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For amorphous materials, the arrangement of atoms does not have long-range symmetry, neither rotational symmetry nor translational symmetry. In real space, it is generally believed that amorphous materials have SRO only in a few angstroms but do not have LRO. It cannot spontaneously embody regular morphology (except spherical), so amorphous materials are generally known as formless (Figure 1.3e). In reciprocal space, the diffraction pattern does not have any diffraction spots or sharp rings but a circular diffraction halo (Figure 1.3f).

Compared with crystalline materials, the features of amorphous materials can be summarized as follows:

1 (1) Atoms in amorphous materials only have fixed atomic arrangement rules in the nearest and the next neighbor (<1 nm). The order of the longer range is still unclear.

2 (2) Because of the long-range disorder of the atomic arrangement, the regular morphology of amorphous materials cannot be obtained by natural growth under non-limited conditions. Therefore, amorphous materials always embody as formless or spherical, driven by surface energy.

3 (3) Amorphous material is physically and chemically isotropic: the homogeneity of the atomic environment determines that they are not as anisotropic as crystals;

4 (4) Compared with crystal, the amorphous material is metastable. The amorphous structure will relax to crystalline state at a high-temperature/high-pressure processing.

5 (5) There is no fixed melting point for amorphous material. It only showed a glass transition temperature. There is no unchanged temperature platform during the phase transition process.

6 (6) Amorphous material does not produce regular X-ray diffraction. The typical X-ray diffraction pattern of amorphous material is a hump at a specific location, rather than a series of peaks in crystal. Its typical electronic diffraction pattern is diffraction halos.

It can be found that the essential difference between amorphous structure and crystals lies in the LRO, and the similarity lies in the high SRO.

SRO means that amorphous atoms only have a high degree of local correlation, which is the result of the strong chemical bonds between the nearest neighbor (including the next neighbor) atoms to maintain as a fixed component solid. This makes the short-range structure of amorphous materials similar to that of crystals, so the SRO is considered as the structural feature of amorphous materials. A large number of simulations and experiments show that the short-order scale of amorphous crystals should be less than 1 nm.

Common diffraction methods, such as X-ray diffraction and selective electron diffraction, are based on LRO. Therefore, it is difficult to directly obtain short-range informations and images of amorphous material. To investigate the average structure information such as the radial distribution function (RDF), the analysis of atomic ordering of amorphous structures is generally based on the fitting results of diffraction (electron, neutron, etc.) or spectroscopy (X-ray fine structure absorption spectroscopy, nuclear magnetic resonance spectroscopy, etc.).

In 2011, Chen Mingwei and Akihisa Inoue [8] of Northeastern University used the most advanced spherical aberration correcting transmission electron microscopy (AC-TEM) technology to reduce the diameter of the coherent electron beam to 3 Å for nanobeam electron diffraction (NBED) analysis to replace traditional selective area electron diffraction (SAED). It was found in the experiment that under the 3.6 Å electron beam, the diffraction pattern of amorphous material showed obvious patterning (Figure 1.4). For the first time, the order of the atomic neighbor and the next-nearest neighbor structure of the amorphous alloy was observed.

For crystal materials, 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.