Theory of Intermediate Twinning and Spontaneous Polarization in Ferroelectric Potassium Sodium Niobate

Potassium sodium niobate is considered a prominent material system as a substitute for lead-containing ferroelectric materials. It exhibits first-order phase transformations and ferroelectricity with potential applications ranging from energy conversion to innovative cooling technologies, thereby addressing important societal challenges. However, a major obstacle in the application of potassium sodium niobate is its multi-scale heterogeneity and the lack of understanding of its phase transition pathway and microstructure. This can be seen from the findings of Pop-Ghe et al. (Ceram Int 47(14):20579-20585, 2021, https://doi.org/10.1016/j.ceramint.2021.04.067) which also reveal the occurrence of a phenomenon they term intermediate twinning during the phase transition. Here, we show that intermediate twinning is a consequence of energy minimization. We develop a geometrically nonlinear electroelastic energy function for potassium sodium niobate, including the cubic-tetragonal-orthorhombic transformations and ferroelectricity. The construction of the minimizers is based on compatibility conditions which ensure continuous deformations and pole-free interfaces. These minimizers agree with the experimental observations, including laminates between tetragonal variants under the cubic to tetragonal transformation, crossing twins under the tetragonal to orthorhombic transformation, intermediate twinning and spontaneous polarization. This shows how the full nonlinear electroelastic model provides a powerful tool in understanding, exploring, and tailoring the electromechanical properties of complex ferroelectric ceramics.