the most essential feature is the orderly arrangement of structural elements. It enables crystal research to be based on mathematics and established standard models. The structural or compositional changes could be fully studied rely on the established model. It can also introduce various defects on the basis of the model and establish a material–structure–property relationship to adjust the performance by tuning materials. This kind of systematic research can not only ensure the continuous follow-up of the theoretical research to the explanation of experimental phenomena but also make medium- and long-term predictions of experimental results. The experimental data will be fed back to the theoretical system at the same time, making it complete and more accurate, forming a perfect closed loop between theory and experiment.
Most of the modern structure detection was built based on crystal models. Thus, for amorphous materials without the LRO, the existing analysis methods can only give average atomic information in the statistical category, which is difficult to get the accurate structural information. Therefore, we have not been able to accurately establish the structural model of amorphous materials to sort out the complex long-range interactions beyond the atomic scale. The existed amorphous research studies have established the relationship between materials, kinetic units, and properties in metallic glass systems. Apart from it, many other research studies are still individual results that are only in the experimental observation stage to summarize the phenomenological rules. This situation may be improved with the development of the basic physics and experimental characterization technique.
Figure 1.4 The ordered diffraction patterns of amorphous material under coherent electron nanobeam with different diameters. Source: Reproduced with permission from Hirata et al. [8]. Copyright 2011, Nature Publishing Group.
1.3 History of Amorphous Materials
Throughout the history of human science and technology, the breakthrough of new technologies is always accompanied by the discovery of new materials. From ancient bone, stone, porcelain, metal materials to modern high-performance plastics, alloys, micro–nanomaterials, which are still developing, all of them have left a deep imprint in the history of science development. Along with the progressing of scientific theory, the ways of exploring new materials have changed significantly (Figure 1.5). For example, it took thousands of years for human beings to distinguish and adjust the composition of substances. From original bone and stone tools to synthetic bronze and iron tools, we finally obtained engineering materials based on precisely controlled alloys and composites. All of them provide the strong support for the industrialization process of human beings. On the other hand, it took decades to achieve material design and control from macroscale to nanoscale, then to atomic scale, laying a structural foundation for discovery of modern high performance energy storage and conversion materials. This accelerated proceeding was strongly supported by various physical and chemical theories and methods and also supported by the rapid development of characterization methods. On the basis of these development, scientists continue to focus on atomic ordering of the materials, which was expected to further improve the mechanical or catalytic properties of traditional crystal materials. With the help of the most advanced characterization methods, such as spherical AC-TEM and synchrotron radiation X-ray fine absorption spectroscopy, scientists try to adjust the atomic arrangement to obtain new structural materials, such as metastable materials, high-entropy alloys, metallic glass, and amorphous materials.
Figure 1.5 The development of materials research in different research orientations.
1.3.1 Establishment of Crystallography
The concept of amorphous is defined in the comparison of crystallography in solid physics. Therefore, the history of amorphous materials should be compared with that of crystallography.
On 25 June 2012, the General Assembly of the United Nations adopted a resolution, which proclaiming the year 2014 as the International Year of Crystallography. It was named to commemorate Max von Laue, who won the Nobel Prize in Physics of 1917, about 100 years ago for characterizing the crystal structure by X-ray. At the same time, it was also commemorated Johannes Kepler proposed the famous article A New Year’s Gift of Hexagonal Snow 400 years ago (1611). He was regarded as the first one to conceptualize the symmetry of crystals which were formed by a regular accumulation of spherical elements. It was considered to be the beginning of the establishment of traditional crystallography.
In 1699, Nicolas Steno observed a large number of ores and proposed that the angle between two identical crystal planes of a crystal is always constant, regardless of the size and shape of the crystal plane [9]. It was called the law of constant angles of the crystal plane, which was generally recognized as the first law of crystals. Prior to the discovery of X-ray, the law laid the foundation for crystal identification, and the word Crystal began to be used to describe substances with regular morphologies and fixed angles.
In 1784, Rene Just Hayuy proposed that each crystal plane was simply composed of blocks of the same size and shape. The crystal structure was described as a regular three-dimensional arrangement, which was an infinite repetition of cells in the three-dimensional directions. On this basis, William Hallowes Miller proposed in 1839 that each crystal plane can be described by three simple integers (h, l, k). That was the Miller Index, as was still used today.
At the end of the nineteenth century, from a mathematical point of view, scientists put forward 32-point groups to describe the symmetry of crystal shape and 230 space groups to nominate the symmetry of microelements. Until now, all the geometric structure characteristics of crystallography have been basically perfected.
In 1912, on the basis of Laue’s work, William Lawrence Bragg proposed the famous Bragg Formula, which laid the foundation for the establishment of modern crystallography and the characterization of crystal structure. Later, together with his father William Henry Bragg, he quickly characterized the crystal structure of various substances, and established modern crystallography soon [10].
From the development history of crystallography, we can find that the confirmation of crystal structure characteristics depends on the discovery of X-ray, but the establishment of geometric theory in crystallography was far before the characterization of its crystal structure. All the elements in the definition of crystals (crystals are solids with regular periodic repetitive arrangement of internal particles in three-dimensional space) are determined before X-ray discovery. The establishment of crystallography depends more on the mathematics-induced theoretical system and physics-drove technique.
1.3.2 Enlightenment of Amorphous Materials
The use of natural amorphous materials can be traced back to prehistoric times when Obsidian was used as a cutting tool. It was a kind of natural glass, formed by the sudden cooling of magma from volcanic lava. With a sharp fracture surface, people used it for cutting as knives.
Because of the simplicity of preparation, glass has become the first amorphous material to be prepared on a large scale. The history of glass preparation can be traced
