Academic literature on the topic 'Ferroelectric Curie Temperature'

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Journal articles on the topic "Ferroelectric Curie Temperature"

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Xu, Lan, Zujian Wang, Bin Su, et al. "Origin of Structural Change Driven by A-Site Lanthanide Doping in ABO3-Type Perovskite Ferroelectrics." Crystals 10, no. 6 (2020): 434. http://dx.doi.org/10.3390/cryst10060434.

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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 (
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WANG, C. L., and M. L. ZHAO. "BURNS TEMPERATURE AND QUANTUM TEMPERATURE SCALE." Journal of Advanced Dielectrics 01, no. 02 (2011): 163–67. http://dx.doi.org/10.1142/s2010135x1100029x.

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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.
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Fantozzi, Gilbert, E. M. Bourim, and Sh Kazemi. "High Damping in Ferroelectric and Ferrimagnetic Ceramics." Key Engineering Materials 319 (September 2006): 157–66. http://dx.doi.org/10.4028/www.scientific.net/kem.319.157.

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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 doma
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Randall, C. A., R. Guo, A. S. Bhalla, and L. E. Cross. "Microstructure-property relations in tungsten bronze lead barium niobate, Pb1−xBaxNb2O6." Journal of Materials Research 6, no. 8 (1991): 1720–28. http://dx.doi.org/10.1557/jmr.1991.1720.

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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 co
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Zhang, J. P., and J. S. Speck. "Identification of the polarized microregions in PLZT." Proceedings, annual meeting, Electron Microscopy Society of America 52 (1994): 556–57. http://dx.doi.org/10.1017/s0424820100170517.

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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
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Hoffmann, Michael, Prasanna Venkatesan Ravindran, and Asif Islam Khan. "Why Do Ferroelectrics Exhibit Negative Capacitance?" Materials 12, no. 22 (2019): 3743. http://dx.doi.org/10.3390/ma12223743.

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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 a
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Fang, Chao, and Liang Yan Chen. "Research of the Mechanism of Ferroelectric Phase Transition in Perovskite: Empty Orbital Model." Applied Mechanics and Materials 130-134 (October 2011): 2809–12. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.2809.

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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 Coulom
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Yoon, Man Soon, and Soon Chul Ur. "Quantitative Analysis of Micro-Macro Domain Transition of PNN-PT-PZ(x) System at Higher PZ Content." Materials Science Forum 510-511 (March 2006): 542–45. http://dx.doi.org/10.4028/www.scientific.net/msf.510-511.542.

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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 cons
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Kumar, Ajay, Sudip Naskar, and Dipankar Mandal. "Synthesis and Investigation of Ferroelectric Curie Transition in BaTiO3." IOP Conference Series: Materials Science and Engineering 1221, no. 1 (2022): 012004. http://dx.doi.org/10.1088/1757-899x/1221/1/012004.

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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.
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Hernández-Moreno, Ana Cristina, Armando Reyes-Montero, Brenda Carreño-Jiménez, Mónica Acuautla, and Lorena Pardo. "Ferroelectric, Dielectric and Electromechanical Performance of Ba0.92Ca0.08Ti0.95Zr0.05O3 Ceramics with an Enhanced Curie Temperature." Materials 16, no. 6 (2023): 2268. http://dx.doi.org/10.3390/ma16062268.

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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 pi
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Dissertations / Theses on the topic "Ferroelectric Curie Temperature"

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Di, Geronimo Camacho Elizabeth Carolina. "Synthesis, high-pressure study and dielectric characterization of two lead-free perovskite materials : SrTi1-xZrxO3 and KNb1-xTaxO3." Thesis, Montpellier, 2016. http://www.theses.fr/2016MONTT208/document.

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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 de
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Krejčí, Josef. "Vlastnosti perspektivních feroelektrických materiálů." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2012. http://www.nusl.cz/ntk/nusl-219810.

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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 s
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Czanadi, Jindřich. "Chování feroelektrik v teplotní oblasti." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2012. http://www.nusl.cz/ntk/nusl-219809.

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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.
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Duan, Runrun. "Investigation of xBi(B')O₃-(1 -- x)PbTiO₃ and xBi(B',B")O3-(1 -- x)PbTiO3 perovskite solid solutions with high transition temperatures." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/24688.

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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
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Xu, Lan. "Novel ferroelectric BiMeO3-PbTiO3 single crystals with a high Curie temperature." Doctoral thesis, 2016. http://hdl.handle.net/10316/30400.

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Tese de doutoramento em Física, na especialidade de Física da Matéria Condensada, apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra<br>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 t
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Cheng-Ming, Hung, and 洪正銘. "Dielectric, Domain structure, and Optical Properties in High-Curie-Temperature Ferroelectric/Piezoelectric Pb(In1/2Nb1/2)1-xTixO3 Single Crystals." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/91050172643288577825.

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碩士<br>輔仁大學<br>物理學系<br>94<br>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
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Allen, Marc Alexander. "Theoretical investigation of size effects in multiferroic nanoparticles." Thesis, 2020. http://hdl.handle.net/1828/11972.

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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. Th
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Amorim, Carlos de Oliveira. "Experimental and modeling studies of magnetoelectric multiferroic heterostructured materials." Doctoral thesis, 2019. http://hdl.handle.net/10773/27751.

