Effective symmetry and physical properties of twinned perovskite ferroelectric single crystals

The effective symmetry and material properties of twinned ferroelectric crystals with perovskite structure were analyzed. The twins or twinbands studied here were formed during ferroelectric phase transitions, which resulted in one of the following symmetry changes: m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar 3$$\end{document}m → 3m, m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar 3$$\end{document}m → 4mm, and m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar 3$$\end{document}m → mm2. It was found that the volume ratios of the two domains in a twin structure were not always equal due to the existence of defect pinning to the domain walls. This unequal partition changed the effective symmetry; hence, the effective macroscopic physical properties of the twin system. Using the data of LiNbO3, BaTiO3, and KNbO3, a detailed analysis has been carried out on macroscopic material property changes caused by the deviation from equal domain volume partition for crystals having 3m, 4mm, and mm2 symmetries.