de Haan, Hendrick

In electron-doped ferroelectrics, the free electrons can become concentrated along the domain walls which act like a conducting surface. We consider the impact of free electrons occupying the t2g orbitals on the domain walls of an electron-doped perovskite ferroelectric. We build an analytical model based on Landau-Ginzburg-Devonshire theory, and a trio of tight-binding Hamiltonians for free electrons. We self-consistently solve for the polarization, potential, and electron density using a finite-difference approximation. We find that the ferroelectric is effectively charge neutral. The free electrons are attracted to the positively-charged domain wall, leaving it with a small residual charge. As the electron density increases, the domain walls tilt to form zig-zag domain walls. Orbital selectivity of the t2g orbitals depends on the relative orientations of the orbital plane and the domain wall. This property influences the rate at which the domain wall tilts as a function of the electron density.

Author Keywords: Charged Domain Wall, Domain Wall, Ferroelectric, Landau-Ginzburg, Perovskite, Strontium Titanate

The appearance of a two-dimensional electron gas (2DEG) in oxide interfaces between strontium titanate (STO) and other materials has become a major area of study. The behaviour of the 2DEG in STO is not well understood in part because the dielectric properties of STO are not well characterized. The differential susceptibility has a major impact on the electric fields within strontium titanate, and therefore to understand the 2DEG a better understanding of the susceptibility is needed. An expression for the soft mode phonon frequency of bulk strontium titanate is derived and used to model the susceptibility as a function of spatially homogeneous electric field, temperature and wavevector. This model is used to discuss the effect of spatially inhomogeneous electric fields and the local vs. nonlocal nature of the susceptibility. The critical exponents and the free energy are determined and discussed.

Author Keywords: critical exponents, differential susceptibility, quantum paraelectric, strontium titanate

The human cornea is required to exhibit specific material properties to maintain its regular shape under typical intraocular pressures which then allow for its correct optical functionality. In this thesis, the basis of continuum solid mechanics and the finite element method are introduced. We use finite element modelling to simulate the extension of an effective-1d, linear-elastic bar, a cornea-like body governed by Poisson's equation, and the deformation of a loaded, linear-elastic, cube. Preliminary results for the deformation of a simulated, linear-elastic, cornea have also been achieved using the finite element approach.

Author Keywords: continuum solid mechanics, corneal biomechanics, finite element method, intraocular pressure

In 2004 it was discovered that a two-dimensional electron gas (2DEG) forms at the interface between lanthanum aluminate (LAO) and strontium titanate (STO). This 2DEG exhibits a variety of electronic and magnetic phenomena, motivating intense research into its applicability to electronic devices. Over the years several models have been developed in theoretical exploration of this system. Here, the transverse Ising model is applied to the LAO/STO interface for the first time. It is shown that the model as it is traditionally formulated cannot accurately predict the structure of the electron density at the interface. I show that this can be fixed with a simple modification of the model, and discuss how this modification affects both the polarization distribution in ferroelectric thin films and the electron density at the LAO/STO interface. The importance of including the depolarizing field when modelling spatially inhomogeneous ferroelectric systems is also explored.

Author Keywords: ferroelectric thin film, lanthanum aluminate, strontium titanate, transverse Ising model, two-dimensional electron gas