Determination of the structure of liquids: an asymptotic approach

Abstract

Accurate determination of a liquid structure, especially at high temperatures, remains challenging, as reflected in the scatter between different measurements. The experimental challenge is compounded by the process of the numerical transformation from the structure factor to the radial distribution function. The resulting uncertainty is often greater than that required to resolve issues associated with changes in the short-range order of the liquid, such as the existence of liquid-liquid phase transitions or correlations between thermophysical properties and structure. In the present contribution it is demonstrated for liquid bismuth as a model system that the structure factor can be obtained to high accuracy, by comparing several independent measurements in different setups. A simple method is proposed for improving the accuracy of the radial distribution functions, based on the extension of the finite range of momentum transfer, q, in the measured data by analytical asymptotic expressions. A unified mathematical formalism for the asymptotic dependence of the structure factor is developed and the asymptotic form of the Percus-Yevick hard-sphere solution is obtained as a special limiting case. The multiple expressions in the literature are shown to reflect uncertainty in the nature of the repulsive interatomic interaction at short separation distances. Applying this asymptotic method, it is shown that it enables access to details of the fine structure of the liquid and its temperature dependence. research papers J. Appl. Cryst. (2013). 46, 1582-1591 Martin Mayo et al. Determination of the structure of liquids 1591

Short range order in elemental liquids of column IV

“…it is well known that interpretation of the liquid structure in real space from the liquid structure factor, and in particular, the identification of small changes in the liquid structure associated with rearrangements or transitions presents a challenge. 13,14 The structure of the liquid is described by the radial distribution function (RDF), which is, however, a limited one dimensional representation of the full three dimensional structure of the liquid and is dominated by the repulsive hardsphere like interactions. Identification of small changes in the three-dimensional liquid structure requires solution of the inverse problem of structure determination from the RDF to high accuracy, e.g., by reverse Monte Carlo (RMC) or similar approaches.…”

“…19 By using an asymptotic analysis of the structure factor, we found that it is possible to extend the experimentally measured range of the wavevector and obtain high quality radial distribution functions in a stable algorithm, provided the original data extended to approximately three times the wavevector of the main scattering peak. 13 These high quality radial distribution functions can then be analysed within the quasi-crystalline model (QCM) [19][20][21][22][23] which has been demonstrated to be able to identify and interpret trends and changes in the short range order of the liquid structure. 19 The QCM approach is not unique in interpreting the structure of liquids, and alternative approaches such as reverse Monte Carlo and molecular dynamics exist.…”

Structure and dynamics in liquid bismuth and Bin clusters: A density functional study

“…Although the pair distribution functions show significant scatter, 14 there is clear evidence of a temperature-driven structural phase transition at 1013 K. 15 Inelastic neutron scattering (INS) measurements of the dynamical structure factor S(Q, ω) near the melting point of Bi show evidence of collective density excitations. 16,17 Bi + n cations 18 have been identified mass spectroscopically to n > 40, and photofragmentation of small Bi cluster cations has been observed.…”

Structure and thermal expansion of liquid bismuth

“…The scattered intensity was measured with an accuracy higher than 2 %. The main structure parameters obtained from the structure factor (SF) and the pair correlation function were calculated according to Mayo et al [27]. The typical uncertainty in PCF obtained by this method is of the order of a few percent.…”