The influence of binomial counting statistics on Mg-Si cluster compositions detected by atom probe tomography in naturally aged AlSiMg

The negative natural ageing (NA) effect, which reduces the strength of heat-treated 6xxx AlMgSi and cast AlSiMg alloys, is commonly attributed to Mg–Si atomic clustering. The reported broadening of Mg–Si cluster compositions at small cluster sizes has supported several proposed mechanisms for this effect. This work examines the extent to which the apparent compositional broadening arises from binomial counting statistics rather than real compositional variation. 3719 clusters identified by atom probe tomography (APT) in a NA AlSi10Mg high-pressure die casting were analysed and compared with synthetic datasets and binomial predictions. The observed compositional spread is quantitatively reproduced by an overdispersed binomial distribution, where the overdispersion is not a function of cluster size, requiring a reassessment of mechanisms linking cluster composition broadening to the negative-NA effect. The findings show the results of APT-clustersearches can be misleading without statistical context, with expected relevance to the general study of nanoscale-clustering by APT.