Littérature scientifique sur le sujet « Ferroelectric Curie Temperature »

Lanthanide doping is widely employed to tune structural change temperature and electrical properties in ABO3-type perovskite ferroelectric materials. However, the reason that A-site lanthanide doping leads to the decrease of the Curie temperature is still not clear. Based on the reported Curie temperature of lanthanides (Ln) doped in two classic ferroelectrics PbTiO3 and BaTiO3 with A2+B4+O3-type perovskite structure, we discussed the relationship between the decrease rate of Curie temperature (ΔTC) and the bond strength variance of A-site cation (σ). For Nd ion doped Pb(Mg1/3Nb2/3)O3-PbTiO3 (Nd-PMNT) ferroelectric crystal as an example, the internal factors of the dramatic decline of the Curie temperature induced by A-site Nd doping were investigated under a systematic study. The strong covalent bonds of Ln-O play an important role in A-site Ln composition-induced structural change from ferroelectric to paraelectric phase, and it is responsible for the significant decrease in the Curie temperature. It is proposed that the cells become cubic around the Ln ions due to the strong covalent energy of Ln-O bonding in A-site Ln doped A2+B4+O3 perovskite ferroelectrics.

In this article, two concepts of temperature, i.e., Burns temperature for relaxor ferroelectrics and quantum temperature scale for quantum paraelectrics, are reviewed briefly. Since both temperatures describe the deviation of the dielectric constant from Curie–Weiss law, their relationship is discussed. Finally the concept of quantum temperature scale is extended to demonstrate the evolution process of quantum paraelectric behavior to relaxor ferroelectric behavior.

High damping materials exhibiting a loss factor higher than 10-2 are generally considered as polymer or metallic materials. But, it will be interesting to consider ferroelectric or ferrimagnetic ceramics, in which internal friction can be due to the motion of ferroelectric or magnetic domains. High level of internal friction can be obtained in these ceramics in a given temperature range. In the case of ferroelectric ceramics, hard ferroelectrics, such as BaTiO3 or PZT, can show some relaxation peaks below the Curie temperature due the motion of domain walls and the interaction between the domain walls and the oxygen vacancies or cationic vacancies. In the case of ferrimagnetic ceramics, some anelastic manifestations due to the ferrimagnetic domain walls appear below the Curie Temperature TC. These peaks are linked to the interaction of domain walls with cation vacancies or cation interstitials or the lattice. Above the Curie temperature, a relaxation mechanism due to the exchange of cations Mn3+ and their vacancies on octahedral sites should occur.

Transmission electron microscopy (TEM) has been used to explore details of the structural phase transitions and corresponding microstructural features in the solid solution of Pb1−xBaxNb2O6 (PBN) tungsten bronze ferroelectrics at compositions embracing the morphotropic phase boundary between orthorhombic and tetragonal ferroelectric phases. In addition to the ferroelectric domain structures that were consistent with the expected symmetries, incommensurate ferroelastic phases were observed. The “onset” and “lock-in” transition temperatures are a function of the Pb/Ba ratio, and for lead-rich compositions it appears that the incommensurate distortion may occur above the ferroelectric Curie temperature in the paraelectric phase.

Relaxor ferroe lee tries are classified by broad or diffuse transitions from their high temperature paraelectric (non-polar phase) to their low temperature ferroelectric phase. This is in contrast to conventional ferroelectrics such as PbTiO3 that show discrete ferroelectric transitions characterized by Curie-Weiss behavior in the dielectric susceptibility near the Curie transition temperature Tc. For relaxor ferroelectrics, the transition has a breadth on the order of 100°C The polarized domains normally show complex nanoscale mottled contrast in either bright field or dark field, two-beam or systematic row scattering contrast images; as an example, this contrast is shown in Fig. 1. The nanoscale contrast appears to be intimately associated with the relaxor phase; however, the physical origins of the contrast remain unclear. It is known that in classical treatments of ferroelectrics, the polarization and strain are the primary order parameters for the paralelectric-ferroelectric phase transition. For classical first order ferroelectric transitions, such as in PbTiO3 or BaTiO3, there is a concurrently spontaneous polarization and strain. However, these order parameters need not be directly coupled, and it may be possible that through the relaxor transition, strain and polarization are uncoupled. In this experimental effort we will demonstrate techniques that separate strain contrast from structure factor contrast, the latter being associated with polarization or compositional fluctuations.

The Landau theory of phase transitions predicts the presence of a negative capacitance in ferroelectric materials based on a mean-field approach. While recent experimental results confirm this prediction, the microscopic origin of negative capacitance in ferroelectrics is often debated. This study provides a simple, physical explanation of the negative capacitance phenomenon—i.e., ‘S’-shaped polarization vs. electric field curve—without having to invoke the Landau phenomenology. The discussion is inspired by pedagogical models of ferroelectricity as often presented in classic text-books such as the Feynman lectures on Physics and the Introduction of Solid State Physics by Charles Kittel, which are routinely used to describe the quintessential ferroelectric phenomena such as the Curie-Weiss law and the emergence of spontaneous polarization below the Curie temperature. The model presented herein is overly simplified and ignores many of the complex interactions in real ferroelectrics; however, this model reveals an important insight: The polarization catastrophe phenomenon that is required to describe the onset of ferroelectricity naturally leads to the thermodynamic instability that is negative capacitance. Considering the interaction of electric dipoles and saturation of the dipole moments at large local electric fields we derive the full ‘S’-curve relating the ferroelectric polarization and the electric field, in qualitative agreement with Landau theory.

