• 
  Wanderka, N.; Lazarev, N.; Chang, C.S.T.; Banhart, J.: Analysis of clustering in Al-Mg-Si alloy by density spectrum analysis of atom probe data. Ultramicroscopy 111 (2011), p. 701-705

10.1016/j.ultramic.2010.11.022

Abstract:
Early stages of cluster formation in anAl–Si–Mg alloy were investigated by atom probe tomography and evaluated by a newly developed statistical method based on the nearest neighbour distributions. After solutionising and quenching,an alloy sample was naturally aged for one week.The atom probe data then measured was analysed for Mg,Si or Mg–Si clusters.For comparison specimen artificial aged with well developed precipitates was also investigated. A general approach for the analysis of density spectra was set up, which reduced the problem to the solution of an integral equation. Application of the method to the atom probe data set allowed us to detect clusters and to evaluate the atomic fractions with in these clusters. This is also possible for an arbitrary number of nucleated phases.The higher -order next nearest neighbour distributions were used for the estimation of cluster sizes. Combining the density distribution method with a Monte Carlo simulation we found very small Si–Si and Mg–Mg clusters consisting of only a few atoms in the naturally aged state.