  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.