The empty orbital model in perovskite ATiO3-type (A=Mg, Ca, Sr and Ba) ferroelectrics with oxygen octahedra has been proposed. In this study, the impact of temperature on the bond energy of Ti-O has been discussed from the point of view of statistical thermodynamics, then the temperature dependence of equilibrium position of Ti ion has been calculated. The results show that because of the existence of empty orbital, with temperatrue decreasing the repulsion energy of Ti and O ions reduces and the Ti ion shift the equilibrium position in the cooling through the Curie temperature owing to Coulomb interaction. Ferroelectric phase transition in perovskite are successfully explained. Theoretical and experimental results for perovskite ATiO3-type ferroelectrics are compared and discussed.

Since the discovery of relaxor behavior in Pb(Mg 1/3 Nb 2/3 )O3 (referred to as PMN), the studies of relaxor ferroelectrics with Pb(B'1/3B"2/3)O3 type perovskites have intensified because of their excellent dielectric and electromechanical properties. The present study is mainly focused on the quantitative analysis of micro-macro domain transition, using dielectric spectroscopy, hot-stage TEM. The deviation from Curie-Weiss behavior was investigated over a broad range of temperature. As the relative contents of PbZrO3 increased, the Curie-Weiss temperature decreased, while the Curie-Weiss constant increased. However, the Lorentz polarization factor (γ) decreased with increasing PbZrO3 content, indicating an enhanced relaxor behavior in the PNN-PT-PZ(x) system at higher PZ content. A microscopic examination demonstrates that the relaxor-normal ferroelectric transition corresponds to a micro-macro domain switching. The long-range ferroelectric domains below the transition temperature were characterized by twin-like 90o macro domains with tetragonal symmetry and by the subdomains, which presumably relieves the internal electrostrictive strains associated with the polarization nonuniformity caused by the polar nanodomains.

Abstract Ferroelectric phase comprising BaTiO3 nanoparticles and nanorods have been prepared by high temperature sintering. The XRD spectra of sintered powder was used to confirm the ferroelectric phase crystallisation. The non-ferroelectric cubic phase to ferroelectric tetragonal phase transition of BaTiO3 was studied by temperature dependent dielectric study. The Curie temperature of 105 °C in sintered nanoparticles was observed from dielectric study of tetragonal phase BaTiO3.

Ba0.92Ca0.08Ti0.95Zr0.05O3 (BCZT8-5) ceramic materials have been scarcely studied as lead-free piezo/ferroelectrics despite their enhanced Curie temperature (>100 °C) with respect to most studied BCZT compositions. In this work, homogeneous dense BCZT8-5 ceramics with grain size in the range of 20 μm, and optimum ferroelectric, dielectric, and electromechanical performance, were prepared by the mixed oxides route using moderate synthesis (1250 °C-2 h) and sintering (1400 °C-2 h) conditions. Thickness-poled thin disks and monomodal shear plate resonators were used for the determination of piezoelectric coefficients, coupling factors, elastic, and dielectric permittivity coefficients, including all losses, by iterative analysis of impedance curves at resonance. Furthermore, the thermal evolution of the piezoelectric characteristics at resonance was determined to assess the enhanced working range of the ceramics (≈100 °C). Ferroelectric hysteresis loops and strains vs. electric-field butterfly loops were also measured and showed soft behavior with Ec = 2 kV/cm, Pr = 12 μC/cm2 after a maximum applied field of 3 kV was used. The ceramics showed a high endurance of P-E cycles to electrical fatigue up to 107 cycles. Moreover, dielectric properties as a function of temperature were also accomplished and showed nearly normal ferroelectric behavior, characteristic of samples with low crystallographic disorder. Overall, these ceramics showed high sensitivity and higher stability than other currently studied BCZT compositions.

