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The structure of liquids, glasses and other non-crystalline solids is characterized by the absence of long-range order which defines crystalline materials. Liquids and amorphous solids do, however, possess a rich and varied array of short to medium range order, which originates from chemical bonding and related interactions. Metallic glasses, for example, are typically well described by the dense random packing of hard spheres, whereas covalent systems, such as silicate glasses, have sparsely packed, strongly bound, tetrahedral network structures. These very different structures result in materials with very different physical properties and applications. The study of liquid and glass structure aims to gain insight into their behavior and physical properties, so that they can be understood, predicted and tailored for specific applications. Since the structure and resulting behavior of liquids and glasses is a complex many body problem, historically it has been too computationally intensive to solve using quantum mechanics directly. Instead, a variety of diffraction, NMR, Molecular dynamics, and Monte Carlo simulation techniques are most commonly used. ==Pair distribution functions & Structure factors== The pair distribution function (or pair correlation function) of a material describes the probability of finding an atom at a separation ''r'' from another atom. A typical plot of ''g'' versus ''r'' of a liquid or glass shows a number of key features: # At short separations (small r), ''g(r)'' = 0. This indicates the effective width of the atoms, which limits their distance of approach. # A number of obvious peaks and troughs are present. These peaks indicate that the atoms pack around each other in 'shells' of nearest neighbors. Typically the 1st peak in ''g(r)'' is the strongest feature. This is due to the relatively strong chemical bonding and repulsion effects felt between neighboring atoms in the 1st shell. # The attenuation of the peaks at increasing radial distances from the center indicates the decreasing degree of order from the center particle. This illustrates vividly the absence of "long-range order" in liquids and glasses. # At long ranges, ''g(r)'' approaches a limiting value of 1, which corresponds to the macroscopic density of the material. The static structure factor, ''S(q)'', which can be measured with diffraction techniques, is related to its corresponding ''g(r)'' by Fourier transformation where ''q'' is the magnitude of the momentum transfer vector, and ρ is the number density of the material. Like ''g(r)'', the ''S(q)'' patterns of liquids and glasses have a number of key features: # For mono-atomic systems the ''S(q=0)'' limit is related to the isothermal compressibility. Also a rise at the low-''q'' limit indicates the presence of small angle scattering, due to large scale structure or voids in the material. # The sharpest peaks (or troughs) in ''S(q)'' typically occur in the ''q''=1-3 Angstrom range. These normally indicate the presence of some ''medium range order'' corresponding to structure in the 2nd and higher coordination shells in ''g(r)''. # At high-''q'' the structure is typically a decaying sinusoidal oscillation, with a 2π/''r1'' wavelength where ''r1'' is the 1st shell peak position in g(r). # At very high-''q'' the ''S(q)'' tends to 1, consistent with its definition. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「structure of liquids and glasses」の詳細全文を読む スポンサード リンク
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