### 3.1.2 Essentials to Chapter 3.1: Diffusion Primer

| There is no technology without diffusion and no "high" technology without controlled diffusion. |  |
| – Diffusion = |
| Fick's first law is the foundation of phenomenological diffusion. |  |
1. | ji | = – | D · Ñ ci
--- | --- | --- | ---
2. | ¶c ¶t | = | div (D · Ñ c) = D · D c
|  | 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)