Symmetry, topology, and crystal deformations: a phase-field crystal approach

Abstract

Crystalline materials are the backbone of modern technology, from semiconductors to structural materials. The properties of these materials, including their strength, conductivity, and optical properties, are strongly influenced by their defects, such as dislocations. Despite their importance, our current understanding of these defects still needs to be improved. The phase-field crystal approach is a relatively new tool that has emerged as a promising way to study crystalline materials. It is a remarkably versatile model, which allows for capturing both the elastic properties of crystals and the dynamics of their defects, including dislocations. In this thesis, I have used the phase-field crystal approach to study the nucleation and motion of dislocations under imposed stress and their interaction with elastic fields. Furthermore, I have extended this approach to various crystal symmetries and dimensions. As a result, my research provides new insights into the behavior of crystals under stress and strain. By improving our understanding of dislocation behavior and its impact on material properties, we can develop new materials with improved properties for various applications, such as electronics, energy storage, and transportation, which in turn may contribute to critical societal and economic issues, including sustainability, energy security, and technological innovation.