Ferroelectric grain boundary complexion transitions

By starting from equilibrium volumetric and interfacial properties of ferroelectric materials, a thermodynamically-consistent phase field framework incorporating polarization and space charge for polycrystalline ferroelectrics is developed. Building on Cahn’s critical point wetting variational analysis, a series of planar $\left[001\right]$ tilt grain boundaries in tetragonal ferroelectrics in the absence of point defects are investigated. We find that grain boundaries with (i) head-to-tail-like polarization configurations have built in E-fields and undergo order–disorder transformations with decreasing temperature or increasing misorientation and those with (ii) head-to-head-like polarization configurations are paraelectric with no E-field and become more structurally disordered with decreasing temperature or increasing misorientation. Results suggest that ordered and disordered grain boundary complexions can coexist in first order ferroelectrics at all temperatures below the Curie temperature, $T_c$. In contrast, in second order ferroelectrics, results suggest that only one complexion will be observed at temperatures just below $T_c$ and, that on further cooling below a critical temperature, a second disordered complexion will develop for some grain boundaries, leading to abrupt changes in material properties.