  Prediction of properties from composition is a fundamental goal of materials
science and can greatly accelerate development of functional materials. It is
particularly relevant for ferroelectric perovskite solid solutions where
compositional variation is a primary tool for materials design. To advance
beyond the commonly used Landau-Ginzburg-Devonshire and density functional
theory methods that despite their power are not predictive, we elucidate the
key interactions that govern ferroelectrics using 5-atom bulk unit cells and
non-ground-state defect-like ferroelectric domain walls as a simple as possible
but not simpler model systems. We also develop a theory relating properties at
several different length scales that provides a unified framework for the
prediction of ferroelectric, antiferroelectric and ferroelectric phase
stabilities and the key transition temperature, coercive field and polarization
properties from composition. The elucidated physically meaningful relationships
enable rapid identification of promising piezoelectric and dielectric
materials.
