Electromechanical properties of orthorhombic 0.24Pb(In_1/2Nb_1/2)O₃–0.43Pb(Mg_1/3Nb_2/3)O₃–0.33PbTiO₃ single-domain crystal

Abstract

Single-domain structure with orthorhombic symmetry has been achieved in morphotropic phase boundary composition 0.24Pb(In_1/2Nb_1/2)O₃ −0.43Pb(Mg_1/3Nb_2/3)O₃–0.33PbTiO₃ ternary single crystal by applying a large field along the pseudo-cubic direction [011]_c. Complete set of elastic, piezoelectric, and dielectric constants has been determined with self-consistency. This crystal shows very large thickness shear piezoelectric coefficient d₁₅=4324 pC/N and extremely high shear electromechanical coupling factor k₁₅=96%. Three-dimensional orientation dependence of the longitudinal piezoelectric constant d₃₃ was calculated and compared with experimental values, which revealed nearly 20% extrinsic contributions in domain engineered [001]_c and [111]_c poled conditions.

1. Introduction

[001]_c poled relaxor-PT single crystals with both rhombohedral and morphotropic phase boundary (MPB) compositions, show excellent longitudinal piezoelectric and electromechanical coupling properties, such as d₃₃=2000 pC/N and k₃₃=92% for [001]_c poled PMN–0.30 PT (R phase), and d₃₃=2820 pC/N and k₃₃ = 94% for [001]_c poled PMN–0.33 PT (MPB composition) single crystals [1,2]. While for [011]_c poling, the macroscopic properties of rhombohedral composition with “2 R” domain structure are significantly different from those of MPB compositions with “1 O” domain structure [3-5]. Especially the longitudinal/transverse piezoelectric properties (d₃₃=340 pC/N, d₃₂= 260 pC/N) of [011]_c poled MPB composition crystals were much lower than that of [011]_c poled rhombohedral crystals (d₃₃=1300 pC/N, d₃₂= −1680 pC/N) [4].

Recently, the coexistence of M_A and M_C phases in as-grown PMN–0.32 PT single crystals were observed at room temperature by polarized optical microscopy [6]. From X-ray diffraction experiments, Singh et al. reported that the structure is tetragonal (T) phase for PMN-xPT with x≥0.35, and R phase for PMN-xPT with x≤0.26. In the MPB regions, monoclinic M_A is stable for 0.27≤x≤0.30, while monoclinic M_C is stable for 0.31≤x≤0.34 [7]. The monoclinic phase (M_C) and orthorhombic phase (O) were induced by electric field E//[001]_c and E//[011]_c for PMN-0.35 PT single crystal, respectively [8].

While after being poled along [011]_c, the MPB composition crystal approximately shows macroscopic orthorhombic mm2 point group symmetry since the monoclinic M_C phase is practically a slightly distorted orthorhombic O phase [5,9]. In this work, we report a complete set of elastic, piezoelectric, and dielectric constants of [011]_c poled 0.24Pb(In_1/2Nb_1/2)O₃–0.43Pb(Mg_1/3Nb_2/3)O₃–0.33PbTiO₃ (0.24PIN–0.43PMN–0.33 PT) ternary single crystal. The poled 0.24PIN–0.43PMN–0.33 PT crystal shows macroscopically orthorhombic mm2 pseudo-single-domain properties. In addition, the three-dimensional orientation dependence of the longitudinal piezoelectric constant d₃₃ has been calculated for 0.24PIN–0.43PMN-0.33 PT based on the measured full matrix single domain data, and compared with the measured d₃₃ under [001]_c and [111]_c poling conditions.

2. Experimental

The 0.24PIN-0.43PMN-0.33 PT single crystals used in this work were grown by the modified Bridgman method [10,11]. The as-grown crystal was oriented by the Laue machine with an accuracy of ±0.5°. Specimens used in the full matrix measurements were cut and polished into parallelepiped with three pairs of parallel surfaces along $[0\stackrel{‒}{1}1{]}_{\mathrm{c}}$, [100]_c, and [011]_c. Moreover, the [001]_c, [111]_c, and [011]_c oriented plates were prepared for the piezoelectric property measurements. The samples were sputtered with gold electrodes on the [001]_c, [111]_c, or [011]_c pair surfaces, respectively, and poled at 15 kV/cm in silicone oil at room temperature. The piezoelectric constant d₃₃ of [001]_c, [111]_c, and [011]_c oriented plates were measured by using a ZJ-2 piezo d₃₃ meter. The combined resonance and ultrasonic methods were used to get the complete set of constants with self-consistency.

