{'fraction_non_alphanumeric': 0.01995305164319249, 'fraction_numerical': 0.007042253521126761, 'mean_word_length': 5.561538461538461, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Theory of Morphotropic Phase Boundary in Solid Solution Systems of Perovskite-Type Oxide Ferroelectrics: Engineered Domain Configurations

Polarization-field and strain-field hysteresis loops with field-induced transition in two types of engineered domain configurations in perovskite-type oxide ferroelectrics were calculated in terms of the Landau-Devonshire type free energy. Using the free energy function truncated at the fourth order with respect to the polarization, it was found that the field-induced transition from the tetragonal phase to the rhombohedral phase under the field along the [111] direction is of the first order, while the transition from the rhombohedral phase to the tetragonal phase under the field along the [001] direction is of the second order. Physical properties of the engineered domain configurations were discussed.