Nobuhisa Fujita

Shape- and size-controlled synthesis in hard templates: sophisticated chemical reduction for mesoporous monocrystalline platinum nanoparticles.

Here we report a novel hard-templating strategy for the synthesis of mesoporous monocrystalline Pt nanoparticles (NPs) with uniform shapes and sizes. Mesoporous Pt NPs were successfully prepared through controlled chemical reduction using ascorbic acid by employing 3D bicontinuous mesoporous silica (KIT-6) and 2D mesoporous silica (SBA-15) as a hard template. The particle size could be controlled by changing the reduction time. Interestingly, the Pt replicas prepared from KIT-6 showed polyhedral morphology. The single crystallinity of the Pt fcc structure coherently extended over the whole particle.

Dodecagonal tiling in mesoporous silica

Recent advances in the fabrication of quasicrystals in soft matter systems have increased the length scales for quasicrystals into the mesoscale range (20 to 500 ångströms). Thus far, dendritic liquid crystals, ABC-star polymers, colloids and inorganic nanoparticles have been reported to yield quasicrystals. These quasicrystals offer larger length scales than intermetallic quasicrystals (a few ångströms), thus potentially leading to optical applications through the realization of a complete photonic bandgap induced via multiple scattering of light waves in virtually all directions. However, the materials remain far from structurally ideal, in contrast to their intermetallic counterparts, and fine control over the structure through a self-organization process has yet to be attained. Here we use the well-established self-assembly of surfactant micelles to produce a new class of mesoporous silicas, which exhibit 12-fold (dodecagonal) symmetry in both electron diffraction and morphology. Each particle reveals, in the 12-fold cross-section, an analogue of dodecagonal quasicrystals in the centre surrounded by 12 fans of crystalline domains in the peripheral part. The quasicrystallinity has been verified by selected-area electron diffraction and quantitative phason strain analyses on transmission electron microscope images obtained from the central region. We argue that the structure forms through a non-equilibrium growth process, wherein the competition between different micellar configurations has a central role in tuning the structure. A simple theoretical model successfully reproduces the observed features and thus establishes a link between the formation process and the resulting structure.

A review of fine structures of nanoporous materials as evidenced by microscopic methods

This paper reviews diverse capabilities offered by modern electron microscopy techniques in studying fine structures of nanoporous crystals such as zeolites, silica mesoporous crystals, metal organic frameworks and yolk-shell materials. For the case of silica mesoporous crystals, new approaches that have been developed recently to determine the three-dimensionally periodic average structure, e.g., through self-consistent analysis of electron microscope images or through consideration of accidental extinctions, are presented. Various structural deviations in nanoporous materials from their average structures including intergrowth, surface termination, incommensurate modulation, quasicrystal and defects are demonstrated. Ibidem observations of the scanning electron microscope and atomic force microscope give information about the zeolite-crystal-growth mechanism, and an energy for unstitching a building-unit from a crystal surface is directly observed by an anatomic force microscope. It is argued how these observations lead to a deeper understanding of the materials.

Incommensurate modulation in the microporous silica SSZ-24

A detailed investigation of the structure of microporous silica, SSZ-24, is presented. It is shown by X-ray powder diffraction and (29)Si MAS NMR experiments that the structure deviates from the previously proposed AlPO(4)-5-type structure. At room temperature, electron diffraction (ED) patterns exhibit extra diffraction spots, which can be attributed to an incommensurate structural modulation along the c axis. This in turn results in a pleat pattern in real space with two different intervals arranged aperiodically along the c axis, as observed with high-resolution electron microscopy (HREM). The modulated structure may easily turn into a disordered one through excessive electron irradiation or heat-treatment. In order to understand the origin of the modulation, soft phonon-modes of the ideal premodulated structure were analyzed by the use of the rigid-unit-mode model. The distribution of soft modes in reciprocal space might correspond roughly to diffuse streaks that could be observed in the diffraction patterns at higher temperatures. It was found that several phonon branches soften at specific wave vectors, which are incommensurate with respect to the original period and might be responsible for the modulation. We present a simple analytic treatment to deduce the wave vectors and associated displacement eigenvectors for the incommensurate soft-modes.

