Shear piezoelectric properties d24 and k24 of a  poled KNNTL-Mn single crystal
The distributions of d24 and k24 in the 3D space of a  poled (K, Na, Li)(Na, Ta)O3:Mn (KNNTL-Mn) single crystal were investigated by the coordinate system rotation method. For the  poled KNNTL-Mn single crystal, the maximum piezoelectric strain constant d24 was 607.4 pC N−1, which was 9.2 times larger than the value in the original coordinate system and higher than d33. The maximum electromechanical coupling coefficient k24 was 0.83, which was 2.7 times larger than the original one. It was found that d24 and d15 as well as k24 and k15 were only equal in the Z-axis direction. In the other directions, d24 and k24 were greater than d15 and k15, respectively. In addition, compared with the 24-shear modes of other four lead-free single crystals (KNN, KNNT, KNNTL, and NBBT95/5) and the PZT-5H piezoelectric ceramics, the 24-shear mode of the KNNTL-Mn single crystals was found to be optimal in the lead-free single crystals. Although the maximum d24 of the KNNTL-Mn single crystal was slightly smaller than that of the PZT-5H piezoelectric ceramics, it was lead-free and had a larger electromechanical coupling coefficient, k24, and a higher Curie temperature than the PZT-5H piezoelectric ceramics. The  poled KNNTL-Mn single crystal is expected to be used in 24-shear mode piezoelectric sensors for non-destructive testing and structural health monitoring.