Generating Intermolecular Potentials from Atom Probe Tomography Experiments

The predictive design of High-Entropy Alloys (HEAs) is hindered by the lack of accurate interaction potentials that would allow molecular simulation to complement existing experimental research. An unambiguous description of the chemical ordering at the atomic scale is necessary to understand how stress and strain at the atomic scale impact the mechanical properties of the alloy. Atom Probe Tomography (APT) experiments provide a set of spatial coordinates and elemental identities for 10⁶ or greater atoms. The traditional “inverse problem” of potential generation uses sets of atomic coordinates, usually from a computational model, to extract a corresponding intermolecular potential with which molecular dynamics (MD) simulations can be performed. The objective of this work is to use APT data sets to generate intermolecular potentials. The obstacle to the direct implementation of APT data in potential generation arises due to the fact that current APT instrumentation produces data sets with two significant issues of data quality: sparsity and noise. Roughly two thirds of the atomic positions are not resolved and there is non-negligible uncertainty in the spatial positions. In an interdisciplinary partnership with computer science and mathematics, we have developed a procedure to extract a distributions of local atomic configurations from the APT data sets, in which atoms have been assigned to lattice points. The procedure uses topological data analysis to create persistence diagrams, which are used to determine the local crystal structure to a high degree (>93% in all cases) of accuracy. With the crystal structure in hand (body centered cubic or face centered cubic in these examples), a statistical formulation of the labeled point set registration problem is employed. This approach invokes a statistical mechanical lattice model to self-consistently identify preferential ordering of atoms, despite the noise in the APT data. An output of this procedure is a set of pairwise nearest-neighbor interaction energies corresponding to the lattice model. The data quality limits of the approach are explored. Progress toward more sophisticated interaction potentials suitable to MD simulation is discussed.