Multiscale simulations of domains in ferroelectrics

This chapter focuses on recent studies of ferroelectrics, where large-scale molecular dynamics (MD) simulations using first-principles-based force fields played a central role in revealing important physics inaccessible to direct density functional theory (DFT) calculations but critical for developing physically-based free energy functional for coarse-grained phase-field-type simulations. After reviewing typical atomistic potentials of ferroelectrics for MD simulations, the chapter describes a progressive theoretical framework that combines DFT, MD, and a mean-field theory. It then focuses on relaxor ferroelectrics. By examining the spatial and temporal polarization correlations in prototypical relaxor ferroelectrics with million-atom MD simulations and novel analysis techniques, this chapter shows that the widely accepted model of polar nanoregions embedded in a non-polar matrix is incorrect for Pb-based relaxors. Rather, the unusual properties of theses relaxor ferroelectrics stem from the presence of a multi-domain state with extremely small domain sizes (2-10 nanometers), giving rise to a greater flexibility for polarization rotations and the ultrahigh dielectric and piezoelectric responses. Finally, this chapter discusses the challenges and opportunities for multiscale simulations of ferroelectric materials.