Doctoral Dissertations

Date of Award

5-2020

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Vasileios Maroulas

Committee Members

Xiaobing Feng, David Keffer, Kody Law, Tim Schulze

Abstract

This thesis comprises a collection of papers whose common theme is data analysis of high entropy alloys. The experimental technique used to view these alloys at the nano-scale produces a dataset that, while comprised of approximately 10^7 atoms, is corrupted by observational noise and sparsity. Our goal is to developstatistical methods to quantify the atomic structure of these materials. Understanding the atomic structure of these materials involves three parts: 1. Determining the crystal structure of the material 2. Finding the optimal transformation onto a reference structure 3. Finding the optimal matching between structures and the lattice constantFrom identifying these elements, we may map a noisy and sparse representation of an HEA onto its reference structure 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 may then develop interaction potentials for molecular dynamics simulations, and make accurate predictions about these novel metallic alloys.

Orcid ID

http://orcid.org/0000-0002-2521-3657

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