Multiwavelength anomalous X-ray diffraction for combined imaging of atomic displacement and strain

The X-ray Bragg coherent diffractive imaging (CDI) technique assumes that the structure factor holds constant over the measured crystal. This approximation breaks down for materials exhibiting variations in the unit-cell configuration, such as piezo- and ferroelectrics. In that case, the strain field cannot be reliably determined from the reconstruction because the lattice deformation and the structure factor contribute concomitantly. Proposed here is a solution to this problem achieved by combining Bragg CDI and the multiwavelength anomalous diffraction approach that measures a Friedel pair of reflections at two different photon energies near an absorption edge. Comparing the obtained reconstructions with a parametric model that includes calculating the scattering amplitude as a function of wavelength and the unit-cell configuration, the contributions of the lattice deformation and the structure factor are separated. Simulations of the ferroelectric material BaTiO₃ demonstrate the possibility of simultaneous probing of the strain and displacement of the Ti atoms. The proposed method opens up an opportunity to apply coherent X-ray diffraction for nanoscale-resolved 3D mapping of polarization domains in micro- and nanocrystals.