Determination of accurate, mean bond lengths from radial distribution functions

Abstract

The mean bond length d between a central atom and its nearest neighbors can be estimated from the position of the first peak in the radial distribution function g(r). However, as we demonstrate here, this estimate does not allow one to deduce temperature-induced changes in d. Instead, skewness has to be included into the analysis, which can be achieved, for example, via the skew normal distribution (SND). Fits to the first peak using the SND give bond length in good agreement with direct measurements of nearest-neighbor distribution functions in crystals as well as with a Voronoi-tessellation based detection of nearest-neighbors in liquids. While the location of the first peak in g(r) may shift to smaller values with increasing temperature for three studied liquids-argon, copper, and the bulk-metallic-glass (BMG) forming alloy Zr60Cu30Al10-we find our improved estimates of d to systematically increase with temperature in all cases. Recent conclusions on temperature-induced bond contractions in simple metallic or BMG-forming liquids may therefore have arisen from the neglect of skewness effects.