{'fraction_non_alphanumeric': 0.02188006482982172, 'fraction_numerical': 0.011345218800648298, 'mean_word_length': 5.465968586387435, '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}}
Study of ferroelectric nanodomains and the effect of grain size in BaTiO3 ceramics

Nanodomains and grain-size effects in BaTiO3 have been studied theoretically. In this article, we have calculated the long-range Coulomb interaction between ferroelectric nanodomains in a single BaTiO3 grain, and obtained information on the domain structure at various temperatures and grain sizes. The relation between transition temperature and the grain size is obtained by incorporating the domain-wall energy, the surface energy, and the stress energy into the Landau–Ginzburg free-energy density. The results show that 180° domains exist in ferroelectric BaTiO3 nanoceramics. At room temperature, with the decreasing grain size, the domain width does not decrease monotonically; when the grain size reduces to 18 nm, the grain becomes a single domain, and when less than 12 nm, the ferroelectric phase disappears. With the decreasing grain size the temperature of the cubic-tetragonal phase transition is reduced, while the temperatures of the tetragonal–orthorhombic and orthorhombic–rhombohedral phase transitions reach a maximum when the grain sizes are in the vicinity of 200 nm. The theoretical results are compared with experimental data.