A three-dimensional polarization domain retrieval method from electron diffraction data.

We present an algorithm for retrieving three-dimensional domains of picometer-scale shifts in atomic positions from electron diffraction data, and apply it to simulations of ferroelectric polarization in BaTiO3. Our algorithm successfully and correctly retrieves polarization domains in which the Ti atom positions differ by less than 3 pm (0.4% of the unit cell diagonal distance) with 5 and 10nm depth resolution along the beam direction, and we also retrieve unit cell strain, corresponding to tetragonal-to-cubic unit cell distortions, for 10nm domains. Experimental applicability is also discussed.