Abstract: The distribution in 3D space of the piezoelectric coefficient d15, d24, d31, d33, d36 and the electromechanical coupling factor k15, k24, k31, k33, k36 of the rhombohedral PMN-0.33PT crystal were investigated by rotating the coordinate system twice.The functions of the coefficients and the factors stated above about the coordinate rotation angle were obtained.The 3D figures, the maximum values of these coefficients and the rotation angle corresponding to the maximum value are achieved by MATLAB program.It is found that d31, d36, k31 and k36 change dramatically in different direction besides d33 and k33.The maximum value of d31 and k31 of the crystal after rotation expand 15 times and 6 times respectively compared with the measured value of the original coordinates.The maximum value of d36 and k36 which are both zero in the original coordinates can reach 1340 pC/N and 0.73 respectively after rotation.It is instructive for the application of the PMN-0.33 PT crystal in piezoelectric sensors and transducers.

Key words: The distribution in 3D space of the piezoelectric coefficient d15, d24, d31, d33, d36 and the electromechanical coupling factor k15, k24, k31, k33, k36 of the rhombohedral PMN-0.33PT crystal were investigated by rotating the coordinate system twice.The functions of the coefficients and the factors stated above about the coordinate rotation angle were obtained.The 3D figures, the maximum values of these coefficients and the rotation angle corresponding to the maximum value are achieved by MATLAB program.It is found that d31, d36, k31 and k36 change dramatically in different direction besides d33 and k33.The maximum value of d31 and k31 of the crystal after rotation expand 15 times and 6 times respectively compared with the measured value of the original coordinates.The maximum value of d36 and k36 which are both zero in the original coordinates can reach 1340 pC/N and 0.73 respectively after rotation.It is instructive for the application of the PMN-0.33 PT crystal in piezoelectric sensors and transducers.