This animation shows several applications of Fick's 2nd law. Select a scenario and click "Continue" to proceed.
In this case of a finite source for diffusion, we have an interstitial impurity located at the end of our piece of metal. We assume that it has a negligible width compared to the width of the metal.
In this situation the interstitial impurity will diffuse through the metal and the metal will not diffuse at all
\(C(x > 0,t = 0) = 0\) (At the start, there are no impurity atoms in the metal)
\(\int {C(x,t).dx = B} \) (The total amount of impurity atoms remains constant)
Where C(x,t) is the concentration of the impurity. The solution for C is:
In this case we have H2 diffusing into steel from one side. We assume that the steel bar has a semi infinite length and that there will be a constant concentration of H2 at the interface of the steel and the H2. From now on we will represent the diffusion with a schematic diagram (top right picture)
In this situation the hydrogen will diffuse into the steel and the steel will not diffuse at all
In this case the boundary conditions for solving Fick's 2nd law are:
\(C(x > 0,t = 0) = 0\) (At the start, there are no impurity atoms in the metal)
\(\int {C(x = 0,t) = B} \) (The concentration at x=0 is constant)
Where C(x,t) is the concentration of the impurity. The solution for C is:
In this case we have two semi-infinite bars placed beside
each other. We assume that both metals will undergo substitutional diffusion
and will therefore diffuse into each other. We also assume that the
two metals have the same diffusivity.
From now on we will using the schematic diagram of the two metals (top
right picture)