle_{\text{DD}}\) axis was parallel to the \(\langle 001\rangle_{\text{SG}}\) side by side, and the unit cell parameter distortion by \(a_{\text{DG}}=a_{\text{DD}}\sqrt{2}/2\). It was also observed that the nodes of one structure were evolved by either pulling apart or merging to fuse with the other structure. As the system contains no chiral chemical components, the symmetry between right-handed and left-handed is preserved. We expect that our finding of the macroporous silica could outline a new concept for understanding the structural relationships of these relevant biological materials and could be applied to further synthesis of these complex architectures.

Fig. 29.43

(ac) HRTEM images of the single-gyroid structure taken from [100], [110] and [111] directions. (d,e) The SEM image of the structural relationships between double diamond and single gyroid. (f) The HRTEM image taken from the sliced sample and the structural model of the intergrowth. Reprinted with permission from [29.176]. Copyright 2016 American Chemical Society

Two-Dimensional Mesoporous Structures

It is very difficult to solve crystal structures solely from powder XRD data, even for the relatively simple 2-D structure. However, the structural features of 2-D mesoporous crystals can be observed by TEM images taken along the channel direction. The mesoporous material FSM-16 has an ordered 2-D structure, which was synthesized from the layered polysilicate kanemite (Fig. 29.44a and b). The HRTEM image of FSM-16 shows highly ordered mesopores with sixfold symmetry along the channel direction, which is difficult to reconcile with their folded sheet formation mechanism, and it can be concluded that the kanemite sheets were dissolved and formed the 2-D hexagonal \(p6mm\) structure by a rearrangement process [29.177]. Another type of 2-D structure mesoporous material, KSW-2, was also synthesized from same the kanemite as for FSM-16, but under more moderate conditions. Nevertheless, KSW-2 shows the \(c2mm\) structure, which is the evidence of the folded sheet mechanism originally proposed for FSM-16, can be clearly identified [29.153]. The HRTEM image and the schematic drawing for the formation mechanism are shown in Fig. 29.44c.

Fig. 29.44

(a) Schematic drawing of a kanemite sheet and the expanding effect of surfactant. (b) HRTEM images of FSM-16 and (c) HRTEM images of KSW-2 and (d) the schematic drawing corresponding to the images. Reprinted from [29.177], with permission from Elsevier

Periodic mesoporous organosilicas are an exciting hybrid inorganic–organic mesoporous crystal reported by Inagaki et al He further succeeded in synthesizing a hybrid benzene-silica mesoporous crystal with a crystal-like pore wall and 3-D structure. This material has a hexagonal mesoporous system with a lattice constant of \({\mathrm{52.5}}\,{\mathrm{\AA{}}}\) and crystal-like pore walls that exhibit structural periodicity with a spacing of \({\mathrm{7.6}}\,{\mathrm{\AA{}}}\) along the channel direction. Reflections from both mesoscopic and atomic orders were observed in an ED pattern. From the HRTEM image, the mesostructures and the atomic ordering were both observed from the same origin/crystal (Fig. 29.45). It is worth noting that in taking HRTEM images, the defocus conditions needed to achieve clear contrasts for mesoscopic structures (at under or over focus conditions that largely deviate from Scherzer focus) and atomic structures (at Scherzer focus condition) are completely different. This is because of the dependence of contrast transfer function (CTF ) on defocus value \(\Updelta f\). In this case, the adjustment of the defocus value \(\Updelta f\) through CTF needs to be well balanced to see the information from both scales [29.154, 29.44].

Fig. 29.45

(a) HRTEM image and ED pattern taken from the [001] direction of the mesoporous benzene-silica, parallel to the channels. (b) Image and ED pattern taken with [100] incidence, perpendicular to the channels. (c,d) Schematic drawing of the uniform mesopores with a diameter of \({\mathrm{38}}\,{\mathrm{\AA{}}}\), and the lattice fringes with a spacing of \({\mathrm{7.6}}\,{\mathrm{\AA{}}}\) are observed in the pore walls. After [29.44]

29.9.5 MOFs and Other New Frameworks

MOFs are a relatively new class of ordered porous solids [29.13]. Their flexibility and structural and functional tenability have converted MOF science into one of the fastest-growing fields in chemistry. The rapid evolution of this area of research has been accompanied by the developments in cluster chemistry, advances in organic chemistry, improvements in characterization techniques and increasing demands in potential industrial applications. MOFs present several virtues such as good thermal stability, very low densities accompanied by large internal areas that can extend beyond \(\mathrm{6000}\) \(\mathrm{m^{2}/g}\) and a great diversity of synthetic methods. As a consequence, MOFs have been widely studied for use in diverse applications including catalysis, gas storage or gas separation, and drug delivery [29.178, 29.179, 29.180, 29.181].

There are currently different synthetic approaches for obtaining targeted MOF materials, and several parameters can be tuned, influencing the structure of the final material; for example, while keeping the topology significant, attention has been paid to the production of new organic linkers with different lengths, bond angles and chirality that will influence the final structure of the MOF. The structural features can be divided into two components: secondary building units (SBU s) formed by clusters or metal ions, and organic molecules linking them; as a result, these parameters give countless combinations for creating novel materials—for example, the SBUs can be substituted while the linker is the same—targeting specific properties.

As might be expected, the characterization of MOFs plays a crucial role in the development of this part of modern chemistry; the choice of analysis is dictated by their periodic structure, SBUs, organic linkers and large surface areas. The most important characteristics of MOFs are precisely controlled surface area and porosity. The former is commonly analyzed by the Brunauer–Emmett–Teller method [29.182]. Thermal stability is a very important characteristic of MOFs, and it will determine many of their industrial applications. A direct method for measuring their thermal stability is thermogravimetric analysis ( ), which measures the mass changes as a function of temperature. As expected, owing to the periodic structure of MOFs, the most common method for analyzing their structure relies on x-ray diffraction (XRD) measurements; this technique enables a structural solution in some cases, providing information about reproducibility or even explaining structural differences between samples obtained through different approaches [29.183]. Neutron diffraction is complementary to XRD and it helps to shed light on structural details, especially in cases of complex architectures. On the other hand, these techniques require a considerable amount of sample, something that is complicated when new methods of synthesis are tested, or the difficulty of obtaining large enough crystals of sufficiently good quality to obtain a response by any of the methods. Transmission electron microscopy studies address this issue and can provide unique information regarding the characterization of this type of materials [29.123, 29.184].


