Microscopic origin and relevant grain size effect of discontinuous grain growth in BaTiO_(3)-based ferroelectric ceramics

Barium titanate[BaTiO_(3)(BT)]-based ceramics are typical ferroelectric materials.Here,the discontinuous grain growth(DGG)and relevant grain size effect are deeply studied.An obvious DGG phenomenon is observed in a paradigmatic Zr^(4+)-doped BT-based ceramic,with grains growing from∼2.2–6.6 to∼121.8–198.4μm discontinuously near 1320℃.It is found that fine grains can get together and grow into large ones with liquid phase surrounding them above eutectic temperature.Then the grain boundary density(D g)is quantitatively studied and shows a first-order reciprocal relationship with grain size,and the grain size effect is dependent on D g.Fine grains lead to high D g,and then cause fine domains and pseudocubic-like phase structure because of the interrupted long-range ferroelectric orders by grain boundary.High D g also causes the diffusion phase transition and low Curie dielectric peak due to the distribution of phase transition temperature induced by internal stress.Local domain switching experiments reveal that the polarization orientation is more difficult near the grain boundary,implying that the grain boundary inhibition dominates the process of polarization orientation in fine-grain ceramics,which leads to low polarization but a high coercive field.However,large-grain ceramics exhibit easy domain switching and high&similar ferroelectricity.This work reveals that the grain boundary effect dominates the grain size effect in fine-grain ceramics,and expands current knowledge on DGG and grain size effect in polycrystalline materials.

Sequential city growth： Theory and evidence from the US

City growth patterns are attracting more attention in urban geography studies. This paper examines how cities develop and grow in the upper tail of size distribution in a large-scale economy based on a theoretical model under new economic geography framework and the empirical evidence from the US. The results show that cities grow in a sequential pattern. Cities with the best economic conditions are the first to grow fastest until they reach a critical size, then their growth rates slow down and the smaller cities farther down in the urban hierarchy become the fastest-growing ones in sequence. This paper also reveals three related features of urban system. First, the city size distribution evolves from low-level balanced to primate and finally high-level balanced pattern in an inverted U-shaped path. Second, there exist persistent discontinuities, or gaps, between city size classes. Third, city size in the upper tail exhibits conditional convergence characteristics. This paper could not only contribute to enhancing the understanding of urbanization process and city size distribution dynamics, but also be widely used in making effective policies and scientific urban planning.