Les matériaux de structure pérovskite de formule générale ABO3 sont les ferroélectriques les plus étudiés pour leurs propriétés intéressantes dans de nombreuses applications technologiques. Cependant leurs propriétés sont directement reliées à la structure et sont fortement conditionnées par les transitions de phases qui dépendent de la température, de la composition chimique et de la pression. Dans le manuscrit de thèse, le comportement sous haute pression de deux matériaux pérovskite SrTi1-xZrxO3 (STZ) et KNb1-XTaXO3 (KNT) est étudié et différentes techniques de frittage pour améliorer la densité des céramiques et optimiser les propriétés ferroélectriques des céramiques K(Nb0.40Ta0.60)O3 et (KxNa1-x)Nb0.6Ta0.4O3 sont examinées.Des analyses sous hautes pressions par spectroscopie Raman et diffraction des rayons X des poudres de SrTi1-xZrxO3 (x= 0.3, 0.4, 0.5, 0.6, 0.7) et KNb1-XTaXO3 (x=0.4, 0.5, 0.6, 0.9) en enclume diamant ont été réalisées. Les spectres Raman montrent une augmentation des modes Raman avec la pression pour les poudres de STZ indiquant que la pression induit des transitions de phases vers des symétries plus basses de la maille dans ces composés.De plus, les expériences de spectroscopie Raman ont fait apparaître une décroissance des modes Raman lorsque la pression est augmentée, montrant bien que la pression induit des transitions de phases vers des structure plus symétriques. L'évolution du mode Raman principal pour les phases orthorhombique et quadratique a été suivi jusqu'à ce que la phase cubique apparaîsse, ce qui nous a permis de proposer un diagramme de phase pression-composition pour les composés KNT.Trois différentes techniques de frittage, utilisation d'additifs, frittage en deux paliers et SPS ont été étudiées pour les céramiques de K(Nb0.4Ta0.6)O3 et (KxNa1-x)Nb0.6Ta0.4O3 . La constante diélectrique et les pertes en fonction de la température des céramiques ont été améliorées par l'utilisation du KF comme additif de frittage et par le frittage en deux paliers. Les échantillons densifiés par SPS présentent une microstructure fine et possèdent les plus fortes densités. Ils ont les meilleurs propriétés ferroélectriques. Aucun changement significatif de la température de Curie ne semble être induit par le taux de Na, et on observe cependant une augmentation de la constante diélectrique et des propriétés ferroélectriques suivant le taux de Na
Perovskite materials whose general chemical formula is ABO3 are one of the most study ferroelectrics due to the interesting properties that they have for technological applications. However, their properties are directly related to structural phase transitions that could depend of temperature, composition and pressure. In the studies presented here, we first examined the high-pressure behavior of two perovskite materials SrTi1-xZrxO3 (STZ) and KNb1-XTaXO3 (KNT), and we later continued to investigate different sintering techniques in order to improve the densification, dielectric and ferroelectric properties of K(Nb0.40Ta0.60)O3 and (KxNa1-x)Nb0.6Ta0.4O3 ceramics.High-pressure Raman scattering and X-ray diffraction investigations of SrTi1-xZrxO3 (x= 0.3, 0.4, 0.5, 0.6, 0.7) and KNb1-XTaXO3 (x=0.4, 0.5, 0.6, 0.9) powders were conducted in diamond anvil cells. Raman scattering experiments showed and increased of Raman modes with pressure for the STZ samples, which indicates that pressure induced phase transitions towards lower symmetry for these compounds.Moreover, high pressure Raman spectroscopy experiments showed a decrease of the Raman modes as the pressure was increased for the KNT samples, showing that pressure induced phase transitions towards higher symmetries. The evolution of the main Raman modes for the orthorhombic and tetragonal phases were followed until the cubic phase was reach, and allowed us to propose a pressure-composition phase diagram for the KNT compounds.Three different sintering techniques, sintered aids, two step sintering and spark plasma sintering, were used on K(Nb0.4Ta0.6)O3 and (KxNa1-x)Nb0.6Ta0.4O3 ceramics. The use of KF as sintered aid and the two step sintering method showed an improvement of the dielectric constant and dielectric losses of these samples. SPS samples presented a fine microstructure with the highest density and the best ferroelectric behavior. We did not detect any changes on the Curie temperature due the amount of Na but and increase of the dielectric constant and the ferroelectric properties was observed due to the amount of Na

This thesis studies the properties and the applications of prospective ferroelectric materials which are used in electrical engineering and electronic industry. Further are physically explained and mathematically described the basic principles running in their structure. The practical part is aimed to build a workplace for measuring the components of the complex permittivity in the frequency and temperature area, controlled by the programmed measurement and service application using the Agilent VEE Pro 8.0 and MS Excel. The functionality of the workplace was verified on the selected material samples by measurement and evaluation of selected properties. For this issue was created electronic text, which can be used as a guide for laboratory exercises and it is an integral part of this work.

The submitted thesis describes characteristics and use of the ferroelectric material which has their utilization in electronics and electro technical industry. The thesis describes behaviour ferroelectrics in temperature range. A suitable workplace was designed and its functionality was verified in selected ferroelectrics samples dependence of temperature of components of complex permittivity.

he extent of BiInO₃ substitution in the perovskite system xBiInO(₃)-(1 - x)PbTiO₃ and the corresponding raise in the transition temperature were investigated using thermal analysis, dielectric measurements, x-ray diffraction, and electron microscopy. Maximum tetragonal perovskite distortion (c/a = 1.082) was obtained for x = 0.20, with a corresponding Curie temperature of 582°C. Phase-pure tetragonal perovskite was obtained for x less than or equal to 0.25. Compound formation after calcining mixed oxide powders resulted in agglomerated cube-shaped tetragonal perovskite particles, which could be fired to 94.7% of theoretical density (TD). Niobium-modified BIPT ceramics with PT contents of 80% and 85% were found to possess significantly lower dielectric loss at elevated temperatures, making it possible to polarize the materials. Piezoelectric properties were measured for a 1.5 mol% Nb -0.15BI-0.85PT composition with a transition temperature of 542°C; the longitudinal piezoelectric coefficient and coercive field were found to be 60 pC/N and 125 kV/cm, respectively. Compositions of xBiLaO₃-(1 − x)PbTiO₃ over the range 0 < x < 0.225 were calcined and sintered. Dielectric constant with temperature and differential scanning calorimetry measurements were in excellent agreement with respect to a Curie-like tetragonal to cubic transformations starting at 495°C for pure PbTiO₃, shifting to lower temperatures with increasing x. For compositions of x > 0.05, a second higher-temperature (∼600°C) endotherm, and matching dielectric anomaly, were consistently observed, for which there were no structural changes indicated by hot-stage x-ray diffraction. This transformation was interpreted to be similar to a Curie transformation in relaxor ferroelectrics in which localized segregation of B-site cations (below the resolution limit of x-ray diffraction) facilitated ferroelectric behavior.