In 2012, Wiktor et al [29.56] reported the results obtained in MOF-5; for that experiment, the accelerated voltage was reduced to \({\mathrm{80}}\,{\mathrm{kV}}\) and the data were acquired using a low-temperature (liquid nitrogen) holder in an aberration-corrected microscope (Fig. 29.46). Electron diffraction micrographs along the [100] zone axis were recorded, proving the cubic nature of MOF-5. Furthermore, high-resolution images were also acquired under almost zero defocus, and the spherical aberration correction allowed together with image simulations the visualization of the organic linkers and the inorganic zinc species, especially after image filtration. The same year, similar observations were performed at \({\mathrm{200}}\,{\mathrm{kV}}\) in a noncorrected column and at liquid nitrogen temperature to observe the lattice fringes of COK-15, which presented repetitive \({\mathrm{5}}\,{\mathrm{nm}}\) mesopores.

Fig. 29.46

(a) High-resolution TEM image of intact MOF-5 crystals. White dashed lines indicate the type of surfaces of a single nanocrystal. Inset: FFT corresponding to the [100] zone axis orientation of MOF-5. (b) Enlarged image of region indicated by the white box in (a). The inset corresponds to the simulated image (\({\mathrm{10}}\%\) of noise). (c) Filtered version of (b). The inset image simulation is noise-free. Reprinted from [29.56], with permission from Elsevier


In this case, Zn-MOF-74 crystals [29.186] with sizes of \({\mathrm{1}}\,{\mathrm{\upmu{}m}}\) were the subject of analysis; this MOF falls in the \(R\bar{3}m\) symmetry, with lattice parameters \(a=b={\mathrm{25.93}}\,{\mathrm{\AA{}}}\), \(c={\mathrm{6.83}}\,{\mathrm{\AA{}}}\); \(\alpha=\beta=90^{\circ}\), \(\gamma=120^{\circ}\). For the preparation of Zn-MOF-74, industrial synthesis conditions were employed, proving the scalability of this synthesis mechanism, at room temperature and with water as solvent [29.186]. Figure 29.47 depicts the schematic model corresponding to Zn-MOF-74 material that would be the product of the preparation described above; the gray polyhedra corresponds to Zn, O appears in red, while C is colored in brown. The structure can be understood in terms of a pore-channel-like system where the organic linkers are connected by triangular Zn clusters forming a three-dimensional porous network. Although the crystals are large enough, allowing a good characterization by powder x-ray diffraction, electron microscopy can provide important information, as it allows the visualization of the porous system. As the \(C_{\mathrm{s}}\)-corrected STEM makes use of an annular dark-field detector, the inorganic clusters may appear much brighter in comparison with the organic linkers. Figure 29.48a-d displays the electron microscopy analysis of one Zn-MOF-74 particle [29.185]. Figure 29.48a-da,b depicts the \(C_{\mathrm{s}}\)-corrected STEM images at different magnifications which were collected using an electron dose of \({\mathrm{0.20}}\,{\mathrm{e^{-}/(A^{2}{\,}s)}}\), with the time of \({\mathrm{10}}\,{\mathrm{\upmu{}s/pixel}}\) and image size of \({\mathrm{1024}}\times{\mathrm{1024}}\) pixels. The high-resolution images show the hexagonal channel conformation through the MOF-74 particle. The Fourier transform presented in Fig. 29.48a-dc shows the resolution achieved this case by the identification of the \((4\bar{5}0)\) diffraction spot situated at \({\mathrm{2.90}}\,{\mathrm{\AA{}}}\). The fact that the maximum capabilities of the modern microscopes (which can easily achieve \({\mathrm{0.8}}\,{\mathrm{\AA{}}}\)) cannot be fully reached is related to the low stability of these materials, which results in a low signal-to-noise ratio image. Nevertheless, the information extracted by electron microscopy methods is of paramount importance in order to observe the structure, analyze defects or study loaded elements in the structure. Figure 29.48a-dd corresponds to the Fourier-filtered data obtained from Fig. 29.48a-db, in which the Zn clusters are evidenced as bright spots. Unfortunately, due to the low stability, atomic columns are not yet elucidated. Figure 29.48a-dd confirms the triangular conformation of the Zn atoms, which are separated from each other by a projected distance of \({\mathrm{2.07}}\,{\mathrm{\AA{}}}\). The experimental pore size measured from the electron microscopy images is \({\mathrm{17.32}}\,{\mathrm{\AA{}}}\), which is in good agreement with the theoretical \({\mathrm{17.28}}\,{\mathrm{\AA{}}}\).

Fig. 29.47

Polyhedral model where Zn appears in gray, C in brown and O in red, projected along the [001] orientation

Fig. 29.48a-d

\(C_{\mathrm{s}}\)-corrected STEM-ADF analysis of Zn-MOF-74. (a,b) Images of the edge of a crystal at different magnifications observing the pore distribution; the Zn clusters appear in white. (c) FFT diffractograms of (b), indexed assuming \(R\bar{3}m\) symmetry. The spot situated at \({\mathrm{2.90}}\,{\mathrm{\AA{}}}\) is marked by a white arrow. (d) Fourier-filtered image of (b), with a magnified image of a pore shown in the inset. The Zn clusters are delimited by dashed lines showing their triangular nature. Reproduced with permission from [29.185]. Copyright © 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Among the numerous benefits that electron microscopy can add to the characterization of porous networks, the analysis of samples that are obtained at the nanoscale which cannot be analyzed by single or powder x-ray diffraction is undoubtedly of critical importance. Some applications of the MOFs would benefit from crystals with very low dimensions [29.187, 29.188, 29.189, 29.190, 29.191, 29.192]; for example, reaction kinetics can be improved due to shorter distance that reactants have to travel into the active sites, or the regeneration of poisoned centers can be carried out more quickly in small materials. On the other hand, characterization of these solids is complicated if the size is too small and falls below the detection limit of conventional x-ray diffractometers.

