Investigation of single and multidomain Pb(In_0.5Nb_0.5)O₃–Pb(Mg_1∕3Nb_2∕3)O₃–PbTiO₃ crystals with mm2 symmetry

Abstract

The piezoelectric properties of Pb(In_0.5Nb_0.5)O₃–Pb(Mg_1∕3Nb_2∕3)O₃–PbTiO₃ crystals with various engineered domain configurations were investigated. Rhombohedral and monoclinic∕orthorhombic crystals poled along their crystallographic [011] directions were found to possess macroscopic mm2 symmetry, with “2R” and “1O” domain, respectively. Crystals with the “2R” domain configuration were found to exhibit high extensional piezoelectric coefficients d₃₃ (∼1300 pC∕N) and d₃₂ (∼−1680 pC∕N), while crystals with the “1O” configuration possessed high shear coefficients d₁₅ (∼3500 pC∕N) and d₂₄ (∼2070 pC∕N), with relatively low extensional piezoelectric coefficients d₃₃ (∼340 pC∕N) and d₃₂ (∼−260 pC∕N). The observed results were explained by “polarization rotation” model, as related to their respective domain configurations.

The ultrahigh piezoelectric properties of [001] poled relaxor-based single crystals are realized through domain engineering, with engineered domain configuration “4R” (4R is one of the domain-engineered structures designated according to the crystal phase and poling direction^{1, 2}). High electromechanical coupling factors (k₃₃s>0.9) and piezoelectric coefficients (d₃₃s>1500 pC∕N) have been reported in Pb(Zn_1∕3Nb_2∕3)O₃–PbTiO₃ (PZNT) and Pb(Mg_1∕3Nb_2∕3)O₃–PbTiO₃ (PMNT) crystals.^{3, 4} Additional stable engineered domain configurations, including “2R,” can be achieved in [011] poled relaxor-based crystals, with comparable piezoelectric properties to the [001] crystals, where electromechanical coupling k₃₃s and piezoelectric coefficients d₃₃s were found to be on the order of ∼0.9 and >1000 pC∕N, respectively. Of particular interest are their ultrahigh transverse properties, with k₃₂ coupling factors and piezoelectric d₃₂ coefficients being on the order of ∼0.9 and −1100∼−1600 pC∕N, respectively.^{5, 6, 7} Furthermore, the mechanical quality factor Qs of [011] poled crystals have been found to be significantly higher, when compared to their [001] poled counterparts (>500 versus ∼100), due to the reduced domain wall mobility. The high Q values, with their yet high piezoelectric properties, indicate [011] oriented crystals promising for high power applications.⁸

Recently, theoretical and practical studies have been carried out on various [011] poled relaxor-PT crystal systems, including PZNT, PMNT, Pb(Mg_1∕3Nb_2∕3)O₃–PbZrO₃–PbTiO₃ (PMN-PZT), Pb(In_0.5Nb_0.5)O₃–Pb(Mg_1∕3Nb_2∕3)O₃–PbTiO₃ (PIN-PMN-PT) crystals.^{9, 10, 11, 12, 13, 14, 15, 16} To date, most of investigations have been carried out on [011] poled rhombohedral crystals with the engineered domain configuration “2R,” focusing on the high transverse piezoelectric d₃₂, with limited reports on the single domain “1O” properties, due to the narrow monoclinic∕orthorhombic compositional region.

In this work, both rhombohedral and orthorhombic PIN-PMN-PT single crystals were poled along the [011] direction, resulting in “2R” and “1O” engineered domain configurations. The longitudinal, transverse, and shear electromechanical properties were explored. Large property variations and strong anisotropic behavior in “2R” and “1O” domain states were analyzed using the “polarization rotation” model, as related to two types of engineered domain configuration.

Ternary xPIN-(1-x-y)PMN-yPT (x=0.25–0.35 and y=0.30–0.32) single crystals were grown using the modified Bridgman technique with [001] oriented seeds. The obtained as-grown crystals were 75 mm in diameter and 100 mm in length. The compositions investigated in this research were selected near the rhombohedral to monoclinic∕orthorhombic morphotropic phase boundaries (MPB). The crystals were oriented using real-time Laue x-ray and the samples were cut into different vibration resonators, according to the IEEE standard on piezoelectricity.¹⁷ Prior to property measurements, the samples were sputtered with gold electrodes on the parallel (011) surfaces. The samples were poled at room temperature using 15 kV∕cm dc field. For transverse 31- and 32-vibration modes, the vibration direction is along [0–11] and [100] orientations, respectively. For shear 15- and 24-vibration modes, the electrodes were subsequently removed from the (011) faces and re-electroded on the (0–11) and (100) faces. The dielectric permittivity of the various samples was determined at 1 kHz, using an HP4284A multifrequency inductance-capacitance-resistance (LCR) meter. The resonance and antiresonance frequencies were measured using an HP4294A impedance-phase gain analyzer. The electromechanical coupling factors (k_ijs) and elastic constants (s_jj∕c_jj) were calculated from the measured resonance and antiresonance frequencies.

