The microstructure of a ferroelectric single crystal is significantly affected by applied loads. Domains evolve through equilibrium states, following a route that minimizes the overall energy. The herringbone pattern is one of the most widely observed domain structures in ferroelectric crystals. In this work, the evolution of four types of herringbone pattern in the tetragonal crystal system is studied by using a variational method. These four herringbone patterns are periodic rank-2 laminates which satisfy compatibility across every domain wall. The unit cell of periodic structure dictates a set of domain walls whose positions may vary while maintaining the same topology. The model allows for a crystal with one type of herringbone domain pattern to switch to another pattern through “pivot states”. In this study, a domain evolution map showing all paths between the four types of rank-2 herringbone pattern and their pivot states is developed. Hysteresis loops such as those observed in ferroelectric single crystals subjected to variety of loads are reproduced.

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