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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 b
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Book chapters on the topic "Ferroelectric Curie Temperature"

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Zhao, Wei, Xiao Hui Wang, Zhi Lun Gui, and Long Tu Li. "Properties of Ultrafine High Curie Temperature (1-x)BiScO3-xPbTiO3 Ferroelectric Ceramics." In Key Engineering Materials. Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-410-3.235.

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Kalyana Lakshmi, Y. "Types, Properties and Characteristics of Piezoelectric Materials." In Materials Research Foundations. Materials Research Forum LLC, 2022. http://dx.doi.org/10.21741/9781644902097-1.

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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.
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Kalyana Lakshmi, Y. "Types, Properties and Characteristics of Piezoelectric Materials." In Materials Research Foundations. Materials Research Forum LLC, 2022. http://dx.doi.org/10.21741/9781644902073-1.

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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.
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"High Curie temperature piezoelectric single crystals of the Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb2/3)O3–PbTiO3 ternary materials system." In Handbook of Advanced Dielectric, Piezoelectric and Ferroelectric Materials. CRC Press, 2008. http://dx.doi.org/10.1201/9781439832882.ch8.

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Yamashita, Y. J., and Y. Hosono. "High Curie temperature piezoelectric single crystals of the Pb(In 1/2 Nb 1/2 )O 3 –Pb(Mg 1/3 Nb 2/3 )O 3 –PbTiO 3 ternary materials system." In Handbook of Advanced Dielectric, Piezoelectric and Ferroelectric Materials. Elsevier, 2008. http://dx.doi.org/10.1533/9781845694005.1.205.

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Newnham, Robert E. "Nonlinear phenomena." In Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.003.0017.

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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.
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Conference papers on the topic "Ferroelectric Curie Temperature"

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Schalles, M., T. Fröhlich, H. T. Langhammer, and D. Boguhn. "Investigation on the Curie temperature of a ferroelectric material as a temperature fixed-point." In TEMPERATURE: ITS MEASUREMENT AND CONTROL IN SCIENCE AND INDUSTRY, VOLUME 8: Proceedings of the Ninth International Temperature Symposium. AIP, 2013. http://dx.doi.org/10.1063/1.4819670.

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Lattanzio, Livio, Giovanni Antonio Salvatore, and Adrian Mihai Ionescu. "Non-hysteretic ferroelectric tunnel FET with improved conductance at Curie temperature." In 2010 68th Annual Device Research Conference (DRC). IEEE, 2010. http://dx.doi.org/10.1109/drc.2010.5551937.

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Salvatore, Giovanni A., Livio Lattanzio, Didier Bouvet, and Adrian M. Ionescu. "The Curie temperature as a key design parameter of ferroelectric Field Effect Transistors." In ESSDERC 2010 - 40th European Solid State Device Research Conference. IEEE, 2010. http://dx.doi.org/10.1109/essderc.2010.5618386.

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Chai, W. K., H. S. Tzou, and S. M. Arnold. "Micro-Structronics and Control of Hybrid Electrostrictive/Piezoelectric Thin Shells." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-42398.

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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 actu
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Liu, T., and C. S. Lynch. "Phase Field Simulation of Ferroelectric Single Crystals." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79622.

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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 externa
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Webjörn, Jonas, Fredrik Laurell, and Gunnar Arvidsson. "Periodically domain-inverted lithium niobate channel waveguides for second harmonic generation." In Nonlinear Guided-Wave Phenomena. Optica Publishing Group, 1989. http://dx.doi.org/10.1364/nlgwp.1989.tha2.

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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.
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Pendergrass, L. L., and R. J. Jungerman. "Ferroelectric Microdomains In Lithium Niobate Optical Modulators." In Integrated and Guided Wave Optics. Optica Publishing Group, 1988. http://dx.doi.org/10.1364/igwo.1988.tud3.

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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 temperatu
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Mimura, T., T. Shimizu, Y. Katsuya, O. Sakata, and H. Funakubo. "Thickness- and orientation-dependence of Curie temperature of ferroelectric epitaxial HfO2 based films." In 2019 International Conference on Solid State Devices and Materials. The Japan Society of Applied Physics, 2019. http://dx.doi.org/10.7567/ssdm.2019.h-2-04.

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Liu, T., and C. S. Lynch. "Phase-Dield Simulation of Rhombohedral and Tetragonal Phases in Ferroelectric Single Crystals." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14945.

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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
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Matiyev, A. Ch, and R. T. Uspazhiev. "INFLUENCE OF POLYTYPY ON PHASE TRANSITIONS IN TlGaSe2 CRYSTALS." In «АКТУАЛЬНЫЕ ВОПРОСЫ СОВРЕМЕННОЙ НАУКИ: ТЕОРИЯ, ТЕХНОЛОГИЯ, МЕТОДОЛОГИЯ И ПРАКТИКА». Международная научно-практическая онлайн-конференция, приуроченная к 60-ти летию член-корреспондента Академии наук ЧР, доктора технических наук, профессора Сайд-Альви Юсуповича Муртазаева. Crossref, 2021. http://dx.doi.org/10.34708/gstou.conf..2021.76.13.002.

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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
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