Solve for a, b, c, d, e and f.

Non-Steady State Diffusion: To determine its diffusion coefficient, gallium (Ga) was coated between two samples of a metal-ceramic composite (aluminum-silicon carbide). Ga wets both Al and SiC, and it has a lower melting point than either Al or SiC. The composite was heat treated at 400C for 24 hours. The Ga diffused into the Al. The behavior followed a thin film solution to the diffusion equation. c(x,t)=4Dtexp4Dtx2 a. Show that this function is a solution to Fick's second Law. In other words, take dc/dx,d2c/dx2 and dc/dt, and obtain an equality. The following chemical data were collected as the Ga penetrated into the Al: boundary condition, c(x=+,t>0)= ? c. Fill in the table above with values for natural log of the Ga concentration ( h,Ga) and position (x) squared. d. Plotting the values with 4Ga on the y axis and x2 on the x axis will give you a trend that should be a straight line of negative slope. The reciprocal of the slope is equal to 4Dt. In other words, you have linearized this equation in order to solve for D. Now solve for D: e. Describe how would you solve for 4Dt, the pre-exponential