  Scanning Transmission Electron Microscopy (STEM) has enabled mapping of
atomic structures of solids with sub-pm precision, providing insight to the
physics of ferroic phenomena and chemical expansion. However, only a subset of
information is available, due to projective nature of imaging in the beam
direction. Correspondingly, the analysis often relies on the postulated known
form of macroscopic Landau-Ginzburg energy, and some predefined relationship
between experimentally determined atomic coordinates and the order parameter
field. Here, we propose an approach for exploring the structure of ferroics
using reduced order parameter models constructed based on experimental data
only. We develop a four sublattices model (FSM) for the analytical description
of A-cation displacement in (anti)ferroelectric-antiferrodistortive perovskites
of ABO3-type. The model describes the displacements of cation A in four
neighboring unit cells and determines the conditions of different structural
phases appearance and stability in ABO3. We show that FSM explains the
coexistence of rhombohedral (R), orthorhombic (O) and spatially modulated (SM)
phases, observed by atomic-resolution STEM in La-doped BiFeO3. Using this
approach, we atomically resolve and theoretically model the sublattice
asymmetry inherent to the case of the A-site La/Bi cation sublattice in
LaxBi1-xFeO3 polymorphs. This approach allows exploring the ferroics behaviors
from experimental data only, without additional assumptions on the nature of
the order parameter.
