## ABSTRACT

According to the thermodynamic laws, the perfect infinite crystals cannot exist in the real world. Various disorders in the forms

of vacancies, interstitial atoms, impurities, dislocations, grain boundaries, surfaces, and other interfaces disrupt the periodicity of otherwise “perfect” crystals and in many cases determine their physical properties. By contrast, highly disordered solids are those solids that are so irregular that the concept of a reference crystal lattice must be abandoned. Such highly disordered materials are called amorphous materials [82]. As Wikipedia, the free encyclopedia, has it: an amorphous (from the Greek term αμορφος, which means “shapeless” or “without form”) solid is a solid, in which there is no translational and orientational long-range order (LRO) of the atomic positions [83]. Early researchers categorized solids as amorphous or crystalline materials based on the macroscopic properties such as their external shapes, fracture mechanisms, and optical properties long before X-ray diffraction techniques and other methods became available to reveal their atomic structures. Only in the past century, an understanding of the microscopic nature of amorphous materials has become possible [82]. However, there is still much debate concerning the exact nature of these materials. For example, in a recent article, Sheng et al., [84] have mentioned: “the atomic arrangements in amorphous alloys remain mysterious at present.” An amorphous structure is distinctly different from a densely packed assembly of microcrystals and is closely related to the structure of a liquid phase. Ideally, an amorphous solid should be described by the model of a perfectly random structure [85]; however, this is the boundary condition. As such, the structure of amorphous solids is normally described in terms of statistical distributions. Nevertheless, prior a further description, one must specify the existing atomic length scales. The shortest length scale usually used to describe the structure of a material consists of an atom and its nearest neighbors, out to perhaps two or three atoms distant. All solids and liquids have some structure on this scale, which is called a short-range order (SRO). For crystalline solids, structural order persists over much longer distances (at least, tens or hundreds of atomic distances), such that the atoms occupy sites in a periodic three-dimensional array. Such materials are said to have a LRO and include most metals and many covalently bonded solids. Non-crystalline solids, including glasses, lack a LRO, and are said to be amorphous even though they can have a SRO that is quite well defined [86].