Tese de doutoramento em Física, na especialidade de Física da Matéria Condensada, apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra
Nesta tese é apresentada a investigação experimental realizada tendo em vista o crescimento de cristais ferroeléctricos com elevada temperatura de Curie da família BiMeO3-PbTiO3 e caraterização das suas propriedades físicas focada nas propriedades estruturais, termodinâmicas, estudo da transição de fase ferroeléctrica, morfologia e microestutura, estrutura de domínios e propriedades de inversão “switching”. As perovesquites com alta temperatura de Curie são materiais particularmente indicados para aplicações em ambientes de temperatura elevada, tais como as aplicações aeronáuticas e na indústria automóvel. Efetuámos o crescimento de monocristais tetragonais com a composição xBiInO3-(1-x)PbTiO3 usando o método de solução de auto-fluxo, onde os óxidos Pb3O4 and Bi2O3 serviram como um fluxo complexo. O refinamento de Rietveld dos dados de difração de RX em pó foi usado para relacionar a estrutura com as propriedades ferroeléctricas e piezoeléctricas. Os monocristaisobtidos e analisados tais como foram sintetizados, sem outros tratamentos, de 0.3BiInO3-0.7PbTiO3 (BIPT03), 0.4BiInO3-0.6PbTiO3 (BIPT04) e 0.5BiInO3-0.5PbTiO3 (BIPT05) possuem temperaturas de Curie próximas de 555 oC. Assim, a adição deBi/Inaumenta a temperatura de Curie do composto de base PbTiO3 (Tc = 490 oC). As propriedades dielétricas, ferro e piezoeléctricas dos monocristais BIPT foram investigadas. A transição de fase ferroeléctrica-paraeléctrica foi estudada no composto BIPT03 por difração de RX a alta temperatura e por calorimetria de varrimento diferencial (DSC). Os estudos de RX a temperatura variável permitiram obter informação sobre a transição estrutural associada à transição da fase ferroeléctrica para a paramagnética. A técnica DSC permitiu caracterizar termodinamicamente a transição. Um estudo detalhado do composto BIPT03 mostrou a existência de histerese térmica, implicando que a transição de fase é de 1ª ordem, com coexistência das fases ferroeléctrica e paraeléctrica num intervalo de temperaturas. Espectroscopia de Infravermelho por transformadas de Fourier (FTIR) foi usada para caracterizar os modos vabriacionais da rede (TiO e PbO). Difração de RX (XRD), espectroscopia de fluorescência de RX (XRF), espectroscopia de RX com análise dispersiva em energia (EDS) e difração de electrões em área selecionada (SAED) permitiram uma caracterização detalhada da estrutura e composição das fases. Microscopia electrónica de varrimento (SEM) foi usada para observar a morfologia dos cristais. As imagens de SAED e os perfis das reflexões de Bragg dos monocristais demonstram que estes são de boa qualidade. As estruturas estáticas dos domínios e as propriedades de inversão (“switching”) dos monocristaisBIPT04 com orientação (010) e dos cristais BIPT03 com orientação (110) foram estudadas por microscopia de força de piezorespostaatómica (PFM). A imagem dos domínios da face (010) dos cristais de BIPT04 e da face (110) dos cristais BIPT03 exibem um padrão de domínios “labiríntico”. As imagens PFM em contraste de fase e de amplitude obtidas aplicando várias tensões de polarização permitiram estudar a evolução da estrutura de domínios em função da polarização externa. As curvas de histerese da piezoresposta da face (010) dos mocristais de BIPT04 permitiram medir as características de inversão da polarização espontânea como a tensão coerciva. Efetuando a comparação com a situação após a aplicação de uma tensão de “poling” de ±25 V na face (010) dos cristais de BIPT04, verificou-se que a tensão coerciva é menor depois do “poling”. Para os cristais de BIPT04, verificou-se que os tamanho dos domínios aumenta e que a tensão coerciva diminui à medida que a espessura da face (010) é reduzida. Cristais tetragonais de composição 0.3BiAlO3-0.7PbTiO3 com temperatura de Curie de 466 oC foram crescidos com sucesso e caracterizados. Infelizmente, as tentativas para crescer cristais puros de 0.2BiYbO3-0.8PbTiO3 (BYPT) e 0.37Bi(Sc0.5Yb0.5)O3-0.63PbTiO3 (BSYPT) não foram bem sucedidas. Outros cristais que foram obtidos no decurso da tese incluem (PbxBi3-x)(TiyYb5-y)O12 que cristaliza numa estrutura de granada com grupo espacial e também de BSYPT, este último com inclusões de uma fase de impureza.
This thesis presents an experimental research on the growth and the physical properties of high Curie temperature BiMeO3-PbTiO3 single crystals, mainly focused on their structural features, thermodynamics, ferroelectric phase transition, morphology and microstructure, domain structure and local switching characteristics. The high Curie temperature perovskite materials are particularly suited for high temperature environments, including space exploration and automotive industry. Tetragonal xBiInO3-(1-x)PbTiO3 (BIPT) single crystals were grown from a high-temperature self-flux solution in which Pb3O4 and Bi2O3 are utilized as a complex flux. Based on the Rietveld refinement of X-ray powder diffraction data, the relationship between their structure and ferroelectric and piezoelectric properties was analysed. The as-grown 0.3BiInO3-0.7PbTiO3 (BIPT03), 0.4BiInO3-0.6PbTiO3 (BIPT04) and 0.5BiInO3-0.5PbTiO3 (BIPT05) single crystals exhibit high Curie temperatures around 555 oC. The addition of Bi/In was shown to increase the Curie temperature (Tc) of the parent ferroelectric PbTiO3 (490 oC). The dielectric, ferroelectric and piezoelectric properties of BIPT single crystals were investigated. The ferroelectric-paraelectric phase transition in BIPT03 was studied using high-temperature X-ray diffraction (XRD) and differential scanning calorimetry (DSC). We have undertaken the XRD study at different temperatures to obtain direct structural information about the phase transition from the ferroelectric to the paraelectric phase. DSC was used to characterize the thermodynamics of this transition. A detailed study of the compound BIPT03 showed “temperature hysteresis”, implying that the transition is of first order, with a coexistence of paraelectric and ferroelectric phases in a range of temperatures. Fourier Transform Infra-Red Spectroscopy (FTIR) was used to characterize the lattice vibrational modes (TiO and PbO modes). XRD and selective area electron diffraction (SAED) were employed to characterize the phase composition and crystal structure; scanning electron microscopy (SEM) was used to observe the morphology of the grown crystals. The observed SAED images and XRD rocking curves indicated that the crystals had a good quality. The static domain structures and local switching properties of relaxor ferroelectric BIPT04 single crystals at (010) crystal orientations and BIPT03 single crystals at (110) crystal orientations where studied using piezoresponse force microscopy (PFM). PFM domain imaging shows that the (010) face of BIPT04 single crystals and the (110) face of BIPT03 single crystals exhibit a labyrinth-like surface domain pattern. Phase and amplitude PFM imaging under different bias voltages were used to study the domain behavior under external polarization. It revealed that bias voltage can effectively control the domain orientation. Piezoresponse hysteresis loops on the (010) face of BIPT04 single crystals enabled to measure local domain switching characteristics, such as the coercive voltage. Comparing with after poling applying ±25 V on the (010) face of BIPT04 single crystals, the coercive voltage was found to be smaller before poling. For BIPT04 single crystals, the domain area grows and the coercive voltage reduces as the thickness of the (010) face decreases. Tetragonal single crystals 0.3BiAlO3-0.7PbTiO3 with Curie temperature of 466oC were also successfully grown and characterized. However, the 0.2BiYbO3-0.8PbTiO3 (BYPT) and 0.37Bi(Sc0.5Yb0.5)O3-0.63PbTiO3 (BSYPT) single crystals could not be obtained as pure samples. Other crystals were obtained during the work of this thesis including (PbxBi3-x) (TiyYb5-y) O12 single crystals that crystallize in the garnet structure with space group and those of BSYPT with inclusions of an impurity phase.
Fundação para a Ciência e Tecnologia

