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Phase-Field Modeling of Relaxor Ferroelectrics and Related Composites

Wang, Shuai (2019):
Phase-Field Modeling of Relaxor Ferroelectrics and Related Composites.
Darmstadt, Technische Universität, [Online-Edition: https://tuprints.ulb.tu-darmstadt.de/8383],
[Ph.D. Thesis]

Abstract

In the 1950s, relaxor ferroelectrics or relaxors were discovered and have lately received a renewed interest in condensed matter physics. Despite the fact that the physical interpretation of the relaxors remains the subject of controversy, their extraordinary electromechanical properties and the resultant potential applications in industries have motivated a vast amount of theoretical studies on different aspects.

In this thesis, based on the random field theory, an electromechanically fully coupled phase-field model is proposed to simulate the peculiar behavior of the relaxor ferroelectrics. The model introduces a quenched local random field to characterize the effect of the chemical disorder. By treating the spontaneous polarization as an independent order parameter and the random field as an internal microforce, a thermodynamic analysis is performed. The deduced nonlinear constitutive and evolution equations are further discretized by the finite element method. Numerical examples show that the model can reproduce typical relaxor features, such as the miniaturization of domain size, the reduction of remanent polarization, and the enhancement of large-signal piezoresponse. The influence of the random field strength on the domain structure and the hysteresis loops is also revealed and validated with the related experimental results.

Subsequently, the phase-field model of relaxors, in combination with the conventional ferroelectric model is applied to analyze the large-signal piezoresponse for relaxor-based composites. More specifically, a series of simulations are presented for the relaxor/ferroelectric layer composites with different types of interfaces. The results confirm that the lateral strain coupling, in addition to the polarization coupling, contributes considerably to the large-signal piezoelectric coefficient. The lateral strain mismatch lowers the remanent strain in the ferroelectric layer and thus increases the macroscopic piezoelectric response. It is worth to be highlighted that the composition ratio of the relaxor constituent is optimized for different electric loadings. The composites with higher relaxor content are inclined to obtain higher large-signal piezoresponse with the increase of the applied electric field. These results can be referred in the future design of high-performance relaxor-based composites.

Finally, the core-shell structures in relaxors, as well as the associated microscale features and mechanisms are explored by the combined ferroelectric-relaxor-flexoelectric phase-field simulations. For BNT-25ST at room temperature, it is found that the increased electric potential beneath the core is responsible for the in-plane domain evolution. The resultant field-induced domains at the coherent core-shell interface play an important role in enhancing the polarization in the non-polar shell region and thus promoting the giant strain.Moreover, at an extreme temperature of 800 degree Celsius, the domain-like nanoregions found in BNT-25ST core-shell nanoparticle are attributed to the flexoelectric effect, where the strain gradient is believed to originate from the Vegard effect. This hypothesis is verified by the comparison between the simulation and experimental results on the electric field mediated redistribution of the polarization.

Item Type: Ph.D. Thesis
Erschienen: 2019
Creators: Wang, Shuai
Title: Phase-Field Modeling of Relaxor Ferroelectrics and Related Composites
Language: English
Abstract:

In the 1950s, relaxor ferroelectrics or relaxors were discovered and have lately received a renewed interest in condensed matter physics. Despite the fact that the physical interpretation of the relaxors remains the subject of controversy, their extraordinary electromechanical properties and the resultant potential applications in industries have motivated a vast amount of theoretical studies on different aspects.

In this thesis, based on the random field theory, an electromechanically fully coupled phase-field model is proposed to simulate the peculiar behavior of the relaxor ferroelectrics. The model introduces a quenched local random field to characterize the effect of the chemical disorder. By treating the spontaneous polarization as an independent order parameter and the random field as an internal microforce, a thermodynamic analysis is performed. The deduced nonlinear constitutive and evolution equations are further discretized by the finite element method. Numerical examples show that the model can reproduce typical relaxor features, such as the miniaturization of domain size, the reduction of remanent polarization, and the enhancement of large-signal piezoresponse. The influence of the random field strength on the domain structure and the hysteresis loops is also revealed and validated with the related experimental results.

Subsequently, the phase-field model of relaxors, in combination with the conventional ferroelectric model is applied to analyze the large-signal piezoresponse for relaxor-based composites. More specifically, a series of simulations are presented for the relaxor/ferroelectric layer composites with different types of interfaces. The results confirm that the lateral strain coupling, in addition to the polarization coupling, contributes considerably to the large-signal piezoelectric coefficient. The lateral strain mismatch lowers the remanent strain in the ferroelectric layer and thus increases the macroscopic piezoelectric response. It is worth to be highlighted that the composition ratio of the relaxor constituent is optimized for different electric loadings. The composites with higher relaxor content are inclined to obtain higher large-signal piezoresponse with the increase of the applied electric field. These results can be referred in the future design of high-performance relaxor-based composites.

Finally, the core-shell structures in relaxors, as well as the associated microscale features and mechanisms are explored by the combined ferroelectric-relaxor-flexoelectric phase-field simulations. For BNT-25ST at room temperature, it is found that the increased electric potential beneath the core is responsible for the in-plane domain evolution. The resultant field-induced domains at the coherent core-shell interface play an important role in enhancing the polarization in the non-polar shell region and thus promoting the giant strain.Moreover, at an extreme temperature of 800 degree Celsius, the domain-like nanoregions found in BNT-25ST core-shell nanoparticle are attributed to the flexoelectric effect, where the strain gradient is believed to originate from the Vegard effect. This hypothesis is verified by the comparison between the simulation and experimental results on the electric field mediated redistribution of the polarization.