Figure 1 shows the dielectric permittivity as function of temperature for [011] poled PIN-PMN-PT crystal samples with compositions close to the R–O MPB. The Curie temperature (T_C) for various crystal samples, crystal I (abbreviated as CI)—crystal III (CIII), were found to be 184 °C, 191 °C, and 198 °C, respectively, indicating that the PT content increased from CI to CIII, according to the phase diagram.¹⁸ Two ferroelectric-ferroelectric (F-F) phase transitions are evident prior to T_C for CI and CII, corresponding to rhombohedral-orthorhombic (T_RO) and orthorhombic-tetragonal (T_OT) phase transitions, respectively. T_RO and T_OT were found to be 99 and 122 °C for CI, being 72 and 115 °C for CII, due to the curved MPB.¹⁸ As shown in Fig. 1, permittivity values in the intermediate temperature range (T_RO−T_OT) for CI and CII were low, indicating the existence of an “1O” metastable single domain state, which was bounded by a low temperature, domain engineered “2R” state and engineered domain configuration “2T” at high temperature. For the CIII composition with the monoclinic∕orthorhombic phase, however, only one F-F transition was observed prior to T_C, corresponding to the O-T phase transition, being on the order of 100 °C. The dielectric permittivity of CIII at room temperature was significantly lower than both CI and CII, suggesting that a pseudosingle domain state “1O” was achieved in [011] poled monoclinic PIN-PMN-PT crystals. It should be noted that both crystals with “1O” and “2R” domain states possess macroscopic mm2 symmetry.

Figure 1.

Dielectric permittivity as function of temperature for PIN-PMN-PT with “1O” and “2R” engineered domain configurations.

Table 1 list the elastic constants (s_jj∕c_jj), electromechanical couplings (k_ij), piezoelectric coefficients (d_ij) and dielectric permittivities (ε_ii∕ε₀) for PIN-PMN-PT single crystals with “1O” (CIII) and “2R” (CI) domain states. The elastic compliances of the extensional vibration modes in “2R” engineering domain state were higher when compared to the values in “1O” single domain, while the shear elastic compliances show higher values in “1O” domain state. The high value of elastic compliance ${\mathrm{s}}_{55}^{\mathrm{E}}$ was found in PIN-PMN-PT with “1O” single domain, being on the order of 288 pm²∕N, corresponding to an ultralow frequency constant of ∼330 Hz m. Electromechanical coupling factors k₃₂, k₃₃, and k₁₅ were found to be 0.901, 0.919, and 0.935, respectively, for crystals with “2R” domain state. The corresponding piezoelectric coefficients d₃₂, d₃₃, and d₁₅ were on the order of −1680, 1300, and 2900 pC∕N. For the single domain state “1O,” however, extensional mode electromechanical coupling factors and piezoelectric coefficients decreased significantly when compared to the values in multi domain “2R” state, while the properties of shear vibration modes (24- and 15 modes) increased greatly.

Table 1.

Piezoelectric properties of PIN-PMN-PT single crystals with single domain “1O” and multidomain “2R” configurations $\left({\mathrm{s}}_{\mathrm{ij}}^{\mathrm{E}}:\mathrm{x}{10}^{-12}{\mathrm{m}}^2∕\mathrm{N};{\mathrm{c}}_{33}^{\mathrm{D}}:\mathrm{x}{10}^{10}\mathrm{N}∕{\mathrm{m}}^2;{\mathrm{d}}_{\mathrm{ij}}:\mathrm{pC}∕\mathrm{N}\right)$.

