Phase field modeling and simulation is employed to study the underlying mechanism of enhancing electromechanical properties in single crystals and polycrystals of perovskite-type ferroelectrics around the morphotropic phase boundary (MPB). The findings include: (I) Coherent phase decomposition near MPB in PZT is investigated. It reveals characteristic multidomain microstructures, where nanoscale lamellar domains of tetragonal and rhombohedral phases coexist with well-defined crystallographic orientation relationships and produce coherent diffraction effects. (II) A bridging domain mechanism for explaining the phase coexistence observed around MPBs is presented. It shows that minor domains of metastable phase spontaneously coexist with and bridge major domains of stable phase to reduce total system free energy, which explains the enhanced piezoelectric response around MPBs. (III) We demonstrate a grain size- and composition-dependent behavior of phase coexistence around the MPBs in polycrystals of ferroelectric solid solutions. It shows that grain boundaries impose internal mechanical and electric boundary conditions, which give rise to the grain size effect of phase coexistence, that is, the width of phase coexistence composition range increases with decreasing grain sizes. (IV) The domain size effect is explained by the domain wall broadening mechanism. It shows that, under electric field applied along the nonpolar axis, without domain wall motion, the domain wall broadens and serves as embryo of field-induced new phase, producing large reversible strain free from hysteresis. (V) The control mechanisms of domain configurations and sizes in crystallographically engineered ferroelectric single crystals are investigated. It reveals that highest domain wall densities are obtained with intermediate magnitude of electric field applied along non-polar axis of ferroelectric crystals. (VI) The domain-dependent internal electric field associated with the short-range ordering of charged point defects is demonstrated to stabilize engineered domain microstructure. The internal electric field strength is estimated, which is in agreement with the magnitude evaluated from available experimental data. (VII) The poling-induced piezoelectric anisotropy in untextured ferroelectric ceramics is investigated. It is found that the maximum piezoelectric response in the poled ceramics is obtained along a macroscopic nonpolar direction; and extrinsic contributions from preferred domain wall motions play a dominant role in piezoelectric anisotropy and enhancement in macroscopic nonpolar direction. (VIII) Stress effects on domain microstructure are investigated for the MPB-based ferroelectric polycrystals. It shows that stress alone cannot pole the sample, but can be utilized to reduce the strength of poling electric field. (IX) The effects of compressions on hysteresis loops and domain microstructures of MPB-based ferroelectric polycrystals are investigated. It shows that longitudinal piezoelectric coefficient can be enhanced by compressions, with the best value found when compression is about to initiate the depolarization process. / Ph. D.

Made available in DSpace on 2016-06-02T20:16:54Z (GMT). No. of bitstreams: 1 6698.pdf: 13275782 bytes, checksum: 2c4bbd5a5c838552f7cbf82ce709e116 (MD5) Previous issue date: 2015-03-09 / Financiadora de Estudos e Projetos / In this work, the lead-free ceramic powders of xBi0,5Na0,5TiO3 - (0,7186 - 0,7143x) Bi0,5K0,5TiO3 - (2814 - 2857x) BaTiO with x = 0,8200; 0,8625; 0,8792, 0,9126 and 0,9300 (BNBK1000x) were prepared by the solid state reaction method, followed by conventional densification. The ceramic bodies showed high density, which was higher than 95% in obtained samples. For the all ceramics were performed structural, micro