碩士
輔仁大學
物理學系
94
Dielectric permittivity, electric hysteresis loops, and domain structures have been measured as functions of temperature, frequency in (001)-cut Pb(In1/2Nb1/2)0.6Ti0.4O3 (PIN-40％PT) and (001)-cut Pb(In1/2Nb1/2)0.7Ti0.3O3 (PIN-30％PT) single crystals. For (001)-cut PIN-40％PT, frequency-dependent dielectric absorption reveals dipolar relaxation processes in the temperature region of 150-300 K which can be described by the Vogel-Fulcher equation. Phase transition from a first-order-type tetragonal/monoclinic to cubic takes place at Tc~486 K. For (001)-cut PIN-30％PT, a diffused phase transition was observed in the temperature region of 430-460 K with strong frequency dispersion. Phase transition from a first-order-type trigonal to cubic occurs inside temperature region 280-400 K. Above the Burns temperature TB~510 K, the dielectric permittivity was found to follow the Curie-Weiss law. An electric-field poling induces macroscopic MA-type monoclinic domains in (001)-cut PIN-30％PT. With temperature increasing near 390 K, these MA-phase clusters significantly reorient and cause an extra dielectric anomaly. Near 415 K, dielectric permittivity has a frequency-dependent anomaly which implies polar nanoclusters appear at 415 K. Above TB~520 K dielectric permittivity follows the Curie-Weiss law. With a prior electric-field poling, both (001)-cut PIN-30%PT and (001)-cut PIN-40%PT show almost no birefringence, indicating that the average structural symmetry is optically isotropic. The crystals exhibit broad transparency in the wavelength region of 0.4-9.0μm.

