flick's law of diffusion

Question

On the basis of Fick’s laws of diffusion, explain why during eutectoid transformation in Fe-C alloys
(as well as in steels) diffusion controlled growth rate of pearlite is inversely proportional to the
interlamellar spacing and directly proportional to the diffusion coefficient.

Answer 1

Pearlite grows by carbon diffusing between layers. When the layers are closer together, carbon travels a shorter distance, so growth is faster, and when the diffusion coefficient is larger, carbon moves more easily, also making growth faster.

Carbon diffusion follows Flick's law: growth rate is proportional to D/λ

meaning,

1. If D is bigger than before → atoms diffuse faster → growth is faster
2. If λ is smaller than before → layers are closer → growth is faster
3. higher diffusion (D) and smaller spacing (λ) balance each other

Example 1:

Sample	D (m²/s)	λ (µm)
A	2.0 x 10-11	0.50
B	1.5 x 10-11	0.25

Question: Which sample has the faster growth rate, and by what factor?

Set up: B/A

(1.5 x 10^-11)/ 0.25 0.75

----------------------- = -------------- = 1.5

(2.0 x 10^-11)/ 0.50 0.50

Sample B goes from 0.25 λ to 0.50 λ

Sample A doesn't change from 0.50 λ

Answer: sample B grows 1.5X faster than sample A

Explain why the pearlite growth rate is proportional to the diffusion coefficient and inversely proportional to the interlamellar spacing using Fick’s law.