Piezoelectric materials for high temperature transducers and actuators

Ferroelectrics typically maintain their spontaneous polarization and post-poling piezoelectric properties with increasing temperature until reaching the Curie point (T_C). At this point the crystal structure transforms into a higher symmetry phase, which relinquishes the asymmetry and alignment of dipoles subsequently causing the material to lose its piezoelectric activity. The increasing temperature effectively ‘softens’ the lattice that increases the ease at which the material can be polarized thus plotting dielectric permittivity versus temperature is a standard method of defining the Curie point. By recording the capacitance on cooling and defining the point at which it reaches a maximum, immediately prior to the ferroelectric phase transition, can be defined as T_C [11].

The thermal re-randomization of the ferroelectric spontaneously formed dipoles also requires the material to be poled at T < T_C in order to restore the piezoelectric properties. This notion of the dipoles tendency to randomize with increasing temperature degrades the piezoelectric properties termed ‘thermal ageing’, which historically limits the operating temperature to a more temperature stable range which is much less than T_C [12]. This operational limit where the material effectively becomes de-poled, is defined as T_d [13] and is typically measured by the small signal resonance method [11, 14] to determine piezoelectric activity as a function of increasing temperature.

The complex a.c. permittivity ɛ* is measured from the complex impedance of a sample:where ε′ and ε″ are the real and imaginary parts respectively. The relative permittivity, or dielectric “constant” ε _r , relates to the sample capacitance and is given by the real part of the complex permittivity:where ɛ ₀ is the vacuum permittivity. ε′ is referred to as the dielectric permittivity in this paper. Dielectric losses are expressed by the loss tangent, or dissipation factor, tan δ:

Perhaps the most ubiquitous figure of merit for piezoelectric materials used throughout the literature is the piezoelectric charge coefficient (d _ij ), which describes the relationship between the direct (Eq. 4a), or converse (Eq. 4b), piezoelectric effect where the application of a mechanical stress is converted to an electrical charge (in C/N) or an applied electric field converted to mechanical strain respectively (m/V).

The stress (T) and strain (x) components are tensor magnitudes, with the origins and more complex orientation-dependent matrix of these coefficients found in detail elsewhere [15]. However, for simplicity and due to symmetry, a reduced notation can be used (Eq. 5), where the three direction is defined as in the direction of poling, with 1 and 2 orthogonal to this vector. For the example of the converse effect, the (d ₃₃) describes the strain induced from the same surface as the applied electric field, and in parallel to the poling direction.

The charge coefficient can be measured by direct or converse effect methods such as resonance [11, 14, 16] and Berlincourt methods respectively, although resonance is preferred and standardized [11, 15]. The magnitude of the charge coefficient in HT materials can range greatly, from <10 pC/N in non-perovskite crystals such as quartz [12], gallium orthophosphate and langasite [1], and exceed 10³ pC/N in ferroelectric single crystals such as PbYbO₃–PbTiO₃ [17] and BiScO₃–PbTiO₃ [18].

An important consideration for transducers is the voltage coefficient (g _ij ) in V/N (Eq. 6). This constant is inversely related to the dielectric permittivity by the charge coefficient and is typically temperature invariant due to the relationship in Eqs. (4a, 4b).

In resonance measurements, piezoelectric properties are commonly expressed as complex coefficients with the imaginary part relating to losses, both dielectric and mechanical. For assessing the piezoelectric properties using the above equations (and for electromechanical coupling factor described in Sect. 2.4) we use the real parts of the coefficients obtained from resonance measurements. At high temperature the dominant factor in the losses is the high electrical conductivity (see Sect. 2.5). We therefore use electrical measurements (see Sect. 2.2) in discussion of losses in this paper.

The fraction of electrical energy that can be converted into mechanical energy, or vice versa, is defined as the electromechanical coupling factor (k ²). As this conversion is never complete, k is always <1, and as such is a limiting factor to attaining high charge coefficients in typically stiffer (or less compliant) polycrystalline materials. This relationship also means the electromechanical coupling factor is relatively temperature insensitive as d, ɛ′ and compliance (s) all increase with temperature, until permanent depoling occurs.

Electromechanical coupling factors are typically found to be in the range of <0.1 for quartz [1], <0.5 for lead free polycrystalline materials [19], 0.8–0.4 for PZT and >0.8 for single crystals [1].

The electromechanical coupling factor can be calculated by the piezoelectric resonance method [11, 14] by measurement of the resonant (f _r ) and anti-resonant (f _a ) frequencies of the desired vibration mode [11]. An effective coefficient can be expressed at any fundamental resonance given by Eq. (7) [1], where the resonant and anti-resonant frequencies are defined by maximum and minimums of impedance (Z) at zero reactance respectively.

The variation of the electromechnical coupling factor and other coeffecients for various modes as a function of temperature for piezoelectric materials, and the principles of measurement are discussed further in Refs. [3, 20].

