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The power of thermodynamics in the calculation of complex chemical and metallurgical equilibria of importance to industry has, over the last 15 years, been considerably enhanced by the availability of computers. It has resulted in the storage of data in databanks, the use of physical but complex models to represent thermodynamic data, the vast effort spent in the generation of critically assessed data and the development of sophisticated software for their application in equilibrium calculations. This thesis is concerned with the generation and application of metallurgical thermodynamic data in which the computer plays a central and essential role. A very wide range of topics have been covered from the generation of data by experiment and critical assessment through to the application of these data in calculations of importance to industry. Particular emphasis is placed on the need for reliable models and expressions which can represent the molar Gibbs energy as a function of temperature and composition. In addition a new computer program is described and used for the automatic calculation of phase diagrams for binary systems. Measurements of the enthalpies of formation of alloys in the Fe-Ti system are reported. All data for this system have been critically assessed to provide a dataset consistent with the published phase diagram. Critically assessed data for a number of binary alloy systems have been combined in order to perform quantitative calculations in two types of steel system. Firstly data for the Cr-Fe-Ni-Si-Ti system have been used to provide information about the long term stability of alloys used in fast breeder nuclear reactors. Secondly very complex calculations involving nine elements have been made to predict the distribution of carbon and various impurities between competing phases in low alloy steels on the addition of Mischmetall. Finally a new model is developed to represent the thermodynamic data for sulphide liquids and is used in the critical assessment and calculation of data for the Cu-Fe-Ni-S system. The phase diagram and thermodynamic data calculated from the assessed data are in excellent agreement with those observed experimentally. The work reported in this thesis, whilst successful, has also indicated areas which will benefit from further study particularly the development of reliable data and models for pure elements, ordered solid phases and liquid phases for high affinity systems.

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Understanding the fundamental mechanisms of solidification and the relative significance of different parameters governing these mechanisms is of vital importance for controlling the evolution of microstructure during solidification, and consequently, for improving the efficacy of a casting process. Towards achieving this goal, the present work attempts to study the effect of convection and shrinkage on solidification and microstructure formation primarily through the development of computational models which are complemented with experimental investigations and analytical solutions. Convection strongly influences the solutal and thermal distribution adjacent to the solidification interface and affects the growth rate and morphology of dendrites. To investigate this, a numerical model based on the enthalpy method is developed for binary alloy dendrite growth in presence of convection. The model results are validated with corresponding predictions using level-set method and micro-solvability theory. Subsequently, the model is applied for studying the effect of convection on the growth morphology of single dendrites. Results show that the presence of flow significantly affects the thermo-solutal distribution and consequently the growth rate and morphology of dendrites. Parametric studies performed using the model predict that thermal and solutal Peclet number and melt undercooling strongly influence the tip velocity of dendrites. Additionally, an analytical model is developed to quantify the effect of convection on dendrite tip velocity through the definition of an equivalent undercooling. An expression for this equivalent undercooling is derived in terms of the flow Nusselt and Sherwood numbers and the analytical equivalent undercooling values are compared with corresponding predictions obtained using the numerical model. Subsequently, the interaction of multiple dendrites growing in close proximity is studied. It is observed that the presence of neighbouring dendrites strongly influences the thermo-solutal distribution in the domain leading to significant changes in growth pattern. The effect of seed density on the growth morphology is investigated and it is observed that a higher initial seeding density leads to more spherical dendritic structure. Comparison with results from chilled casting of Al-6.5% Cu alloy with and without grain refiners show qualitative similarity in both the cases. The next part of the thesis presents a eutectic solidification model developed using the general enthalpy-based framework for dendritic solidification. New parameters and rules are defined and suitable modifications are made to incorporate the physics of eutectic solidification and account for the additional complexities arising due to the presence of multiple solid phases. The model simulates the presence of buoyancy driven convection and its interaction with the solidification process. i The model predictions are found to be in good agreement with the Jackson-Hunt theory. At first, the model is applied to simulate regular eutectic growth in a purely diffusive environment and it is observed that the model predicts the variation in interface profile with change in lamella width similar to those observed in experimental studies on eutectic solidification. Subsequently, a few case studies are performed to demonstrate the ability of the model in handling complex scenarios of eutectic growth such as width selection, lamella division and presence of solutal buoyancy. It is observed that solutal buoyancy gives rise to flow cells ahead of the eutectic interface facilitating the transfer of solute between the two phases. Apart from forced and natural convection, another important factor affecting solidification is the presence of shrinkage. Currently, solidification shrinkage is mostly modelled using empirical relations and criteria functions. In the present work, a phenomenological model for shrinkage driven convection is developed by incorporating the mechanism of solidification shrinkage in an existing framework of enthalpy based macro-scale solidification model. The effect of shrinkage flow on the free surface deformation is accounted for by using the volume-of-fluid method. The results predicted by the model are found to be in excellent agreement with analytical solutions for one-dimensional solidification with unequal phase densities. A set of controlled experiments are designed and executed for validating the numerical model. The experiments involve in-situ X-ray imaging of casting of pure aluminium in a rectangular cavity. The numerical predictions for solidification rate, free surface movement and temperature profiles are compared with corresponding experimental results obtained from the in-situ X-ray images and thermocouple data. Subsequent case studies, performed using the model, show significant influence of applied heat flux and mould geometry on the formation of shrinkage cavities. The shrinkage flow model provides the foundation for development of a generalized model to accurately predict the formation and morphology of internal porosity. The validated macro-scale shrinkage model is extended to the microscopic scale to study the influence of shrinkage flow on the growth rate of dendrites. Results demonstrate that shrinkage driven convection towards the dendrite strongly influences the solutal and thermal distribution adjacent to the solidification interface and consequently decreases the growth rate of the dendrite. Additionally, an analytical model is developed to quantify the effect of shrinkage driven convection through the definition of an equivalent undercooling for shrinkage flow. The present models provide significant physical insight into various mechanisms governing the process of solidification. Moreover, due to their similar framework, the individual models have the potential to be an effective foundation for the development of a generalized multi-scale solidification model incorporating the presence of important phenomena such as shrinkage and convection.

