Advanced Statistical Methods for Atomic-Level Quantification of Multi-Component Alloys

Advances in materials design have produced novel compounds, such as high-entropy alloys and entropy-stabilized oxides, that exhibit remarkable properties stemming from an amorphous and highly-disordered structure. Due to their high-configurational entropy and nanoscale disorder, such materials are not amenable to traditional techniques that characterize the local atomic-structure. Instead, we invoke techniques such as atom probe tomography that create information-rich datasets containing elemental type and spatial coordinates. The technique used to view these materials at the nanoscale produces a large but sparse dataset, comprised of approximately 10⁷ atoms. However, it is corrupted by nontrivial amounts of observational noise. The advent of such material design techniques necessitate new developments in statistical methodologies and data flows to fully capture the structural variations of these materials at an appropriate scale. A thorough analysis of these atomic-level variations unlock the capability for rapid material discovery. To fully explore and analyze such materials requires developing efficient and thoughtfully designed material descriptors. These descriptors may be continuous or discrete, but must be quantifiable in order to be employed by a statistical learning methodology. Our goal is to develop statistical methods to quantify the atomic structure of these materials. Our strategy is decomposed into three parts: i. Classifying the lattice structure of the material, ii. Mapping the perturbed observational data onto a model crystal lattice, and iii. Finding the optimal matching between observed data and the model lattice, and identifying the elemental type of the atoms in the model lattice. From these three parts, we could map a noisy and sparse representation of a metallic alloy onto its reference lattice and determine the probabilities of different elemental types that are immediately adjacent, i.e., first neighbors, or are one-level removed and are second neighbors. Having these elemental descriptors of a material, researchers could then develop interaction potentials for molecular dynamics simulations, and make accurate predictions about these novel metallic alloys.