Theory of intermediate twinning and spontaneous polarization in the phase transformations of ferroelectric potassium sodium niobate

Potassium sodium niobate is considered a prominent material system as a substitute for toxic lead-containing ferroelectric materials. It exhibits first-order phase transformations and ferroelectricity with potential applications ranging from energy conversion to innovative cooling technologies, hereby addressing urgent 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 2021 et al. [1] which also reveal the occurrence of intermediate twinning during the phase transition. Here we show that intermediate twinning is a consequence of energy minimization. We employ 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 the 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.