<p> This investigation is concerned with the development of a general ternary diffusion analysis for the diffusion-controlled oxidation of binary alloys based on the concept of local equilibrium and phenomenological diffusion theory and its application to appropriate experimental systems. </p> <p> The theoretical analysis is in two parts. In the first part diffusion equations for the alloy and oxide phases are obtained and tested against experiments for Ni-10.9% Co alloy at 1000°C. In the second part phenomena observed in binary alloy oxidation such as supersaturation, internal oxidation and morphological instability are qualitatively discussed and the concept ot the stationary diffusion path on the isotherm is applied to binary alloy oxidation. In general the ternary diffusion analysis satisfactorily accounts for the diffusion-controlled oxidation properties of several binary alloys. </p> <p> An experimental investigation of the oxidation of nickel-iron alloys at 1000°C is described. In the first part of the experimental investigation, thermodynamics of the ternary iron-nickel-oxygen system at 1000°C has been investigated in support of the oxidation studies. The second part is comprised of a detailed kinetic and metallographic study of nickel-iron alloys containing upto 25% iron exposed to oxygen atmospheres at 1000°C and determination of the metal concentration profiles in the oxide and alloy phases. The experimental results for these alloys are in good agreement with the theoretical calculations. </p> / Thesis / Doctor of Philosophy (PhD)

The primary focus of the present work is to model the entire casting process from filling stage to complete solidification. The model takes into consideration any phase change taking place during the filling process. An implicit volume of fluid (VOF) based algorithm has been employed for simulating free surface flows during the filling process and the model for solidification is based on a fixed-grid enthalpy-based control volume approach. Solidification modelling is coupled with VOF through User Defined Functions (UDF) developed in commercial fluid dynamics (CFD) code FLUENT 6.3.26. The developed model is applied for the simultaneous filling and solidification of pure metals and binary alloy systems to study the effects of filling process on the solidification characteristics, evolution of mushy zone and the final macrosegregation pattern in the casting. The numerical results of the present analysis are compared with the conventional analysis assuming the initial conditions to be a completely filled mould cavity with uniform temperature, solute concentration and quiescent melt inside the cavity. The effects of process parameters, namely the degree of superheat, cooling temperature and filling velocity etc. are also investigated. Results show significant differences on the evolution of mushy zone and macrosegregation between the present analysis and the conventional analysis. The application of present model to simulate three dimensional sand casting is also demonstrated. The three dimensional competetive effect of filling generated residual flow and the buoyancy-induced convective flow pattern cause significant difference in macrosegregation pattern in casting.

<p>Premelting is the formation of a thin, thermodynamically stable, liquid-like film at an interface for temperatures below the equilibrium melting temperature. Using a Monte Carlo technique, the underlying short range structural forces for premelting at the grain boundary can be directly calculated. This technique is applied to a (i) Σ9 ⟨115⟩ 120^o twist boundary and a (ii) Σ9 ⟨011⟩ {411} symmetric tilt boundary in an embedded atom model of Aluminum-Magnesium alloy. Both grain boundaries exhibit disordered structures near the melting point that depend on the concentration of Magnesium. The behavior is described quantitatively with sharp interface thermodynamics, involving an interfacial free energy that depends on width of the grain boundary, referred to as the disjoining potential. The disjoining potential calculated for boundary (i) displays a decreasing exponential dependence on width of the grain boundary, while the disjoining potential of (ii) features a weak attractive minimum. This work is discussed in relation to a previous study using pure Nickel, results of which can be useful to the theoretical study of thermodynamic forces underlying grain boundary premelting in an alloy.</p> / Master of Science (MSc)

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