Nanometer-range atomic order directly recovered from resonant diffuse scattering

Abstract

The method for three-dimensional imaging with an atomic resolution, based on the measurement of resonant scattering of x rays, is presented and tested on a nanoscale-range occupational ordering of niobium and magnesium ions in the lead magnesium niobate (${\mathrm{PbMg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_{3}$) single crystal. X-ray diffuse scattering experiments performed at two wavelengths close to the absorption edge of niobium allowed us to record two $1024\ifmmode\times\else\texttimes\fi{}1024\ifmmode\times\else\texttimes\fi{}1024$ data sets of scattering intensities covering densely a large volume of the reciprocal space (up to ${Q}_{\mathrm{max}}=8.5\phantom{\rule{0.16em}{0ex}}{\AA{}}^{\ensuremath{-}1}$, with steps smaller than $\ensuremath{\delta}Q=0.05\phantom{\rule{0.16em}{0ex}}{\AA{}}^{\ensuremath{-}1}$). It is demonstrated that the anomalous part of the scattering intensity, including both discrete diffraction spots and diffuse scattering, can be employed to reconstruct the local atomic environment around the niobium cation up to the distance of several nanometers.