Spent fuel from power reactors contains mixtures, alloy subsets, and compounds of elements; but the aggregate atomic densities in spent fuel are dominated by uranium and oxygen atoms. With the exception of some UO2 fuels with burnable poisons (primarily gadolinia in BWR rods), the other elements with significant atomic densities in spent fuel evolve during reactor operation from neutron reactions and fission plus fission decay events. Due to nuclear decay processes, the intrinsic chemical composition and activity of spent fuel will continue to evolve after it is removed from reactors as its radioactivity decays over time. During the time interval when the radioactivity levels are significant, which is the time interval relevant for design and for performance assessment of a geological repository, it is important to develop an understanding and to develop models that describe potential chemical responses in spent fuel and its potential degradational impacts on repository design and performance. One such potential impact is the oxidation response of spent fuel. The oxidation of spent fuel results in an initial phase change of the UO2 lattice to a U4 O9 lattice, and the next phase change is probably to U3 O8 although it has not been observed yet at low temperatures (<200°C). The U4 O9 lattice is non-stoichiometric with a oxygen to uranium weight ratio (O/U) at ~ 2.4. Preliminary indications are that the UO2 has a O/U of ~ 2.4 at the time just before it transforms into the U4 O9 phase.[1,2] Also, in the oxygen weight gain versus time response, a plateau appears as the O/U approaches ~ 2.4. Part of this plateau response is due to geometrical effects of a U4 O9 phase change front propagating into UO2 grain volumes. However, the plateau time response may be indicative of a metastable phase change delay kinetics or a diffusional related delay time until the oxygen density can attain a critical value to satisfy the stoichiometry and energy conditions for phase changes. In a previous paper and as a first step, a kinematic and thermodynamic ayalysis was developed to model spatially homogeneous oxidation phase transitions. However, the experimental data clearly show a front of U4 O9 lattice structure propagating into grains of the UO2 lattice structure. To describe this spatially inhomogeneous oxidation phase transition, as well as the expected U3 O8 phase transition from the U4 O9 lattice, lattice models are developed and spatially discontinuous kinematic and energetic expressions are derived. The approach will use concepts from statistical mechanics, discontinuum mechanics, and non-equilibrium thermodynamics. In addition, analytical techniques from shock wave analysis will be used to derive the surface discontinuity energetic expressions across the propagating oxidation phase front.