Quantitative binomial distribution analyses of nanoscale like‐solute atom clustering and segregation in atom probe tomography data

Abstract

The applicability of the binomial frequency distribution is outlined for the analysis of the evolution nanoscale atomic clustering of dilute solute in an alloy subject to thermal ageing in 3D atom probe data. The conventional chi(2) statistics and significance testing are demonstrated to be inappropriate for comparison of quantity of solute segregation present in two or more different sized system. Pearson coefficient, mu, is shown to normalize chi(2) with respect to sample size over an order of magnitude. A simple computer simulation is implemented to investigate the binomial analysis and infer meaning in the measured value of mu over a series of systems at different solute concentrations and degree of clustering. The simulations replicate the form of experimental data and demonstrate the effect of detector efficiency to significantly underestimate the measured segregation. The binomial analysis is applied to experimental atom probe data sets and complementary simulations are used to interpret the results.

Precipitate modification in PH13-8 Mo type maraging steel

“…Data reconstruction and statistical evaluation was conducted using the software package IVASe 3.4.3 from Imago Scientific Instruments (Madison, WI). Frequency distribution analysis [37,38] was performed to examine the distribution of elements in the analyzed volume. Clusters were detected by applying a cluster search algorithm based on the maximum separation method [39].…”

Atom Probe Tomography of Solute Distributions in Mg-Based Alloys

“…To evaluate solute clustering in the atom probe data, a range of statistical approaches, such as frequency distribution, [12] contingency table, [13] binomial distribution, [14] and autocorrelation function analyses [15,16] have been developed. [8] These techniques have been applied to evaluate solute clustering behaviors mostly in a single alloy subject to different aging treatments.…”

Design of a twinning-induced plasticity high entropy alloy

“…The quality of the fit was quantified using several parameters, as listed in the insert chart. The normalized homogenization parameter, referred to as l, ideally ranges from 0 to 1, where 0 refers to total randomness while 1 represents complete ordering [38,39]. For all four alloying elements, the l values are close to 0, confirming the random distribution of elements in this alloy.…”