Phase-field Models of Piezoelectric and Multiferroic Responses of Ferroelectric and Multiferroic Nanostructures

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TECHNICAL SUMMARYThis award supports theoretical and computational research on electro-magneto-mechanical couplings in ferroelectric and multiferroic nanostructures. Ferroelectrics and multiferroics are multi-functional materials that have many applications in devices such as actuators, sensors, and memory storage. The main objective of the project is to fundamentally understand the roles of mechanical and electrical boundary conditions in their ferroic responses. The focus is on the piezoelectric responses of nanoferroelectrics and the magnetoelectric coupling of self-assembled epitaxial nanocomposites of ferroelectric and ferromagnetic crystals. The phase-field approach will be employed in combination with mesoscale elasticity, electrostatic theory, and micromagnetics. The particular goals of the project are as follows:(1) The PI will develop and implement efficient numerical algorithms based on the spectral method for solving the phase-field, mechanical, electrostatic, and magnetostatic equations while taking into the appropriate electric and mechanical boundary conditions.(2) The PI will investigate the dependence of piezoelectric responses of ferroelectric nanostructures on substrate constraints as well as on the inhomogeneous stress distributions within a nanostructure due to presence of defects such as dislocations.(3) The PI will study the correlation between the multiferroic nanocomposite microstructure and the magnitude of magnetoelectric coupling effect. This research program involves active collaborations with applied mathematicians on the implementation of advanced numerical algorithms and with experimentalists on experimental validation of computational predictions and findings. The research under this award is expected to (i) significantly contribute to the fundamental understanding of the piezoelectric responses of nanoferroelectrics and magnetoelectric coupling effect of multiferroic nanocomposites, (ii) yield new phase-field formulations for modeling multiferroic domain structures, and (iii) produce advanced numerical algorithms for solving phase-field equations involving non-periodic boundary conditions. This award supports training graduate as well as undergraduate students through thesis and summer research. Software tools developed from the project will be incorporated into two graduate courses and an undergraduate course. The research findings will be disseminated to a wide audience through archival publications and conferences, review and overview papers, and active participation and lectures at interdisciplinary workshops. NON-TECHNICAL SUMMARYThis award supports theoretical and computational research on the properties and functionalities of ferroelectric and multiferroic oxides. Ferroelectrics and multiferroics are multi-functional materials that can produce two or more different types of responses when they are subjected to an external field. They have many potential applications in devices such as actuators, sensors, and computer memory storage. For example, a ferroelectric crystal can change both its shape and electric polarization when it is subject to an external mechanical stress. Electric polarization results when the negative electronic charge distribution is shifted from the positive charge distribution of the atomic nuclei in a crystal. In a multiferroic material, the magnitude and direction of both the magnetization and electric polarization can be altered by externally applying either an electric or a magnetic field. The research program has two main thrusts: The PI will investigate the so-called "piezoelectric response", which is related to the magnitude of the change in electric polarization under a mechanical stress or the degree of crystal shape deformation under an electric field. These effects will be examined in bulk ferroelectrics as well as in tiny structures of sizes that are approximately one billionth the size of the human hair. Secondly, the PI will investigate the so-called "magnetoelectric" coupling, which is related to the change in electric polarization under an applied magnetic field or the change in magnetization under an applied electric field. The PI will develop and apply various computational tools in these investigations. The overall goal is to optimize the multi-functionalities of such materials through computer simulations. The research program involves active collaborations with applied mathematicians on the implementation of advanced numerical algorithms and with experimentalists on experimental validation of computational predictions and findings.The project will contribute to human resource development by training graduate as well as undergraduate students through thesis and summer research. Software tools developed from the project will be incorporated into two graduate courses and an undergraduate course. The research findings will be disseminated to a wide audience through archival publications and conferences, review and overview papers, and active participation and lectures at interdisciplinary workshops.