  X-ray analysis of ferroelectric thin layers of Ba1/2Sr1/2TiO3 with different
thickness reveals the presence of internal strain gradients across the film
thickness and allows us to propose a functional form for the internal strain
profile. We use this to calculate the direct influence of strain gradient,
through flexoelectric coupling, on the degradation of the ferroelectric
properties of thin films with decreasing thickness, in excellent agreement with
the observed behaviour. This work highlights the link between strain relaxation
and strain gradients in epitaxial films, and shows the pressing need to avoid
strain gradients in order to obtain thin ferroelectrics with bulk-like
properties.