The electrical resistivity (ρ) of the material is an important property that is strongly affected by temperature. Polarisation changes resulting from an applied stress will, over a period of time, be nulled by charge movement due to conduction within the material. The rate at which this occurs is determined by the time constant (τ) of the circuit formed by the sample’s capacitance (C) and its electrical resistance (R). R is dependent on the conductivity of the material and the sample dimensions. At high frequency, the rate of change of charge due to the changing applied stress is much faster than the time constant, so charge compensation due to conductivity is negligible. At low frequency, however, the signal from a sensor or generator may be significantly attenuated. An indication of the minimum useful frequency, or lower limiting frequency (f _LL ) is given by the reciprocal of the time constant (Eq. 8), representing an attenuation of the signal by a factor of \(\sqrt 2\). RC time constants for PZT at room temperature are typically >100 s [20] (f _LL  < 0.01 Hz). The capacitance of a ferroelectric material is also strongly temperature dependent, so the temperature dependence of f _LL combines the effects of both capacitance and resistance, providing a useful figure of merit for sensor or transducer applications.

In this work resistivity was determined from AC fields below 0.01 Hz.

A further consideration for high temperature piezoelectric materials for use in high temperature devices is the thermal coefficient of expansion (TCE) (α) given in m/m K, or K⁻¹, and is typically temperature dependent [21]. TCE is required to match appropriate electrodes and package the piezo-elements into a device to meet tolerances. For example the TCE of PZT and other piezo-oxides parallel to the poled direction is in the order of −1 to −10 × 10⁻⁶ K⁻¹, or perpendicularly +1 to +8 × 10⁻⁶ K⁻¹, whereas metals, i.e. gold and stainless steel for electroding and acoustic matching layer respectively, are in the order of +10 to +80 × 10⁻⁶ K^−1.

Poled ferroelectric, piezoelectric materials are also typically anisotropic, with a negative TCE in the poled direction and positive orthogonal directions. TCE can be measured by interferometry or dilatometry to measure the displacement of a short-circuited piezoelectric sample, as a function of temperature.

After the discovery of BaTiO₃ researchers were stimulated to finding materials that exhibited piezoelectric properties over a wider range of temperatures. In the 1950s [22] that came in the form of the perovskite, lead zirconate titanate (PZT), probably the most diversely used and popular commercial piezoelectric with much of its success due to the ability to tailor its properties to specific applications by means of doping. Substitutionally doping on to the A or B site alters the movement of domain boundaries and modifies the electrical properties, but at the cost of lowering T_C.

PZT forms from the combination of ferroelectric PbTiO₃ and antiferroelectric PbZrO₃ to create a continuous solid solution with formula Pb(Zr_x Ti_1−x)O₃ where 0 < x < 1. The solid solutions where x < 0.9 are all ferroelectric, with T_C ranging from 220 to 490 °C depending on composition (x = 0.9–0 respectively) [15].

The structure of PZT goes through several transitions with increasing temperature, but at ambient between 0.52 < x < 0.545 there lies a morphotropic phase boundary [23] between two ferroelectric phases. Piezoelectric properties are at an optimum for most applications at this MPB composition [24] due to a peak in permittivity, to which the piezoelectric coefficient is proportional (Eqs. 4a, 4b).

This affords MPB compositions of PZT with d₃₃ values ~200 pC/N [15], which can be further increased by donor doping, to form soft PZT’s, with ions such as Nb to exceed d₃₃ values of 350 pC/N [25] but with a reduced T_C = 360 °C [12]. PZT suffers from rapid aging, leading to depoling, which means it is not typically suitable for use above ~200 °C [12, 26]. The properties of PZT are summarised in Table 1.

Phase transitions are characteristic of ferroelectrics, with the most important in the scope of this work being between the ferroelectric and paraelectric phase at T_C. Upon cooling through the Curie point, the crystallographic structure of the ferroelectric is associated with a small distortion of the paraelectric structure, lowering the symmetry.

Many materials also undergo further transitions below T_C, as well as within the lower symmetry ferroelectric phase associated with an change in orientation of the polar axis; for example from tetragonal to rhombohedral. These are termed polymorphic phase transitions [61], and can occur not only with variations in temperature, but also mechanical stress or applied electric field [62‐66].

Many ferroelectric solid solutions including the commercially popular PZT possess a morphotropic phase boundary (MPB), an abrupt structural change with composition [15], separating two ferroelectric phases of differing crystallographic symmetry, or polar axis rotation. For compositions near the MPB, the competing phases (and occasionally simultaneous existence of both in a mixed phase [57] ), allow polarization rotation to occur between the two symmetries, enhancing the piezoelectric and dielectric properties. However, these enhancements at the MPB are strongly temperature dependent [7] due to the dielectric permittivity and compliance components described in Eqs. (4a, 4b) being temperature dependent, further enhanced at the crystallographic boundary do to the increased electrical and mechanical degrees of freedom inherent with the presence of two different polar phases that can change with minimal energy. For optimal utility of these materials in application it is preferable they exhibit as linear a temperature dependence as possible.

