Finite element analysis of the effect of non-ferroelectric second phases in Pb(Mg1/3Nb2/3)O3

Non-ferroelectric second phases such as pores and pyrochlore usually exist in PbMg_1/3Nb_2/3O₃ (PMN) unless special production techniques are employed. A detailed 2D model was developed to assess the effects of these non-ferroelectric inclusions in terms of stress and electric field concentrations they create. Field induced anisotropy, and electric field dependence of elastic stiffness, dielectric permittivity and electrostrictive coefficients were included in the model where the material behavior was considered at T_max (zero hysterisis). Dielectric breakdown was also taken into account if the local electric field intensity exceeded an assumed dielectric strength. The results suggest that the electric and mechanical field concentrations depend on the geometry and alignment of the inclusions with respect to the applied field. Electric field concentration and depletion cause stresses up to 25 and 42 MPa, respectively. If dielectric breakdown occurred, it grew dendritically towards the electrodes and formed a region depleted of electric field in its surrounding. The results provide an insight to the mechanism of decreased performance of PMN due to the existence of nonferroelectric inclusions