structural, electric and anelastic characterizations. The X-ray diffraction (XRD) analysis indicated the formation of the complex perovskite type crystaline structure for all compositions analyzed without the presence of spurious phases. By the structural refinement by the Rietveld method of XRD data and by Raman spectroscopy were observed that for BNBK912 and BNBK930 compositions, at room temperature, the predominant symmetry is rhombohedral (R3c), while the BNBK820 composition exhibits a tetragonal crystalline symmetry (P4mm). For the BNBK879 and BNBK826 compositions presented a mixture of phases, possibly with rhombohedral and tetragonal symmetry, reaveling the morphotropic phase boundary (MPB) of this system. The microstructure of BNBK1000x ceramics was investigated by scanning electron microscopy (SEM), where the morphology grains with irregular sizes and shapes, where the increased levels of K+ and Ba2+ ions suppressed the growth of the grains. The characterizations by Raman spectroscopy at room temperature showed broad Raman modes, due to the chemical and/or structural disorder related to the substitution of elements Bi and Na for Ba and K. The ferroelectric characterizations at room temperature of the BNBK1000x ceramics showed that all compositions studied are ferroelectric. Through the comparison among the measurements of electrical impedance and mechanical spectroscopy, was possible to identify the different structural and electric phase transitions that were employed in the construction of a pseudodiagram of phases for the BNBK1000x compositions. / Neste trabalho, os pós-cerâmicos livres de chumbo xBi0,5Na0,5TiO3 - (0,7186 - 0,7143x) Bi0,5K0,5TiO3 - (2814 - 2857x) BaTiO com x = 0,8200; 0,8625; 0,8792, 0,9126 e 0,9300 (BNBK1000x) foram obtidos através do método de reação de estado sólido, seguido por densificação convencional. Os corpos cerâmicos obtidos apresentaram elevada densificação, sendo maior que 95% nas amostras produzidas. Para todas as cerâmicas foram realizadas caracterizações estruturais, microestruturais, elétricas e anelásticas. As análises por difração de raios-X (DRX) indicaram a formação da estrutura cristalina tipo perovkista complexa para todas as composições analisadas, sem a presença de fases espúrias. O refinamento estrutural, pelo método de Rietveld, dos resultados de DRX e os resultados de espectroscopia Raman apontam que para as composições BNBK930 e BNBK912 a simetria predominante em temperatura ambiente é romboédrica (R3c), enquanto que a composição BNBK820 apresenta a simetria cristalina tetragonal (P4mm). Já as composições BNBK879 e BNBK862 apresentaram uma mistura de fases, possivelmente com simetrias romboédrica e tetragonal, evidenciando o contorno de fase morfotrópico (CFM) deste sistema. A microestrutura das cerâmicas de BNBK1000x foi investigada por microscopia eletrônica de varredura (MEV), onde a morfologia apresentada pelas diferentes composições estudadas possuíam grãos com tamanhos e formatos irregulares, sendo que o aumento dos teores dos íons de K+ e Ba2+ inibiram o crescimento dos grãos. A caracterização por espectroscopia Raman, em temperatura ambiente, apresentou modos Raman amplos, mostrando um elevado grau de desordem química e/ou estrutural devido à substituição dos elementos Bi e Na por Ba e K. As caracterizações ferroelétricas, também em temperatura ambiente das cerâmicas de BNBK1000x mostraram que todas as composições estudadas possuem propriedades ferroelétricas. Através da comparação entre as medidas de impedância elétrica e anelástica, levando em consideração as caracterizações estruturais e ferroelétricas com temperatura, foi possível identificar diferentes transições de fase estruturais e elétricas, que foram empregadas na construção de um pseudo-diagrama de fases para as composições de BNBKx.

