Property matrices of [011]-poled rhombohedral Pb(Zn_1/3Nb_2/3)O₃–(4.5-7)%PbTiO₃ single crystals

Relaxor-based Pb(Zn_1/3Nb_2/3)O₃-xPbTiO₃ (PZN-xPT) domain-engineered single crystals, where x=0.045-0.09, exhibit much superior piezoelectric properties and electromechanical coupling factors compared to conventional Pb(Zr_xTi_1-x)O₃ polycrystalline ceramics.^1–9 They have been used as the active materials in a number of high performance transducers for demanding applications.

For instance, PZN-(0.06-0.08)PT single crystals, notably PZN-(6.5-7.0)%PT (for which k₃₃ ≥ 0.92, d₃₃ ≈ 2400-2900 pC/N, T_RT ≈ 85-104 °C, E_c ≈ 0.30-0.40 kV/mm for [001]-poled crystals;^1–8 k₃₂ ≥ 0.92, d₃₂ ≈ −(2400-3200) pC/N, T_RO ≈ 90-104 °C and E_c ≈ 0.48-0.60 kV/mm for [011]-poled crystals^8,9), are ideal active materials for compact yet high sensitivity sensors including hydrophones,¹⁰ accelerometers^11,12 and 3D acoustic vector sensors,¹⁰ broadband transducers of moderate power density such as medical phased array probes,^13–17 laminate composite magnetoelectric sensors,¹⁸ and piezoelectrically tunable devices.^19–22 Exhibiting comparatively superior piezoelectric coefficients but of higher transformation properties, PZN-(0.05-0.06)PT single crystals, or more specifically PZN-5.5%PT (for which k₃₃ ≥ 0.91, d₃₃ ≈ 1950-2600 pC/N, T_RT ≈ 105-115 °C, E_c ≈ 0.35-0.40 kV/mm for [001]-poled crystals;^8,23,24 k₃₂ ≥ 0.89, d₃₂ ≈ −(1850-2450) pC/N, T_RO ≈ 104-115 °C and E_c ≈ 0.45-0.55 kV/mm for [011]-poled crystals^9,12,24,25), find applications in high-performance compact broadband underwater projectors,^10,12,26 large stroke linear actuators,²⁷ etc. In contrast, PZN-(0.045-0.05)PT single crystals, or PZN-(4.5-4.75)%PT in particular (for which k₃₃ ≥ 0.89, d₃₃ ≈ 1400-2100 pC/N, T_RT ≈ 115-125 °C, E_c ≈ 0.25-0.35 kV/mm for [001]-poled crystals;^{3,6,8,28–30} k₃₂ ≥ 0.88, d₃₂ ≈ −(1200-1800) pC/N, T_RO ≈ 116-127 °C and E_c ≈ 0.32-0.45 kV/mm for [011]-poled crystals^{9,12,23,29–31}), are used in applications where improved temperature stability are sought despite having slightly reduced performance characteristics. These include land based and underwater transducers,¹⁰ phased array medical probes,³² and recently developed “Hi-Fi Stake” piezo single crystal actuators.³³ 

Due to their application potential, three different nominal PZN-xPT crystal compositions, i.e., x = 0.045, 0.07 and 0.08, are included in the recently published IEEE standard for relaxor-based single crystals.³⁴ In the current version, only [001]-poled crystal properties are listed. In a recently concluded Piezoelectric Single Crystal Standards Committee meeting held in conjunction with the 2018 International Workshop for Acoustic Transduction Materials and Devices (IWATMD 2018), it was recommended that [011]-poled properties of the various PZN-PT compositions including PZN-5.5%PT be included in the to-be-published, final version.³⁵ 

Single crystals are anisotropic in properties. For device design and modelling purposes, complete property matrices of the desired crystal composition and cut are required. For the range of PT content described above, PZN-PT single crystals are of rhombohedral structure at room temperature with spontaneous polarization along <111> crystal directions. When poled along a [011] crystal direction, the crystal displays mm2 symmetry with 17 independent material constants: 9 elastic, 5 piezoelectric and 3 dielectric constants.

