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A Phase-Field Model for Inhomogeneous Multiferroic Materials

Jafari, Bahram | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53084 (07)
  4. University: Sharif University of Technology
  5. Department: Materials Science and Engineering
  6. Advisor(s): Tavakoli, Rouhollah
  7. Abstract:
  8. In this thesis, by deliberately embedding “emplacements” in the system to locally break the inversion and the time reversal symmetries, the manifold of all possible microstructures is navigated in pursuit of the one that can give rise to maximal magnetoelectric effect mediated by elastic energy of piezoelectric-piezomagnetic phases via their interface --- needless to mention the low intensity of such an effect in single-phase multiferroics. The configuration with the maximal coupling is sought within the context of phase-field modeling. In order to numerically track the conserved dissipative dynamics of the interface (namely, the Cahn-Hilliard equation) --- that is nonlocal by the nature of the long-range interactions --- in a semi--energy-stable scheme and by means of Fourier spectral methods, we managed to discover periodic rod-shaped configurations in lower volume fractions other than those layered microstructures predicted by Y. Ni and A. G. Khachaturyan (2007) in equal volume fractions of piezoelectric and piezomagnetic phases. It was of pivotal importance not to think of the phase-field modeling as a mere computational getaway from the otherwise costly sharp-interface approach, but to be cognizant of its physical meaning and the physics of the energy functional. Since the pertinent field theory should interweave electrostatics, magnetoestatics and micro-elasticity, an apt statistical ensemble should be sought in which not only is the effective Hamiltonian functional thermodynamically stable, it also respects Maxwell's equations that describe the state of the very system, as one anticipates from coarse-graining a microscopic Hamiltonian. A large portion of the thesis is allocated to justify and expound on the corresponding effective field theory, together with the thermodynamics of magnetoelectroelastic materials and exploring the best suited functional describing them in different ensembles. Many of the assertions are made by addressing statistical field theory
  9. Keywords:
  10. Multiferroic ; Composite ; Phase Field Model ; Effective Field Theory ; Electrostatic ; Magnetostatic ; Piezomagnetic ; Piezoelectric ; Landa Dynamics Method

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