Elastic Heterophase Domains in Ferroelectric Epitaxial Films
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Elastic Heterophase Domains in Ferroelectric Epitaxial Films A. L. Roytburd1,*, J. Ouyang2,*, B. M. Boyerinas1, H. A. Bruck1, J. Slutsker1, A. Artemev3 1 University of Maryland, College Park, MD 20742, U. S. A. 2 Key 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, Shandong 250061, People’s Republic of China 3 Carleton University, Ottawa, ON KIS 5B6, Canada. *: Corresponding authors: [email protected], [email protected]. ABSTRACT A heterophase polydomain structure has been recently discovered in BiFeO3 epitaxial ferroelectric films, which provides large electromechanical responses. In this work, the formation of such a microstructure is explained by theory of elastic domains. The thermodynamics of the heterophase polydomain microstructure is analyzed to predict the equilibrium volume fraction of domains at different film-substrate lattice misfits. Extrinsic mechanical and piezoelectric properties are discussed for the heterophase polydomains. It is shown that an applied electric field, which increases electrostatic interaction between domains, may lead to dramatic increase of piezo response. The results of this work are in good agreement with experimental data for BiFeO3. INTRODUCTION Polydomain structures consisting of elastic domains are a typical phenomenon in solids undergoing phase transformations.[1,2] Relaxation of internal stresses arising in the course of mechanically constrained transformations results in formation of modulated arrangement of differently oriented domains of the same phase (twins) or domains of different phases. The trend to minimize the elastic energy of internal stresses can lead to appearance of phases which do not exist in stress-free solids.[3] A constraint effect can be used to design polydomain structures in epitaxial films. Theoretical prediction of the formation of polydomain structures consisting of twin domains and heterophase domains in epitaxial films was made in 1976.[4] There have been numerous theoretical and experimental studies of polytwin epitaxial films, making these structures a well established phenomenon.[5] The theory and modeling of the formation and evolution of heterophase polydomain structures during polymorphic transformation has also been developed.[6-8] However, there are only few experimental observations of these structures.[9,10] Therefore, a recent discovery of a rhombohedral-tetragonal (R-T) polydomain structure in epitaxial ferroelectric BiFeO3 films [11] is especially important for verification of the theory of heterophase domains and its expansion to ferroic films. The task of this paper is to determine equilibrium heterophase and ferroelectric domain structures in epitaxial films depending on filmsubstrate misfit and estimate their response to external fields due to domain interface movement. In the absence of external electric field, internal long range electrostatic field in ferroelectri
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