As of to-date, only the complete property matrix of [011]-poled PZN-7%PT single crystals has been reported by Zhang et al.³⁶ However, the reported piezoelectric coefficients, as well as those reported by the same authors in an earlier work,³⁰ i.e., d₃₂ ≈ −(1460-1900) pC/N, are significantly lower than the optimum value of –(2400-3200) pC/N reported by other researchers;^8,25 so are their reported k₁₅ and k₃₁ values. Other than the above work, the complete property matrices for [011]-poled PZN-xPT single crystals of other compositions (i.e., x = 0.045, 0.055 and 0.065) are unavailable as of to-date. This remains so despite that these PZN-PT compositions have been used by contemporary scientists and researchers in a number of successful applications.

In view of the above and ad-hoc requests received by us from contemporary researchers for property matrices for [011]-poled PZN-PT single crystals, in this work, we measured the elastic, dielectric and piezoelectric properties of [011]-poled rhombohedral PZN-PT single crystals of various useful compositions using the resonance and anti-resonance method. The measured and deduced properties are compiled to form the complete property matrices for use by contemporary scientists and researchers working in the field.

The PZN-xPT single crystals used, x = 0.0475, 0.055 and 0.065, were grown by the high temperature flux method at Microfine Materials Technologies P/L (Singapore).⁶ Table I shows the dimensions, crystal orientations and intended vibration modes of the various [011]-poled PZN-PT single crystal samples used in the present work. These samples were prepared according to the Institute of Radio Engineers (IRE)³⁷ and Institute of Electrical and Electronic Engineers (IEEE) standards.³⁸ 

A schematic showing the various crystal cuts is provided in Figure 1. The opposite L×W faces (Table I) of all the samples were sputter-coated with Au-Pd electrode. Then, the samples were optimally poled at room temperature in the [011] crystal thickness direction (marked T in Table I), which is assigned as the 3-axis of the poled crystals (Figure 1). The poling fields used were 0.6 kV/mm for both PZN-4.75%PT and PZN-5.5%PT and 0.5 kV/mm for PZN-6.5%PT. For sample nos. 3(b) and 4(b), the poling electrodes were removed and new electrodes were sputtered onto their smallest W×T opposite faces (Figure 1) as the working electrode. Care was exercised to ensure that no crystal depoling occurred in the application of the working electrode.

The dielectric constants $εijT$ were obtained from capacitance measurement (nos. 1, 3b and 4b samples) at 1 kHz. The electromechanical coupling factors k_ij and selected elastic constants (⁠$s11E$⁠, $s22E$⁠, $s33D$⁠, $c33D$⁠, $c44E$⁠, and $c55E$⁠) of the extensional and shear single crystals were determined from the resonance behaviors of sample nos. 1-4 using expressions (1) to (6) below. Both the resonance and dielectric measurements were performed using an impedance analyzer (Wayne Kerr 6500B) at ambient conditions.

And

where f_r and f_a are the resonance and anti-resonance frequencies, l and t the resonating length and thickness directions of respective samples, and ρ the crystal density. The longitudinal and transverse elastic constants, $c33E$⁠, $s11D$⁠, $s22D$ and $s33E$⁠, and shear compliances $s44E$ and $s55E$ were derived using equations (7) to (10) below.

Based on the obtained elastic compliances $sijE$⁠, electromechanical coupling factors k_ij, and dielectric constants $εiiT$⁠, the various piezoelectric strain coefficients d_ij were calculated using equation (11). The other piezoelectric constants e_ij, g_ij and h_ij, and dielectric constants β_ij were derived using standard piezoelectric relations contained in IEEE standard.³⁸ 

The off-diagonal matrix components $s12E$⁠, $s23E$ and $s13E$⁠, and the shear compliance $s66E$ were obtained from sample nos. 5(a) – 5(c) using equations (12)–(14) below.

With all the elastic compliances $sijE$ obtained, the undetermined elastic stiffness constants $cijE$ were calculated using the matrix inversion technique. The $c33E$ values obtained from the matrix inversion technique and equation (7) are almost the same, which also serves as self-consistency check. Other elastic constants, i.e., those under constant dielectric displacement conditions, i.e., $cijD$ and $sijD$⁠, were determined using equations (15) and (16) below. These two expressions were also used for self-consistency check purposes, i.e., to remove occasionally too-high or too-low measured or deduced property values resulting from possible compositional variations among the crystal samples. That is, the final property values provided satisfactorily fulfil these two expressions and all the obtained electromechanical coupling factors are meaningful and reasonable.