Over the last two decades, great progress has been made in the understanding of multiferroic materials, ones where multiple long-range orders simultaneously exist. However, much of the research has focused on bulk systems. If these materials are to be incorporated into devices, they would not be in bulk form, but would be miniaturized, such as in nanoparticle form. Accordingly, a better understanding of multiferroic nanoparticles is necessary. This manuscript examines the multiferroic phase diagram of multiferroic nanoparticles related to system size and surface-induced magnetic anisotropy. There is a particular focus on bismuth ferrite, the room-temperature antiferromagnetic-ferroelectric multiferroic. Theoretical results will be presented which show that at certain sizes, a bistability develops in the cycloidal wavevector. This implies bistability in the ferroelectric and magnetic moments of the nanoparticles. This novel magnetoelectric bistability may be of use in the creation of an electrically-written, magnetically-read memory element.
Graduate

Multiferroic materials are a very exotic type of materials which present simultaneously two or more ferroic properties. Magnetoelectric multiferroics, in particular, are a very prominent class of materials, mainly due to their outstanding foreseen applications such as magnetic sensors, energy harvester/conversion devices, and high efficiency memories. However, intrinsic magnetoelectric materials are quite rare and do not have, yet, the adequate properties to the everyday applications. One of the reasons for this to occur is due to the requirements for magnetism and ferroelectricity in matter being a priori contradictory, since the former needs unfilled dn orbitals, while the latter favours d0 orbitals. Nevertheless, extrinsic magnetoelectric multiferroics do not suffer from this problem because they do not share the same phase, hence being a very promising approach to engineer adequate magnetoelectric multiferroics. This thesis focus on the study of Fe and BaTiO3 systems as a means of achieving novel magnetoelectric effects. It is shown that a peculiar type of BaTiO3:Fe auto-composite presents an ordered magnetic behaviour, despite the concentration of Fe being as low as 113 atomic ppm. The Fe magnetization displays two abrupt changes in its spontaneous value, one with M/M ≈ 32% and the other with M/M ≈ 14%. These magnetic transitions are correlated the BaTiO3 orthorhombic↔tetragonal and tetragonal↔cubic ferroelectric phase transitions. This magnetoelectric auto-composite was the motivation to resort to Density Functional Theory (DFT) modeling as a means to discover the microscopic mechanism(s) behind such a strong magnetoelectric effect. The study of an iron monolayer placed upon several possible BaTiO3 unit cells lead to the discovery of several interfaces with abrupt changes in their spontaneous magnetization, either through the enhancement and reduction of the Fe magnetic moments, or through the change between antiferromagnetic and ferromagnetic order of the Fe monolayer. However, the highlight of these DFT studies lies in the discovery of a particular kind of interfaces, namely in the BTO221_2ndFe and BTO99_2ndFe supercells, where there is a High-Spin–Low-Spin state transition which can quench completely the atomic magnetic moment of each of Fe atom, depending on the local crystal field felt by the Fe atoms. Based on this specific effect, where it is possible to turn on and off the magnetic moments of the Fe atoms, a magnetoelectric multiferroic device was proposed. Knowing the importance of the crystal field for the High-Spin–Low-Spin state transition, a thorough study regarding the Electric Field Gradient (EFG) of each possible BaTiO3 site was performed, resorting to a combined study of DFT and Perturbed Angular Correlations (PAC) spectroscopy. In this study, it was concluded that the PAC spectroscopy is not the most adequate hyperfine technique to be used in a quantitative study of the BaTiO3/Fe interfaces EFG tensor, due to the non-negligible effects of the radioactive probe on the BaTiO3 matrix. Finally, the deposition of BTO/Fe heterostructures on LaAlO3, MgO, Al2O3 and SrTiO3 substrates using RF-Sputtering, and the Molecular Beam Epitaxy (MBE) deposition of Fe layers on BaTiO3 cut at the (100), (110) and (111) planes were performed as an attempt to recreate the interfaces with the most appealing magnetoelectric effects predicted in the DFT modeling. The thin films deposited using sputtering showed the growth of many Fe, Ba-Ti-O and Fe-Ti-O oxides depending strongly on their substrate, as well as in the deposition and annealing conditions. Still no magnetoelectric coupling was observed in such thin films. On the other hand the Fe thin films deposited on BaTiO3 substrates showed large magnetoelectric couplings between the BaTiO3 ferroelectric phase transitions and the magnetization of the Fe layers (similarly to what happened in the BaTiO3:Fe auto-composite). The magnitude of this magnetoelectric couplings is strongly correlated with the BTO interface where the Fe was deposited, showing a huge change in spontaneous magnetization and coercivity for the rhombohedral↔orthorhombic ferroelectric phase transition up to M/M ≈ 148% and HC/HC ≈ 183% respectively for the (110) case.