Among other techniques such as \(\mathrm{N_{2}}\) adsorption/desorption isotherms, thermogravimetric analyses or FTIR spectroscopy, electron microscopy will provide additional information for a complete characterization. First of all, it will help to extract an accurate particle size; Fig. 29.49a shows a \(C_{\mathrm{s}}\)-corrected STEM-ADF image of several nanocrystals of Zn-MOF-74 with an average size of \({\mathrm{15}}\,{\mathrm{nm}}\times{\mathrm{50}}\,{\mathrm{nm}}\). Although they seem to be partially aggregated, they can be clearly identified as individual entities. The morphology can be described as elongated, faceted nanoparticles similar to those found in the conventional micrometer-sized Zn-MOF-74. Figure 29.49b shows a fully oriented \({\mathrm{20}}\,{\mathrm{nm}}\) crystal along the [001] direction with the pores parallel to the electron beam, exhibiting a hexagonal pore arrangement similar to the conventional MOF-74 presented in Fig. 29.49. With this data, it is now possible to conclude the successful synthesis of nanosized MOF-74 crystals. Figure 29.49c corresponds to a magnified image of the pores, with the fast Fourier transform ( ) shown in the inset, confirming the \(R\bar{3}m\) symmetry. Figure 29.49d displays another nanoparticle with the channels oriented perpendicular to the electron beam, sitting on the [211] direction.

Fig. 29.49

(a\(C_{\mathrm{s}}\)-corrected STEM-ADF image of several nanosized Zn-MOF-74 crystals. (b) Nanoparticle faced along the [001] zone axis. (c) Fourier-filtered image of (b) displaying the hexagonal array of pores with the FFT shown in the inset. (d) A different crystal oriented along the [211] zone axis with the FFT inset. Reprinted with permission from [29.192]. Copyright 2014 American Chemical Society

HRTEM observations were also performed for direct observations of several members of a series of compounds having the structures of expanded versions of MOF-74, M2(2,5-DOT) (M \(=\) \(\mathrm{Zn^{2+}}\), \(\mathrm{Mg^{2+}}\); DOT \(=\) dioxidoterephthalate) [29.123]. These MOF materials have the structures 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 a series of isoreticular (that means having the same topology) MOF-74 structures (named IRMOF-74-I to XI) with their pore sizes ranging from \(\mathrm{1.4}\) to \({\mathrm{9.8}}\,{\mathrm{nm}}\). In this study, the crystalline structures including defect structures of several kinds of MOF and COF materials are visualized by HRTEM. The transmission electron microscope used for HRTEM observations is a JEM-2010F equipped with a CEOS post-specimen spherical aberration corrector (\(C_{\mathrm{s}}\) corrector) operated at \({\mathrm{120}}\,{\mathrm{kV}}\). In order to reduce the electron beam damage, the beam densities were reduced to \({\mathrm{50}}\approx{\mathrm{150}}\,{\mathrm{e^{-}/(nm^{2}{\,}s)}}\) during observations. a series of images (up to \(\mathrm{10}\) frames) was taken with an exposure time for each frame of \(\mathrm{0.5}\) or \({\mathrm{1}}\,{\mathrm{s}}\). In order to increase the signal-to-noise ratios (SNRs) of the images, several frames were superimposed after sample drift compensations. Simulations for HRTEM images were performed using MacTempas software. Figure 29.50 shows the HRTEM images of arrangements of pores (or channels) of IRMOF-74-VII (Fig. 29.49a) and IRMOF-74-IX (Fig. 29.50b). Ordered pores of the six-membered ring (surrounded by six channels) arranged in a honeycomb hexagonal structure can be easily identified. The fast Fourier transform () patterns of the corresponding square areas in RMOF-74-VII and IRMOF-74-IX are inserted in the top left side of Fig. 29.50a,b. In each FFT pattern, six reflection spots corresponding to the {110} planes can be clearly identified. The \(d\)-spacings were measured at \(\mathrm{3.95}\) and \({\mathrm{5.57}}\,{\mathrm{nm}}\) for IRMOF-74-VII and IRMOF-74-IX, respectively. These values are in good agreement with the \(d\)-spacing values of \({\mathrm{4.59}}\,{\mathrm{nm}}\) (IRMOF-74-VII) and \({\mathrm{5.69}}\,{\mathrm{nm}}\) (IRMOF-74-IX) derived from the x-ray crystal structure analyses. The HRTEM image in Fig. 29.50c shows the defects formed in the four-membered ring (surrounded by four channels) and eight-membered ring (surrounded by eight channels).

Fig. 29.50

(a) HRTEM image of IRMOF-74-VII, inset with the FFT pattern of the square area. (b) HRTEM image of RMOF-74-IX, inset with the FFT pattern of the square area. (c) Defects formed in the four-member-ring (surrounded by four channels) and eight-member-ring in the channel arrangement of RMOF-74-IX


The metal organic frameworks designated as -\(n\) (Materials of the Institute Lavoisier) series were first synthesized by Ferey's group in 2002 [29.193]. The MIL-\(n\) type of nanoporous materials are of particular interest due to their simple structure and higher thermal stability compared to other MOFs. Among the MIL-\(n\) materials, MIL-53(Al or Cr) has been found to adsorb large amounts of gases such as \(\mathrm{CH_{4}}\) and \(\mathrm{CO_{2}}\) [29.194, 29.195]. This uptake is afforded through a singular mechanism known as breathing allowing the material to accommodate a larger amount of gases by severe and reversible structural transformation, which takes place at different pressure depending on the nature of the gas guest. In other words, MIL-53(Al or Cr) is able to adjust its cell volume in a reversible manner to optimize interactions between the guest molecules and the framework, with no evidence of bond breakage. Considerable effort has been devoted to the characterization of the breathing effect in MIL-53 [29.196, 29.197]. On our side, we tried to image MIL-53(Al) prepared in an environmentally sustainable manner, i. e., room temperature and water as a solvent via the use of linker salt instead of acid [29.186].

