Probing the polarity of ferroelectric thin films with x-ray standing waves

An x-ray-diffraction method that directly senses the phase of the structure factor is demonstrated and used for determining the local polarity of thin ferroelectric films. This method is based on the excitation of an x-ray st anding-wave field inside the film as a result of the interference between-t he strong incident x-ray wave and the weak kinematically Bragg-diffracted x -ray wave from the film. The method is used to sense the displacements of t he Pb and Ti sublattices in single-crystal c-domain PbTiO3 thin films grown by metal-organic chemical-vapor deposition on SrTiO3(001) substrates.