ZrO2 is typically a stochiometric oxide dominated by Schottky defects. Consider the addition of a small amount of Ta2O5 to ZrO2 that can dissolve into the ZrO2 lattice. If a sufficient amount of Ta2O5 is present, it can upset the balance of Zr and O vacancies that results from the Schottky defect reaction. When this is the case, the ZrO2 defects are considered to be in the "extrinsic" regime. If the amount of Ta2O5 is sufficiently small, the Schottly defect balance is not upset and this is considered the "intrinsic" regime. a) Provide the balanced reaction for the incorporation of Ta2O5 into ZrO2 b) Provide an expression as detailed as possible for the oxygen self-diffusivity, "Do, in the intrinsic regime, assuming a vacancy mechanism for oxygen diffusion. c) Provide an expression as detailed as possible for the oxygen self-diffusivity, D0 in the extrinsic regime, assuming a vacancy mechanism for oxygen diffusion. d) Provide a sketch (plot) of the variation of ln(D0 ) (along vertical axis) as a function of 1/T (along horizontal axis), including both intrinsic and extrinsic regimes and indicate the slopes expected for ln(D0) versus (1/T) for portions that are linear