The topological transitions of the grain boundary network during grain growth under uniform grain boundary energies are believed to be known. However, this is not true for more realistic materials with varying grain boundary energies that, in principle, allow many different grain boundary configurations. A grain growth simulation for such a material therefore requires a procedure to enumerate all possible topological transitions and select the most energetically favorable one. Such a procedure is developed and implemented here for a microstructure represented by a volumetric finite element mesh. The method is implemented as a C++ library called VDlib based on SCOREC, an open source massively parallelizable library for finite element simulations with adaptive meshing. To test the implementation, a Voronoi tessellated microstructure composed of one hundred grains is generated and evolved under constant grain boundary properties until half of the grains remained. The evolution of the individual grains is compared to what is expected from the MacPherson-Srolovitz relation and is found to be in good match.

As with all numerical techniques, it is important to identify systematic sources of error. Such studies for grain growth simulations are either missing from or not uniform across the literature. To address this issue and enable comparison across grain growth simulations, a set of benchmark cases, one for each boundary type of surfaces, lines, and points with analytical solutions are identified. These are used to compare a recently developed discrete-interface method for microstructure evolution to a state of the art diffuse interface (multiphase field method). In each case, the discrete method is found to meet or outperform the multiphase field method in terms of accuracy for comparable levels of refinement, demonstrating its potential efficacy as a numerical approach for microstructure evolution.

Last, a novel invariant of ideal grain growth process is defined that ideally can be used to calculate the number of topological entities in a microstructure and only changes as the topology changes. VDlib is used to test the invariant on a simulated microstructure composed of a periodic arrangement of Kelvin cells. A convergence study reveals that the invariant converges to the ideal case with increasing levels of refinement, however predicting the number of entities without bounds on number of entities proves unpractical. Two error measures based on this novel invariant are proposed which can potentially be used to quantitavely measure how much simulations deviate from ideal grain growth process and experimental microstructures.

Computational models can support materials development by identifying the key factors that a ect materialproperties and by guiding the search for optimal chemical and processing conditions. However, the success of this venture assumes the ability to accurately model material structures and the relationship of those structures to material properties. State-of-the-art tools in high-performance computing and machine learning are continually improving the performance of these models, thereby furthering their integration into the process of developing better materials including advanced alloys. This dissertation includes three projects that use atomic simulations to support the development of advanced alloys for applications in extreme conditions. First is the construction of a novel framework for machine learning potentials (MLPs). MLPs could dramatically accelerate simulations of atomic systems while providing the accuracy of electronic structure techniques through the use of supervised regression algorithms. MLPs do still have a higher computational expense than empirical potentials though, both during their construction and for every evaluation of the potential energy. With the purpose of reducing these costs and alleviating the necessity for enormous training data sets, our framework for producing MLPs combines an e cient implementation of a sparse Gaussian process algorithm with a novel set of descriptors for atomic environments. Second, molecular dynamics is used to investigate energy storage and heat evolution during high-strain-rate deformation of the refractory metal Ta. This is encapsulated in a quantity known as the Taylor{Quinney coe cient, which is critical to models of material failure in conditions where direct experimental measurement of the temperature is infeasible. Other than developing a phenomenological model for the energy stored in the material, this chapter identi es that a signi cant amount of the energy is stored in the form of point defects. Third, molecular dynamics is used to study the defect structures that evolve in irradiated materials in the low temperature and high radiant ux regime. The algorithm used involves the successive insertion of Frenkel pairs and relaxation of the simulation cell, and allowed the study of Fe, equiatomic CrCoNi, and a  ctitious metal with identical bulk properties to the CrCoNi up to the equivalent of 2.0 displacements per atom (dpa). Several areas requiring further research are identi ed, including the mechanisms by which Shockley partials develop in FCC metals at low dpa and robust ways to measure point defect concentrations in heavily-damaged FCC materials.