Correlations between Crystal Structure and Elastic Properties of Piezoelectric Crystals: Tourmalines and Relaxor Ferroelectrics of the type CaxBa1-xNb2O6 and Ce:CaxBa1-xNb2O6 DISSERTATION zur Erlangung des akademischen Grades eines “Doktor der Naturwissenschaften” an der Fakultät für Geowissenschaften der Ruhr-Universität Bochum Germany von Chandra Shekhar Pandey aus Bareilly (India) Bochum, 2010 1. Gutachter Prof. Dr. Jürgen Schreuer 2. Gutachter Prof. Dr. Ladislav Bohatý Datum der Vorlage 20.10.2010 Datum der Disputation 17.12.2010 “If we knew what we were doing, it wouldn't be research” Albert Einstein This thesis is dedicated to My Love Arti & My sweet ‘n’ cute loving daughter Aditi Abstract In this thesis the elastic properties of two distinct groups of piezoelectric crystals are presented: one is natural tourmaline occurring with a vast variability in chemical compositions with a stable phase over a wide temperature range and hence allowing to examine the influence of chemical composition on its physical properties; while the other is synthetically grown relaxor ferroelectric calcium barium niobate (CBN) exhibiting a ferroelectric-paraelectric phase transition and thus invoking the interest to investigate the variation of elastic properties in both phases as well as in the vicinity of the phase transition. To this end the non-destructive innovative method of resonant ultrasound spectroscopy (RUS) was employed. The full sets of elastic, piezoelectric, dielectric constants and coefficients of thermal expansion of five natural single crystal tourmalines of gem quality have been determined between 100 K and 903 K. The main influence of Li and Fe on elastic, piezoelectric and dielectric properties of tourmalines was studied. Some tourmalines showed an unexpected irreversible softening of resonance frequencies during first heating, which is probably due to order/disorder processes on certain cation sites. The anomalous elastic behaviour was observed in Czochralski-grown pure and cerium doped Ca0.28Ba0.72Nb2O6 (CBN-28) single crystals between room temperature and 1503 K. Doping of Ce in pure CBN leads to lowering of Curie temperature (Tc) by ~ 70°C, and stiffening of all elastic constants. Below about 900 K all resonances of the freely vibrating samples show rapid softening when approaching Tc. In the ferroelectric phase ultrasound dissipation effects were too strong to observe enough resonances to refine elastic constants, which are probably related to interactions between sound waves and ferroelectric domain walls. Initiation of Burns temperature was clearly observed in the temperature range of 890-910 K. Contents Abbreviations 1 Introduction 1 2 Theoretical background 5 2.1 Elastic properties of materials 5 2.1.1 Generalized Hooke’s law 5 2.1.2 Elastic anisotropy 7 2.1.3 Deviation from Cauchy relations 7 2.1.4 Temperature dependence of the elastic constants 8 2.2 Piezoelectricity 8 2.2.1 Constitutive equations 12 2.2.2 Piezoelectric materials 13 2.3 Ferroelectricity 14 2.4 Relaxor ferroelectrics 17 2.5 Resonant ultrasound spectroscopy 19 2.5.1 The forward problem 22 2.5.2 The inverse problem 24 3 Experimental techniques 25 3.1 Sample preparation 25 3.2 Chemical and structural characterization 26 3.2.1 Electron microprobe analysis 26 3.2.2 X-ray diffraction 26 3.2.3 Density determination 26 x Contents ________________________________________________________________________ 3.3 Thermal analysis 27 3.3.1 Dilatometry 27 3.3.2 Differential scanning calorimetry 27 3.4 Dielectric properties 28 3.4.1 Substitution method 28 3.4.2 Geometric method 29 3.5 Elastic and Piezoelectric constants 30 3.5.1 Resonant ultrasound spectroscopy 30 4 Elastic and piezoelectric properties of tourmalines 33 4.1 Crystal chemistry of tourmalines 33 4.2 Chemical and structural characterization 36 4.3 Dielectric constants 41 4.4 Thermal properties 46 4.4.1 Thermal expansion 46 4.4.2 Specific heat capacity 48 4.5 Elastic and piezoelectric properties 48 4.5.1 Correlation between crystal structure and elastic properties 54 4.5.2 Isotropic elastic moduli and Debye temperature 57 4.5.3 Temperature evolution of elastic and piezoelectric constants 59 4.6 Summary and conclusions 62 5 Anomalous elastic behavior of Ca0.28Ba0.72Nb2O6 single crystal in the paraelectric phase 65 5.1 Thermal expansion 69 5.2 Elastic properties 73 5.2.1 Deviation from Cauchy relations 78 5.2.2 Isotropic elastic properties 80 5.2.3 Temperature evolution of eigen modes 81 5.3 Summary and conclusions 82 6 Elastic properties of Ce:Ca0.28Ba0.72Nb2O6 single crystal in paraelectric phase 83 6.1 Comparison of pure and Ce doped CBN-28 85 Contents xi ________________________________________________________________________ 6.1.1 Thermal expansion 85 6.1.2 Elastic properties 87 6.1.3 