MIL-53 is built from infinite chains of corner-sharing \(\mathrm{M_{4}(OH)_{2}}\) octahedra (M \(=\) \(\mathrm{Al^{3+}}\), \(\mathrm{Cr^{3+}}\), \(\mathrm{Fe^{3+}}\)), interconnected by the dicarboxylate groups of the benzenedicarboxylate units. The chemical formula is given by M\({}^{\text{III}}\)(OH)(BDC) or M(OH)(\(\mathrm{O_{2}C}\)\(\mathrm{C_{6}H_{4}}\)\(\mathrm{CO_{2}}\)) [29.198]. In this way, a 3-D microporous framework with 1-D diamond-shaped channels with a free internal diameter of about \({\mathrm{0.85}}\,{\mathrm{nm}}\) is formed (Fig. 29.51a,b).

Crystal data reported for MIL-53(Al) synthesized using hydrothermal method [29.196] are as follows: orthorhombic system, Pnma, (no. \(\mathrm{62}\)) \(a={\mathrm{17.129}}(2)\), \(b={\mathrm{6.628}}(1)\), \(c={\mathrm{12.182}}(1)\,{\mathrm{\AA{}}}\) which changes the orthorhombic system, Imma (no. \(\mathrm{74}\)), \(a={\mathrm{6.608}}(1)\), \(b={\mathrm{16.675}}(3)\), \(c={\mathrm{12.813}}(2)\,{\mathrm{\AA{}}}\) upon calcination into MIL-53(Al). The application of the room-temperature synthesis yielded a MIL-53(Al) material formed by agglomerates of nanosized particles having small domains of crystallinity, making its characterization more difficult. In this case, our observations reveal the formation of elongated crystals constituting the agglomerated material, with sizes typically reaching \({\mathrm{200}}\,{\mathrm{nm}}\times{\mathrm{40}}\,{\mathrm{nm}}\) (Fig. 29.52a-ca). The structural lattice of MIL-53(Al)-RT is revealed in Fig. 29.52a-cb along the [100] orientation, proving the diamond-shaped porous system. FFT is shown in the inset, proving the good crystallinity that can be achieved with this synthesis method. Because of the high sensitivity of this material, in order to improve the SNR in the images, the data were Fourier-filtered, as depicted in Fig. 29.52a-cc, which shows a magnified image of the channels. The distances obtained in this case were \(\mathrm{17.1}\) and \({\mathrm{13.0}}\,{\mathrm{\AA{}}}\), similar to those reported for MIL-53(Al) synthesized using the hydrothermal method; however, no significant differences were observed in the material activated for three days in terms of lattice constants and crystallinity.

Fig. 29.51a,b

Schematic representations of MIL-53(Al) (a) showing the channel system. (b) Projection of the infinite chains formed by the octahedra sharing corners, connected by the 1,4-benzenedicarboxylate ligands. Color code: Al \(=\) blue; C \(=\) gray; Fe \(=\) brown; O \(=\) red

Fig. 29.52a-c

\(C_{\mathrm{s}}\)-corrected STEM-ADF images of MIL-53(Al). (a) Low-magnification image showing several crystals. (b) High-resolution image of one MIL-53(Al) particle, with the FFT shown in the inset. (c) Magnified image of the pore system proving the diamond-shaped pores

Observing the breathing effect may be difficult in conventional electron microscopy due to the high vacuum inside the column that would evacuate the material. The recent advances regarding the in situ electron microscopy observations under variable atmospheres may shed light on these transformations. For this purpose, scanning electron microscopy ( ) [29.199] was used at \({\mathrm{70}}\,{\mathrm{Pa}}\) and without previous metallic coating, by means of a Quanta 250 environmental SEM-FEG, at \({\mathrm{10}}\,{\mathrm{kV}}\) and spot size of \(\mathrm{3.5}\). Prior to SEM observations of the MOF, MIL-53(Al) particles were attached to a glass in order to avoid the carbon tape which could interfere with the MOF. While observing an isolated MIL-53(Al) particle, an interesting phenomenon occurred (Fig. 29.53). The volume of the crystal began a transformation over time, and the width decreased while the length increased. This transformation took around \({\mathrm{20}}\,{\mathrm{s}}\) until it was finished. Although the measurements were carried out in an environmental SEM under low pressure, the stimuli that initiated the breathing effect seemed to be the electron beam through an increment of temperature. As expected and as previously reported [29.196], upon heating, the organic molecules trapped inside the pores may be removed and MIL-53(Al) could adopt the ht configuration Imma symmetry, a fact that was observed under the high vacuum of the transmission electron microscope. Despite these conditions, the behavior observed in the environmental SEM did not fulfill that expectation, since the particles attached to the glass seemed to shrink with the electron beam observations; the fact that the MOF particles allow the adsorption of toluene during the attachment treatment [29.199, 29.200] causes the MIL-53(Al)\({}_{\text{tol}}\) behave in a different manner from MIL-53(Al)\({}_{\text{lt}}\); according to lattice constants measured for MIL-53(Al)\({}_{\text{tol}}\) and data reported for xylene-loaded MIL-53(Al) [29.200, 29.201], it seems that when toluene is present, the structure is an intermediate between those of MIL-53(Al) after m- and \(p\)-xylene adsorption through the interaction of the methyl group itself and the carboxylate groups of two opposing terephthalate framework ligands [29.200]. Inside the environmental SEM, as the electron beam rastered over the sample, the toluene desorption began, leading to the formation of the intermediate phase, and in fact explaining the particle shrinkage instead of the expansion that would be expected for MIL-53(Al)\({}_{\text{lt}}\).

