Nuclear and gas turbine power plants, computer chips, and other devices and industries are running hotter than ever for longer than ever. With no apparent end to the trend, the potential arises for a phenomenon known as thermotransport to cause undesirable changes in these high temperature materials. The diffuse-interface method known as the phase-field model is a useful tool in the simulation and prediction of thermotransport driven microstructure evolution in materials. The objective of this work is to develop a phase-field model using practical and empirical properties of thermodynamics and kinetics for simulating the interdiffusion behavior and microstructural evolution of single and multiphase binary alloy system under composition and/or temperature gradients. Simulations are carried out using thermodynamics and kinetics of real systems, such as the U-Zr solid metallic fuel, with emphasis on the temperature dependencies of the kinetics governing diffusional interactions in single-phase systems and microstructural evolution in the presence of multiple driving forces in multi-phase systems. A phase field model is developed describing thermotransport in the γ phase of the U-Zr alloy, a candidate for advanced metallic nuclear fuels. The model is derived using thermodynamics extracted from the CALPHAD database and temperature dependent kinetic parameters associated with thermotransport from the literature. Emphasis is placed upon the importance of the heat of transport, Q*, and atomic mobility, β. Temperature dependencies of each term are estimated from empirical data obtained directly from the literature, coupled with the textbook phenomenological formulae of each parameter. A solution is obtained via a finite volume approach with the aid of the FiPy® partial differential equation solver. Results of the simulations are described based on individual flux contributions from the gradients of both composition and temperature, and are found to be remarkably similar to experimental results from the literature. iv In an additional effort the thermotransport behavior of a binary two-phase alloy is modeled, for the first time, via the phase-field method for a two-phase (γ + β) U-Zr system. The model is similarly built upon CALPHAD thermodynamics describing the γ and β phases of the U-Zr system and thermotransport parameters for the γ phase from literature. A parametric investigation of how the heats of transport for U and Zr in the β phase affect the redistribution is performed, and the interplay between system kinetics and thermodynamics are examined. Importantly, a strict control over the microstructure that is placed into the temperature gradient ( ) is used to eliminate the randomness associated with microstructural evolution from an initially unstable state, allowing an examination of exactly how the β phase thermotransport parameters affect the redistribution behavior of the system. Results are compared to a control scenario in which the system evolves only in the presence of thermodynamic driving forces, and the kinetic parameters that are associated with thermotransport are negligible. In contrast to the single-phase simulations, in the presence of a large thermodynamic drive for phase transformation and stability, the constituent redistribution caused by the thermotransport effect is comparatively smaller.

The diffuse-interface phase-field model is a powerful method to simulate and predict mesoscale microstructure evolution in materials using fundamental properties of thermodynamics and kinetics. The objective of this dissertation is to develop phase-field model for simulation and prediction of interdiffusion behavior and evolution of microstructure in multiphase binary and ternary systems under composition and/or temperature gradients. Simulations were carried out with emphasis on multicomponent diffusional interactions in single-phase system, and microstructure evolution in multiphase systems using thermodynamics and kinetics of real systems such as Ni-Al and Ni-Cr-Al. In addition, selected experimental studies were carried out to examine interdiffusion and microstructure evolution in Ni-Cr-Al and Fe-Ni-Al alloys at 1000°C. Based on Onsager’s formalism, a phase-field model was developed for the first time to simulate the diffusion process under an applied temperature gradient (i.e., thermotransport) in single- and two-phase binary alloys. Development of concentration profiles with uphill diffusion and the occurrence of zeroflux planes were studied in single-phase diffusion couples using a regular solution model for a hypothetical ternary system. Zero-flux plane for a component was observed to develop for diffusion couples at the composition that corresponds to the activity of that component in one of the terminal alloys. Morphological evolution of interphase boundary in solid-to-solid two-phase diffusion couples (fcc-γ vs. B2-β) was examined in Ni-Cr-Al system with actual thermodynamic data and concentration dependent chemical mobility. With the instability introduced as a small initial compositional fluctuation at the interphase boundary, the evolution of the interface morphology was found to vary largely as a function of terminal alloys and related composition-dependent chemical mobility. In a binary Ni-Al system, multiphase diffusion couples of fcc-γ vs. L12-γ′, γ vs. γ+γ′ and γ+γ′ vs. γ+γ′ were simulated with alloys of varying compositions and volume fractions of second phase (i.e., γ′). Chemical mobility as a function of composition was employed in the study with constant gradient energy coefficient, and their effects on the final interdiffusion microstructure was examined. Interdiffusion microstructure was characterized by the type of boundaries formed, i.e. Type 0, Type I, and Type II boundaries, following various experimental observations in literature and thermodynamic considerations. Volume fraction profiles of alloy phases present in the diffusion couples were measured to quantitatively analyze the formation or dissolution of phases across the boundaries. Kinetics of dissolution of γ′ phase was found to be a function of interdiffusion coefficients that can vary with composition and temperature. The evolution of interdiffusion microstructures in ternary Ni-Cr-Al solid-to-solid diffusion couples containing fcc-γ and γ+β (fcc+B2) alloys was studied using a 2D phase-field model. Alloys of varying compositions and volume fractions of the second phase (β) were used to simulate the dissolution kinetics of the β phase. Semi-implicit Fourier-spectral method was used to solve the governing equations with chemical mobility as a function of compositions. The simulation results showed that the rate of dissolution of the β phase (i.e., recession of β+γ twophase region) was dependent on the composition of the single-phase γ alloy and the volume fraction of the β phase in the two-phase alloy of the couple. Higher Cr and Al content in the γ alloy and higher volume fraction of β in the γ+β alloy lower the rate of dissolution. Simulated results were found to be in good agreement with the experimental observations in ternary Ni-CrAl solid-to-solid diffusion couples containing γ and γ+β alloys. For the first time, a phase-field model was developed to simulate the diffusion process under an applied temperature gradient (i.e., thermotransport) in multiphase binary alloys. Starting from the phenomenological description of Onsager’s formalism, the field kinetic equations are derived and applied to single-phase and two-phase binary system. Simulation results show that a concentration gradient develops due to preferential movement of atoms towards the cold and hot end of an initially homogeneous single-phase binary alloy subjected to a temperature gradient. The temperature gradient causes the redistribution of both constituents and phases in the two-phase binary alloy. The direction of movement of elements depends on their atomic mobility and heat of transport values.