Piezoelectric and electro optic properties of tetragonal (1 − x )Pb(Mg 1/3 Nb 2/3 )O 3 − x PbTiO 3 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 1/3 Nb 2/3 )O 3 – x PbTiO 3 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 1/3 Nb 2/3 )O 3 – x PbTiO 3 single crystals have the first-order cubic-tetragonal phase transitions. The dielectric constants are in great agreement with the experimental results. The piezoelectric coefficients d 33 and d 31 at room temperature are about 145 pC/N and −62 pC/N respectively which are smaller than that of (1 − x )Pb(Mg 1/3 Nb 2/3 )O 3 – x PbTiO 3 single crystals around the morphotropic phase boundary. Moreover, tetragonal (1 − x )Pb(Mg 1/3 Nb 2/3 )O 3 – x PbTiO 3 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.