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Simulation par éléments finis à partir de calculs ab-initio du comportement ferroélectrique

Abstract : Physicals properties of ferroelectric materials mainly arise from the fact that the polarizationis strongly influenced by strain and electrical boundary conditions, which may changeits orientation and magnitude. At small scales, this influence is even stronger and unusualdomain structures are produced like vortices in quantum dots or stripes in thin films. For thecalculation of domain structures, at small scales, first-principle-based effective Hamiltonianare widely used whereas at higher scales, continuum models are predominants. Nevertheless,in between there is no computational method connecting both scales. Therefore„ thegoal of this dissertation is to develop and build new approaches in order to bridge these twoseparated scales.Our model stems for classical effective Hamiltonian, written for barium titanate as afunction of the polarization and strain. This Hamiltonian is then formulated in order tocorrespond to a continuous description. Difficulties arise from non local interactions. In theend, the Hamiltonian is transformed into a set of partial differential equations describing theequilibrium and the boundary conditions. The temperature is then introduced in such a waythat makes evolve the coefficients of those sets of equations. We therefore reconstructed aLandu-like model.Such approach can be applied in quantum dots and thin films where the domain organizationdepend on the size. The results show how to apply finite element in order to obtainpatterns of polarizations with the wanted precision. The vortices shapes of domain patternin quantum dots is well reproduced. The stripes-like polarization pattern is also well reproducedin thin films. Besides expanding thickness of those films change the periodicity ofthose stripes, behaviour described by the Kittel law. This law is calculated and compared tomeasurements.
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Submitted on : Friday, December 10, 2010 - 10:42:16 AM
Last modification on : Wednesday, July 8, 2020 - 11:10:20 AM
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  • HAL Id : tel-00545426, version 1



David Albrecht. Simulation par éléments finis à partir de calculs ab-initio du comportement ferroélectrique. Autre. Ecole Centrale Paris, 2010. Français. ⟨NNT : 2010ECAP0007⟩. ⟨tel-00545426⟩



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