Optimal working regime of lead–zirconate–titanate for actuation applications

Abstract

The large-signal unipolar behavior of PZT is characterized under combined electrical, thermal, and mechanical loading. Maximum strain S_max and polarization P_max feature a pronounced sensitivity on stress with a field-dependent peak evolving at around −50 MPa that is associated with enhanced non-180° domain switching. As notable strains are achieved in excess of the quasi-statically measured blocking stress, it is suggested that the testing procedure presented within this work is suited to supplement blocking force measurements in order to comprehensively evaluate the electromechanical performance of a piezoceramic. With the suppression of non-180° domain switching at high stress levels, S_max(σ) decreases at a faster rate than P_max(σ). Accordingly, the electrostrictive coefficient Q₁₁ is shown to be stress-dependent. This observation is rationalized with the stress-dependent change of domain processes. It is furthermore found that Q₁₁ features a notable dependence on temperature, increasing from 0.018 m⁴ C⁻² at 25 °C to 0.028 m⁴ C⁻² at 150 °C under zero-stress. To assess the actuatoric efficiency, a novel figure of merit η* is defined to quantify the fraction of input energy utilized for mechanical work.

Introduction

The electromechanical coupling in piezoceramics is utilized for numerous applications [1], [2], [3]. Here, actuation is one of the most important tasks that can be addressed since piezoelectric actuators offer a natural solution wherever high precision, quick response, and high force are required [4], [5], [6]. Owing to its good electromechanical properties, the perovskite ceramic PbZr_xTi_1−xO₃ (PZT) is the material of choice for more than 98% of all produced piezo-actuators [7], [8]. Stacked actuators are currently the state of the art technology for producing piezo-actuators, which consist of thin laminated PZT layers that are separated from one another by electrodes. This configuration allows for large stroke and force production at low driving voltages [4], [9], [10], [11].

In each actuation application, work is performed against external force. In order to design and match an actuator to its application, it is necessary to know the strain behavior under the specific mechanical loading regime. This can be addressed by obtaining the blocking force, which is defined as the maximum force the actuator can generate against an infinitely stiff clamping [12], [13]. The measurement is conducted by elongating the previously poled actuator under an electric field and subsequently compressing the actuator to its initial height with an external mechanical load [14]. This kind of measurement provides only the electromechanical properties under stress in quasi-static testing conditions. In contrast, real-world applications are often dynamic in nature with the actuator being electrically cycled under mostly uni- or sesquipolar conditions at frequencies into the kHz regime [15], [16], [17], [18].

To evaluate the actuation performance, several authors reported large-field properties under uniaxial mechanical pre-load on soft PZT [19], [20], [21], [22]. It was found that the maximum strain S_max and polarization P_max during unipolar electric field loading increased for applied compressive stress up to approximately −50 MPa. For even higher stresses, S_max and P_max decrease, yielding a peak in the S_max(σ) and P_max(σ) curves [19], [20]. This observation can be explained by non-180° domain wall processes and will be discussed in more detail in Section 4 [19], [23].

However, these previous experimental investigations of unipolar P(E) and S(E) curves under compressive load have been restricted to room-temperature [19], [20], [21], [23], [24], [25]. In real operation, actuators must also operate under harsh conditions and elevated temperatures such as in automotive or aviation applications [11], [26]. Although previous reports discussed the large-signal behavior of PZT at elevated temperatures [27], [28], [29], [30], they did not consider mechanical pre-stresses. For this reason, we report here on the field-induced polarizations and strains of soft PZT under compressive stresses up to −448 MPa at temperatures from 25 °C to 150 °C. To the best of our knowledge this is the first report that features such a versatile and comprehensive loading scenario for the large-signal behavior of a ferroelectric ceramic.

It was demonstrated previously that the electric field-induced strain S_i follows a linear relation with the polarization $P_j^2$ in PZT even if the S(E) and P(E) loops are significantly nonlinear and hysteretic [31]. Using the Voigt-notation, the relation is expressed as [32], [33]

$$S_i=Q_{ij}{P}_j^2$$

where Q_ij are the electrostrictive coefficients and can be extracted from strain data fitting [30], [31], [34]. However, these previous studies on PZT are limited to mechanically free conditions at room temperature. Knowledge of the electrostrictive properties as a function of stress and temperature would be desirable as Q_ij is often needed in modeling of ferroelectric behavior [35], [36], [37], [38]. Therefore, we also report the stress- and temperature-dependent Q₁₁ up to 150 °C and −384 MPa in the present work.