The first chapter introduces the basic principles governing the phenomenon like ferroelectricity, piezoelectricity and pyroelectricity, which influences the material properties for its device applications. An effort is made to examine the present status of material issues, measurement techniques and applications pertaining to the lead based PZT type systems. This chapter also highlights the objectives and the scope of work. The second chapter deals with the various basic experimental techniques and principles adopted for the synthesis and characterizations of materials which include phase and quantitative analysis by X-ray diffraction, density measurements, microstructures by scanning electron microscopy, electrical properties such as dielectric permittivity, dielectric loss, and piezoelectricity by impedance analyzer and piezometer etc. The materials were synthesized via two step solid state reaction by adopting a low temperature calcinations route. Further, hot processing was employed for densification and better control of microstructure of the ceramics. In the third chapter PZT1-x –PZNx (x=0, 0.1, 0.2 & 0.3) compositions prepared by the single step low temperature calcination method have been described. It is seen that the pyrochlore free perovskite phase could be obtained up to x=0.2 compositions. The effect of additives like Li and Mn on the structure, sinterability, microstructure, density and dielectric properties has been investigated. The improvement in densification and ferroelectric properties were observed for Li addition favor tetragonal phase while Mn addition compositions were inclined to pseudocubic phase. Further, the addition of Mn led to the significant decrease in Tc than the parent compositions compared to Li added compositions. In the fourth chapter, the X-ray diffraction data on pbzrx Ti1-x O3 (PZT) for x=0.48 to 0.52 are presented. High resolution x-ray studies for composition x=0.5 show the MPB which consists of monoclinic Zr rich studies and tetragonal Ti rich phase at room temperature. The refined structural parameters for MPB compositions have been obtained using least square Rietveld refinement program, FULLPROF 2006. The evolutions of lattice parameters of the system were also studied with respect to the temperature. The phase transformation in the system has been analyzed by x-ray diffraction pattern and dielectric measurements. The monoclinic phase transforms to tetragonal phase at 270oC after which the tetragonal phase transforms to paraelectric cubic phase at 370DoC. Dielectric properties show signature of the phase transformation. Hence, it is concluded to pole the MPB samples below 270o C to gain the advantage of increased ease of polarization reorientation for monoclinic phase. The fifth chapter deals with the systematic structural investigation on PZT1-y-PNZy (PZT-PNZ) and PZT1-y-PMNy (PZT-PMN) systems. In this chapter, an effort has been made to determine quantitatively the MPB phase contents and variation in Zr/Ti ratio of PZT-PZN and PZT-PMN systems. High resolution XRD data has been used for quantitative phase analysis using FULLPROF 2006. The correlation between the width of MPB and grain size has also been discussed for these systems. It is found that the addition of PMN and PZN to PZT system shifts the MPB towards pbZrO3 (PZ). The MPB can be regained by tuning the Zr/Ti ratio in the system. Further, there exists an inverse relation between the grain size and coexistence region in the system. It is seen that the MPB range is from x=0.48 to 0.58 and x=0.44 to 0.58 for 10% and 20% PZN concentration respectively. Similar trend has been obtained for the PZT-PMN system. The MPB ranges from x=0.46 to 0.53 and x=0.42 to 0.50 for 10% and 20% PMN respectively. The broadening of coexistence width is attributed to the lower grain size of our samples synthesized by adopting low temperature calcinations route. The sixth chapter deals with the hot pressing technique employed (adopting low temperature calcinations) for the synthesis of various PZT-PMN compositions with an intention of obtaining highly dense piezoceramics with fine, homogeneous and uniform microstructure. It also describes the dielectric, pyroelecrtic and pi ezoelectric properties were enhanced by hot processing technique. Li and Mn addition further improved the properties of the system. The seventh chapter investigates various nominal compositions of PZT-(Li, Nb) compositions based on certain assumptions. The attempt was made to introduce Li at A site and B site of ABO3 perovskite lattice. The ball milled, calcined powders were densified at<1000oC using hot pressing technique to prevent Li and Pb loss. High density ceramics have been studied for structural, dielectric, piezoelectric and pyroelectric properties. Through the clear cut evidence for the identification of Li site in the PZT system could not be established but the system which were synthesized under the assumption that Li substitutes A-site of the perovskite, favored the tetragonal phase and led to the enhancement in the dielectric, pyroelectric and piezoelectric properties. Further, their transition temperature was higher compared to the compositions where Li was tried to substitute B-site, which makes them promising candidates for transducer applications. The key finding in this thesis has been carried out by the candidate as part of the ph. D. programme. She hopes that this would constitute a worthwhile contribution towards the understanding of the behavior of lead based perovskites and in tailoring the properties of these ceramics towards device applications by the introduction of suitable additives in the system.

