Phase stability and ionic transport in post-spinel CaV$_2$O$_4$ cathode

Calcium-ion batteries (CBs) represent an alternative to lithium-ion technology but their advancement is limited by the lack of high-performance intercalation cathodes. Identified via computational screening, post-spinel CaV$_2$O$_4$ has emerged as a promising candidate, though its practical application is hindered by limited electrochemical capacity. Hence, we investigate the thermodynamic and ionic transport characteristics of Ca$_x$V$_2$O$_4$ ($0 \leq x \leq 1$) in this work, by integrating the cluster expansion formalism with Monte Carlo simulations and density functional theory based calculations. We construct the temperature-composition phase diagram of Ca$_x$V$_2$O$_4$ revealing several stable phases ($\alpha$ through $\zeta$) that can appear during electrochemical operations at different voltages. Importantly, we observe the formation of the $\varepsilon$ phase at $x \sim 0.83$ across a 370-590~K temperature window via invariant reactions, which agrees with observations in the experimental voltage profiles. Further, migration barrier calculations confirm that Ca mobility is severely impeded within the $\alpha$ ($x \sim 0$) and $\gamma$ ($x \sim 0.5$) phases. With the strong Ca-vacancy ordering contributing to the high barrier in $\gamma$ and the persistent two-phase region stretching across the $\delta$ ($x \sim 0.67$) and the $\gamma$ phases, we expect the accessible electrochemical capacity in the CaV$_2$O$_4$ system to be kinetically limited to at most half the theoretical capacity at 298~K, in agreement with experiments. Strategies including cation doping and particle size reduction can be considered to flatten the potential energy landscape of $\gamma$ and improve Ca mobility. Our computational findings highlight the interplay between stability and transport and provide design strategies that can enable the practical use of CaV$_2$O$_4$ as a CB cathode.