Fig. 29.53

Environmental SEM images recorded at 0, 6, 12, 16 and \({\mathrm{20}}\,{\mathrm{s}}\). The graphic shows the particle width and length variations as a function of time. Reprinted from [29.199], with permission from Elsevier


Another example is the observation of metal catecholates (CAT s) synthesized by solvothermal reactions of 2,3,6,7,10,11-hexahydroxytriphenylene (HHTP ) with metal (II) ion (Co and Ni) MOF structures [29.184]. Figure 29.54 shows an HRTEM image of the activated metal catecholate (CAT) Ni-CAT-1 material. Both uniform honeycomb hexagonal arrangement of channels (while an incident electron beam is parallel to the channels) and the channel lateral walls' direction (while an incident electron beam is perpendicular to the channels) can be observed in this image. Defects in the arrangement of the channel lateral walls can be directly found as indicated by the arrow. Aside from the defect structure, the terminal structure of activated Ni-CAT-1 can also be clearly identified from HRTEM observation. Figure 29.55a is an HRTEM image showing the terminated structures of a particle of the activated Ni-CAT-1 material as indicated by the arrows. In order to determine the terminal structure, image simulations are performed. The layered 2-D model is geometrically optimized using molecular mechanics with the MM+ force field. This optimized model and the simulated image using this model are shown in Fig. 29.55b. However, this model is slightly different from the structure deduced by synchrotron radiation XRD analysis of the as-synthesized Ni-CAT-1 single crystal. The main difference is the metal atomic positions of the interlayer complexes. This fact indicates that after the activation process and under the high-vacuum acquisition conditions for HRTEM observations, small changes in the orientation of the complexes may occur.

Fig. 29.54

HRTEM image showing the channel structures of the activated Ni-CAT-1. The defect in channel arrangement is indicated by the arrow. Reprinted with permission from [29.184]. Copyright 2012 American Chemical Society

Fig. 29.55

(a) HRTEM image of activated Ni-CAT-1 showing the terminal structure as indicated by the arrows. (b) Simulated TEM image and the optimized 2-D model structure used for the TEM image simulation. Reprinted with permission from [29.184]. Copyright 2012 American Chemical Society

HRTEM images can provide the detailed crystalline structure of the activated Ni-CAT-1 material. Figure 29.56 shows such an HRTEM image inset with two FFT patterns of their corresponding square areas indicated by the arrows. The honeycomb hexagonal arrangement of the pores in the left side of Fig. 29.56 is along the \(\langle 001\rangle\) direction, which allowed the calculation of the unit cell lattice parameter of \(a={\mathrm{2.02}}\,{\mathrm{nm}}\). This result is in agreement with the value obtained from the x-ray powder diffraction study of Ni-CAT-1 (\(a={\mathrm{2.19}}\,{\mathrm{nm}}\)). It is interesting to find fringes perpendicular to the channel walls in the region inside the yellow square area (right-hand side) of Fig. 29.56. The broad arc 001 reflection in the corresponding inset FFT pattern in the top right of Fig. 29.56 demonstrates that the fringes perpendicular to the pore walls are wavy, which can also be clearly identified in Fig. 29.57a, suggesting the fluctuation of the Ni atomic positions. The curvatures of the lattice fringes along the \(c\) directions were roughly deduced as \(\pm 15^{\circ}\) through analysis of the full width at half maximum of the 001 arc line reflection intensity. The average spacing between these wavy fringes calculated from the FFT patterns is about \({\mathrm{0.32}}\,{\mathrm{nm}}\), which is corresponding to the inter-layer distance of Ni-CAT-1 structure (\({\mathrm{0.33}}\,{\mathrm{nm}}\) according to the x-ray data). The comparison between the HRTEM and simulated image along the [001] direction is shown in Fig. 29.57b. The characteristic six dots in black contrasted inside the white circles in both HRTEM and simulated images match well, further proving the proposed changes in the structure (Fig. 29.57b).

It is also a challenge to observe MOFs using scanning transmission electron microscopy (STEM) , since in STEM mode, a focused beam that has a higher beam density than that in TEM mode is used during observations. Usually, zeolites and mesoporous silicas are damaged much faster in STEM mode than in conventional TEM mode. However, we were able to overcome this challenge and observe a crystalline MOF material for the first time by using STEM mode at \({\mathrm{60}}\,{\mathrm{kV}}\). A JEOL 2100F with a cold field-emission gun equipped with a newly designed DELTA \(C_{\mathrm{s}}\) corrector operated at \({\mathrm{60}}\,{\mathrm{kV}}\) was used for STEM mode observation. In order to analyze the chemical composition in the sample, a Gatan GIF quantum equipped on the above JEM-2100F was used to perform electron energy-loss spectroscopy ( ) analysis in STEM mode at \({\mathrm{60}}\,{\mathrm{kV}}\). In Fig. 29.58a, which is a high angle annular dark-field ( ) image of the activated Ni-CAT-1, the uniform honeycomb arrangement of the channels (in HAADF mode, the channels are in dark contrast) in activated Ni-CAT-1 is clearly observed. However, the crystalline structure collapsed to amorphous after the electron beam scanning at a speed of \({\mathrm{38}}\,{\mathrm{\upmu{}s/pixel}}\) that is used for obtaining adequate SNRs for the HAADF image. The electron energy-loss spectrum in Fig. 29.58b shows the existence of Ni (\(\mathrm{L}\)-edge) and O (\(\mathrm{K}\)-edge) that demonstrates the chemical composition of the activated Ni-CAT-1.