Deviation from Cauchy relations 91 6.1.4 Isotropic elastic properties 92 6.1.5 Eigen modes behavior 93 6.2 Hypothesis for Ce position in Ce:CBN 94 6.3 Summary and conclusions 97 7 Summary and outlook 99 Bibliography 103 Abbreviations ai Crystallographic system α Coefficients of linear thermal expansion B Bulk modulus C Mean elastic stiffness CBN, CBN-28 Calcium Barium Niobate Ce:CBN, Ce:CBN-28 Cerium doped Calcium Barium Niobate cijkl, cij Elastic stiffness constants ei Cartesian reference system εij Strain tensor є ij Dielectric constant at constant strain є ij Dielectric constant at constant stress eijk, eij Piezoelectric stress constants EMPA Electron Micro-Probe Analysis f Frequency G Shear modulus gmn Deviation from Cauchy relations μ Poisson’s ratio Q Quality factor ρb Buoyancy density ρg Geometric density RUS Resonant Ultrasound Spectroscopy σij Stress tensor T Temperature tan δ Dielectric loss TB Burns temperature xiv Abbreviations ________________________________________________________________________ Tc Curie temperature ΘD Debye temperature Tij Thermoelastic constants Tm Temperature of maximum dielectric constant VD Mean wave velocity VL Longitudinal wave velocity VS Shear wave velocity Angular frequency Wt % Weight percent XRD X-ray Diffraction Chapter 1 Introduction The elastic properties of a solid correspond to its response to an applied stress and are of fundamental importance to science and technology because they are related to the forces acting between the constituent atoms or ions and thus give useful information about the present network of bonding interactions in the material. The evolution of elastic properties with respect to temperature is considered valuable to study phase transitions in a material. Further, the elastic constants are closely connected to thermodynamic properties of the material such as specific heat, thermal expansion, and the Debye temperature. The knowledge of elastic constants is essential for many practical applications related to the mechanical properties of a solid, for example load-deflection, thermoelastic stress, internal strain or residual stress, sound velocities and fracture toughness [1-3]. In piezoelectric crystals elastic waves are additionally accompanied by electric fields giving rise to electromechanical coupling effects which can be used to convert electrical → mechanical energy and vice-versa. Today, crystal species like LiNbO3, Ca3Ga2Ge4O14 and α-quartz, are well investigated and widely used in piezoelectric devices. However, they suffer from phase transitions or strong ultrasound dissipation effects etc. A promising candidate to overcome these limitations is tourmaline. Tourmaline, a structurally complex ring silicate, has been attractive for researchers due to its promising piezoelectric properties. The use of transparent tourmaline in the studies on polarized light is well known. The application of tourmaline at temperatures up to about 1000 K is not limited by phase transitions, electrical conductivity or strong ultrasound dissipation effects. Tourmaline offers 2 Introduction Chapter 1 ________________________________________________________________________ certain advantages over most other materials, especially for operation at higher frequencies [4]. For example, (a) the attenuation is extremely low, being about one order of magnitude smaller than in α-quartz [5], (b) for transducer applications, tourmaline can be used up to 1100 MHz [4], while widely used α-quartz only till 800 MHz, and (c) it has high acoustic velocities [4] (relative to those in α-quartz and LiNbO3) together with a high Debye temperature [6]. Tourmaline can also be used as high-frequency surface-acoustic-wave devices, where the combination of low acoustic loss, high acoustic velocities and moderate piezoelectric effect make it attractive for high frequency work [5]. No success has yet been achieved in growing synthetic tourmaline of more than 1mm in diameter in laboratory [7-8]. Therefore, for any practical application, one has to depend only on natural tourmalines. However, natural tourmalines exist in a broad range of chemical compositions, leading to variations in their physical properties. Thus, it becomes important to study the behavior of the desirable properties of tourmalines with chemical composition. The available literature on elastic constants of tourmalines [9-13] are without any discussion on the chemical composition except the work by [12] and [13], whereas piezo- and dielectric properties are missing in those literatures too. Moreover, a systematic study of elastic, piezoelectric and dielectric properties, their systematic variation with chemical composition and, more importantly, the temperature evolution of these physical properties up to the decomposition