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

TL;DR

This paper introduces a data-driven approach to model ferroic phenomena at the atomic scale using reduced order parameter models derived solely from experimental STEM data, enabling detailed analysis of phase coexistence and sublattice asymmetry in La-doped BiFeO3.

Contribution

It develops a four sublattices model (FSM) for describing atomic displacements in ABO3 perovskites directly from experimental data, bypassing traditional assumptions about order parameters.

Findings

Explains coexistence of multiple structural phases in La-doped BiFeO3.

Atomically resolves sublattice asymmetry in La/Bi cation distribution.

Provides a new framework for analyzing ferroic behaviors from experimental data.

Abstract

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.