Table 2.

Measured and calculated materials properties of tetragonal PIN–PMN–PT crystals poled along [001] direction. The data of PMN–42PT and PZN–12PT crystals were obtained from the Refs. ¹⁶, ²¹ for comparison.

	Dielectric constants					Electromechanical coupling factor
Materials	${\epsilon }_{33}^{\text{T}}$	${\epsilon }_{33}^{\text{S}}$		${\epsilon }_{11}^{\text{T}}$	${\epsilon }_{11}^{\text{S}}$	k31(45°)	k31	k33		k15		kt
PIMNTa	1090	310		15 000	4800	0.58	0.50	0.84		0.85		0.61
PMN–42PTb	660	260		8600	3100		0.39	0.78		0.8		0.62
PZN–12PTc	870	210		12 000a	5100a	0.58	0.52	0.87		0.78a		0.55
Piezoelectric constants
	dij (pC∕N)			eij (C∕m2)			hij (×108 N∕C)			gij (×10−3 m2∕C)
Materials	d31	d33	d15	e31	e33	e15	h31	h33	h15	g31	g33	g15
PIMNTa	−200	530	2350	−4.2	9.5	46.4	−16.5	34.9	10.8	−20.6	55.0	16.4
PMN–42PTb	−91	260	1310	−2.1	12.2	37.5	−9.2	53.2	15.9	−15.6	44.5	13.9
PZN–12PTc	−200	560	1450a	−2.2	8.5	41.3a	−12.0	45.9	9.1a	−26	75.1	13.6a
Elastic constants sij (×10−12 m2∕N)
Materials	${\text{s}}_{11}^{\text{E}}$	${\text{s}}_{12}^{\text{E}}$	${\text{s}}_{13}^{\text{E}}$	${\text{s}}_{33}^{\text{E}}$	${\text{s}}_{44}^{\text{E}}$	${\text{s}}_{66}^{\text{E}}$	${\text{s}}_{11}^{\text{D}}$	${\text{s}}_{12}^{\text{D}}$	${\text{s}}_{13}^{\text{D}}$	${\text{s}}_{33}^{\text{D}}$	${\text{s}}_{44}^{\text{D}}$	${\text{s}}_{66}^{\text{D}}$
PIMNTa	17.1	−3.3	−14.2	41	55.0	25.0	12.3	−7.1	−2.5	12.1	15.1	25.0
PMN–42PTb	9.4	−1.7	−6.2	19.2	35.0	12.5	8.0	−3.1	−2.1	7.6	12.4	12.5
PZN–12PTc	22.4	−3.5	−20.9	58.0	38.1a	27.9	16.3	−9.7	−4.8	14.9	15.4a	27.9
Elastic constants cij (×1010 N∕m2)
Materials	${\text{c}}_{11}^{\text{E}}$	${\text{c}}_{12}^{\text{E}}$	${\text{c}}_{13}^{\text{E}}$	${\text{c}}_{33}^{\text{E}}$	${\text{c}}_{44}^{\text{E}}$	${\text{c}}_{66}^{\text{E}}$	${\text{c}}_{11}^{\text{D}}$	${\text{c}}_{12}^{\text{D}}$	${\text{c}}_{13}^{\text{D}}$	${\text{c}}_{33}^{\text{D}}$	${\text{c}}_{44}^{\text{D}}$	${\text{c}}_{66}^{\text{D}}$
PIMNTa	20.6	15.5	12.5	12.5	1.8	4.5	21.3	16.3	10.9	19.4	6.8	4.5
PMN–42PTb	17.5	8.5	8.3	10.5	2.9	8.0	17.7	8.7	7.2	17.0	8.1	8.0
PZN–12PTc	15.2	11.4	9.7	8.72	2.9a	3.6	15.4	11.6	8.9	12.5	7.3a	3.6

^aPresent work.

^bReference ¹⁶.

^cReference ²¹.