PIN-PMN-PT	${\mathrm{s}}_{11}^{\mathrm{E}}$	${\mathrm{s}}_{22}^{\mathrm{E}}$	${\mathrm{s}}_{33}^{\mathrm{E}}$	${\mathrm{s}}_{44}^{\mathrm{E}}$	${\mathrm{s}}_{55}^{\mathrm{E}}$	${\mathrm{c}}_{33}^{\mathrm{D}}$
1O (CIII)	17.6	18.1	22.1	45.9	288	23.2
2R (CI)	24.8	89.9	52.1	16.1	160	18.7
PIN-PMN-PT	k31	k32	k33	k24	k15	kt
1O (CIII)	0.670	0.654	0.820	0.827	0.944	0.412
2R (CI)	0.750	0.901	0.919	0.427	0.935	0.500
PIN-PMN-PT	d31	d32	d33	d24	d15
1O (CIII)	260	−260	340	2070	3490
2R (CI)	730	−1680	1300	200	2900
PIN-PMN-PT	${\epsilon }_{11}^{\mathrm{T}}∕{\epsilon }_0$	${\epsilon }_{22}^{\mathrm{T}}∕{\epsilon }_0$	${\epsilon }_{33}^{\mathrm{T}}∕{\epsilon }_0$	TC (°C)	TFF (°C)	EC (kV∕cm)
1O (CIII)	5360	15 500	900	198	100	6.3
2R (CI)	6810	1480	4360	184	122∕99	6.1

In order to elucidate the large variations in piezoelectric coefficients for “2R” and “1O” domain states, the “polarization rotation” model is considered. There are eight possible degenerate domain variants in the rhombohedral state, two of which will be energetically favored upon the application of an electric field along the [011]_C direction, being equally inclined to the poling direction at an angle of 35.5°, thus, only 71° domain walls remain. However, for crystals with the O phase, the spontaneous polar vectors are along the [011]_C crystallographic directions, thus a single domain “1O” state can be realized as a result of applying an electric field along the [011]_C. According to the IEEE standard, the orthorhombic principle axes are notated as [001]_O, [010]_O, and [100]_O, being equal to [011]_C, [0-11]_C, and [100]_C cubic axes, respectively, via a simple coordinate transform.

Due to the facilitated polarization rotation process in relaxor-PT based crystals,⁵ high transverse dielectric (ε₁₁ and ε₂₂) and shear piezoelectric properties (d₁₅ and d₂₄) are expected in “1O” single domain crystals, as shown in Fig. 2 and evident in Table 1. For “2R” domain engineered crystals, however, it is interesting to note that the level of the d₂₄ coefficient is only ∼200 pC∕N, much lower than that of d₁₅ (∼2900 pC∕N), though the crystals show the same macroscopic mm2 symmetry as “1O” domain state. As shown in Fig. 3, upon application of the electric field E₁, polarization rotation of domains I and II will contribute to the shear piezoelectric deformation S₅, leading to high piezoelectric coefficients (d₁₅). If an electric field E₂ applied, however, contributions to the shear deformation S₄ through polarization rotations of domains I and II are opposed, negating one another. As a consequence, the apparent piezoelectric coefficient d₂₄ is minimized. Analogous to the above analysis, the small shear piezoelectric coefficients observed for [001] poled “4R” domain engineered crystals (∼100–200 pC∕N) (Refs. ^{19, 20}) are the results of the negated shear deformations.

Figure 2.

Two independent shear piezoelectric responses (15- and 24-mode) and related polarization rotation paths in crystals with “1O” pseudosingle domain state.

Figure 3.

Two independent shear piezoelectric responses (15- and 24-mode) and related polarization rotation paths in crystals with “2R” engineered domain state, where the shear deformations were contributed by polarization rotation of domain I (DI) and domain II (DII).

As observed in crystals with the “4R” engineered domain configuration,^{1, 2, 3} [011] poled “2R” crystals exhibit relatively high extensional d₃₁, d₃₂, and d₃₃ values, due to the facilitated polarization rotation (high level of shear piezoelectric coefficient in single domain state “1R”), by the application of electric field E₃, as shown in Fig. 4. It should be noted that the extensional piezoelectric coefficients of “2R” crystals increased as the composition approaching R-O phase boundary, due to the flattening of free energy,⁵ where the d₃₃s were on the order of 1300 pC∕N and 1500 pC∕N for CI and CII, respectively. However, these extensional piezoelectric coefficients are small in “1O” single domain crystals, due to the electric field E₃ coincides with the spontaneous polarization direction, where no “polarization rotation” occurs and the collinear piezoelectric effect dominates.⁵

Figure 4.

Extensional piezoelectric response and related polarization rotation paths in crystals with “1O” and “2R” domain states.

In summary, [011] poled PIN-PMN-PT single crystals with “2R” and “1O” domain states were investigated. High extensional piezoelectric coefficients d₃₃∕d₃₂ were observed in engineered multi domain “2R” crystals, as a result of the facilitated polarization rotation. Of particular interest is the high shear piezoelectric coefficient d₂₄ found in crystals with the “1O” domain state (∼2070 pC∕N), when compared to the value of “2R” multidomain configuration (∼200 pC∕N), owing to the negated shear deformation S₄ in “2R” domain engineered structure.