Phase-field modeling for energy storage optimization in ferroelectric ceramics capacitors during heat treatment process

Ferroelectric ceramic capacitors have potential advantages in energy storage performance, such as high energy storage density and fast discharge speed, making them widely applicable in different energy storage devices. During heat treatment, ferroelectric ceramics undergo an evolution of grain growth leading to changes in dielectric properties. Optimizing the energy storage properties of ferroelectric ceramics during heat treatment is a crucial issue. In this work, a phase field modeling for dielectric breakdown coupled with a grain growth model is developed to give a fundamental understanding of the effect of grain growth on dielectric breakdown. In addition, this work proposes a breakdown detection method to shorten the computational time of the model. The results indicate the existence of a local maximum of the breakdown field strength during grain growth, leading to a local maximum of the energy storage density. It is found that the dielectric breakdown strength and the pattern of the final breakdown path are significantly influenced by the grain size and distribution. The model is also applicable to various dielectrics and provides guidance for the design of high-energy storage dielectrics.