Modelling of precipitate hardening in ferroelectric materials

This investigation presents a mechanical model to determine energetically favourable particle shapes, motivated by precipitation hardening in ferroelectric materials. We examine Li-doped \(\text {NaNbO}_3\) ${\text{NaNbO}}_3$ and propose a system of equations to derive the correct material constants for this material system. To model the elongated precipitate shape we introduce two approaches: An elliptic shape and a shape based on cubic B-spline-curves. We subject both definitions to an optimisation routine that yields equilibrium shapes. We further use the spline approach to derive configurational forces on the interface.