Atomic migration and the diffusion coefficient

Similarly, the numbo- moving from plane 2 to plane 1 is 721, where 

The net movement, often called the flux, between the planes, 7, is given by  

If the process is random, the jump frequency is independent of direction and we can set Fi 2 equal to F2i- Moreover, if the jump frequency is independent of direction, then half of the jumps, on average, will be in one direction and half will be in the opposite direction, so we can write 

The number of mobile atoms on plane 1 is n per unit area, so that the concentration per unit volume at plane 1 is n la, or ci. Similarly, the number of mobile atoms per unit area on plane 2 is ri2, so that the concentration per unit volume at plane 2 is 2/a, or C2. Thus  

The concentration gradient, dc/dx, is given by the change in concentration between planes 1 and 2 

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