Piezoelectric materials find use as actuators and sensors in automotive, aerospace and other related industries. Automotive applications such as fuel injection nozzles and engine health monitoring systems require operating temperatures as high as 300-500 oC. The commercially used piezoelectric material PbZr1-xTixO3 (PZT) is limited to operating temperatures as low as 200 oC due to the temperature induced depolarization effects. PZT, in the undoped state exhibits a piezoelectric coefficient (d33) of 223 pC/N and ferroelectric-paraelectric transition temperature (Tc) of 386 oC. The enhanced properties of PZT occur at a region between the tetragonal and rhombohedral phases, called the Morphotropic Phase Boundary (MPB). Therefore, search for new materials with higher thermal stability and better sensing capabilities were focused on systems that exhibit a PZT-like MPB. This led to the discovery of (x)BiScO3-(1-x)PbTiO3 (BSPT), which exhibits an MPB with enhanced Tc (450 oC) and exceptionally high piezoelectric response (d33 = 460 pC/N). Theoretical studies have shown that the mechanism of enhanced piezoresponse in ferroelectric systems is related to the anisotropic flattening of the free energy profiles. An alternative view point attributes the anomalous piezoelectric response to the presence of high density of low energy domain walls near an inter-ferroelectric transition. Diffraction is a versatile tool to study the structural and microstructural changes of ferroelectric systems upon application of electric field. However, characterization of electric field induced structural and microstructural changes is not a trivial task, since in situ electric field dependent diffraction studies almost invariably give diffraction patterns laden with strong preferred orientation effects, due to the tendency of the ferroelectric/ferroelastic domains to align along the field direction. Additionally, diffraction profiles of MPB compositions exhibit severe overlap of Bragg peaks of the coexisting phases, and hence, it is difficult to ascertain with certainty, if the alteration in the intensity profiles upon application of electric field is due to change in phase fraction of the coexisting phases or due to preferred orientation induced in the different phases by the electric field. The characterization of electric field induced phase transformation in MPB systems, has therefore eluded researchers and has been considered of secondary importance, presumably due to the difficulties in unambiguously establishing the structural changes upon application of electric field. In fact, majority of the in situ electric field dependent diffraction studies have been carried out on compositions just outside the MPB range, i.e. on single phase compositions. In such studies, the focus has been mainly on explaining the piezoelectric response in terms of motions of the non-180° domain walls and field induced lattice strains. In this dissertation, the BSPT system has been systematically investigated with the view to understand the role of different contributing factors to the anomalous piezoelectric response of compositions close to the MPB. Using a comparative in situ electric field dependent diffraction study on a core MPB composition exhibiting highest piezoelectric response and a single phase monoclinic (pseudo-rhombohedral) composition just outside the MPB, it is demonstrated that, inspite of the significantly large domain switching and lattice strain (obtained from peak shifts) in the single phase composition, as compared to the MPB composition, the single phase composition shows considerably low piezoelectric response. This result clearly revealed that the anomalous piezoelectric response of the MPB composition is primarily associated with field induced inter-ferroelectric transformation and the corresponding field induced interphase boundary