Place of Publication: Darmstadt
Divisions: 11 Department of Materials and Earth Sciences
11 Department of Materials and Earth Sciences > Material Science
11 Department of Materials and Earth Sciences > Material Science > Mechanics of functional Materials
11 Department of Materials and Earth Sciences > Material Science > Nonmetallic-Inorganic Materials
Exzellenzinitiative
Exzellenzinitiative > Graduate Schools
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Date Deposited: 10 Feb 2019 20:55
Official URL: https://tuprints.ulb.tu-darmstadt.de/8383
URN: urn:nbn:de:tuda-tuprints-83837
Referees: Xu, Prof. Dr. Bai-Xiang and Kleemann, Prof. Dr. Wolfgang
Refereed / Verteidigung / mdl. Prüfung: 16 January 2019
Alternative Abstract:
Alternative abstract Language
Relaxor-Ferroelektrika (Relaxoren) wurden in den 1950er Jahren entdeckt und haben erneut Interesse in der Physik der kondensierten Materie erhalten. Trotz der Tatsache dass die physika- lische Deutung der Relaxoren ein Streitgegenstand bleibt, motivierten die außergewöhnlichen elektro-chemischen Eigenschaften sowie die sich daraus ergebenden potenziellen Anwendungs- gebiete in der Industrie eine Vielzahl an Studien zu verschiedenen Aspekten. Auf der Zufallsfeldtheorie basierend wird in der vorliegenden Arbeit erstmalig ein voll elek- tromechanisch gekoppeltes Phasenfeldmodell vorgestellt, um das sonderbare Verhalten der Re- laxoren zu simulieren. Dabei wird ein lokales Zufallsfeld eingeführt, um den Effekt der chemi- schen Fehlordnung zu charakterisieren. Desweiteren wird eine thermodynamische Analyse un- ternommen, bei der die spontane Polarisierung als ein unabhängiger Ordnungsparameter und das Zufallsfeld als eine interne Mikrokraft behandelt werden. Die resultierenden nichtlinearen Material- und Evolutionsgleichungen werden anschließend mit der Finite-Elemente-Methode diskretisiert. Numerische Simulationen zeigen, dass dieses Modell die Merkmale von Relaxoren wiedergeben kann, beispielsweise die Miniaturisierung der Domänengröße, die Reduzierung der remanenten Polarisierung und die Verstärkung der Großsignal-Piezo-Antwort. Es wird insbeson- dere der Einfluss der Zufallsfeldstärke auf die Domänenstruktur und die Hysteresen diskutiert und durch Versuchsergebnisse validiert. Im nächsten Schritt wird das Phasenfeldmodell zusammen mit dem Modell für herkömmliche Ferroelektrika auf die Analyse und das Design der Relaxor-basierten Verbundwerkstoffe ange- wandt. In diesem Zusammenhang wird eine Reihe von Simulationen für die ferroelektrischen Verbundwerkstoffe mit verschiedenen Typen der Grenzschicht ausgeführt. Die Ergebnisse be- stätigen, dass zusätzlich zur Polarisierungskopplung, die laterale Verzerrungskopplung einen beachtlichen Beitrag zum Groçsignal-Deformationskoeffizienten liefert. Die laterale Verzer- rungsfehlanpassung senkt die remanente Verzerrung in der ferroelektrischen Schicht und erhöht dadurch die makroskopische piezoelektrische Reaktion. Erwähnenswert ist die Optimierung der Zusammensetzungsverhältnise der Relaxoren in Be- zug auf verschiedene elektrische Ladungen. Besonders die Verbundwerkstoffe mit einem höhe- ren Gehalt an Relaxor sind geneigt, erhöht Großsignalige-Piezo-Antwort für höhere elektrische Felde zu erhalten. Diese Erkenntnisse können in die weitere Entwicklung von Relaxoren und ferroelektrische Verbundwerkstoffe mit verbesserter Leistung einfließen. Abschließend werden die core-shell-Strukturen in Relaxoren sowie die assoziierten mikros- kaligen Merkmale und Mechanismen durch kombinierte ferroelektrisch-relaxor-flexoelektrische Phasenfeldsimulationen untersucht. Bei Raumtemperatur wird für BNT-25ST festgestellt, dass das erhöhte elektrische Potenzial unterhalb des Kerns für die Domänenentwicklung in der Ebene verantwortlich ist. Die resultierenden Feld-induzierten Domänen am kohärenten Core-Shell-Interface spielen eine wichtige Rolle für die Steigerung der Polarisation in der nonpolaren Schalenregion und damit für die Erzeugung großer Verzerrungen. Für die extrem hohen Tem- peraturen von 800 ◦C lassen sich die domänenartigen Nanoregionen in BNT-25ST core-shell- Nanopartikeln zurückführen auf den flexoelektrischen Effekt, wobei der Verzerrungsgradient seinen Ursprung wohl im Vegard-Effekt besitzt.German
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