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Scanning Transmission Electron Microscopy (STEM) has enabled mapping ofatomic structures of solids with sub-pm precision, providing insight to thephysics of ferroic phenomena and chemical expansion. However, only a subset ofinformation is available, due to projective nature of imaging in the beamdirection. Correspondingly, the analysis often relies on the postulated knownform of macroscopic Landau-Ginzburg energy, and some predefined relationshipbetween experimentally determined atomic coordinates and the order parameterfield. Here, we propose an approach for exploring the structure of ferroicsusing reduced order parameter models constructed based on experimental dataonly. We develop a four sublattices model (FSM) for the analytical descriptionof A-cation displacement in (anti)ferroelectric-antiferrodistortive perovskitesof ABO3-type. The model describes the displacements of cation A in fourneighboring unit cells and determines the conditions of different structuralphases appearance and stability in ABO3. We show that FSM explains thecoexistence of rhombohedral (R), orthorhombic (O) and spatially modulated (SM)phases, observed by atomic-resolution STEM in La-doped BiFeO3. Using thisapproach, we atomically resolve and theoretically model the sublatticeasymmetry inherent to the case of the A-site La/Bi cation sublattice inLaxBi1-xFeO3 polymorphs. This approach allows exploring the ferroics behaviorsfrom experimental data only, without additional assumptions on the nature ofthe order parameter.

Building Free Energy Functional from Atomically-Resolved Imaging: Atomic Scale Phenomena in La-doped BiFeO3