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.

Uranium-zirconium (U-Zr) alloys comprise a class of metallic nuclear fuel that is regularly considered for application in fast nuclear energy systems. The U-10wt%Zr alloy has been demonstrated to very high burnup without cladding breach in the Experimental Breeder Reactor-II (EBR-II). This was accomplished by successfully accommodating gaseous fission products with low smear density fuel and an enlarged cladding plenum. Fission gas swelling behavior of the fuel has been experimentally revealed to be significantly affected by the temperature gradient within a fuel pin and the multiple phase morphologies that exist across the fuel pin. However, the phase effects on swelling behavior have not been yet fully accounted for in existing fuel performance models which tend to assume the fuel exists as a homogeneous single phase medium across the entire fuel pin. Phase effects on gas bubble nucleation and growth in the alloy were investigated using transmission electron microscopy (TEM). To achieve this end, a comprehensive examination of the alloy system was carried out. This included the fabrication of uranium alloys containing 0.1, 2, 5, 10, 20, 30, 40, and 50 wt% zirconium by melt-casting. These alloys were characterized using electron probe micro-analysis (EPMA), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA). Once the alloys were satisfactorily characterized, selected U-Zr alloys were irradiated with 140 keV He^(+) ions at fluences ranging from 1 × 10^(14) to 5 × 10^(16) ions/cm^(2). Metallographic and micro-chemical analysis of the alloys indicated that annealing at 600 °C equilibrates the alloys within 168 h to have stable α-U and δ-UZr_(2) phase morphologies. This was in contrast to some reported data that showed kinetically sluggish δ-UZr_(2) phase formation. Phase transformation temperatures and enthalpies were measured using DSC-TGA for each of the alloys. Measured temperatures from different time annealed alloys have shown consistent matches with most of the features in the current U-Zr phase diagram which further augmented the EPMA observed microstructural equilibrium. Nevertheless, quantitative transformation enthalpy analysis also suggests potential errors in the existing U-Zr binary phase diagram. More specifically, the (β-U, γ2) phase region does not appear to be present in Zr-rich (> 15 wt%) U-Zr alloys and so further investigation may be required. To prepare TEM specimens, characterized U-Zr alloys were mechanically thinned to a thickness of ~150 μm, and then electropolished using a 5% perchloric acid/95% methanol electrolyte. Uranium-rich phase was preferentially thinned in two phase alloys, giving saw-tooth shaped perforated boundaries; the alloy images were very clear and alloy characterization was accomplished. During in-situ heating U-10Zr and U-20Zr alloys up to 810 °C, selected area diffraction (SAD) patterns were observed as the structure evolved up to ~690 °C and the expected α-U → β-U phase transformation at 662 °C was never observed. For the temperature range of the (α-U, γ2) phase region, phase transformation driven diffusion was observed as uranium moved into Zr-rich phase matrix in U-20Zr alloy; this was noted as nonuniform bridging of adjacent phase lamellae in the alloy. From the irradiation tests, nano-scale voids were discovered to be evenly distributed over several micrometers in U-40Zr alloys. For the alloys irradiated at the fluences of 1 × 10^(16) and 5 × 10^(16) ions/cm^(2), estimated void densities were proportional to the irradiation doses, (250 ± 40) and (1460 ± 30) /μm^(2), while void sizes were fairly constant, (6.0 ± 1.5) and (5.2 ± 1.2) nm, respectively. Measured data could be foundational inputs to the further development of a semi-empirical metal fuel performance model.