Evaporation maps for ternary non-ideal liquid mixtures

This thesis deals with the evaporation of non-ideal liquid mixtures using a multicomponent mass transfer approach. It develops the concept of evaporation maps as a convenient way of representing the dynamic composition changes of ternary mixtures during an evaporation process. Evaporation maps represent the residual composition of evaporating ternary non-ideal mixtures over the full range of composition, and are analogous to the commonly-used residue curve maps of simple distillation processes. The evaporation process initially considered in this work involves gas-phase limited evaporation from a liquid or wetted-solid surface, over which a gas flows at known conditions. Evaporation may occur into a pure inert gas, or into one pre-loaded with a known fraction of one of the ternary components. To explore multicomponent masstransfer effects, a model is developed that uses an exact solution to the Maxwell-Stefan equations for mass transfer in the gas film, with a lumped approach applied to the liquid phase. Solutions to the evaporation model take the form of trajectories in temperaturecomposition space, which are then projected onto a ternary diagram to form the map. Novel algorithms are developed for computation of pseudo-azeotropes in the evaporating mixture, and for calculation of the multicomponent wet-bulb temperature at a given liquid composition. A numerical continuation method is used to track the bifurcations which occur in the evaporation maps, where the composition of one component of the pre-loaded gas is the bifurcation parameter. The bifurcation diagrams can in principle be used to determine the required gas composition to produce a specific terminal composition in the liquid. A simple homotopy method is developed to track the locations of the various possible pseudo-azeotropes in the mixture. The stability of pseudo-azeotropes in the gas-phase limited case is examined using a linearized analysis of the governing equations. Algorithms for the calculation of separation boundaries in the evaporation maps are developed using an optimization-based method, as well as a method employing eigenvectors derived from the linearized analysis. The flexure of the wet-bulb temperature surface is explored, and it is shown how evaporation trajectories cross ridges and valleys, so that ridges and valleys of the surface do not coincide with separation boundaries. Finally, the assumption of gas-phase limited mass transfer is relaxed, by employing a model that includes diffusion in the liquid phase. A finite-volume method is used to solve the system of partial differential equations that results. The evaporation trajectories for the distributed model reduce to those of the lumped (gas-phase limited) model as the diffusivity in the liquid increases; under the same gas-phase conditions the permissible terminal compositions of the distributed and lumped models are the same.

A tight-binding analysis of the electronic properties of III-nitride semiconductors

This thesis divides into two distinct parts, both of which are underpinned by the tight-binding model. The first part covers our implementation of the tight-binding model in conjunction with the Berry phase theory of electronic polarisation to probe the atomistic origins of spontaneous polarisation and piezoelectricity as well as attempting to accurately calculate the values and coefficients associated with these phenomena. We first develop an analytic model for the polarisation of a one-dimensional linear chain of atoms. We compare the zincblende and ideal wurtzite structures in terms of effective charges, spontaneous polarisation and piezoelectric coefficients, within a first nearest neighbour tight-binding model. We further compare these to real wurtzite structures and conclude that accurate quantitative results are beyond the scope of this model but qualitative trends can still be described. The second part of this thesis deals with implementing the tight-binding model to investigate the effect of local alloy fluctuations in bulk AlGaN alloys and InGaN quantum wells. We calculate the band gap evolution of Al1_xGaxN across the full composition range and compare it to experiment as well as fitting bowing parameters to the band gap as well as to the conduction band and valence band edges. We also investigate the wavefunction character of the valence band edge to determine the composition at which the optical polarisation switches in Al1_xGaxN alloys. Finally, we examine electron and hole localisation in InGaN quantum wells. We show how the built-in field localises the carriers along the c-axis and how local alloy fluctuations strongly localise the highest hole states in the c-plane, while the electrons remain delocalised in the c-plane. We show how this localisation affects the charge density overlap and also investigate the effect of well width fluctuations on the localisation of the electrons.