Statistical Physics of Multicomponent Alloys

We consider the application of techniques from statistical physics to problems concerning the phase behaviour of multicomponent alloys. We begin by introducing the site-wise occupancies (discrete) and site-wise concentrations (continuous), which are variables used to concisely specify the configuration (or a set of configurations) of atoms in an alloy. The concept of a free energy is then briefly outlined, and a discussion of Landau theory is given. The majority of the chapter is then dedicated to the derivation of a tractable form of the alloy free energy for use in a Landau-type linear response theory, and to the physical interpretation of results obtained using this theory. The chapter concludes by presenting some intuitive examples of ‘toy’ alloy systems where the internal energy takes a simple, pairwise form, and analysing these using the Landau theory in conjunction with lattice-based Monte Carlo simulations.