ficks law of diffusion _________________

Ficks law

1. Fick’s First Law of Diffusion Based on analogy between material transfer in a solution and heat transfer by conduction .   J=rate of transfer of solute per unit area or diffusion flux N= concentration of solute (function of x and t only) x=coordinate axis in the direction of solute flow t=diffusion time D=diffusivity (Diffusion constant ) Statement : The local rate of transfer of solute per unit area per unit time is proportional to the concentration gradient of the solute and defines the proportionality constant as diffusivity of the solute. The negative sign shows the flow towards lower concentration of solute. 1

2. Here, d is the distance between tetrahedral sites. Let n 1 and n 2 be the no. of atoms in layers1 and 2 respectively . C 1 and C 2 ---- their respective concentration A----------------- Area of concentration N1, N2--------- Volume concentration of layer 1 and layer 2 2

3. We assume atoms jump at a frequency of v such that,half of them jump right and the other half jump left. So , the net flow of atoms across plane R in direction of x is = Similarly, net flow across the plane = =   3

4. n1 = & n2 = = Concentration gradient = = = ) = ) = ) =   4

5. Lets introduce j ---- flux density flux -------------number of units passing through a boundary area per unit time . = and d are constants ------------ D ----------------------Flicks first law of diffusion Statement : Flux density or rate of change of atoms per area is directly proportional to the concentration gradient or change in volume concentration ( ) for a given displacement.   5

6. 6 Limitation of first law Though it describes diffusion process accurately. But, has no convenient measure of current density of the impurity. Thus, second law developed to describe the concept with more readily measurable quantities.

7. 7 Flick’s second law of diffusion Moving from P1 to P2 impurity concentration changes and so does flux density from j1 to j2 We know, Let flux density entering at plane P1 = Aj & Let flux density entering at plane P2 = A dj Now, if the plates are separated by a distance dx, the rate of accumulation of the particles in the region between the planes = The change in flux is equal to the accumulation of the particles in the region between the plates, = - A dj  

8. 8 Flick’s second law of diffusion = - A dj = But, ----------------------Flicks first law of diffusion = ) = D Statement: The rate of change of volume concentration is directly proportional to the derivate of concentration gradient