Thermodynamics of formation of tetragonal and rhombohedral heterophase polydomains in epitaxial ferroelectric thin films

In this work, the thermodynamics of formation of tetragonal and rhombohedral heterophase polydomains in ferroelectric films is explained by the theory of elastic domains. The energetics of the heterophase polydomain microstructure are analyzed. The three major energy terms determining the crystalline orientation of the interdomain interface, i.e. interdomain elastic energy, interdomain electrostatic energy and domain interface energy, are investigated and compared. The crystalline orientation of the elastically best fitting plane between the two phases is analytically solved under an isotropic approximation of elasticity. It is found that a {1 1 2} type of domain interface minimizes interdomain elastic energies. Using available material parameters, it is found that the {1 1 2} domain interface prevails in Pb(Zr, Ti)O3, Pb(Mg1/3 Nb2/3)O3–PbTiO3 and BiFeO3 heterophase polydomains under zero applied electric field, as elastic energy is the dominant factor of interdomain interactions in all three systems. On the other hand, an increasing interdomain electrostatic energy under a poling field may induce a different domain interface, which is beneficial to extrinsic electromechanical responses.