Piezoelectric and electro—optic properties of tetragonal (1-x)Pb(Mg_1/3Nb_2/3)O₃—xPbTiO₃ single crystals by phenomenological theory

An eighth-order Landau–Devonshire theory is constructed to investigate the piezoelectric and electro–optic properties of tetragonal (1-x)Pb(Mg_1/3Nb_2/3)O₃–xPbTiO₃ single crystals (x=0.38 and x=0.4). The dielectric stiffness coefficients of the Landau potential are obtained by fitting to the dielectric properties and the phase transition temperature between cubic phase and tetragonal phase. It is indicated that tetragonal (1-x)Pb(Mg_1/3Nb_2/3)O₃–xPbTiO₃ single crystals have the first-order cubic-tetragonal phase transitions. The dielectric constants are in great agreement with the experimental results. The piezoelectric coefficients d₃₃ and d₃₁ at room temperature are about 145 pC/N and -62 pC/N respectively which are smaller than that of (1-x)Pb(Mg_1/3Nb_2/3)O₃–xPbTiO₃ single crystals around the morphotropic phase boundary. Moreover, tetragonal (1-x)Pb(Mg_1/3Nb_2/3)O₃–xPbTiO₃ single crystals have the linear electro–optic coefficients r_c=33.7 pm/V and r_c=28.8 pm/V for x=0.38 and x=0.4, respectively which are in accordance with the measurements.