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Abstract. When a capillary bridge of a constant volume is formed between two surfaces, the shape of the liquid bridge will change as the separation between those surfaces is varied. To investigate the variable forces and Laplace pressure of the capillary bridge, as the shape the bridge evolves, a pseudo-three-dimensional force model of the capillary bridge is developed. Based on the characteristics of the slender structured surface, an efficient method is employed to directly solve the differential equations defining the shape of the capillary bridge. The spacing between the plates satisfying the liquid confined within the hydrophobic region of the structured surface is calculated. The method described in this paper can prevent meshing liquid surfaces such that, compared with Surface Evolver simulations, the computing speed is greatly improved. Finally, by comparing the results of the finite element simulations performed with Surface Evolver with those of the method employed in this paper, the practicality of the method is demonstrated.

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[Formula: see text] (SLTO) ceramics ([Formula: see text] = 0.05, 0.10, 0.15) were prepared with giant dielectric constant by the traditional solid-state method at 1350[Formula: see text]C. The temperature dependence of the dielectric constant was obtained at the temperature ranging from 29[Formula: see text]C to 500[Formula: see text]C and the frequency ranging from 2 kHz to 2 MHz. Two sets of relaxation peaks appear in the low temperature (region I) and the high temperature (region II), respectively. For region I, we conclude that the relaxation behavior is related to the oxygen vacancy migration. For region II, the two relaxation processes are caused by grain boundary for high frequency and Sr or Ti defects at grain interior for low frequency. With the doping amount reaching 0.15, the relaxation peaks disappear and become a common phase transition because of the aggravation of lattice distortion. These possible physical mechanisms of two sets of relaxation peaks are briefly discussed.

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