Structure of this Thesis Sample Clauses

Structure of this Thesis. ‌ In this thesis, we first introduce the background electronic structure theory in Chap- ter 2. This chapter is a presentation of known results. Starting with the Born- Xxxxxxxxxxx approximation and ending with a derivation of the simple-metal limit of the GPT in its modern self-consistent KS-DFT formalism. We derive self-consistently screened interatomic potentials for Mg using the GPT formalism. Using these po- tentials, we develop the so-called adaptive GPT (aGPT) in Chapter 3. In a bulk elemental metal, the aGPT and GPT are guaranteed to be equivalent representations. However, the aGPT adds a many-body correction when free surfaces or volumes are encountered. We derive expressions for the forces and stress tensor, and apply these expressions to a range of properties including the relaxed vacancy formation energy. In Chapter 4, we use the GPT alloy theory to derive self-consistent interatomic po- tentials for the Mg-Ca alloy system. The central problem for industrial applications of wrought Mg is the plastic anisotropy. This is not unique to Mg and is found across hcp metals (although the plastic anisotropy in Mg is particularly severe). We explore the thermodynamic and mechanical stability of the body-centred cubic (bcc) phase in this alloy system, as the bcc phase is inherently more isotropic. We conclude in Chapter 5, outlining future research directions in the GPT and aGPT.