The effect of nonlinear stress and temperature on the ferroelectric properties of perovskites. Part 1: Phenomenological equations

Abstract

Ferroelectric material properties strongly depend on the external and internal stress and electric fields. This strong dependency is due to the coupling of the nonlinear switching polarization to the nonlinear switching strain of the BO₆ octahedra of the ABO₃ perovskite structure. Therefore any changes imparted to this atomic octahedral configuration either by external or internal mechanisms would lead in an average sense to changes in the material properties.

In the current paper, a first order phase transition Landau model is modified by making the nonlinear dielectric stiffness, α₁₁ temperature, T ₃ dependent and retaining the nonlinear c _ijk, elastic stiffnesses. Due to these modifications, stress induced phase transition shift is observed as well as shifting of the first order transition to second order transition under the applied stress which agrees well with the experimental observations. The model can also predict critical points where multiple phases coexist, the phase stability, thin film stress effects, grain size effects, doping effects and single domain material properties, which are presented in follow up papers. The free energy equations and the material properties derivation with the necessary justifications are presented in the current paper.

Keywords:

• Ferroelectrics
• piezoelectrics
• Landau model
• nonlinear stress
• phase diagrams
• perovskites
• electromechanics
• PZT
• barium titanate