Modelling Magnetic Phase Transitions

with Density Functional Theory and the Finite Element Method

Bachelor thesis (2019)

Authors

M. van Diepen Applied Sciences

Contributors

N.H. van Dijk RST/Fundamental Aspects of Materials and Energy - AS (supervisor 1)
F.J. Vermolen Numerical Analysis - EEMCS (supervisor 1)
Faculty
Applied Sciences
Copyright: © 2019 Mischa van Diepen
Finite Element Method Magetic phase transitions Curie Temperature Density Funtional Theory
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Published Date

04-07-2019

Language

English

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Faculty

Applied Sciences

Abstract

The present thesis discusses two modelling endeavours that serve to provide insights into both the magnetic and structural dynamics associated with a first order magnetic phase transition.
Firstly, density functional theory has been used to model the lithiation of a supercell of 2x2x2 the conventional unit cell of the ferromagnet Fe2P. Subsequently, the magnetic moments in the resulting structure were set to proxy a paramagnetic state and compute the energy difference between the ferromagnetic and paramagnetic state. It has been found that non-magnetic Li-atoms substitute for magnetic Fe-atoms at 3g-positions in the a,b-plane. Moreover, since these are the positions of Fe-atoms that carry a high magnetic moment and induce a magnetic moment on the Fe-atoms in the 3f-layer, the lithiation of the respective positions leads to a reduction of the magnetic moment per formula unit. The energy difference between the ferromagnetic state and the selected proxy of a paramagnetic state showed to decrease linearly in the fraction of lithiated 3g-positions. This deviates from experimental findings suggesting an increase of Tc of the structure upon lithiation. This difference can stem from the fact that the lithiation fractions considered here were higher than those achieved experimentally or that the selected proxy of a paramagnetic state was incorrect.
Secondly, the finite element method has been applied to approximate the displacement field of a 2D structure consisting of grains distributed over two structural phases with different associated lattice parameters. The development of shear stress discontinuities across grain boundaries has been studied in relation to the degree of porosity in a domain. The replacement of grain boundaries by voids appears, after correction for the orientation of edges at these grain boundaries, to lead to a reduction in the values for these discontinuities. More delicate development of the grid to correspond to physically realistic orientations of grain boundaries is needed to gain more robust quantitative measures for this relation. Moreover, the relation between the orientation of grain boundaries and shearing stresses at these boundaries forms an interesting venue for further research to which the present FEM-model can be readily applied.