The investigation of Ni2MnGa ferromagnetic shape memory alloys relies on accurate and complete phase diagrams for the various phase transitions these materials exhibit. However, very little work has been performed to investigate the high temperature order/disorder phase transitions. This project tries to fill some of the gap in the phase diagram through a systemic composition based investigation of Ni2-XMn1+XGa (X=-0.2, 0.0, 0.2, 0.8 and 1.0) using high temperature specific heat measurements. The work has produced a phase diagram in the composition range measured and demonstrated that the order/disorder transition temperatures and Curie temperatures follow the predicted trend as seen in similar studies of different alloy compositions. This work has also characterised the melt temperature of the five compositions measured. As part of the investigation of the high temperature phase transitions, a 'High Temperature Adiabatic Calorimeter' was developed, which was commissioned using four reference samples (copper, Stainless steel, graphite and molybdenum). The developed system used a linearly drifting baseline to improve the speed, accuracy and stability of the system. This modification to the standard adiabatic calorimeter measurement scheme required extensive development of the analysis techniques and development of new approaches (e.g. heating phase analysis and finite element modelling analysis). The system was demonstrated to operate well between room temperature and 1350 K, producing accurate specific heat data that compared well with the standard data for the commissioning samples. Due to time constraints this system was not used for the Ni2MnGa investigation.

Strix Ltd is the world leader in the manufacture of thermostatic controls for water boiling applications in the domestic appliance industry. At the heart of every control are one or more snap-action bimetal thermostatic switches called `blades'. In 2003, Strix Ltd manufactured over 100 million blades and demand is increasing. In this research finite element models have been used to simulate key stages of the blade manufacturing process and the subsequent measurement of the blade switching temperatures. The purpose of this research has been to identify sensitive material and manufacturing process parameters in order to gain an understanding of the observed process variability. There are two key stages within the blade manufacturing process; a high-speed metal forming stage, and a heat treatment stage. Only the metal forming stage is modelled in this work due to the time constraints of the project, however, suitable material models are produced for both stages. The material phenomena relevant to the blade manufacturing process are, elasticity, plasticity and creep. In the first part of this work a series of experiments have been carried out to characterise the relevant material behaviour; uni-axial tensile testing and Vickers hardness testing to characterise the elastic and plastic material parameters, and uni-axial creep testing to characterise creep behaviour of the two constituent bimetal alloys. A constitutive material model is developed; linear elasticity and classical metal plasticity are used to model strain-rate and temperature dependent elasticity and plasticity. Creep deformation mechanisms in metals and techniques for modelling creep are examined and a set of creep constitutive equations selected. The experimental data is used to calibrate the material model which is then implemented within the commercial finite element code `ABAQUS'. A novel and original technique is developed to enable the calibration of cold reduction and goods-in residual stress present within bimetal strip. The boundary conditions describing the interaction of the blade-forming press tool with the blade are investigated and defined. A finite element simulation of the blade metal forming process is then developed. The residual stresses present within the blade after each metal forming operation are evaluated and their compatibility with known process sensitivities examined. A finite element simulation of the blade temperature measurement process is developed using the results of the residual stress calculations from the blade metal forming simulation as input. The snap-through switching temperatures of the simulated blade are established and the stress state of the blade is evaluated to gain an understanding of the blade operating cycle. Sensitivity studies are carried out using the finite element models above to evaluate the impact of variation of material and metal forming process parameters on blade performance. Three sensitive metal forming process parameters, and two sensitive material parameters are identified and their relative sensitivities quantified. The results from the finite element models are then compared against experimental data to establish the accuracy and validity of the approach used. The sensitive parameters identified are examined to establish their compatibility with the top five problems experienced in normal blade production. Finally, the new understanding of the sensitive material and process parameters is used to formulate recommendations to improve current and future blade manufacturing processes within Strix.

