Lead-Free Piezoelectric Materials. Jing-Feng Li

1 Fundamentals of Piezoelectricity

      1.1 Introduction

      In 1880, Pierre Curie and Jacques Curie discovered the (direct) piezoelectric effect in quartz (SiO₂) and other single crystals, which generates an electric charge proportional to a mechanical stress. The converse piezoelectric effect, a geometric strain proportional to an applied voltage, was also soon realized. Since then, quartz has been one of the most well‐known and widely used piezoelectric materials. Many decades later, polycrystalline piezoelectric ceramics (oxides) have been discovered. The first one is BaTiO₃ that was discovered during the World War II, which was used as dielectric materials for solid condensers at first [1]. In 1947, Roberts found that BaTiO₃ ceramics (polycrystals) showed good piezoelectricity, about 100 times higher than that of quartz, after they were poled under a high voltage [2]. Since then, BaTiO₃ ceramics have been widely applied to transducers, sensors, and filters, particularly in Japan. In 1952, Shirane et al., reported that solid solutions can be formed between PbTiO₃ and PbZrO₃ [3, 4]. One year later, ferroelectricity and antiferroelectricity were found in the solid solutions [5]. In 1954, Jaffe et al. studied the piezoelectric properties of PbTiO₃–PbZrO₃ solid solution ceramics, and found that its piezoelectric constants were twice as high as that of BaTiO₃, and its Curie temperature (above which the piezoelectricity disappears) was over 300 °C [6]. Now, the PbTiO₃–PbZrO₃ solid solutions, abbreviated as PZT, are the most widely used piezoelectric ceramics [7–10]. The PZT ceramics show greatly enhanced piezoelectric and dielectric properties when the Zr/Ti ratio is close to 52/48, where exists a morphotropic phase boundary (MPB) separating the rhombohedral and tetragonal regions [7]. It is generally understood that the piezoelectricity enhancement stems from the effect of phase coexistence enabled by the existence of MPB.

Despite the facts that BaTiO₃ is lead‐free and was also discovered before PZT, the markets of piezoceramic applications have been dominated by PZT‐based ceramics mainly because of its following advantages compared with BaTiO₃: (i) excellent and adjustable piezoelectric properties, (ii) relatively high Curie temperature, and (iii) relatively low sintering temperature. Recently, environmental protection has become a major global concern, and environmental‐friendly materials and technology are one of the main tasks to be resolved in this new century. The manufacturing, handling, and disposal of PZT ceramics, which contain >60 wt% of lead, pose harmful influences on the workers' safety and soil environment as well as water supply. That is why many countries have incentivized the development of lead‐free piezoelectric materials [11–18].

      For the R&D of lead‐free piezoelectric materials, it is very important to get a full understanding of piezoelectric principles and the piezoelectric mechanisms of existing piezoelectric materials, especially PZT ceramics. However, because PZT ceramics have many important applications, and in some sense, its application research has moved faster compared with the fundamental research on its piezoelectric mechanism, there are still a lot of things remaining very unclear. For example, the phase diagram of PZT around the MPB has been renewed even after half a century passed since the discovery of PZT [19–21], and rigorous descriptions still lack for unambiguous understanding of the MPB's contribution to piezoelectricity. The fundamental structure–property mechanisms revealed in lead‐containing piezoelectric materials can be also operational in lead‐free systems and at a minimum, should be considered as starting guidelines for the development of lead‐free piezoelectrics from the aspects of composition modification, microstructure tailoring, property characterizations, device applications, etc.

1.2 Piezoelectric Effects and Related Equations

The piezoelectric effect or piezoelectricity is the generation of electric charges on the surface of certain non‐conducting materials in response to applied mechanical stress, or conversely, the generation of a mechanical strain in such materials when they are subjected to an electric field, as schematically shown in Figure 1.1 [17]. The piezoelectric effect is a reversible process, so the materials exhibiting the direct piezoelectric effect also exhibit the converse piezoelectric effect. As such, piezoelectricity is referred to as both direct and converse effects, even though the word “piezoelectricity” often leads us to the meaning of the direct piezoelectric effect of the internal generation of electrical charges resulting from an applied mechanical force.

Figure 1.1 (a) The direct piezoelectric effect provides an electric charge upon application of a mechanical stress, whereas (b) the converse piezoelectric effect describes the situation where strain develops under an applied electric field.

      Source: Reproduced with permission from Roedel and Li [17]. Copyright 2018, Cambridge University Press.

      In a narrow sense, piezoelectricity can be understood as a linear electromechanical interaction between the mechanical and the electrical states. The constant for such a linearly proportional relation is defined as the piezoelectric coefficient d, which is a third‐rank tensor coupling the first‐rank tensor or vector (electric displacement or field) and the second‐rank tensor (stress or strain). Hence, the piezoelectric equations may be written in the following form (i, j, k = 1, 2, 3) [22]

      (1.1)

      (1.2)

      where D_i is electric displacement (C/m²), E_i is electric field component (V/m), S_ij is strain component, Τ_ij is stress component (N/m²), and d_kij or d_kij^* is component of the piezoelectric charge or strain constant. It should

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