Micromechanics of residual stress and texture development due to poling in polycrystalline ferroelectric ceramics

This paper presents micromechanics based analysis of elastic strain and changes in the texture of poled polycrystalline ferroelectric PZT ceramics for direct comparison with synchrotron X-ray measurements. The grains are modelled as spherical inclusions, to which transformation strains are assigned depending on the fractions of different ferroelectric domains. Eshelby's inclusion problem with the classical self-consistent method is applied to evaluate the elastic state of the grains. In particular, the elongation due to lattice elastic strain is calculated as a function of inclination Ψ relative to the polar axis. The ratio of diffraction peak intensities, corresponding to the domain fractions, is also expressed as a function of Ψ. This analysis identifies the special character of the {111} reflection, for which the lattice strain along 〈111〉 in the stress free state is independent of ferroelectric domain population and hence unaffected by poling. The elongation due to the lattice strain parallel to 〈111〉 and peak intensity ratio are expressed in terms of the overall macroscopic strain of a poled specimen, each having a cos2Ψ dependence.