The study explores the role of lattice disorder in classic ferroelectricity, particularly in ATiO3 perovskites. Traditional models often overlook the local structural perturbations (short-range lattice disorder) that significantly influence material behavior. While experimental techniques reveal average crystal structures, computational methods are needed to understand the underlying lattice disorder. The authors challenge the 'displacive' model, proposing instead a dynamic model where Ti cations hop across <111> directions. This hopping is governed by minimum potential energy pathways along <100> directions, leading to spatially modulated polarization nanoclusters. The emergence of soft phonon modes during phase transitions is also linked to this cation hopping. Existing research using techniques like Raman spectroscopy and X-ray Absorption Fine Structure (XAFS) provided seemingly contradictory results, but the authors suggest these can be reconciled through a dynamic framework encompassing the hopping of Ti cations. This dynamic paradigm is explored using high-resolution phonon dispersion analyses, molecular dynamics (MD) simulations and density functional theory (DFT) simulations, providing a more complete picture of the relationship between atomic-scale processes and macroscopic ferroelectric properties.

The introduction extensively reviews the existing literature on lattice disorder and its implications for ferroelectricity in perovskite materials. It discusses conflicting experimental results from Raman spectroscopy and XAFS, which initially supported both displacive and order-disorder models. The authors highlight previous theoretical work, including effective Hamiltonian and MD approaches, that have provided insights into the hopping processes of central cations and their connection to ferroelectric properties. They reference studies on soft phonon modes in perovskites, linking them to disorder-related phenomena. The review emphasizes the limitations of previous studies, which often relied on quasi-static or vanishing-temperature simulations, motivating the need for the finite-temperature dynamic analyses presented in this work.

The research utilizes a combination of molecular dynamics (MD) simulations and density functional theory (DFT) calculations. Large-scale MD simulations, employing an anharmonic core-shell potential model, were conducted with triclinic supercells containing up to 1 million atoms. The core-shell model represents each atom with two particles: a positively charged core and a negatively charged shell, allowing for the simulation of atomic polarization. The simulations incorporated short-range interactions between shells and long-range electrostatic interactions using the computationally efficient Wolf method. Different parameter sets were used for BaTiO3 and PbTiO3, reflecting the different bonding characteristics. Simulations were performed under various conditions, including different temperatures, applied electric fields, and mechanical stresses. The analysis included assessments of lattice disorder, polarization nanocluster evolution, phonon spectra calculations, and domain wall structure investigations. The DFT calculations, performed with the Vienna Ab initio Simulation Package (VASP), provided a complementary approach to calculate phonon dispersion curves. A detailed description of the method for calculating lattice polarization (accounting for both core and shell particle positions), configurational energy, and phonon spectra is included. The computational details, including supercell sizes, time steps, ensembles used, and computational resources, are thoroughly described.

The study's key findings center on the dynamic nature of lattice disorder and its influence on polarization, nanocluster formation, and domain wall structures in perovskite materials. MD simulations revealed that disordered perovskite phases consist of dynamically distorted rhombohedral lattices, with minimum configurational energy associated with <100> pathways. The distribution of these distorted lattices correlates with the distribution of configurational energy. The hopping of Ti atoms along these <100> pathways generates scattered soft phonon modes across phase transitions, as evidenced by high-resolution phonon dispersion analyses. These analyses demonstrate that the delocalized nature of these soft modes is a characteristic of disordered phases. The study further reveals the formation of polarization nanoclusters resulting from long-range polarization modulation. Ultrafast, soliton-like propagation of these nanoclusters was observed along the <100> directions. The simulations showed that while intrinsic nanoclusters in defect-free regions evolve dynamically, extrinsic nanoclusters, stabilized by electric charge defects, appear more stable and potentially observable experimentally. The analysis of domain walls (DWs) at room temperature demonstrated that in stable 180° and 90° head-to-tail DWs, polarization variations are accommodated by rearrangements of lattice disorder, while unstable head-to-head DWs are characterized by larger thicknesses and local orthorhombic structures. The study also examined the influence of mechanical stress, showing that applied shear strain leads to monoclinic lattice configurations, with more significant rotation in disordered BTO compared to ordered PTO. Furthermore, the application of biaxial pressure to a 90° head-to-tail DW resulted in the self-assembly of a monoclinic substructure, characterized by zig-zagged polarization rotations and twin boundaries. This finding has implications for understanding morphotropic phase boundaries (MPBs). Finally, the research suggests a method to distinguish between ordered and disordered ferroelectrics based on their response to applied shear strain.

The study addresses the research question by demonstrating a strong link between lattice disorder, the dynamic behavior of Ti cations, and the macroscopic ferroelectric properties of perovskite materials. The findings extend previous understanding by providing a dynamic framework that integrates seemingly contradictory experimental results. The discovery of ultrafast polarization nanocluster propagation and the correlation between cation hopping and soft phonon modes are significant contributions. The study's insights into the structure and stability of domain walls offer a potential mechanism for explaining light-induced domain wall mobilization. The results related to pressure-induced phase transitions and the formation of monoclinic nanostructures provide a new perspective on morphotropic phase boundaries, which are crucial for designing high-performance piezoelectric devices. The work highlights the power of large-scale MD simulations coupled with DFT calculations in unraveling the complexities of ferroelectric materials at different length scales. The results challenge experimental assertions, pointing to the need for advanced characterization techniques to observe dynamic nanocluster structures.

This research provides a comprehensive understanding of the interplay between lattice disorder, domain wall structures, and morphotropic phase boundaries in perovskite materials. Key findings include the identification of minimum energy pathways for cation hopping, the formation and propagation of polarization nanoclusters, and the impact of mechanical stress on phase transitions. The authors propose a new method for distinguishing between ordered and disordered ferroelectrics based on their response to shear strain. Future research could focus on further experimental validation of the predicted dynamic nanocluster behavior and the exploration of novel material processing routes to tailor MPB formation in thin-film structures.

The study primarily focuses on model perovskite systems (BaTiO3 and PbTiO3). While the core-shell potential model captures essential features of the materials' behavior, it is a simplification of the complex interactions in real systems. The simulations assume periodic boundary conditions, which might not perfectly represent real materials with finite size effects and surfaces. While the study suggests that extrinsic nanoclusters stabilized by charge defects may be observable experimentally, direct experimental observation of the ultrafast dynamic nanocluster evolution in defect-free regions remains a challenge. The interpretation of phonon spectra relies on post-processing of MD trajectories and might be influenced by the chosen analysis parameters.