Fig. 29.56

HRTEM image of activated Ni-CAT-1 showing the channel structures. The inset FFT patterns are corresponding to the square areas indicated by the arrows. The magenta arrow indicates a terminal structure of one activated Ni-CAT-1 particle. Reprinted with permission from [29.184]. Copyright 2012 American Chemical Society

Fig. 29.57

(a) FFT pattern of the activated Ni-CAT-1 channel walls demonstrating the wavy characterization of the inter-layers perpendicular to the channel walls. (b) Comparison between the simulated image (upper part) using the 2-D model shown in Fig. 29.56b and the HRTEM image (lower part) taken from the [001] direction. Reprinted with permission from [29.184]. Copyright 2012 American Chemical Society

Fig. 29.58

(a) High-angle annular dark-field (HAADF) image of activated Ni-CAT-1 taken at \({\mathrm{60}}\,{\mathrm{kV}}\). (b) Electron energy-loss spectrum of activated Ni-CAT-1 showing the existence of Ni (\({L}\)-edge) and O (\({K}\)-edge). Reprinted with permission from [29.184]. Copyright 2012 American Chemical Society


In a recent report [29.202], atomic-resolution HRTEM imaging was performed on MOF ZIF-8 with an ultralow electron dose to unravel surface and interfacial structures. In this study, the stability of various MOFs including ZIF-8 was first evaluated under a \({\mathrm{300}}\,{\mathrm{kV}}\)-accelerated electron beam. The results reveal differences in beam tolerance among the MOFs, but they are all highly beam-sensitive in general. They began to lose their crystallinity when the cumulative electron dose reached \(5{-}30\,{\mathrm{e^{-}/\AA{}^{2}}}\), as determined by the fading of the electron diffraction spots (Fig. 29.59). Considering the inevitable exposure to the electron beam during the specimen searching process, the electron dose that can be used for HRTEM imaging is in fact very limited (\(<{\mathrm{10}}\,{\mathrm{e^{-}/\AA{}^{2}}}\)). Conventional scintillator-based cameras cannot render useful images with such a low electron dose . Therefore, a direct-detection electron-counting ( ) camera that exhibits a much higher detective quantum efficiency was used for image acquisition.

Fig. 29.59

Dose-dependent electron diffraction patterns of ZIF-8 crystals displayed in a logarithmic scale. A dose rate of \({\mathrm{1}}\,{\mathrm{e^{-}/(\AA{}^{2}{\,}s^{-1})}}\) was used. The results show that the crystals begin to lose crystallinity when the cumulative dose reaches \({\mathrm{15}}\,{\mathrm{e^{-}/\AA{}^{2}}}\). After [29.202]

The ZIF-8 crystals examined in this work are uniform in size (\(\approx{\mathrm{85}}\pm{\mathrm{15}}\,{\mathrm{nm}}\)) and shape (rhombic dodecahedron). An HRTEM image of ZIF-8 along the [111] incidence is shown in Fig. 29.60, which was taken on an uncorrected FEI Titan electron microscope with a \(C_{\mathrm{s}}\) of \({\mathrm{1.2}}\,{\mathrm{mm}}\), a convergence angle of \({\mathrm{0.2}}\,{\mathrm{mrad}}\) and a focal spread of \({\mathrm{4.5}}\,{\mathrm{nm}}\) at \({\mathrm{300}}\,{\mathrm{kV}}\), using a DDEC ( Gatan K2 summit) camera. The camera counting frame rate is \(\mathrm{400}\) frames per second ( ), and the final image output rate is \({\mathrm{40}}\,{\mathrm{fps}}\) at \({\mathrm{4}}\,{\mathrm{k}}\times{\mathrm{4}}\,{\mathrm{k}}\) resolution. With an exposure of \({\mathrm{3}}\,{\mathrm{s}}\), an image stack of \(\mathrm{120}\) individual frames was obtained at a magnification of \(\mathrm{43000}\) (pixel size: \({\mathrm{0.86}}\,{\mathrm{\AA{}}}\)) with a total electron dose as low as \(\approx{\mathrm{3.0}}\,{\mathrm{e^{-}/pixel}}\) (\(\approx{\mathrm{4.1}}\,{\mathrm{e^{-}/\AA{}^{2}}}\)). The \(\mathrm{120}\) frames were merged into 1 image after alignment. Fast Fourier transform of this image indicates information transfer as high as \({\mathrm{2.1}}\,{\mathrm{\AA{}}}\) (Fig. 29.60a, inset).

The very low framework density of MOFs greatly decreases their effective scattering thickness, and consequently, it is safe to apply the weak-phase object approximation to MOFs for a wide range of thicknesses up to \(\approx{\mathrm{100}}\,{\mathrm{nm}}\). Therefore, a single image can be made more interpretable by correcting the contrast inversion caused by the contrast transfer function (CTF ), if the absolute defocus of the image is known. The defocus value of the image was determined to be \({\mathrm{-550}}\,{\mathrm{nm}}\) by analyzing the Fresnel fringe that appeared at the crystal's edge. In the CTF-corrected image, individual Zn atomic columns in triplet and imidazole rings with two different configurations (edge-on/face-on) in the ZIF-8 structure were identified after denoising by Wiener filtering (Fig. 29.60b, left). Imposing a projection symmetry (\(p31m\)) to the lattice-averaged image results in a very good match to the structural model of ZIF-8 projected along the [111] direction (Fig. 29.60b, middle) and the corresponding simulated projected potential map (Fig. 29.60b, right). These results confirm the intactness of the ZIF-8 crystal structure under the carefully chosen imaging conditions. This confirmation of structural integrity is crucial because it ensures that the observed structural features are intrinsic rather than produced by beam irradiation.