Materiais Multiferróicos são um tipo de materiais bastante exótico que apresentam simultaneamente dois ou mais tipos de propriedades ferróicas. Multiferróicos magnetoelétricos, em particular, são uma classe de materiais muito proeminente, principalmente devido às suas espantosas aplicações tecnológicas, tais como sensores magnéticos, dispositivos de conversão/colheita de energia, e memórias the alta eficiência. Todavia, materiais magnetoelétricos intrínsecos são verdadeiramente raros e ainda não possuem propriedades adequadas ao uso do dia-a-dia. Uma das razões para que isto aconteça prende-se com o facto dos requisitos para existência de magnetismo e ferroeletricidade na matéria serem a priori contraditórios, uma vez que enquanto os primeiros necessitam de orbitais dn semipreenchidas, os últimos tendem a favorecer orbitais d0. Porém, Multiferróicos magnetoelétricos extrínsecos não sofrem desta limitação pois não partilham a mesma fase sendo portanto uma abordagem promissora para a construção de um bom Multiferróico magnetoelétrico. Esta tese focar-se-á no estudo de sistemas contendo Fe e BaTiO3 como meio de se alcançarem novos efeitos magnetoelétricos. Um auto-compósito de BaTiO3:Fe é apresentado, que apesar da sua diminuta concentração de Fe (apenas 113 ppm atómicas), ainda assim apresenta um comportamento magnético ordenado. A magnetização do Fe apresenta duas variações bruscas no seu valor espontâneo, uma com M/M ≈ 32% e outra com M/M ≈ 14%. Estas transições magnéticas estão correlacionadas com as transições de fase ferroelétricas do BaTiO3 (ortorrômbica↔tetragonal e tetragonal↔cúbica). Este auto-compósito magnetoelétrico foi a motivação par ao uso da Teoria de Densidade Funcional (DFT) como meio para descobrir os mecanismos microscópicos por trás deste acoplamento magnetoelétrico tão intenso. O estudo de uma mono-camada de Fe colocada sobre várias células unitárias de BaTiO3 levaram à descoberta de várias interfaces com mudanças abruptas na sua magnetização espontânea, ora através do aumento ou diminuição dos momentos magnéticos do Fe, ora através da mudança entre a natureza antiferromagnética ou ferromagnética da camada de Fe. Contudo, o destaque dos estudos de DFT reside na descoberta de um tipo particular de interfaces onde ocorre uma transição de estado High-Spin–Low-Spin que consegue colapsar completamente o momento magnético atómico dos átomos de Fe, dependendo do campo cristalino local sentido por esses mesmos átomos. Baseado neste efeito, um dispositivo Multiferróico magnetoelétrico foi proposto. Sabendo a importância do campo cristalino para as transições de estado High-Spin–Low-Spin state, um estudo minucioso foi feito relativo ao gradiente de campo elétrico (EFG) nos sítios possíveis do BaTiO3, usando um estudo combinado entre Correlações Angulares Perturbadas (PAC) e DFT. Neste estudo, concluiu-se que PAC não é uma técnica hiperfina adequada para o estudo quantitativo do tensor EFG de interfaces de BaTiO3/Fe, dados os efeitos não desprezáveis das sondas radioativas na matriz de BaTiO3. Finalmente, foi feita a deposição de Heteroestruturas de BTO/Fe em substratos de LaAlO3, MgO, Al2O3 e SrTiO3 usando RF-Sputtering, assim como deposição de camadas de Fe em substratos de BaTiO3 cortados nos planos (100), (110) e (111) planes, usando Molecular Beam Epitaxy (MBE), numa tentativa de recrear as interfaces com efeitos magnetoelétricos mais apelativos, previstos pela modelação DFT. Os filmes finos depositados por sputtering mostraram o crescimento de múltiplos óxidos de Fe, Ba-Ti-O e Fe-Ti-O dependendo fortemente do substrato onde foram crescidos, assim como das condições de deposição e tratamentos térmicos. Porém, nenhum efeito magnetoelétrico foi observado nestes filmes. Por outro lado, os filmes depositados nos substratos de BaTiO3 mostraram grandes acoplamentos magnetoelétricos entre as fases ferroelétricas do BTO e a magnetização das camadas de Fe (à semelhança do que aconteceu no auto-compósito de BaTiO3:Fe). A ordem de grandeza destes acoplamentos está fortemente correlacionada com a interface do BTO onde o Fe foi depositado, apresentando uma enorme variação na magnetização espontânea e na coercividade para o caso da transição romboédrica↔ortorrômbica, até M/M ≈ 148% e HC/HC ≈ 183% respetivamente para o caso da orientação (110).
Tese realizada com apoio financeiro da FCT através da bolsa SFRH/BD/93336/2013.
Programa Doutoral em Física