Cluster-packing geometry for Al-based F-type icosahedral alloys

This paper presents a new, highly stable, periodic approximant to the Al-based F-type icosahedral quasicrystals, i-Al–Pd–TM (TM = transition metals). The structure of this intermetallic Al–Pd–Cr–Fe compound is determined ab initio using single-crystal X-ray diffraction, where the space group is identified to be Pa{\overline 3} and the lattice constant 40.5 A. The structure is well described as a dense packing of clusters of two kinds, which are called the pseudo-Mackay-type and the mini-Bergman-type clusters. Adjacent clusters can be markedly interpenetrated, while the structure requires no glue atoms to fill in the gaps between the clusters. It is shown that the clusters are centred at the vertices of a canonical cell tiling, which corresponds to a 2 × 2 × 2 superstructure of Henleys cubic 3/2 packing, and that the parity of each vertex determines the kind of associated cluster. The proper quasi-lattice constant for describing the cluster packing is 1/τ (τ = golden mean) times the conventional one used to describe Al-based P-type icosahedral alloys. The superstructure ordering of the present approximant turns out to be of a different kind from the P-type superstructure ordering previously reported in i-Al–Pd–Mn. The present results will greatly improve the understanding of atomic structures of F-type icosahedral quasicrystals and their approximants.

Band structure of the P, D, and G surfaces

A theoretical study on the band structures for electrons constrained to move along triply periodic minimal surfaces is presented. The P, D, and G surfaces, which belong to the same Bonnet family, are considered, and their band structures are calculated numerically. The interrelations between the band structures of these surfaces are discussed in terms of the six-dimensional algebra of the Bonnet transformations [C. Oguey and J.-F. Sadoc, J. Phys. I France 3, 839 (1993)]. Specifically, the coincidence of energy eigenvalues between the surfaces, observed at several wave vectors, are explained in a systematic way. We also analyze in detail the symmetry properties of the band structures. It turns out that there is a close connection between the symmetry properties and the occurrence of nodal lines in the eigenstates. This analysis proves to be useful in understanding the overall characteristics of the band structures. The global connectivity of the band structures is considerably different between the surfaces because of their topological differences. The present study may provide a basis for understanding further the connection between the topology and the band structures.

Quantum particles constrained on cylindrical surfaces with non-constant diameter

We present a theoretical formulation of the one-electron problem constrained on the surface of a cylindrical tubule with varying diameter. Because of the cylindrical symmetry, we may reduce the problem to a one-dimensional equation for each angular momentum quantum number m along the cylindrical axis. The geometrical properties of the surface determine the electronic structures through the geometry dependent term in the equation. Magnetic fields parallel to the axis can readily be incorporated. Our formulation is applied to simple examples such as the catenoid and the sinusoidal tubules. The existence of bound states as well as the band structures, which are induced geometrically, for these surfaces are shown. To show that the electronic structures can be altered significantly by applying a magnetic field, Aharonov–Bohm effects in these examples are demonstrated.

The role of curvature in silica mesoporous crystals

Silica mesoporous crystals (SMCs) offer a unique opportunity to study micellar mesophases. Replication of non-equilibrium mesophases into porous silica structures allows the characterization of surfactant phases under a variety of chemical and physical perturbations, through methods not typically accessible to liquid crystal chemists. A poignant example is the use of electron microscopy and crystallography, as discussed herein, for the purpose of determining the fundamental role of amphiphile curvature, namely mean curvature and Gaussian curvature, which have been extensively studied in various fields such as polymer, liquid crystal, biological membrane, etc. The present work aims to highlight some current studies devoted to the interface curvature on SMCs, in which electron microscopy and electron crystallography (EC) are used to understand the geometry of silica wall surface in bicontinuous and cage-type mesostructures through the investigation of electrostatic potential maps. Additionally, we show that by altering the synthesis conditions during the preparation of SMCs, it is possible to isolate particles during micellar mesophase transformations in the cubic bicontinuous system, allowing us to view and study epitaxial relations under the specific synthesis conditions. By studying the relationship between mesoporous structure, interface curvature and micellar mesophases using electron microscopy and EC, we hope to bring new insights into the formation mechanism of these unique materials but also contribute a new way of understanding periodic liquid crystal systems.

New classes of quasicrystals and marginal critical states

One-dimensional quasilattices, namely, the geometrical objects that represent quasicrystals, are classified into mutual local-derivability (MLD) classes. Besides the familiar class, there exist an infinite number of new MLD classes, and different MLD classes are distinguished by the inflation rules of their representatives. It has been found that electronic properties of a new MLD class are characterized by the presence of marginal critical states, which are considered to be nearly localized states.

Point substitution processes for decagonal quasiperiodic tilings

A general construction principle for the inflation rules for decagonal quasiperiodic tilings is proposed. The prototiles are confined to be polygons with unit edges. An inflation rule for a tiling is the combination of expansion and division of the tiles, where the expanded tiles can be divided arbitrarily as long as the set of prototiles is maintained. A certain kind of point decoration process turns out to be useful for the identification of possible division rules. The method is capable of generating a broad range of decagonal tilings, many of which are chiral and have atomic surfaces with fractal boundaries. Two new families of decagonal tilings are presented; one is quaternary and the other ternary. The properties of the ternary tilings with rhombic, pentagonal and hexagonal prototiles are investigated in detail.