Modestly (<5 %) donor doped modified ceramic powders of the 0.567BF-0.188KBT-0.245PT (D2) ternary system [87] were prepared by conventional solid-state synthesis, as it was expected to improve the resistivity and offer stable high temperature properties for metrology. Herein, this material nomenclature will be D2+, where as reported elsewhere in detail, stoichiometric quantities of the starting reagents were mixed with yttria stabilized zirconia balls in isopropyl alcohol using a high energy bead mill (Willy A. Bachofen, Basel, Switzerland) for 30 min, followed by drying and sieving through 200 μm. The subsequent powder was calcined at 800 °C for 4 h in covered crucibles. Binder was subsequently added and the powder pressed into 12 mm diameter pellets and sintered at 1050 °C for 2 h, before being ground and polished with SiC (Buehler, Germany) to 1 mm thick. Finished pellets were electroded by sputtering with 50 nm of Ti, and 200 nm of Au as layers (Quorum Technologies ltd. Lewes, UK). Density was measured using the Archimedes method and established to be 7700 kg/m³.

Samples were poled at 6 kV/mm at 100 °C in silicone oil for 10 min before being left for 24 h and subsequent measurements taken. The current was recorded throughout to determine high field resistivity. X-ray diffraction (Phillips X’Pert MPD, Almelo, The Netherlands) was used to identify the crystal structure on poled non-electroded samples (Fig. 1).

Parallel capacitance (C_P) was measured at 1 kHz–1 MHz as a function of temperature using an Agilent 4294A, with a non-inductively wound furnace. The T_C was determined from the maximum in calculated dielectric permittivity (Eq. 2) upon cooling (at 2 °C/min) from 600 °C on un-poled samples. The operating temperature was defined as T_d, and characterized from resonance, where three geometries were cut from discs and poled to meet the requirements for the various vibration modes described in BS EN 50324-1 [11]. This included a longitudinal length mode bar, transverse length plate and thickness shear plate, with a radial mode served by the as-made discs.

Each geometry was placed into a modified TA Instruments Thermal Mechanical Analyser (TMA) at NPL (Fig. 2), connected to an Agilent 4294a impedance analyser, with frequency sweeps controlled with LabVIEW (National Instruments, TX, USA) at 20 °C steps when heated at 2 °C/min. Calibration runs were taken across the frequency limits of the 4294a in open and short configuration for fixture compensation in post processing.

The frequency range and parameters set for each geometry are outlined in Table 4, and analysis conducted by identification of f_s and f_p from maxima and minima in conductance and resistance respectively [88]. Impedance spectroscopy was completed on un-poled discs at 50 °C intervals, with data collected from frequencies spanning 10 MHz–0.01 Hz at 10 points per decade using a ModuLab MTS (Solartron Analytical, UK), with data fitted to a circle from Z′/Z″ plots for analysis (Table 5).

X-ray diffraction reveals a mixed, rhombohedrally and tetragonally distorted, perovskite phase structure with no discernable insoluble phases. It is observed that little has been modified by the addition of the donor dopant, with the tetragonal a and c lattice vectors varying insignificantly, retaining a spontaneous strain of 3.5 % as per the un-modified D2 material. It is expected then that the Berlincourt measured d₃₃ should remain approximately the same between D2 and D2+ as these are intrinsically linked. Indeed a value of 197 pC/N is measured for a disc, which is in agreement, within the error of the measurement, with the un-doped variant [87]. Derived dielectric permittivity from the measured parallel capacitance (C_P) on cooling from 600 °C exhibits a peak for 1 kHz at 467 °C for T_C in the D2+ system (Fig. 3), which indicates a 45 °C increase in the ferroelectric to paraelectric phase transition T_C from D2. However an increase in T_C for the D2+ material is not expected compared with typical doping studies [49, 89] of similar materials.

Resistivity data supports this, with the doping regime exhibiting an order of magnitude increase in volume resistivity across the temperature range measured (22–400 °C) (Fig. 4), where the D2 material exhibits a resistivity of 3050 Ω m at 400 °C, which equates to a f _LL  = 2.2 kHz; Sufficiently in excess of the 1 kHz measurement, to prevent the material from charging fully and represented by the increasing tanδ loss. For the D2+ material, the increased resistivity maintains a f _LL  = 527 Hz at 400 °C (Fig. 5), but extrapolates to 1 kHz around the assumed T_C at 467 °C. This indicates that the conductivity mechanism is dominating the capacitance measurement, rather than a true ferroelectric-paraelectric phase transition. This obviously indicates further work is required to establish a true T_C, and that the resistivity as a function of temperature is likely to provide the frequency dispersion observed in Fig. 3.

Importantly for this work, the piezoelectric properties calculated from resonance determine a room temperature k_t = 0.5 and k_p = 0.36. The effect of temperature on d₃₁ from resonance is shown in Fig. 6 where the near linear proportional increase is ideal for the purposes of both metrology and device integration. A de-poling temperature is determined at T_d = 416 °C where the piezoelectric properties cease, and are independent of conductivity, where the resonance measurements undertaken are at frequencies much greater than the f _LL for the de-poling temperature.

A disc used for calculating the planar measurements was subsequently re-poled after the permittivity measurement, and re-tested using the resonance method. It is shown that the material exhibits excellent agreement for the calculated k_p as the first run, indicating that the temperature excursions have little effect on the materials composition and structure. A maximum long term operating temperature was therefore established as 380 °C.