motion. A simple strategy has been employed to establish the field induced structural transformation for the MPB compositions, by overcoming the experimental limitation of in situ electric field dependent diffraction studies. The idea stemmed from the fact that, if the specimens for diffraction study can be used in powder form instead of pellet, the problems associated with preferred orientation effects can be eliminated, and the nature of field induced structural changes can be accurately determined. A comparative study of the diffraction profiles from poled (after subjecting the specimen to electric field) and unpoled (before subjecting the specimen to electric field) powders could precisely establish the nature of electric field induced phase transformation for the MPB compositions of BSPT and provided a direct correlation between the electric field induced structural changes and the enhanced piezoelectric response. A new ‘powder poling’ technique was devised, which involves application of electric field to powder form of the specimen. Using this technique, it was possible to study separately, the effect of stress and electric field on the nature of structural transformation. A unique outcome of this study was, it could demonstrate for the first time, analogous nature of the stress and electric field induced structural transformation. A comparative study of the dielectric response of poled and unpoled samples was used to show a counterintuitive phenomenon of field induced decrease in polarization coherence for the MPB compositions. This approach was used to suggest that the criticality associated with the MPB extends beyond the composition boundary conventionally reported in literature based on bulk diffraction techniques (x-ray and neutron powder diffraction). The layout of the dissertation is as follows: Chapter 1 gives a brief introduction of the fundamental concepts related to ferroelectric materials. The theories that explain the enhanced piezoresponse of MPB based ferroelectric systems have been outlined. Detailed information of the existing literature is presented in the relevant chapters. Chapter 2 presents the details of the solid state synthesis of BSPT compositions and structural analysis using diffraction studies. The dielectric measurements were used to establish the Tc for the different compositions. The enhanced ferroelectric and piezoelectric properties were observed for the MPB compositions, which were shown to exhibit coexistence of tetragonal and monoclinic phases from structural studies. The critical MPB composition exhibiting highest piezoelectric and ferroelectric properties was established to be x = 0.3725. The thermal stability of the critical MPB composition was established to be 400 oC using ex situ thermal depolarization studies. The common approach of structural analysis in the unpoled state failed to provide a unique relationship between the anomalous piezoelectric response and the structural factors at the MPB, emphasizing the need to characterize these system using electric field dependent structural studies. Chapter 3 presents the results of in situ electric field dependent diffraction measurements carried out at Argonne National Laboratory, USA. The quasi-static field measurements could successfully quantify the non-180o domain switching fractions and the field induced lattice strains. The changes in the integrated intensities were used to obtain the non-180o domain switching fraction and the shift in peak positions were used to quantify the field induced lattice strains. The in situ studies could successfully explain the macroscopic strain response for the single phase pseudo-rhombohedral (monoclinic) composition on the basis of domain switching mechanisms and field induced lattice strains. The MPB compositions were shown to have additional contributions from interphase boundary