  In epitaxially strained ferroelectric thin films and superlattices, the
ferroelectric transition temperature can lie above the growth temperature.
Ferroelectric polarization and domains should then evolve during the growth of
a sample, and electrostatic boundary conditions may play an important role. In
this work, ferroelectric domains, surface termination, average lattice
parameter and bilayer thickness are simultaneously monitored using in-situ
synchrotron x-ray diffraction during the growth of BaTiO$_3$/SrTiO$_3$
superlattices on SrTiO$_3$ substrates by off-axis RF magnetron sputtering. The
technique used allows for scan times substantially faster than the growth of a
single layer of material. Effects of electric boundary conditions are
investigated by growing the same superlattice alternatively on SrTiO$_3$
substrates and 20nm SrRuO$_3$ thin films on SrTiO$_3$ substrates. These
experiments provide important insights into the formation and evolution of
ferroelectric domains when the sample is ferroelectric during the growth
process.
