The local structure of ${\mathrm{Bi}}_4{\mathrm{W}}_{2/3}{\mathrm{Mn}}_{1/3}{\mathrm{O}}_8\mathrm{Cl}$ is determined using quantitative transmission electron microscopy. The electron exit wave, which is closely related to the projected crystal potential, is reconstructed and used as a starting point for statistical parameter estimation. This method allows us to refine all atomic positions on a local scale, including those of the light atoms, with a precision in the picometer range. Using this method one is no longer restricted to the information limit of the electron microscope. Our results are in good agreement with x-ray powder diffraction data demonstrating the reliability of the method. Moreover, it will be shown that local effects can be interpreted using this approach.

• Received 15 November 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.096106