Piezoelectric materials are an important class of materials that find application in science and technology, in engineering and in modern warfare as pressure transducers, sensors and energy harvesting devices. Selection of suitable piezoelectric materials relies on several factors such as the type, Curie temperature, environmental stability, different physical properties and their characterization depending different measurement techniques. Several aspects and typical characteristic constants that are necessary for selection of suitable piezoelectric composition are very broadly highlighted in this chapter. Fundamental properties obtained from different characterization tools were concisely discussed with respect to piezoelectric materials which also show ferroelectric behavior.

Piezoelectric materials are an important class of materials that find application in science and technology, in engineering and in modern warfare as pressure transducers, sensors and energy harvesting devices. Selection of suitable piezoelectric materials relies on several factors such as the type, Curie temperature, environmental stability, different physical properties and their characterization depending different measurement techniques. Several aspects and typical characteristic constants that are necessary for selection of suitable piezoelectric composition are very broadly highlighted in this chapter. Fundamental properties obtained from different characterization tools were concisely discussed with respect to piezoelectric materials which also show ferroelectric behavior.

The physical properties discussed thus far are linear relationships between two measured quantities. This is only an approximation to the truth, and often not a very good approximation, especially for materials near a phase transformation. A more accurate description can be obtained by introducing higher order coefficients. To illustrate nonlinearity we discuss electrostriction, magnetostriction, and higher order elastic, and dielectric effects. These phenomena are described in terms of fourth and sixth rank tensors. Many of the recent innovations in the field of electroceramics have exploited the nonlinearities of material properties with factors such as electric field, mechanical stress, temperature, or frequency. The nonlinear dielectric behavior of ferroelectric ceramics (Fig. 15.1), for example, has opened up new markets in electronics and communications. In these materials the electric polarization saturates under high fields. Electric displacement Di varies with applied electric field Ej as . . . Di = εijEj + εijkEjEk + εijklEjEkEl +· · · , . . . where εij is the dielectric permittivity and εijk and εijkl are higher order terms. The data in Fig. 15.1 were collected for a relaxor ferroelectric in its paraelectric state above Tc where the symmetry is centrosymmetric. Therefore the third rank tensor εijk is zero, and the shape of the curve is largely controlled by the first and third terms. For cubic crystals, the fourth rank tensor εijkl is similar in form to the elastic constants discussed in Chapter 13. Tunable microwave devices utilize nonlinear dielectrics in which the polarization saturates as in Fig. 15.1. By applying a DC bias the dielectric constant can be adjusted over a wide range.

Certain ferroelectric materials possess dual electrostrictive and piezoelectric characteristics, depending on their specific Curie temperatures. These materials exhibit piezoelectric characteristics in the ferroelectric phase when the temperature is below the Curie point. However, they become electrostrictive in the paraelectric phase (non-polar phase) as the temperature exceeds the Curie point. The (direct) electrostrictive effect is a quadratic dependence of stress or strain on applied electric field. The nonlinear electromechanical effect of electrostrictive materials provides stronger actuation performance as compared with that of piezoelectric materials. Due to the complexity of the generic ferroelectric actuators, micro-electromechanics and control characteristics of generic electrostrictive/piezoelectric dynamics system deserve an in-depth investigation. In this study, electro-mechanical dynamic system equations and generic boundary conditions of hybrid electrostrictive/piezoelectric double-curvature shell continua are derived using the energy-based Hamilton’s principle, elasticity theory, electrostrictive/piezoelectric constitutive relations, and Gibb’s free energy function. Moreover, the second converse electrostrictive effect and the direct piezoelectric effect are all considered in the generic governing equations. Simplifications of the generic theory to other common geometries or specific materials are demonstrated and their electromechanical characteristics are also evaluated.

Ferroelectric materials exhibit spontaneous polarization and domain structures below the Curie temperature. In this study a cubic to tetragonal phase transformation and the evolution of domain structures in ferroelectric crystals are simulated by using the time-dependent Ginzburg-Landau equation. The effects of electric boundary conditions on the formation of domain patterns and field induced polarization switching are discussed. The phase field model is used to simulate the formation of domain structures, domain wall motion and the macroscopic response of ferroelectric materials under external fields.

It is known that ferroelectric domain inversion can occur at the positive face when c-cut lithium niobate is treated at temperatures near the Curie-temperature [1]. Domain inversion has also been noted as a problem during waveguide fabrication based on titanium indiffusion, which requires high diffusion temperatures [2,3,4]. The titanium was seen to affect the inversion process.

Degradation of lithium niobate integrated optical device performance due to the reversal of ferroelectric micro-domains in localized regions has been described in Ref. 1. However, it has been assumed that these reversals can take place only at extremely high temperatures (near the Curie point) or with very high applied electric fields. Indeed, it has been shown theoretically (Ref. 2) that for pure lithium niobate at room temperature, an electric field of about 3 × 10 9 V/m applied along the crystalline c axis would be necessary to cause domain reversal. Titanium diffusion at elevated temperatures was identified in Ref. 1 as the cause of these reversals and usage of -Z-cut substrates rather than +Z-cut substrates was proposed to reduce their occurrence.

Ferroelectric materials exhibit spontaneous polarization and domain structures below the Curie temperature. In this work the phase field approach has been used to simulate phase transformations and the formation of ferroelectric domain structures. The evolution of phases and domain structures was simulated in ferroelectric single crystals by solving the time dependent Ginzburg-Landau (TDGL) equation with polarization as the order parameter. In the TDGL equation the free energy of a ferroelectric crystal is written as a function of polarization and applied fields. Change of temperature as well as application of stress and electric fields leads to change of the free energy and evolution of phase states and domain structures. In this work the finite difference method was implemented for the spatial description of the polarization and the temporal evolution of polarization field was computed by solving the TDGL equation with an explicit time integration scheme. Cubic to tetragonal, cubic to rhombohedral and rhombohedral to tetragonal phase transformations were modeled, and the formation of domain structures was simulated. Field induced polarization switching and rhombohedral to tetragonal phase transition were simulated.

It is shown that, in the C-polytype of TlGaSe2 crystals, the structural PT, which occurs at a temperature of T ~ 108 K, is accompanied by an abrupt change in the value of the parameter c (∆c ~ 0.004 Å). For the 2C-TlGaSe2 polytype, the c (T) dependence shows only one clearly pronounced maximum at the temperature Tc2. Moreover, at temperatures that are T1 ~ 30 K higher and T2~ 5 K below Tc2, the Curie-Weiss law is fulfilled. The absence of a fourfold increase in the parameter from the unit cell for 2C-TlGaSe2 samples in the temperature range T = 100-300 K indicates that spontaneous polarization is the order parameter of the ferroelectric PT