Contributions to the Piezoelectric Effect in Ferroelectric Single Crystals and Ceramics Dragan Damjanovic* ,w Ceramics Laboratory, Materials Science and Engineering Institute, E ´ cole polytechnique fe´ de´ rale de Lausanne-EPFL, CH-1015 Lausanne, Switzerland The piezoelectric effect in ferroelectric single crystals and ce- ramics is investigated considering intrinsic (lattice), and extrin- sic (originating mainly from displacement of domain walls) contributions. The focus of the study of intrinsic properties is on piezoelectric anisotropy, which was examined using the Landau–Ginsburg–Devonshire phenomenological theory. It is shown that the enhanced piezoelectric response along nonpolar directions, observed in many perovskite systems, is a conse- quence of the flattening of the Gibbs free energy profile. This flattening is common for temperature-, composition-, and exter- nal field-induced enhancement of the piezoelectric properties along nonpolar axes. A brief review of recent advances in un- derstanding the origins of the piezoelectric nonlinearity, hyster- esis, and frequency dispersion is also given. I. Introduction T HE last several years have witnessed tremendous progress in the development of ‘‘new’’ piezoelectric materials (relaxor ferroelectric single crystals, 1 solid solutions with high transition temperature, 2 lead-free materials 3 ) and in understanding of mechanisms of the piezoelectric coupling in ferroelectric piezo- electrics. 4,5 Most of the progress has been centered on the dis- covery of the enhanced piezoelectric response along nonpolar directions in perovskite crystals. This discovery was, for exam- ple, the driving force behind extensive crystallographic studies that questioned the commonly assumed nature of the morpho- tropic phase boundary (MPB) at x 5 0.48 in lead zirconate ti- tanate [Pb(Zr 1x Ti x )O 3 or PZT] 6–8 and in unprecedented efforts in first-principles calculations to interpret the properties of sim- ple and complex perovskites. 4,9–12 At the same time, consider- able efforts were made to understand details of extrinsic (nonlattice) contributions to the piezoelectric effect, revealing complex mechanisms, several of which sometimes operate si- multaneously in a given material. 13–18 From the application point of view, these extrinsic contributions play an important role as they directly affect the performance of high precision devices. 19 In this paper, intrinsic and extrinsic contributions to the pi- ezoelectric response of single-crystal and ceramic perovskite ferroelectrics are discussed. In the first section, the anisotropy of piezoelectric properties in the vicinity of the MPB in PZT, the most widely used piezoelectric ferroelectric, is considered using the Landau–Ginsburg–Devonshire (LGD) 20–27 thermodynamic theory. An attempt is made to show that the nature of the high piezoelectric response along nonpolar directions can be inter- preted in terms of the anisotropic flattening of the Gibbs free energy profile as the composition changes from either end mem- ber toward MPB. The analogy is made with similar behavior of the Gibbs free energy in barium titanate, BaTiO 3 , in the vicin- ity of the temperature-driven ferroelectric–ferroelectric phase transitions. Thus, a common mechanism is proposed for the temperature- and composition-induced enhancement of piezo- electric properties along nonpolar axes. Moreover, a comment is made that the same approach can be extended to include the effects of external elastic and electric fields on the enhancement of piezoelectric properties. These results are than used to em- phasize the important, and often ignored, role of shear piezoe- lectric coefficients on the high piezoelectric properties of ceramic samples with MPB composition. The presented results, while specifically discussing PZT and BaTiO 3 , have broad implica- tions as they can be applied to other perovskite materials, in- cluding relaxor–ferroelectric solid solutions and could help in designing new, high-performance materials. Finally, it will be shown that the mechanism of the piezoelectric properties en- hancement is not limited to polarization rotation processes. The focus of the second part (Section III) is on the extrinsic contributions to piezoelectric properties. The extrinsic contribu- tions are believed to originate mostly from the displacement of domain wall boundaries and phase interfaces, although the ev- idence for operation of other mechanisms will be presented. Both the field and the frequency dependence of the piezoelectric properties are examined, including the resulting hysteresis. II. Intrinsic Effects: Piezoelectric Enhancement and Anisotropic Instability of the Gibbs Free Energy Before discussing the free energy aspects of the piezoelectric anisotropy, a short background is given of the most important J ournal J. Am. Ceram. Soc., 88 [10] 2663–2676 (2005) DOI: 10.1111/j.1551-2916.2005.00671.x r 2005 The American Ceramic Society Feature D. Green—contributing editor This work was financed in part by the Swiss National Science Foundation. *Member, American Ceramic Society. w Author to whom correspondence should be addressed. e-mail: dragan.dam janovic@epfl.ch Manuscript No. 20489. Received April 30, 2005; approved June 30, 2005.