Fig. 29.60

(a) Raw HRTEM image of two connected ZIF-8 crystals taken along the [111] zone axis. Inset is the FFT of the highlighted area, showing an information transfer of \({\mathrm{2.1}}\,{\mathrm{\AA{}}}\). (bLeft, CTF-corrected and denoised (using a Wiener filter) image from the bulk region; middle, symmetry-imposed and lattice-averaged image with a structural model of ZIF-8 embedded; right, simulated projected potential map with a point spread function width of \({\mathrm{2.1}}\,{\mathrm{\AA{}}}\) and a crystal thickness of \({\mathrm{100}}\,{\mathrm{nm}}\). Blue rectangles highlight representative regions where individual atomic columns of Zn and imidazole rings can be identified. After [29.202]

In the first report of HRTEM of ZIF-8 [29.202], the zone axis image was obtained by sampling a large number of randomly oriented crystals. This is an inefficient trial-and-error process and success is not guaranteed. More recently, a suite of methodologies has been developed, including a software to achieve one-step, fast alignment of zone axis to minimize beam damage, an amplitude filter to restore the high-resolution information from noisy low-dose images, and a method to determine the absolute defocus value of the HRTEM image [29.203]. With these methods, the HRTEM of MOFs is becoming a nearly routine process, and a series of MOF materials (ZIF-8, UiO-66, HKUST-1, MIL-101, etc.) has been successfully imaged from multiple zone axes with resolution greater than \({\mathrm{2}}\,{\mathrm{\AA{}}}\) [29.203, 29.204].

Imaging in liquid environments can be achieved in either STEM or TEM mode; for that purpose, a liquid flow cell holder and silicon nitride chips were used [29.205]. For this study, both UiO-66 and ZIF-8 MOF materials were synthesized; UiO-66(Zr) was tested for beam damage purposes, while ZIF-8 was subjected to the nucleation mechanism (Fig. 29.61a-h). To avoid/minimize beam damage, the dose was kept below the threshold value previously obtained [29.206]. The first observation of the initial growth of individual ZIF-8 nanoparticles was observed after \({\mathrm{11}}\,{\mathrm{min}}\) (Fig. 29.61a-ha–d), with a diameter of \({\mathrm{15}}\,{\mathrm{nm}}\) that reached values of \({\mathrm{50}}\,{\mathrm{nm}}\) (Fig. 29.61a-he). The final material was extracted from the cell and also analyzed under dry conditions (Fig. 29.61a-hf) together with selected area electron diffraction (SAED), which confirmed the formation of ZIF-8 (Fig. 29.61a-hg). A graphic with particle size versus time in seconds is presented in Fig. 29.61a-hh, which was in agreement with previous results on the kinetics of ZIF-8 [29.207, 29.58] and suggesting the negligible effect on the electron beam on the ZIF-8 growth.

Fig. 29.61a-h

LCTEM analysis of ZIF-8 self-assembling. (ad) represents the evolution of the ZIF-8 with time. (e) Final image still in liquid environment. The red dashed box indicates the area where Fig. (ad) were recorded. (f) Image of the same area after the cell was dried and (g) the correspondent SAED. (h) Plot showing the mean growth kinetics of individual particles. Reprinted with permission from [29.206]. Copyright 2015 American Chemical Society


Another study presented here deals with the sustainable synthesis of a MOF-100(Fe), which is similar to the current commercial Fe-BTC. The synthesis procedure is based on previously reported sustainable methods [29.208]. For comparison purposes, Basolite F300-like semiamorphous Fe-BTC material was prepared exactly following the same published recipe, but at room temperature [29.209]. To confirm the different structural nature of both Fe-BTC materials prepared at room temperature, the samples MIL-100(Fe)-RT and Fe-BTC-RT were exhaustively studied by STEM using the experimental conditions described in cases above. The observations revealed that MIL-100(Fe)-RT grows in faceted platelets of medium size (\({\mathrm{500}}\,{\mathrm{nm}}\) to \({\mathrm{1}}\,{\mathrm{\upmu{}}}\)). These particles allowed tilting series in the microscope, yielding three different crystal orientations, as shown in Fig. 29.62a-d, corresponding to [211], [111] and [110] orientations of this structure. The FFT shown in the inset confirms the crystal orientation, and it can be indexed assuming \(Fd\bar{3}m\) with a unit cell of \(a={\mathrm{70.74}}\,{\mathrm{\AA{}}}\). The reported unit cell parameter for MIL-110(Fe) with this spatial group is \({\mathrm{73.34}}\,{\mathrm{\AA{}}}\). A closer observation is depicted in Fig. 29.62a-dd, which for better clarity was Fourier-filtered. Because of the large number of atoms forming the unit cell, making MIL-100(Fe)-RT a highly complex material, obtaining atomic resolution data results is tremendously complex. The observations of the semi-amorphous Fe-BTC-RT yielded the exact same structural units as in MIL-100, except that it was found to be extremely difficult to find a crystalline-like particle in the microscope. The only crystal found in Fe-BTC-RT showed a small contraction of the unit cell from \(\mathrm{70.74}\) to \({\mathrm{67.76}}\,{\mathrm{\AA{}}}\). Nevertheless, according to the electron microscopy results, the two materials show an identical structure, that of MIL-100, although with a significant loss of crystallinity in the case of the Fe-BTC Basolite F300 type of material.

