Na- and K-ion batteries are attractive "beyond Li-ion" technologies for large-scale energy storage applications due to their low cost. However, the development of robust electrode materials to host these larger ions remains a challenge. Layered oxide intercalation compounds, which have been extensively adopted as cathodes for Li-ion batteries, tend to undergo many structural phase transitions and stabilize complex ion-vacancy orderings when intercalated with Na or K. These effects produce stepwise voltage profiles and can lead to mechanical degradation and sluggish diffusion during battery cycling.
To understand this behavior, we have examined the thermodynamics of several layered oxide chemistries for Na/K intercalation using our CASM (a Clusters Approach to Statistical Mechanics) software package. Energies obtained from density functional theory were used to train cluster expansion effective Hamiltonians that allow for rapid evaluation of the energies of arbitrary ion-vacancy configurations. This enables the prediction of low-energy phases and the simulation of finite-temperature properties using Monte Carlo techniques.
We discovered several families of stable Na/K orderings that are common to the systems studied. At intermediate Na/K content, the orderings consist of regions of a single ordering periodically separated by antiphase boundaries (APBs) that accommodate changes in composition. This yields a near continuum, or "Devil's staircase," of ordered ground states, which give rise to voltage profiles resembling those measured experimentally. Through a detailed investigation of possible diffusion pathways, we predict that Na diffusion in the APB-based ordered phases is mediated by APB migration occurring via the formation and expansion of kinks in the boundaries. We turn to kinetic modeling to understand the macroscopic implications of this unusual diffusion mechanism.
