A multiscale model for reversible ferroelectric behaviour of polycrystalline ceramics

A multiscale model for the behaviour of ferroelectric polycrystalline materials under electro-mechanical loading is proposed. It is based on an energetic description of the equilibrium at the single crystal scale using a statistical estimate of the ferroelectric domain structure. A self-consistent scheme is then used to establish the behaviour of polycrystalline materials. The approach is anhysteretic but hysteresis effects can be added afterwards so as to obtain butterfly ferroelectric loops. It is applied to a tetragonal Lead Zirconate Titanate (PZT). The model allows the investigation of crystallographic texture effects on the overall behaviour and provides an estimate of internal stresses within the material. By way of an example a 〈100〉 fibre texture is predicted to generate as much as 150% more longitudinal strain and 33% more electric induction at 1 MV/m compared to an isotropic polycrystal.