Fig. 29.62a-d

\(C_{\mathrm{s}}\)-corrected STEM-ADF images of MIL-100(Fe)-RT recorded along different orientations (a) [211], (b) [111] and (c) [110] with the FFT shown in the inset. (d) Fourier-filtered data for (c) with the simulated data in the inset. Reprinted with permission from [29.208]. Copyright 2017 American Chemical Society


The final example is a recently synthesized COF whose structure has been solved by combining 3-D EDT data, HRTEM imaging, structure modeling, geometry optimization and powder x-ray diffraction ( ) refinement. COF-505 [29.107] is a woven framework that has helical organic threads interlacing a woven crystal structure. It was synthesized by imine condensation of aldehyde-functionalized copper (I)-bis-phenanthroline tetrafluoroborate, \(\mathrm{Cu(PDB)_{2}(BF_{4})}\) and benzidine (BZ ). However, the crystal structure cannot be solved using single-crystal XRD, as the particles are small and seriously aggregated. The crystallinity is also not good enough to solve the structure using the PXRD pattern. Instead, we solve the structure using methods based on electron crystallography. Three-dimensional electron diffraction data were collected from a single submicrometer-sized particle. Both Laue class and unit cell parameters were determined from the reconstructed 3-D reciprocal lattice. The structure of COF-505 was identified as a \(C\)-centered orthorhombic Bravais lattice, and the unit cell parameters were determined to be \(a={\mathrm{18.9}}\,{\mathrm{\AA{}}}\), \(b={\mathrm{21.3}}\,{\mathrm{\AA{}}}\) and \(c={\mathrm{30.8}}\,{\mathrm{\AA{}}}\). The reflection conditions were summarized as \(hkl:h+k=2n\); \(hk0:h,k=2n\); \(0kl:k=2n\). This suggests five possible space groups: \(Cm2a\), Cmma, Cmca, \(Cc2a\) and Ccca. Figure 29.63a-dd shows an HRTEM image of COF-505 taken along \([1\bar{1}0]\) incidence. The plane-group symmetry was identified as pgg, as a result of which three possible space groups—\(Cm2a\), Cmma and Ccca—were excluded. The Fourier analysis of the HRTEM image after imposing space group symmetries was performed to reconstruct a 3-D potential map. The positions of eight copper atoms were located from the maxima of the map. As the chemical compositions have been determined by elemental analysis, the number of building units could also be determined, that is, one unit cell contains 8 \(\mathrm{Cu(PDB)_{2}}\) and 16 biphenyl units. Based on the copper positions and the geometry of the \(\mathrm{Cu(PDB)_{2}}\) complex, the structure of COF-505 was built in the materials studio by putting \(\mathrm{Cu(PDB)_{2}}\) units at copper positions and connecting them through biphenyl molecules. However, symmetry operations of the space group Cmca require two PDB units connected to one copper on a mirror plane perpendicular to the \(a\)-axis, which is not energetically favorable. Therefore, the final space group was determined to be \(Cc2a\). The crystal structure was further geometrically optimized and refined against the PXRD pattern.

Fig. 29.63a-d

Morphology and electron microscopy studies of COF-505. (a) Crystallites aggregated on a crystalline sphere observed by SEM. (b) 2-D projection of the reconstructed reciprocal lattice of COF-505 obtained at \({\mathrm{298}}\,{\mathrm{K}}\) from a set of 3-D-EDT data (the inset shows an image of used crystal). (c) HRTEM image of COF-505 taken with the \([1\bar{1}0]\) incidence (inset shows a 2-D projected potential map obtained by imposing pgg plane-group symmetry). (d) Reconstructed 3-D electrostatic potential map (threshold: \(\mathrm{0.8}\))

29.10 Conclusions

Overall, despite the difficulty in applying transmission electron microscopy to MOF science, the number of publications in this area is growing rapidly due to the great interest that these materials have created. In the current chapter, the main results achieved by TEM have been collected, paying special attention to imaging conditions. The working conditions have evolved from low voltages and liquid nitrogen temperature when the first reports appeared, to working under high accelerating voltage (\({\mathrm{300}}\,{\mathrm{kV}}\)) where controlling the beam dose is crucial in order to acquire the best images possible.

Similarly, as with other cases of porous solids, such as zeolites, or ordered mesoporous materials, mastery of the imaging conditions in the electron microscope is required to obtain information that cannot be obtained by other means. Further studies should continue in the direction of improving the environment to allow for fully exploiting the capabilities of electron microscopes, developing more sensitive detectors and faster acquisition procedures, and of course achieving a better understanding of the damage mechanisms, with the hope of eventually obtaining analytical information of the same quality as that obtained from radiation-insensitive materials.



This work was supported by the Shanghai Pujiang Program (17PJ1406400), Shanghai Natural Science Fund (17ZR1418600), the Young Elite Scientist Sponsorship Program By CAST (2017QNRC001) (Y.M.), the National Natural Science Foundation of China 21571128, the National Excellent Doctoral Dissertation of China 201454, and the Shanghai Rising Star Program 17QA1401700 (L.H.), JST (Japan), VR and Wallenberg Foundation (Sweden) and Foreign Expert Recruiting Program (China) (O.T.). This work is partially supported by CℏEM, SPST, ShanghaiTech under the grant #EM02161943 (Y.M., A.M., P.O. and O.T.). O.T. acknowledges Sir John Meurig Thomas for introducing and guiding him to his fascinating field, the structural study of nanostructured materials by electron crystallography and imaging.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Physical Science and TechnologyShanghaiTech UniversityShanghaiChina
  2. 2.Dept. of MathematicsTongji UniversityShanghaiChina
  3. 3.Inorganic Functional Materials Research InstituteNational Institute of Advanced Industrial Science and Technology (AIST)NagoyaJapan
  4. 4.School of Science and TechnologyShanghaiTech UniversityShanghaiChina
  5. 5.Institute of Catalysis and Petroleum ChemistrySpanish National Research Council (CSIC)MadridSpain
  6. 6.Dept. of PhysicsShanghaiTech UniversityShanghaiChina
  7. 7.Dept. of Crystaline Materials ScienceNagoya UniversityNagoyaJapan
  8. 8.Physical Science and Engineering DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  9. 9.Gatan, Inc.Pleasanton, CAUSA
  10. 10.College of Chemical EngineeringZhejiang University of TechnologyHangzhouChina
  11. 11.Physical ScienceOsaka Prefecture UniversitySakaiJapan
  12. 12.School of Chemistry and Chemical EngineeringShanghai Jiao Tong UniversityShanghaiChina
  13. 13.Centre for High-resolution Electron Microscopy, School of Physical Science and TechnologyShanghaiTech UniversityShanghaiChina

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