Based on the obtained data, the complete sets of elastic, dielectric and piezoelectric properties of [011]-poled PZN-4.75%PT, PZN-5.5%PT and PZN-6.5%PT rhombohedral multidomain single crystals were constructed and are provided in Table II. Also provided in Table II are the rhombohedral-to-orthorhombic transformation temperature (T_RO), coercive field strengths (E_c), and density (ρ) of the various crystal compositions. It is evident from this table that rhombohedral PZN-(4.75-6.5)%PT single crystals have extremely high (d₁₅, k₁₅) shear and (d₃₂, k₃₂) transverse properties, with k₃₂ ≈ k₁₅ ≥ 0.89, d₁₅ ≈ (4000-5000) pC/N and d₃₂ ≈ −(1800-2800) pC/N.

A comparison is made with the property matrix for [011]-poled PZN-7%PT crystal reported by Zhang et al.³⁶ Their value of elastic stiffness $c66E$ is extremely high (i.e., > 9× higher) and of d₁₅ is significantly lower (i.e., < 0.5×) than the values obtained in the present work (see Table II). This has probably resulted in the lower values of their other piezoelectric properties (notably d₃₂, d₃₁, d₂₄, k₃₁ and k₂₄), as it has been shown that a high d₁₅ value contributes, in a large part, to the high d_ij values of [001]- and [011]-poled rhombohedral relaxor-PT single crystals.³⁹ The crystal used in Ref. 36 (and Ref. 30 as well) was grown by the solution Bridgman growth technique. It had been reported that solution Bridgman grown PZN-PT crystals exhibited large compositional variations, notably in the region close to the initial growth portion as well as the last formed portion.^40,41 It has also been reported that for [011]-oriented crystals with composition close to the morphotropic phase boundary (MPB), they could become overpoled with degraded piezoelectric properties if the crystals were poled at sufficiently high field.^8,9,42 That is, they could be poled into the orthorhombic state, either globally or locally, and the transformed part of the poled crystal would remain in such a state even after field removal. As orthorhombic crystal displays much lower piezoelectric coefficients, so do the overpoled crystals.^8,9,42 It is thus possible that the crystal used in Ref. 36 and 30 could have been overpoled and hence was not truly rhombohedral. For the above reason, we have decided not to list and compare the result of Zhang et al.³⁶ in Table II, to avoid unnecessary confusion.

In summary, selected elastic, dielectric and piezoelectric constants for [011]-poled flux-grown PZN-4.75%PT, PZN-5.5%PT and PZN-6.5%PT single crystals of rhombohedral phase have been measured from the resonance technique and used to construct the complete property matrices of [011]-poled PZN-PT crystals. Self-consistency checks using established piezoelectric relations were performed to avoid measured or deduced values which could be too high or too low due to possible crystal composition non-uniformity.

The results show that [011]-poled PZN-PT single crystals display excellent transverse and shear properties (k₃₂ ≥ 0.90, k₁₅ ≈ 0.92, d₃₂ ≈ –(2400-3200) pC/N, d₁₅ ≈ 4800 pC/N, T_RO ≈ 90-104 °C for PZN-6.5%PT and k₃₂ ≥ 0.90, k₁₅ ≈ 0.89, d₃₂ ≈ –(1850-2400) pC/N, d₁₅ ≈ 4200 pC/N, T_RO ≈ 105-115 °C for PZN-5.5%PT). These unique piezoelectric properties of [011]-poled PZN-PT crystals, together with the property matrices provided in this work, can be used advantageously to design high-performance single crystal transducers of transverse or shear activation/sensing modes to suit various application needs. The present work further shows that for [011]-cut PZN-xPT single crystals of close to MPB composition, i.e., x ≥0.07, care must be exercised to avoid overpoling during crystal processing which could result in degraded piezoelectric properties.

The single crystal samples used in the present work were provided by Microfine Materials Technologies Pte Ltd (Singapore). The authors wish to acknowledge the technical support rendered by the staff of MMT.