motion, resulting from change in phase fraction of the coexisting phases. The results emphasized the need to investigate the electric field induced transformation for MPB compositions, in order to give a comprehensive picture of the various contributions to the macroscopic piezoreponse. While Rietveld analysis could be used to investigate the phase transformation behaviour upon application of electric field, textured diffraction profiles obtained using in situ studies, in addition to the severely overlapping Bragg reflections of the coexisting phases for the MPB compositions hindered reliable estimation of the structural parameters. An alternate approach to investigate the field induced phase transformation is presented in Chapter 4. The stroboscopic measurements on the MPB composition showed evidence of non-180o domain wall motion even at sub-coercive field amplitudes as low as 0.1 kV/mm. Chapter 4 presents the results of the ex situ electric field dependent structural study, wherein the diffraction profiles collected from poled powders is compared to that of unpoled powders. The diffraction profiles from the poled powders did not exhibit any field induced crystallographic texture and could successfully be analyzed using Rietveld analysis. High resolution synchrotron diffraction studies (ESRF, France) carried out on closely spaced compositions revealed that, the composition exhibiting the highest piezoelectric response is the one, which exhibits significantly enhanced lattice polarizability of both the coexisting (monoclinic and tetragonal) phases. The enhanced lattice polarizability manifests as significant fraction of the monoclinic phase transforming irreversibly to the tetragonal phase after electric poling. The monoclinic to tetragonal transformation suggested the existence of a low energy polarization rotation pathway towards the [001]pc direction in the (1 1 0)pc pseudocubic plane of the monoclinic phase. The results are discussed on the basis of the existing theories that explain piezoresponse in MPB systems and are in support of the Polarization rotation model, in favor of a genuine monoclinic phase. Chapter 5 discusses the ferroelectric-ferroelectric stability of the MPB compositions in response to externally applied stress and electric field independently. Using the newly developed ‘powder poling’ technique, which is based on the concept of exploiting the irreversible structural changes that occur after application of electric field and stress independently, it was possible to ascertain that, both moderate stress and electric field induce identical structural transformation - a fraction of the monoclinic phase transforms irreversibly to the tetragonal phase. The powder poling technique was also used to demonstrate field induced inter-ferroelectric transformation at sub-coercive field amplitudes. In addition, the analysis of the dielectric response before and after poling revealed a counterintuitive phenomenon of poling induced decrease in the spatial coherence of polarization for compositions around the MPB and not so for compositions far away from the MPB range. Exploiting the greater sensitivity of this technique, it was demonstrated that, the criticality associated with the inter-ferroelectric transition spans a wider composition range than what is conventionally reported in the literature based on bulk x-ray/neutron powder diffraction techniques. Chapter 6 presents the closure and important conclusions from the present work and summarizes the key results, highlighting the proposed mechanism of enhanced piezoresponse in BSPT. The last part of the chapter deals with suggestions for future work from the ideas evolved in the present study. vi

