  Reversible topotactic transitions between oxygen-vacancy-ordered structures
in transition metal oxides provide a promising strategy for active manipulation
of material properties. While transformations between various oxygen-deficient
phases have been attained in bulk ABO$_{3-\delta}$ perovskites, substrate
clamping restricts the formation of distinct ordering patterns in epitaxial
films. Using in-situ scanning transmission electron microscopy (STEM), we image
a thermally driven reversible transition in
La$_{0.5}$Sr$_{0.5}$CoO$_{3-\delta}$ films on SrTiO$_3$ from a multidomain
brownmillerite (BM) structure to a uniform phase wherein oxygen vacancies order
in every third CoO$_x$ plane. Because temperature cycling is performed over a
limited temperature range (25 {\deg}C - 385 {\deg}C), the oxygen deficiency
parameter $\delta$ does not vary measurably. Under constant $\delta$, the
topotactic transition proceeds via local reordering of oxygen vacancies driven
by thermal strain. Atomic-resolution imaging reveals a two-step process whereby
alternating vertically and horizontally oriented BM domains first scale in size
to accommodate the strain induced by different thermal expansions of
La$_{0.5}$Sr$_{0.5}$CoO$_{3-\delta}$ and SrTiO$_3$, before the new phase
nucleates and quickly grows above 360 {\deg}C. Upon cooling, the film transform
back to the mixed BM phase. As the structural transition is fully reversible
and $\delta$ does not change upon temperature cycling, we rule out
electron-beam irradiation during STEM as the driving mechanism. Instead, our
findings demonstrate that thermal strain can solely drive topotactic phase
transitions in perovskite oxide films, presenting opportunities for switchable
ionic devices.