The transport properties of the rare earth elements exhibit many interesting features, especially around the magnetic transition temperatures. The little data available on the thermal conductivity of the heavy rare earth metals cover mostly the high temperature range (5-300°K). The results reported at the lower end of this temperature range are unexpected, the thermal conductivity largely exceeding the value derived from the electrical conductivity via the Wiedemann-Franz law. For example, the Lorenz numbers given varied from 3 to 12 x 10^-8 watts- ohms- K^-2 (theoretical value 2.45 x 10^-8 watts- ohms-K^-2). These authors concluded that mechanisms of heat transport other than the usual dominant electronic term must also be present. Recently some anomalous results were reported for some of the heavy rare earths in the He⁴ temperature range and the results did not extrapolate to the origin at 0°K. These discrepancies and the hope that at sufficiently low temperatures a predominantly electronic thermal conductivity obeying Wiedemann-Franz law would emerge were good reasons for a detailed investigation down to a lower limit of temperature. In this thesis we present a systematic thermal conductivity study of the heavy rare earth metals in the temperature range 0.4 to 4.2°K. covered by two different cryostats - a He³ and a He⁴ cryostat. The specimens studied were gadolinium (2 samples), dysprosium (2 samples), holmium (2 samples), erbium (2 samples), terbium (1 sample) and ytterbium (1 sample). The results obtained by us show no anomaly and are very consistent. The thermal conductivity of all the specimens can be separated into a linear and a small quadratic term in temperature. Furthermore our results do not confirm the anomalously high Lorenz numbers previously referred to in the literature but when we relate the linear temperature dependence of the thermal conductivity to the residual electrical resistivity using Wiedemann-Franz law we obtain, for all the specimens, Lorenz numbers which are remarkably close to the theoretical value. We therefore conclude that the linear term represents an electronic contribution, with the electron mean free path limited by 'impurity' scattering. To account for the small quadratic contribution, we have invoked other carriers - phonons and magnons. We have observed this term in specimens which have spin waves and also in those which have no spin waves below 4°K. Further measurements were done to see the effects of dislocations on this small quadratic contribution. The results of these experiments lead us to believe that the major contribution to this quadratic term in thermal conductivity is due to phonon conduction limited by electron scattering. We may have not reached the upper limit, for there may be a little additional scattering of the phonons due to dislocations, which has the same temperature dependence. The thesis is divided into three chapters. In chapter one a brief account of the theory of thermal conduction in metals at low temperatures is presented. We have also given some magnetic properties of the rare earth ferromagnets in this chapter. The second chapter describes the He³ cryostat, which we designed and built for measuring the thermal conductivity below 1°K. Also discussed are the techniques used. Finally in the third chapter the results are discussed.

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In this thesis we study super-cooled liquids through simulations of hard interacting particles: hard disks in two dimensions, and hard spheres in three dimensions. These systems provide simple models of glass-forming liquids in general and are good models for colloidal glass-forming systems specifically. Whether static structure exists, and the nature of any collective motion are two key questions about super-cooled liquids. Both involve correlation, and this motivates us to use information theory: we use Shannon entropy and mutual information to provide general, unbiased measurements of disorder and correlation. We use mutual information to define an order agnostic order parameter in ther hard disk system and show that static correlations are short-ranged in these simulations. Many of the simulations described in this thesis are performed in the isoconfigurational ensemble. This technique gives access to probability distributions of particle trajectories conditioned on the initial system configuration. By using information theory to investigate these distributions we are able to answer questions about predictability in quantitative terms. We measure the predictability of the dynamics of our hard sphere system; then, by classifying the structure of the initial configuration, we search for the salient features that have predictive power over the dynamics. We find that classifying the initial configuration in terms of geometrical motifs and local volume fraction gives some predictive power. By using information theory to quantify dynamic correlations between particles we show that this predictivity exists because the initial configuration specifies the positions of early-relaxing particles and slow-relaxing relatively stable regions. Most particles belong to neither of these regions and are presumably responsible for the unpredictable behaviour of the system. The final results chapter in this thesis measures changes in shape of the dynamical regions in our model systems using fractal dimension.

In this second part of the thesis, we turn to the study of thermodynamics at the quantum scale, with a special focus on small thermal machines. To begin with, in Chapter 4, we look at the concept of a virtual temperature, as introduced in [43]. This is a temperature calculated for any pair of energy levels in a diagonal state by matching the ratio of its populations to the Gibbs state. The small quantum fridge introduced in Chapter 5, as well as all of the other small quantum thermal machines may be understood in terms of the virtual temperatures that they are able to generate within a system. We use the concept of virtual temperatures to construct an elegant and illuminating proof of the notion of complete passivity. A passive state [44] is one from which no work may be extracted from a unitary, while complete passivity refers to the property that no work can be extracted from multiple copies of a state.

Molecular dynamics simulation was used to study and to estimate the effect of thermally resistive mechanisms in non-metallic crystalline solids. The first part of this work focused on line dislocations parallel to the heat flow. At a dislocation density of 1013 cm-2 , edge dislocations caused by an extra half-plane of atoms parallel to the heat flow were found to reduce the thermal conductivity of gallium nitride to 54% of the defect-free value. Using an extrapolation procedure, at dislocation densities of 1012 and 1011 cm-2 , the conductivity was estimated to be 82% and 98% of the defect-free value respectively. For a dislocation density of 2 x 1012 cm-2 , open-core screw dislocations were found to cause a greater reduction, by a factor of about 1.2. These results suggest that, in principle, dislocations parallel to the heat flow can have a significant impact on the thermal conductivity only when the dislocation density is very high.

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