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| Effect of elastic domains on electromechanical response of epitaxial ferroelectric films with a three-domain architecture |
| Jun OUYANGa*,Wei ZHANGa,S. Pamir ALPAYb,Alexander L. ROYTBURDc* |
aKey Laboratory for Liquid–Solid Structural Evolution and Processing of Materials (Ministry of Education), Engineering Ceramics Laboratory, School of Materials Science and Engineering, Shandong University, Jinan 250061, Shandong, China bMaterials Science and Engineering Program and Institute of Materials Science, University of Connecticut, Storrs 06269, Connecticut, USA cDepartment of Materials Science and Engineering, University of Maryland, College Park 20742, Maryland, USA |
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Abstract Thermodynamics of (001) epitaxial ferroelectric films completely relaxed due to the formation of elastic domains with a three-domain architecture is presented. The polydomain structure and electromechanical response of such films are analyzed for two cases corresponding to immobile and mobile elastic domain walls. It is shown that immobile elastic domains provide additional constraint which increases the mechanical and electrical clamping, thereby significantly reducing the piezoelectric and dielectric responses. On the other hand, a polydomain ferroelectric film adapts to the variations in the applied electric field by reversible domain wall displacements in the case of mobile domain walls. The comparison of the theory with experiments shows that the elastic domain walls are mobile in the fully relaxed films of ~ 1?μm thickness. In addition, if the substrate constraint is reduced via decreasing lateral size of a polydomain ferroelectric film, its piezoresponse will increase dramatically, as is experimentally verified on small islands of polydomain ferroelectric films. The general conclusions can be readily applied to other constrained polydomain films.
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Received: 28 January 2013
Published: 15 September 2015
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Corresponding Authors:
Jun OUYANG,Alexander L. ROYTBURD
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(a) From left to right, the cubic paraelectric phase, the three ferroelectric tetragonal variants, and the atomic force microscopy image of the cellular domain structure existing in PZT thick films; (b) schematic evolution of the domain architecture as a function of the a-domain fraction; (c) phase–field modeling of domain evolution.
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α0*) as functions of zirconium content in tetragonal PbZrxTi1-xO3 solid solutions.">
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Variations in δ and equilibrium c-domain fraction (1-α0*) as functions of zirconium content in tetragonal PbZrxTi1-xO3 solid solutions.
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Two different cases showing schematic domain arrangements due to the applied electric field E: (a) immobile 90° domain walls and (b) mobile 90° domain walls, with 180° domain walls within the polydomains adjust to E. The arrows in the domains represent the polarization vectors.
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d33f(Δα=0)/d33 as a function of the a-domain fraction α0 and ξ.">
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Normalized piezomodulus of the constrained film d33f(Δα=0)/d33 as a function of the a-domain fraction α0 and ξ.
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| Thickness (nm) | Substrate | a-domain fraction (%) | d33 predicted by theory (pm/V) | d33 in experiment (pm/V) | | Intrinsic | Extrinsic | Total | Film | Island | | 1000 | SrTiO3 | 50 | 20 | 58 | 78 | 60 [13] | 100–250 [13] | | 1000 | Si | 60 | 14 | 64 | 78 | 50 [23] | 100–400 [23] |
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Piezomoduli d33 of epitaxial polydomain Pb(Zr0.2Ti0.8)O3 films
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