Electronic Structure Ab Initio

We outline the details of a theory underpinning the description of the electronic ‘glue’ of an alloy, bonding atoms together and driving atomic ordering tendencies. The chapter begins with a brief review of the underlying theory of the electronic structure of condensed matter, and how density functional theory (DFT) makes it possible to (approximately) describe the electronic structure of many systems in a computationally tractable manner. We then proceed to outline the details of the Korringa-Kohn-Rostoker (KKR) formulation of density functional theory, which enables us to review both the coherent potential approximation (CPA) and the disordered local moment (DLM) picture. We then outline the \(S^{(2)}\) theory for multicomponent alloys and state the set of coupled equations which must be solved self-consistently to evaluate the atomic short-range order ab initio. We also state the reduced form of these equations in the so-called ‘band-only’ approximation. The chapter concludes by discussing the electronic structure of some well-known metals and alloys, to provide intuition to the reader.