Piezokeramischen Werkstoffe auf der Basis von Bleizirkonat - Titanat (PZT) zeigen Extremwerte der elektromechanischen Eigenschaften im morphotropen Phasenübergangsbereich. Durch Modifikation des Verhältnisses von rhomboedrischer und tetragonaler Phase im Gefüge können die piezoelektrischen Eigenschaften des Werkstoffs entsprechend den jeweiligen Anforderungen angepasst werden. Es wurde eine Methode vorgestellt, einen mathematisch kohärenten Satz piezoelektrischer Kleinsignalkoeffizienten vollständig und mit hoher Genauigkeit über einen breiten Temperatur-(-200°C...+200°C) und Zusammensetzungsbereich (0...1 rh/tet) zu bestimmen. Desweiteren wurden die piezoelektrischen Eigenschaften dem Phasenanteil im Gefüge zugeordnet.:Danksagung II Symbolverzeichnis IV Abkürzungsverzeichnis VI Inhalt VII 1 Einleitung 1 1.1 Piezoelektrische Werkstoffe 1 1.2 Zielstellung 2 1.3 Materialsystem 3 1.4 Lösungsansatz 3 2 Grundlagen 5 2.1 Klassifizierung dielektrischer Keramiken 5 2.1.1 Wirkung elektrischer Felder auf dielektrische, keramische Werkstoffe 5 2.1.2 Piezoelektrizität einkristalliner und keramischer Dielektrika 7 2.1.3 Pyroelektrizität keramischer Dielektrika 8 2.1.4 Ferroelektrizität keramischer Dielektrika 8 2.2 Piezokeramische Werkstoffe des Systems PZT 10 2.2.1 Blei- Zirkonat- Titanat (PZT) 11 2.2.2 Domänenstruktur des PZT 12 2.2.3 Intrinsische und extrinsische Beiträge zu den piezoelektrischen Eigenschaften nach der Polung 13 2.2.4 Der morphotrope Phasenübergang im PZT 14 2.2.5 Entwicklung von PZT Werkstoffen mit spezifischen Eigenschaften 15 2.2.6 Das Werkstoffsystem Pb(ZrXTi1-X)O3-Sr(K0,25 Nb0,75)O3 (PZT/SKN) 18 2.3 Das Phasendiagramm des Werkstoffsystems PZT 20 2.4 Beschreibung der piezoelektrischen Eigenschaften 26 2.4.1 Die Komponenten der piezoelektrischen Eigenschaftsmatrix für perowskitische, piezokeramische Werkstoffe 28 2.4.2 Definition der Kohärenz von piezoelektrischen Eigenschaftsmatrizen 30 2.4.3 Mathematische Kohärenz 30 2.4.4 Physikalische Konsistenz 31 2.5 Schwingungsmoden piezokeramischer Probenkörper 32 2.5.1 Longitudinalschwingung (3-3 Schwingung) 34 2.5.2 Transversalschwingung (3-1 Schwingung) 34 2.5.3 Planarschwingung (Radial- Schwingung) 35 2.5.4 Dicken- Dehnungs- Schwingung (Dickenschwingung) 35 2.5.5 Dicken- Scher- Schwingung (1-5 Schwingung) 36 3 Messmethoden 37 3.1 Bestimmung der Matrix der piezoelektrischen Komponenten nach DIN Standard 37 3.2 Impedanzanalyse 38 3.2.1 Das Impedanzspektrum piezoelektrischer Proben 39 3.3 Röntgen- Diffraktometrie (XRD) 43 4 Experimentelle Durchführung 45 4.1 Verwendete Werkstoffe und Probenvorbereitung 46 4.1.1 Dichtebestimmung 48 4.2 Temperaturabhängige Kleinsignalimpedanzmessung 49 4.3 Röntgen– Diffraktometrie– Untersuchungen (XRD) 56 4.4 Keramographie 58 4.5 Automatisierung des Messsystems 59 5 Datenaufbereitung und Primärdatenerfassung 59 5.1 Kompensation von Messfehlern 59 5.2 Datenverarbeitung 59 5.3 Ermittlung einer optimierten piezoelektrischen Eigenschaftsmatrix 60 5.3.1 Bestimmung der vorläufigen Eigenschaftsmatrix 61 5.3.2 Berechnung einer optimierten Eigenschaftsmatrix und Minimierung der Messfehler 64 5.4 Bestimmung der Phasenlage mittels Röntgen- Diffraktometrie- Untersuchungen 65 5.5 Temperatur- und Zusammensetzungs- Eigenschafts- Mappings 71 5.6 Einführung von „Pseudo- Phasengrenzen“ 72 6 Ergebnisse und Diskussion 75 6.1 Ergebnisse der keramographischen Untersuchungen 75 6.2 Ergebnisse der XRD Untersuchungen 80 6.3 Ergebnisse der temperaturabhängigen Kleinsignalimpedanzmessungen 85 6.4 Korrelation von Phasenlage und PbZrO3-Anteil 91 6.5 Erstellen einer vollständigen, kohärenten Eigenschaftsmatrix an einem konkreten Beispiel 100 6.6 Selbstkonsistenzprüfung anhand eines FEM Modells in ANSYS 112 6.7 Bestimmung der Phasenlage anhand einfacher, temperaturabhängiger Messungen 118 6.7.1 Bestimmung der absoluten Phasenlage bei Proben des Systems PZT/SKN 119 6.8 Fehlerdiskussion 121 7 Zusammenfassung 123 8 Ausblick 124 9 Abschließende Anmerkungen 125 10 Literaturverzeichnis 126 / Piezoceramic materials based on