Structure and Properties of Aperiodic Materials

Liquids are equilibrium systems which represent a longstanding problem for physics and chemistry. We now know a great deal about their structures and properties in conditions without large fluctuations, and the physics of liquids near the critical point has now been elucidated. Proteins and DNA in water are the current target of physics. The physics and chemistry of amorphous metals have made much progress during the last thirty years and they are now widely used in industry. Quasicrystals were discovered in 1984 and this brought about a kind of revolution in our understanding of materials: until then, every textbook had stated in the first few pages that the five-fold rotational symmetry was prohibited in long-range ordered systems. We now know that this is not the case. Furthermore, quite a few quasicrystalline systems are in an equilibrium phase.

Small-angle X-ray scattering (hereafter referred to as SAXS) has been widely used for studying structural features of materials in various fields such as physics, chemistry, metallurgy, and biology, because SAXS data enable us to obtain important microstructural parameters such as particle volume and shape of so-called structural inhomogeneities with colloidal size [1–3]. Since SAXS signals are analyzed on the basis of coherent scattering due to electron density inhomogeneities in the sample, SAXS studies are usually made using radiation whose energy is far from an atomic absorption edge of constituent elements, where the atomic scattering factor for each element is almost proportional to the atomic number. Therefore, the conventional SAXS analysis produces a theoretical difficulty in detecting the structural inhomogeneities caused by the distribution of near-neighbor elements.

Magnetic properties of 3d transition metals (TMs) and alloys are decided by the balance between the magnitude of the electron correlation and the kinetic energy of 3d electrons [1–4]. In other words, the magnetic properties are influenced by the atomic structures, because the transfer probability of 3d electrons is easily influenced by the interatomic distance and the coordination number [1, 3], accompanied by the changes in magnitude of both the electron correlation and the kinetic energy of 3d electrons. Such features of 3d electrons are closely correlated to the origins of various important and attractive problems in magnetism. A unified model of itinerant- and localized-electron models by taking spin fluctuations (SFs) into consideration successfully explains various magnetic properties in crystalline homogeneous systems [2].