Using non-parametric statistical testing to quantify solute clustering in atom probe reconstructions

Abstract

Atom probe tomography (APT) is routinely used to investigate nano-scale solute architecture within multicomponent systems. However, there is no consensus on how to best quantify solute clustering within APT data. This contribution leverages recent developments in the field of non-parametric hypothesis testing of nearest-neighbour distributions to address this critical gap. We adapt a goodness-of-fit-type test statistic known as ‘the level of heterogeneity’ to quantitatively discern whether solute distributions exhibit clustering behaviour beyond what would be expected from a random distribution. Further, comparing APT datasets remains difficult due to the inability to directly compare their nearest-neighbour distributions. We present a method that leverages Monte-Carlo simulations, already used to calculate the non-parametric statistic, as a means of comparing APT data. The method is more powerful than comparing datasets through the Pearson coefficient, as is conventionally done.