Lead- Zirconate- Titanate (PZT) show extreme electromechanic properties in the area of morphotropic phase transition. PZT materials can be tailored to specific demands by modifying the ratio of volume of the rhombohedral and tetragonal phase within the micro structure. A method was introduced to accurately determine a complete and mathematically coherent set of piezoelectric small signal coefficients. This was done over a wide range of temperature (-200°C…+200°C) and phase composition (0…1 rh/tet). Additionally, the piezoelectric properties were correlated to the ratio of rhombohedral and tetragonal phases.:Danksagung II Symbolverzeichnis IV Abkürzungsverzeichnis VI Inhalt VII 1 Einleitung 1 1.1 Piezoelektrische Werkstoffe 1 1.2 Zielstellung 2 1.3 Materialsystem 3 1.4 Lösungsansatz 3 2 Grundlagen 5 2.1 Klassifizierung dielektrischer Keramiken 5 2.1.1 Wirkung elektrischer Felder auf dielektrische, keramische Werkstoffe 5 2.1.2 Piezoelektrizität einkristalliner und keramischer Dielektrika 7 2.1.3 Pyroelektrizität keramischer Dielektrika 8 2.1.4 Ferroelektrizität keramischer Dielektrika 8 2.2 Piezokeramische Werkstoffe des Systems PZT 10 2.2.1 Blei- Zirkonat- Titanat (PZT) 11 2.2.2 Domänenstruktur des PZT 12 2.2.3 Intrinsische und extrinsische Beiträge zu den piezoelektrischen Eigenschaften nach der Polung 13 2.2.4 Der morphotrope Phasenübergang im PZT 14 2.2.5 Entwicklung von PZT Werkstoffen mit spezifischen Eigenschaften 15 2.2.6 Das Werkstoffsystem Pb(ZrXTi1-X)O3-Sr(K0,25 Nb0,75)O3 (PZT/SKN) 18 2.3 Das Phasendiagramm des Werkstoffsystems PZT 20 2.4 Beschreibung der piezoelektrischen Eigenschaften 26 2.4.1 Die Komponenten der piezoelektrischen Eigenschaftsmatrix für perowskitische, piezokeramische Werkstoffe 28 2.4.2 Definition der Kohärenz von piezoelektrischen Eigenschaftsmatrizen 30 2.4.3 Mathematische Kohärenz 30 2.4.4 Physikalische Konsistenz 31 2.5 Schwingungsmoden piezokeramischer Probenkörper 32 2.5.1 Longitudinalschwingung (3-3 Schwingung) 34 2.5.2 Transversalschwingung (3-1 Schwingung) 34 2.5.3 Planarschwingung (Radial- Schwingung) 35 2.5.4 Dicken- Dehnungs- Schwingung (Dickenschwingung) 35 2.5.5 Dicken- Scher- Schwingung (1-5 Schwingung) 36 3 Messmethoden 37 3.1 Bestimmung der Matrix der piezoelektrischen Komponenten nach DIN Standard 37 3.2 Impedanzanalyse 38 3.2.1 Das Impedanzspektrum piezoelektrischer Proben 39 3.3 Röntgen- Diffraktometrie (XRD) 43 4 Experimentelle Durchführung 45 4.1 Verwendete Werkstoffe und Probenvorbereitung 46 4.1.1 Dichtebestimmung 48 4.2 Temperaturabhängige Kleinsignalimpedanzmessung 49 4.3 Röntgen– Diffraktometrie– Untersuchungen (XRD) 56 4.4 Keramographie 58 4.5 Automatisierung des Messsystems 59 5 Datenaufbereitung und Primärdatenerfassung 59 5.1 Kompensation von Messfehlern 59 5.2 Datenverarbeitung 59 5.3 Ermittlung einer optimierten piezoelektrischen Eigenschaftsmatrix 60 5.3.1 Bestimmung der vorläufigen Eigenschaftsmatrix 61 5.3.2 Berechnung einer optimierten Eigenschaftsmatrix und Minimierung der Messfehler 64 5.4 Bestimmung der Phasenlage mittels Röntgen- Diffraktometrie- Untersuchungen 65 5.5 Temperatur- und Zusammensetzungs- Eigenschafts- Mappings 71 5.6 Einführung von „Pseudo- Phasengrenzen“ 72 6 Ergebnisse und Diskussion 75 6.1 Ergebnisse der keramographischen Untersuchungen 75 6.2 Ergebnisse der XRD Untersuchungen 80 6.3 Ergebnisse der temperaturabhängigen Kleinsignalimpedanzmessungen 85 6.4 Korrelation von Phasenlage und PbZrO3-Anteil 91 6.5 Erstellen einer vollständigen, kohärenten Eigenschaftsmatrix an einem konkreten Beispiel 100 6.6 Selbstkonsistenzprüfung anhand eines FEM Modells in ANSYS 112 6.7 Bestimmung der Phasenlage anhand einfacher, temperaturabhängiger Messungen 118 6.7.1 Bestimmung der absoluten Phasenlage bei Proben des Systems PZT/SKN 119 6.8 Fehlerdiskussion 121 7 Zusammenfassung 123 8 Ausblick 124 9 Abschließende Anmerkungen 125 10 Literaturverzeichnis 126