Nanoscale Modelling of Substitutional Disorder in Battery Materials

Over the last decades, Density Functional Theory (DFT) has been the standard quantum mechanical method for the atomistic modelling of solids, giving an insight into the functional properties of applied materials. However, current materials innovation requires the screening of increasingly large and complex chemical spaces for both disordered and metastable structures that can display superior multi-functional properties. This usually involves the complete configurational exploration of beyond ternary and high-entropy alloys and ceramics, unachievable due to the computational costs of performing such an immense number of DFT calculations. A typical way to reduce computational costs is to employ the Cluster Expansion (CE) method, but with the development of Machine Learning (ML) in recent years, new methods have been gaining momentum. In this chapter, we guide the reader through the key computational models available to deal with the ever-increasing complexity of configurational space, with a particular focus on the application of these models to battery materials. Section 1 starts with a brief introduction to the general concepts on configurational thermodynamics, then in Sect. 2 we review a selection of studies highlighting configurational disorder in battery materials. In Sect. 3 we discuss current conventional methods of determining the partition function based on exact symmetry-adapted configurational modelling techniques, as well as the approximations utilized to reduce the number of configurations sampled such as the CE formalism. In Sect. 4 we discuss current ML approaches, and finally, in Sect. 5 we give our general conclusions and perspectives on the direction of the field.