Real-space imaging of polar and elastic nano-textures in thin films via inversion of diffraction data

algorithm with unsupervised machine learning to invert the diffuse scattering in conventional x-ray reciprocal-space mapping into real-space images of polar and elastic textures in thin epitaxial films. We first demonstrate our imaging in PbTiO 3 /SrTiO 3 superlattices to be consistent with published phase-field model calculations. We then visualize strain-induced ferroelastic domains emerging during the metal-insulator transition in Ca 2 RuO 4 thin films. Instead of homogeneously transforming into a low-temperature structure (like in bulk), the strained Mott insulator splits into nanodomains with alternating lattice constants, as confirmed by cryogenic scanning transmission electron microscopy. Our study reveals the type, size, orientation, and crystal displacement field of the nano-textures. The non-destructive imaging of textures promises to improve models for their dynamics and enable advances in quantum materials and microelectronics. patterns (white grid is set according to the thickness fringes minimum positions at 300K). The 300K fringes indicate a film thickness of 16.9 nm, while the 7K fringes indicate a thickness of 14 nm. The cause of the disparity of the thickness fringes under different temperatures is unclear. One plausible explanation is the illuminated region upon the thin film drifted during the dramatic change of temperatures because of the thermal expansion of the sample holder. And a thickness change of ~3nm is possible on CRO/LAO film as observed in the STEM. (c, d) The real space pixel size in the phase retrieval algorithm is directly related to the reciprocal space range. By tuning the input reciprocal space image size, we perform reconstructions with support thickness of 16.9 nm and 14nm. The reconstructed diffraction patterns with support thickness of (c) 16.9nm and (d) 14 nm. (e) The comparison of the thickness fringes of measured and reconstructed patterns. An obvious difference exists between the two measured fringes especially at the off-center regions. The fringe of the 16.9 nm reconstruction agrees with the measured 300K fringe, and the 14 nm reconstruction fringe agrees with the measured 7K fringe. Therefore, the support thickness is directly related to the thickness fringes of the reconstructed pattern and a support thickness of 14 nm is selected to reconstruct the data measured at 7K. Compared to the support thickness, the horizontal size of the support has less effect on the reconstruction. Reconstructions with thickness of 14nm and various horizontal support size of 169.5nm, 150.5nm, 133.7nm, 116.8nm. All the reconstructed diffraction patterns well retained the features of the measured data and resemble each other. And the width of the fine vertical lines within the reconstructed pattern is inversely related to the support horizontal size, as the a ‘thickness fringes’ analogue in the horizontal direction. Although the reconstructions are with different support size, similar repeating patterns are observed in all the reconstructed real space object with different number of periods.