### 3.1.2 Essentials to Chapter 3.1: Diffusion Primer

There is no technology without diffusion and no "high" technology without controlled diffusion.

Fick's first law is the foundation of phenomenological diffusion.
1.            ji  =  –  D · Ñci

2.            c
t
=  div (D · Ñc)  =  D · Dc
Fick's second law is simply the continuity equation for diffusing entities (without changing the total particle number).

Diffusion is synonymous with "random walk". The basic equation for random walk relates the diffusion length L to the number of jumps N and the (average) distance a covered in one jump.
L2   =  a2 · 3N

The relation between the atomic point of view and the phenomenological point of view goes back to Einstein; n is the jump frequency N/t.
D  =  g · a2 · n

=  D0 · exp – HM
kT
The important parameter for atomic diffusion is now the migrations enthalpy HM of the atom (or better defect) under consideration, and, somewhat less important, the pre-exponential factor D0 that contains the migration entropy SM and the lattice parameters.

If we combine the equations for D with the one for random walk, we obtain the Einstein-Smolukowski relation
D  =  L2
6t

Read backwards it tells us that the diffusion lengtt L is given by the square root of diffusion coefficient D times diffusion time t.

© H. Föll (Defects - Script)