In the incoherent precipitate growth of planar, given the balance of diffusion flux and transition of solute atom B from matrix to precipitate as

$D\frac{dC}{dx}=v(C_{}-C_{eq})$

From the concentration profile in the matrix as shown in figure, by using the balance of solute $(C_{}-C_0)x=\frac{1}{2}L{C}_0,$ show that precipitate thickening obeys a parabolic growth law as

$x=\frac{x_0}{(x_{}-x_{eq})}\sqrt[\phantom{2}]{Dt}$