  The intercalation of alkali ions into layered materials has played an
essential role in battery technology since the development of the first
lithium-ion electrodes. Coulomb repulsion between the intercalants leads to
ordering of the intercalant sublattice, which hinders ionic diffusion and
impacts battery performance. While conventional diffraction can identify the
long-range order that can occur at discrete intercalant concentrations during
the charging cycle, it cannot determine short-range order at other
concentrations that also disrupt ionic mobility. In this article, we show that
the use of real-space transforms of single crystal diffuse scattering, measured
with high-energy synchrotron x-rays, allows a model-independent measurement of
the temperature dependence of the length scale of ionic correlations along each
of the crystallographic axes in a sodium-intercalated V$_2$O$_5$. The
techniques described here provide a new way of probing the evolution of
structural ordering in crystalline materials.
