TABLE I.

Measured and derived material constants of orthorhombic PIN-PMN-PT:Mn single crystals poled along [011] direction with “1O” single domain state.

Elastic stiffness constants: $c_{\mathit{i}\mathit{j}}^E$, $c_{\text{ij}}^E$(1010 N/m2)
$c_{11}^E$	$c_{12}^E$	$c_{13}^E$	$c_{22}^E$	$c_{23}^E$	$c_{33}^E$	$c_{44}^E$	$c_{55}^E$	$c_{66}^E$
20.0	10.6	4.64	14.9	10.2	15.0	1.84	0.49	7.14
$c_{11}^D$	$c_{12}^D$	$c_{13}^D$	$c_{22}^D$	$c_{23}^D$	$c_{33}^D$	$c_{44}^D$	$c_{55}^D$	$c_{66}^D$
20.1	10.3	5.34	15.7	8.34	19.2	6.69	4.33	7.14

Elastic compliance constants: $s_{\text{ij}}^E$, $s_{\text{ij}}^E$(10−12 m2/N)
$s_{11}^E$	$s_{12}^E$	$s_{13}^E$	$s_{22}^E$	$s_{23}^E$	$s_{33}^E$	$s_{44}^E$	$s_{55}^E$	$s_{66}^E$
8.59	−7.99	2.75	19.9	−11.0	13.3	54.3	204	14.0
$s_{11}^D$	$s_{12}^D$	$s_{13}^D$	$s_{22}^D$	$s_{23}^D$	$s_{33}^D$	$s_{44}^D$	$s_{55}^D$	$s_{66}^D$
7.49	−4.96	0.07	11.6	−3.64	6.76	14.9	23.1	14.0

Piezoelectric coefficients: $d_{\mathit{i}\mathit{j}}$(10−12 C/N), $e_{\mathit{i}\mathit{j}}$(C/m2), $g_{\text{ij}}$(10−3 Vm/N), $h_{\mathit{i}\mathit{j}}$(108 V/m)
$d_{15}$	$d_{24}$	$d_{31}$	$d_{32}$	$d_{33}$	$e_{15}$	$e_{24}$	$e_{31}$	$e_{32}$	$e_{33}$
3100	2435	110	−302	267	15.2	44.8	2.38	−6.23	14.5
$g_{15}$	$g_{24}$	$g_{31}$	$g_{32}$	$g_{33}$	$h_{15}$	$h_{24}$	$h_{31}$	$h_{32}$	$h_{33}$
58.4	16.2	10.0	−27.5	24.3	25.3	10.8	4.80	−12.5	29.2

Dielectric permittivity: ${\epsilon }_{\text{ij}}$/${\epsilon }_0$, ${\beta }_{\mathit{i}\mathit{j}}$(10−4/${\epsilon }_0$)
${\epsilon }_{11}^S$	${\epsilon }_{22}^S$	${\epsilon }_{33}^S$	${\epsilon }_{11}^T$	${\epsilon }_{22}^T$	${\epsilon }_{33}^T$	${\beta }_{11}^S$	${\beta }_{22}^S$	${\beta }_{33}^S$	${\beta }_{11}^T$	${\beta }_{22}^T$	${\beta }_{33}^T$
679	4672	561	6000	17000	1240	14.7	2.14	17.8	1.67	0.59	8.06

Electromechanical coupling factors: $k_{\mathit{i}\mathit{j}}$ and mechanical quality factors Qm
$k_{15}$	$k_{24}$	$k_{31}$	$k_{32}$	$k_{33}$	$k_t$
94%	85%	36%	65%	70%	47%
$Q_{15}$	$Q_{24}$	$Q_{31}$	$Q_{32}$	$Q_{33}$	$Q_{\mathrm{\text{t}}}$
70	30	490	390	1230	220