Determination of the structure of liquids: an asymptotic approach

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.