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

Ferroelectric material properties strongly depend on the external and inter nal stress and electric fields. This strong dependency is due to the coupli ng of the nonlinear switching polarization to the nonlinear switching strai n of the BO6 octahedra of the ABO(3) perovskite structure. Therefore any ch anges imparted to this atomic octahedral configuration either by external o r internal mechanisms would lead in an average sense to changes in the mate rial properties. In the current paper, a first order phase transition Landau model is modifi ed by making the nonlinear dielectric stiffness, alpha(11) temperature, T-3 dependent and retaining the nonlinear c(ijk), elastic stiffnesses. Due to these modifications, stress induced phase transition shift is observed as w ell as shifting of the first order transition to second order transition un der 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 follo w up papers. The free energy equations and the material properties derivati on with the necessary justifications are presented in the current paper.