Single domain and multidomain piezoelastic relationships in piezoelectric single crystals

Abstract

This paper presents a new method to compute the piezoelastic properties of multidomain single crystals from their single domain state. Based on a quasistatic assumption, a PMN- xPT multidomain is defined as a periodic medium with a lattice composed of layers of two domains in a twin structure. This latter is assumed to have charged domain walls that imply adapted lattice media and boundary conditions. A numerical computation has been performed for a PMN-33PT single crystal. The effective elastic, piezoelectric and dielectric constants of the macroscopic structure are quantified, calculations of the degree of anisotropy and of the wave velocities in different domain pattern configurations are reported. I. INTRODUCTION Relaxor based ferroelectric single crystals, such as (1- x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 and (1-x)Pb(Zn1/3Nb2/3)O3- xPbTiO3, can reach excellent piezoelectric properties due to the formation of engineered domain configurations (1), (2). In such materials, the functional properties of macroscopic systems with multidomain structures will not only depend on the single domain properties but also on extrinsic contributions of domain walls. These two effects have thus to be taken into account to predict the effective properties of multidomain single crystals. In the present paper, a quasistatic homogenization model is proposed to calculate the effective tensor properties of twin single domains. Defining a lattice medium and appropriate electrical boundary conditions at the interface between two domains, the method allows to distinguish the intrinsic contri- butions due to domain orientation and volume averaging from the extrinsic effect of domain walls. This model has been used to calculate the multidomain properties of a PMN-xPT single crystal from its single domain properties in the rombohedral phase. Numerical results are given for a PMN-33PT single crystal in term of piezoelastic tensor and degree of anisotropy in different configurations of domain pattern.