Below given diffusion couple has been prepared with $C_0$ and $C_0^{\text{'}}$ compositions from the substitutionally solid solution forming A$-$B alloy system, which contains inert markers at the initial interface. In the A$-$B alloy system $B$ has a higher diffusivity than $A.$

a$)$ Using the provided hypothetical phase diagram sketch the time series composition profiles at times $t_0,t_1,t_2$ and $t_{}$ for this diffusion couple at $T_0.$

b$)$ In parallel to the composition profiles you have plotted in part a$)$ sketch the changes that will occur in the diffusion couple with time at $T_0.$ Explain your sketch by supporting it with appropriate profiles etc. in correlation with the phase diagram.