3. Results and discussions

The measured and derived elastic, piezoelectric and dielectric constants of the 0.24PIN-0.43PMN-0.33 PT single crystal poled along [011]_c direction have been determined and given in Table 1. Material constants marked with a star (*) were determined directly by resonance or ultrasonic measurements while others were derived values. It was found that the longitudinal/transverse piezoelectric constants d₃₃=229 pC/N, d₃₂= 291 pC/N, and d₃₁=110 pC/N with “1 O” structure are much smaller compared to that of [011]_c poled rhombohedral crystals with “2 R” structure, which possess large longitudinal/transverse properties withd₃₃= 1068 pC/N, pC/N, d₃₂ 1693 and d₃₁=675 pC/N for [011]_c poled 0.24PIN-0.46PMN-0.30 PT [12]. In addition, both shear piezoelectric constants d₁₅ and d₂₄ are very large with d= 4324 pC/N and d₂₄= 1063 pC/N for [011]_c poled 0.24PIN-0.43PMN-0.33 PT single crystal, which is significantly different from [011]_c poled 0.24PIN–0.46PMN–0.30 PT with large shear d₁₅=3122 pC/N but lowd₂₄=142 pC/N [12]. This is because the polarization rotation is easier in the “1 O” domain structure under electric field parallel to $[0\stackrel{‒}{1}1{]}_{\mathrm{c}}$ or [100]_c, since there is only one polarization orientation remains. Hence, both the shear piezoelectric constants d₁₅ and d₂₄ are large for the “1 O” single domain structure [4].

Table 1.

Measured and derived material constants of [011]_c poled 0.24P1N-0.43PMN-0.33 PT single crystal. [Directly measured constants are marked by a star (*).]

Elastic stiffness constants: $C_{ij}^E$ and $C_{ij}^D$ (1010 N/m2)
$C_{11}^{E_{\ast }}$	$C_{12}^E$	$C_{13}^E$	$C_{22}^{E_{\ast }}$	$C_{23}^E$	$C_{33}^E$	$C_{44}^{E_{\ast }}$	$C_{55}^{E_{\ast }}$	$C_{66}^{E_{\ast }}$
20.35	10.93	6.67	13.25	9.13	15.31	4.92	0.32	7.42
$C_{11}^D$	$C_{12}^D$	$C_{13}^D$	$C_{22}^D$	$C_{23}^D$	$C_{33}^{D_{\ast }}$	$C_{44}^{D_{\ast }}$	$C_{55}^{D_{\ast }}$	$C_{66}^D$
21.00	10.30	8.44	13.87	7.41	20.11	7.62	4.33	7.42
Elastic compliance constants: $S_{ij}^E$ and $S_{ij}^D$ (10−12 m2/N)
$S_{11}^{E_{\ast }}$	$S_{12}^E$	$S_{13}^E$	$S_{22}^{E_{\ast }}$	$S_{23}^E$	$S_{33}^E$	$S_{44}^E$	$S_{55}^E$	$S_{66}^E$
8.89	−7.92	0.85	19.86	−8.40	11.17	20.33	312.50	13.48
$S_{11}^D$	$S_{12}^D$	$S_{13}^D$	$S_{22}^D$	$S_{23}^D$	$S_{33}^{D_{\ast }}$	$S_{44}^D$	$S_{55}^D$	$S_{66}^D$
7.80	−5.03	−1.42	12.23	−2.39	6.45	13.13	23.10	13.48
Piezoelectric coefficients: eiλ(C/m2), diλ(1012 C/N), giλ(103 Vm/N), and hiλ(108 V/m)
e 15	e 24	e 31	e 32	e 33	d 15	d 24	$d_{31}^{\ast }$	$d_{32}^{\ast }$	$d_{33}^{\ast }$
13.84	52.30	5.82	−5.67	15.80	4324	1063	110	−291	229
g 15	g 24	g 31	g 32	g 33	h 15	h 24	h 31	h 32	h 33
66.93	6.78	9.90	−26.21	20.60	28.98	5.16	11.18	−10.89	30.36
Dielectric constants: εij(ε0) and β(104/ε0)
${\epsilon }_{11}^{S_{\ast }}$	${\epsilon }_{22}^{S_{\ast }}$	${\epsilon }_{33}^{S_{\ast }}$	${\epsilon }_{11}^{T_{\ast }}$	${\epsilon }_{22}^{T_{\ast }}$	${\epsilon }_{33}^{T_{\ast }}$	${\beta }_{11}^{S_{\ast }}$	${\beta }_{22}^{S_{\ast }}$	${\beta }_{33}^{S_{\ast }}$	${\beta }_{11}^{T_{\ast }}$	${\beta }_{22}^{T_{\ast }}$	${\beta }_{33}^{T_{\ast }}$
540	11,450	588	7300	17,730	1256	18.54	0.87	17.00	1.37	0.56	7.96
Electromechanical coupling factors kij and density
k 15	k 24	$k_{31}^{\ast }$	$k_{32}^{\ast }$	$k_{33}^{\ast }$	$k_t^{\ast }$	Density (kg/m3)
0.96	0.60	0.35	0.62	0.65	0.49	8198

