Читать книгу Amorphous Nanomaterials - Lin Guo - Страница 13

For crystal materials, the atomic arrangement has both translational symmetry and rotational symmetry. In real space, its structural elements (atoms or molecules) are arranged periodically in three-dimensional space according to certain rules. Therefore, periodicity is considered as the most essential characteristic of a crystal structure. Its morphology is mostly manifested as a highly symmetrical polyhedron (Figure 1.3a). In reciprocal space, the periodically arranged structural units of a single crystal material would produce diffraction spots with translation and rotation repeatability. The diffused diffraction spots form diamond patterns centered on the transmission spot (Figure 1.3b). The diamond angle and edge length are the direct transformation of crystal lattice parameters. For polycrystalline materials, the diffraction patterns are sharp diffraction rings centered on the transmission spot.

Figure 1.3 The morphologies of three different kinds of solid materials, as well as their corresponding electron diffraction patterns. (a, b) Crystal, (c, d) quasicrystal, and (e, f) amorphous materials. Source: Panels (a, b) Reproduced with permission from Zhang et al. [4]. Copyright 2009, Royal Society of Chemistry. Panel. (c) Reproduced with permission from Fisher et al. [5]. Copyright 2000, Elsevier Inc. Panel. (d) Reproduced with permission from Zhang et al. [6]. Copyright 1985, Taylor and Francis Group. Panel. (f) Reproduced with permission from Yue et al. [7]. Copyright 2015, Science China Press.

For quasicrystal materials (Figure 1.3c), the atomic arrangement has rotational symmetry but does not have translational symmetry. Its biggest feature is the symmetry that is incompatible with the traditional crystal space lattice (e.g. fifth symmetric axis). In reciprocal space, it also exhibits similar diffraction patterns as the crystals with regular and diffused diffraction spots (Figure 1.3d). The difference is that there is only rotation regularity and no translation regularity.

Because crystals and quasicrystals have great consistency in structure, modern solid-state physics is also accustomed to classifying quasicrystals together into crystals, i.e. materials with sharp diffraction spots (i.e. periodic arrangement of atoms in real space) as crystals, which have the following characteristics:

1 (1) The atomic arrangement of crystal units has long-range symmetry and regularity.

2 (2) Crystals show self-limitation, which means natural-grown crystals without external interference will eventually grow into regular morphologies with high symmetry. It is the geometric basis for the determination of crystals.

3 (3) Crystals obey the law of constancy of interfacial angles, which is the first law of geometric crystallography, and is also the basis for judging crystals in morphology. It states that the angles between two corresponding faces on the crystals of any solid chemical or mineral species are constant and are characteristic of the species. The law holds for any crystals, regardless of size, locality of occurrence, or whether they are natural or man-made.

4 (4) Single crystals are anisotropic.

5 (5) Crystal material has a fixed melting point, and its temperature remains unchanged during the phase transition process.

6 (6) Crystals can produce X-ray diffraction with specific regularity: It is the basis for modern crystallography to judge whether a substance is a crystal or not.