Study On The Piezoelectric Properties And The Cut Directions Of PMN-xPT Crystal

The PMN-xPT single crystal has excellent piezoelectric properties and is expected to replace the traditional piezoelectric ceramics.The piezoelectric properties of ceramic materials are transversely isotropic,while the piezoelectric properties of PMN-xPT crystals are anisotropic.So,the piezoelectric properties of the crystal can be better utilized only when the anisotropic is taken into account in practical applications to cut the piezoelectric crystal.In this paper,the anisotropy of the commonly used piezoelectric moduli and electromechanical coupling coefficients of PMN-xPT（x=0.30,0.33,0.38,0.42）piezoelectric crystals are investigated by the coordinate system Z-X rotated twice The results are as follows:For the rhombohedral phase PMN-0.33PT single crystal,d₃₃3 and k₃₃ changed from 190pC/N and 0.69 to 2410.9 pC/N and 0.94,with corresponding rotation angles of（-63°/0°）and（-70.5°/0°）,increased by 12.6 times and 1.36 times,respectively;d₃₁1 and k₃₁ changed from-90 pC/N and 0.15 to 1342.9 pC/N and 0.92,with the corresponding rotation angles（94.5°/0°）and（112.5°/0°）,respectively,which are respectively 15 times and 6.1times larger than the original ones.d₃₆6 and k₃₆6 do not exist in the original coordinate system and the maximum value after rotation reaches 1340 pC/N and 0.73 corresponding to the rotation angles（45°/90°）and（148.5°/46.5°）,respectively.The values of piezoelectric modulus d₁₅5 and d₂₄ before rotation are both 4100 pC/N,and the maximum values of rotation are 4898.2 pC/N and 4279.7 pC/N,respectively.In addition,the electromechanical coupling coefficients k₁₅ and k₂₄ do not need coordinate rotation to reach the maximum.The tetragonal phase PMN-xPT crystals（x=0.30、0.33、0.38、0.42）have a 4mm structure.The piezoelectric coefficients d₁₆,d₂₁,d₂₂,d₂₃,d₃₄ and the electromechanical coupling coefficients k₁₆,k₂₁,k₂₂,k₂₃,k₃₄ have no initial values in the original coordinate system.After the rotation of the coordinate system,the maximum value can be obtained.However,they are equal to the value of a certain component before the coordinate system is rotated.Such a rotation has no real meaning and is therefore not considered.The piezoelectric moduli of x=0.30,0.33 and 0.42 are completely the same in the three-dimensional space.And only the value of d₂₄ has increased to some extent after Z-X coordinate rotation（-54°/-180°）、（54°/0°）and（-49.5°/0°）,respectively.The values of d₂₄ in PMN-0.33PT[001]and PMN-0.30PT crystals are 146.1pC/N and 190.3pC/N in the original coordinate system,which are much less than the values of 2833pC/N and 1981 pC/N for d₃₃,respectively.The maximum values were 3170.4 pC/N and 2197.5 pC/N,which increased by 21.7 times and 11.5 times,respectively,much larger than the values of d₃₃.The d24value of PMN-0.42PT crystal is 131 pC/N,the maximum value after the second rotation is250.3 pC/N,which is still less than the value of d33 of 300 pC/N,so rotary cutting has little significance.For PMN-0.38PT crystals,the piezoelectric modulus component does not produce new values after the second rotation,so rotary cutting makes no sense.The electromechanical coupling coefficient of the four kinds of crystals having a 4 mm structure of x=0.30,0.33,0.38 and 0.42 have the following characteristics.All of the electromechanical coupling coefficients of PMN-0.33PT and PMN-0.30PT crystals are completely the same in three-dimensional space.Compared with the above two kinds of crystals,only the distribution of electromechanical coupling coefficients k₃₁1 of PMN-0.38PT crystals is the same.And only the law of maximum value of k₂₄ is changed.For the number of maximum values of k₂₄,it is no longer eight,but two along the±Z axis.The distribution of k₁₅5 and k₃₃3 of PMN-0.42PT crystal is the same as that of PMN-0.38 PT,and the rest is the same as that of the crystal of 0.30 and 0.33.The rotation of the coordinate system can significantly increase the k₂₄、k₃₁1 of PMN-0.33PT and PMN-0.30PT crystals,and has little effect on the PMN-0.42PT crystals.Moreover,it has no effect on the PMN-0.38PT crystals.In this paper,the research results on the piezoelectric anisotropy of PMN-xPT crystal are of theoretical significance for its application in piezoelectric devices.