Electromechanical properties of single domain PZN–12%PT measured by three different methods Guennou Mael a, * , Dammak Hichem a , Dje ´ mia Philippe b , Moch Philippe b , Pham-Thi Mai c a Laboratoire SPMS, UMR 8580 CNRS, E ´ cole Centrale Paris, Grande Voie des Vignes, 92295 Cha ˆtenay-Malabry, France b LPMTM CNRS (UPR 9001), Universite´ Paris 13, 93430 Villetaneuse, France c Thales Research & Technology France, 91767 Palaiseau, France article info Article history: Received 19 January 2009 Received in revised form 20 February 2009 Accepted 18 March 2009 Available online xxx Keywords: Piezoelectricity Resonance–antiresonance method Brillouin scattering Resonant ultrasound spectroscopy abstract In this paper, we compare the electromechanical properties of tetragonal single domain PZN–12%PT single crystals obtained by different methods: resonance–antiresonance method, Brillouin scattering, and resonant ultrasound spectroscopy. The agreement between the different measurements is found satisfactory for many elastic constants within experimental uncertainties. Differences are notable for the elastic constants associated to the propagation of shear waves (c 66 E and c 44 E ). This can be accounted for by imperfections of the sample in acoustic spectroscopy and specific difficulties of shear resonators used for the resonance method. Strong discrepancies are noted for the hardened elastic constant c 33 D asso- ciated to longitudinal waves propagating along the polarization direction; we suggest this can arise from a frequency dependence of the dielectric constant. Ó 2009 Elsevier Masson SAS. All rights reserved. 1. Introduction Pb(Zn 1/3 Nb 2/3 )O 3 –xPbTiO 3 (PZN–xPT) and Pb(Mg 1/3 Nb 2/3 )O 3 – xPbTiO 3 (PMN–xPT) single crystals have raised considerable interest for more than 10 years due to their excellent piezoelectric proper- ties, which offer promising improvement perspectives for piezo- electric transducers and actuators. In those systems, the highest piezoelectric coefficients d 33 are obtained for compositions close to the morphotropic phase boundary (x z 9% for PZN–xPT, 35% for PMN–xPT) when poled along a [001] direction [1]. The electrome- chanical properties of such crystals are fully characterized by a pie- zoelastic tensor that consists in elastic, piezoelectric and dielectric constants. The accurate determination of the constants is essential from a practical point of view for the prediction of device perfor- mances, as well as for a proper understanding of the different contributions and mechanisms that come into play. The aim of this study is to measure the electromechanical properties of tetragonal single domain PZN–12%PT by different methods and discuss the discrepancies observed. The paper is organized as follows. Section 2 describes the sample preparation, Section 3 describes the different measurements performed. The results are then compared and discussed in Section 4. 2. Sample preparation PZN–12%PT single crystals were grown by the flux method (PbO flux) as described elsewhere [2]. They are orientated using the Laue back-scattering technique. Crystals are cut with a wire saw along appropriate crystallographic directions. Crystal faces are polished on silicon carbide disks with grain sizes down to 1 mm to obtain mirror-like surfaces. Gold electrodes (not thicker than 0.15 mm) are sputtered on the relevant surfaces of the samples. Samples are then annealed at 400  C for 2 h to release stress induced by polishing. The crystals are poled by the field cooling method whereby the sample is heated up into the cubic phase (490 K), an electric field is applied along a [001] direction and the sample is slowly cooled down. For all samples, we used an electric field of 1 kV/cm and a cooling rate of 2  C/min. PZN–12%PT crystals are tetragonal with a spontaneous polari- zation lying along a [001] direction [3]. When poled along one of the 6 equivalent directions, the crystal is in a tetragonal single domain state labelled 1 T with macroscopic symmetry 4 mm. We had previously shown that the single domain state could be unstable in plates thinner than 300 mm [4] and checked by optical microscopy that the polarization is homogeneous throughout the samples. In the single domain state, the electromechanical prop- erties are then fully characterized by 11 independent coefficients. Choosing the stress T l and electric field E i as independent variables, they are divided into 6 elastic constants s 11 E , s 12 E , s 13 E , s 33 E , s 55 E and s 66 E , * Corresponding author. E-mail address: mael.guennou@supaero.org (M. Guennou). Contents lists available at ScienceDirect Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie ARTICLE IN PRESS 1293-2558/$ – see front matter Ó 2009 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2009.03.026 Solid State Sciences xxx (2009) 1–4 Please cite this article in press as: M. Guennou, H. Dammak, et al., Electromechanical properties of single domain PZN–12%PT measured by three different methods, Solid State Sci. (2009), doi:10.1016/j.solidstatesciences.2009.03.026