  Short-range ordering in cation-disordered cathodes can have a significant
effect on their electrochemical properties. Here, we characterise the cation
short-range order in the antiperovskite cathode material Li$_2$FeSO, using
density functional theory, Monte Carlo simulations, and synchrotron X-ray
pair-distribution-function data. We predict partial short-range
cation-ordering, characterised by favourable OLi$_4$Fe$_2$ oxygen coordination
with a preference for polar cis-OLi$_4$Fe$_2$ over non-polar
trans-OLi$_4$Fe$_2$ configurations. This preference for polar cation
configurations produces long-range disorder, in agreement with experimental
data. The predicted short-range-order preference contrasts with that for a
simple point-charge model, which instead predicts preferential
trans-OLi$_4$Fe$_2$ oxygen coordination and corresponding long-range
crystallographic order. The absence of long-range order in Li$_2$FeSO can
therefore be attributed to the relative stability of cis-OLi$_4$Fe$_2$ and
other non-OLi$_4$Fe$_2$ oxygen-coordination motifs. We show that this effect is
associated with the polarisation of oxide and sulfide anions in polar
coordination environments, which stabilises these polar short-range cation
orderings. We propose similar anion-polarisation-directed short-range-ordering
may be present in other heterocationic materials that contain cations with
different formal charges. Our analysis also illustrates the limitations of
using simple point-charge models to predict the structure of cation-disordered
materials, where other factors, such as anion polarisation, may play a critical
role in directing both short- and long-range structural correlations.
