ABSTRACT:

This thesis addresses the phenomenon of plastic embrittlement by describing elastic stiffening with quantum elastodynamics (QED). The primary objective is to develop an artificial intelligence (AI) and machine learning (ML) approach for material discovery with theory-guided algorithms informed by spectroscopy for comparative validation of material design for commercial applications and industrial processes. The dissertation analyzes band structures and elastic tensors obtained from density functional theory quantum mechanical self-consistent, nonlinear field calculations based on Hohenberg-Kohn theorems, mathematically formulated by Euler-Lagrange, and described by Kohn-Sham equations. Results are investigated for the interpretation of stiffening towards embrittlement based on the agreement of classical and quantum mechanical formulations with experimental spectroscopic measurements.

This research contributes to understanding plastic embrittlement, elastic stiffening, and quantum elastodynamics. A novel approach for demixing by Cahn-Hilliard spinodal decomposition using free energy is developed, and stable spinodal compositions are identified. The elastic tensor is obtained through Kohn-Sham quantum mechanical solutions to the Schrodinger energy eigenstate equation, enabling the calculation of elastic moduli from atomic positions that minimize the energy functional through the ground state electron density. Stiffening is determined by analyzing the elastic tensor, facilitating a high throughput screening of embrittlement. The origin of embrittlement is determined as thermoelastic activations in dislocations that induce a topological transition in the Fermi surface, detectable by spin-polarized transport measurements. Numerical simulations with surface-state Green's functions, tight-binding theory, and full-counting statistics were then applied to study the emergence of protected topological states in one-dimensional wire systems, such as Majorana fermions and multiple Andreev reflections.

This research then addresses computational constraints that limit the scope of material design. Due to these limitations, previous results employed simplistic models for underlying computations. To demonstrate more complex and realistic models, matrix-free Anderson extrapolation-based vector-to-vector mapping was applied to simple potentials and was found to accelerate convergence compared to gradient descent and momentum-based optimizations. This pivotal finding motivated accelerated computational scaling studies, enabling more realistic simulations with high atom counts with AI and ML for material discovery. Such advancements in computational capabilities enhance these models' precision and applicability, thereby propelling applications in material design and industrial processes with QED.