The three-dimensional orientation of d₃₃ by the coordinate transformation using the “1 O” full matrix data is shown in Fig. 1, which revealed large spatial anisotropy. The theoretical value of $d_{33}^{\left[001\right]}$ was calculated in the $[0\stackrel{‒}{1}1{]}_{\mathrm{c}}-{\left[001\right]}_{\mathrm{c}}$ plane to be 1649 pC/N by Eq. (1), which accounts for 81% of the measured d₃₃=2038 pC/N for [001]_c poled 0.24PIN-0.43PMN-0.33 PT multi-domain crystal. It shows that the orientation effect plays an important role in the material properties of domain engineered relaxor-PT ferroelectric crystals but the extrinsic contribution for this system is also significant. We can also conclude that the origin of this large piezoelectric coefficient $d_{33}^{\left[001\right]}$ is mainly from the large shear property d₁₅ of the single-domain crystal.

$$d_{33}^{\left[001\right]}=\frac{1}{2\sqrt{2}}(d_{15}^{\mathrm{O}}+d_{31}^{\mathrm{O}}+d_{33}^{\mathrm{O}})$$ (1)

Fig. 1.

Calculated three-dimensional orientation dependence of d₃₃ by the co-ordinate transformation using the “1O” full matrix data of 0.24PIN-0.43PMN-0.33 PT single crystal.

Similarly, the theoretical value of $d_{33}^{\left[111\right]}$ was calculated in the [100]_c-[011]_c plane to be 334 pC/N by using Eq. (2), which contributed 83% of the measured d₃₃=400 pC/N for [111]_c poled 0.24PIN–0.43PMN–0.33 PT domain engineered crystal. It is important to note that this is consistent with the fact that higher piezoelectric strain is obtained under an electric field along [001]_c than a field along [111]_c [11]. Based on Eq. (2), the origin of piezoelectric properties $d_{33}^{\left[111\right]}$ is mainly from the shear piezoelectric constant d₂₄, since the d₂₄ is much higher than d₃₂ and d₃₃ in the orthorhombic single-domain crystal.

$$d_{33}^{\left[111\right]}=\frac{\sqrt{2}}{3\sqrt{3}}(d_{24}^{\mathrm{O}}+d_{32}^{\mathrm{O}})+\frac{2\sqrt{2}}{3\sqrt{3}}{d}_{33}^{\mathrm{O}}$$ (2)

On the other hand, for domain engineered 0.24PIN–0.43PMN–0.33 PT single crystal, the extrinsic (domain structure) contribution is about ~20%, much higher than that in domain engineered rhombohedral crystal with only ~5% extrinsic contribution [13]. In the case of relaxor-PT single crystal, ferroelectric domain structures miniaturize down to nanometer scales when the composition approaches the MPB, which implies that domain structures play a greater role near the MPB since high density of domain walls are present in the crystals [14].

4. Summary and conclusions

A complete set of elastic, piezoelectric, and dielectric constants of [011]_c poled 0.24Pb(In_1/2Nb_1/2)O₃–0.43Pb(Mg_1/3Nb_2/3)O₃–0.33PbTiO₃ ternary single crystal with orthorhombic symmetry has been measured. The [011]_c poled single crystal shows macroscopic orthorhombic single-domain properties with ultra-large thickness shear mode piezoelectric coefficient d₁₅=4324 pC/N and very high shear electromechanical coupling factor k₁₅=96%. Both polarization rotation effect and domain wall motions play important roles in the enhanced macroscopic properties for the domain engineered [001]_c poled 0.24PIN-0.43PMN-0.33 PT single crystals.