  An atomistic study of the order-effect occurring in Li$_{x}$CoO$_{2}$ at
$x=0.5$ is presented and an explanation for the computationally and
experimentally observed dip in the Li diffusivity is proposed. Configurations
where a single half-filled Li layer arranged in either a linear or a zig-zag
pattern are simulated. It is found that the lowest energy phase is the zig-zag
pattern rather than the linear arrangement that currently is considered to be
of lowest energy. Atomic interactions are modeled at the DFT level of accuracy
and energy barriers for Li-ion diffusion are determined from searches for first
order saddle points on the resulting potential energy surface. The determined
saddle points reveal that the barriers for diffusion parallel and perpendicular
to the zig-zag phase differ significantly and explain the observed dip in
diffusivity.
