The Effective Electromechanical Moduli of Domain Engineered Ferroelectric Crystals
We present a micromechanical analysis to explain the enhanced electromechanical coupling of domain engineered ferroelectric single crystals. The theory starts with energy-minimization approach, where the energy minimizing domain configurations are characterized as the convex hull of the ferroelectric energy wells, and are constructed by multi-rank laminations. The electromechanical moduli of ferroelectric single crystal with engineered domain configuration can then be determined by the homogenization theory. Using this approach, we analyzed the engineered domain configuration in tetragonal single crystal BaTiO3 poled in <111> direction, where d33 70% higher than those poled in <001> direction has been demonstrated, consistent with experimental observation. It is also found that the two-variant domain configurations have higher enhancement than three-variant systems, suggesting an optimal domain configuration for the enhanced piezoelectric properties. The theory reveals the fundamental property enhancement mechanism in ferroelectric single crystals with engineered domain configuration, and offers insight on the design and optimization of ferroelectric single crystals with superior functional properties.