Field evaporation events as Markov chains: A time-of-flight atom-probe study of iridium, Pt-Rh alloys, and metallic glasses

Abstract

Field evaporation events in time-of-flight atom-probe analyses were treated as Markov chains. Both the random chain and the chain with a given distribution of cluster sizes were considered. The validity of the analysis was checked with a set of atom-probe data of iridium. The data agree with a random distribution of the two isotopes. Two sets of atom-probe data were collected from Pt-Rh alloys, and were analyzed and compared with these models. It is found that the experimental distributions fit best with the distributions including slight degrees of clustering in the field evaporation events. Thus, microclustering of Rh and Pt atoms occurs in Pt-Rh alloys, which are generally believed to be complete random solid solutions over the entire composition range. From the atom-probe data, however, we are not yet able to estimate the cluster size distribution of Rh and Pt atoms in the alloys. Our atom-probe data of a metallic glass agree well within the statistical uncertainty of the data with a random distribution of the constituents. If microclustering occurs, it is still beyond the sensitivity of the method as constrained by the amount of data available.

Quantifying Compositional Homogeneity in Pb(Zr,Ti)O3 Using Atom Probe Tomography

“…The field evaporation of long chains of Zr and Ti were not detected in the Markov analysis. Furthermore, formation of ionic clusters during field evaporation in the atom probe will result in apparent clustering of the material; hence, the results are inconclusive …”

“…Quantification of elemental nearest neighbors of a selected atom is possible in the atom probe reconstruction via spatial distribution mapping, use of a pair correlation function, Markov chain analysis, or cluster analysis using binomial distribution routines. [24][25][26][27][28][29][30] These statistical techniques have been applied in metal alloys [30][31][32] and elemental clustering in irradiated reactor pressure vessel steels has also been reported. 27 However, to date, cluster analysis on complex oxides has not been demonstrated.…”

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

“…A range of statistical tools have been developed or adapted specific to the analysis of the large 3D point data sets generated by APT (Hetherington et al, 1986;Miller, 2000;. Key algorithms routinely applied for these analyses include frequency distributions techniques (Camus and Abromeit, 1994a,b;Langer et al, 1975;Moody et al, 2007), autocorrelation (Camus and Abromeit, 1994a,b;Vurpillot et al, 2003), Markov chain (Tsong et al, 1982), and cluster identification algorithms such as maximum separation (Heinrich et al, 2003;Hyde and English, 2001;Stephenson et al, 2007;Vaumousse et al, 2003).…”

Atom Probe Tomography: A Technique for Nanoscale Characterization

“…In addition to these methods, several of the statistical methods developed for the original atom probe have been adapted for the analysis of the three-dimensional data generated in modern atom probes. These statistical methods include autocorrelograms to determine characteristic distance measurements of particle size and complex interconnected network structures~Hyde, 1993; Miller et al, 1996!, Markov chain~Johnson & Klotz, 1974!, and the ABBA methods Tsong et al, 1982! to detect solute clustering and ordering.…”