1. Uranium oxide (UO2) is the most common fuel used in nuclear fission reactors. To make fuel pellets for these reactors, uranium containing ore is calcined to U3O8, heated further at 700°C to form UO2, and finally cold pressed with organic binder to form a pellet shape. These shapes are fired and sintered with the goal of forming a dense solid with minimal pores. Using the equations provided during in the notes on sintering and the attached paper (see Tables 2 and 3): i. Using excel, calculate the lattice, surface, and grain boundary diffusion as well as the vapor pressure at 1000°C. ii. Find the H values for surface diffusion, lattice diffusion (surface), vapor transport, grain boundary diffusion, and lattice diffusion (volume) iii. Construct a table for a particle radius, a, of 10 μm and another for a diameter 100 nm. Find the values of neck growth (x/a) and for densification (AL/Lo) at 10, 100, and 10,000 seconds. iv. Change the temperature to 1500°C and comment on which mechanisms are driving sintering at the two temperatures (1 paragraph). Ensure that coarsening mechanisms are differentiated from those that lead to densification. v. Will the powder coarsen or densify? Which will ensure minimal porosity? Which powder size leads to further densification? vi. More recent work by Balakrishna et al. (2001) has shown that sintering of uranium dioxide shows a coarsening-densification transition temperature (CDTT). This temperature was found to be 953°C for UO2. Assuming the data used was for low temperature sintering and that coarsening is minimized, what mechanism will drive densification in UO2 at higher temperatures?