Atomic diffusion in crystallized phases

J is the flow of atoms passing through a unit surface, per time unit, D the diffusion coefficient of the species that diffuses and c its concentration. 

The force that acts on the atom that diffuses is the opposite of the chemical potential gradient. The mobility of the atom i is Bi, the quotient of the speed of the atom by the driving force  

Dj = kTBj, where k is the Boltzmann constant Therefore, the diffusion coefficient is proportional to the atomic mobility. Besides, dg/dx is proportional to the pressure gradient dP/dx  

The difference in pressure between the two sides of an interface causes a matter flow that is proportional to the pressure difference and to the diffusion coefficient of the mobile species [PHI 85], 

- D = DQexp(-Q/RT), so despite the presence of the term kT in the denominator of [3.8], it is the exponential of the numerator that is more important an increase of T results in a rapid increase of J. 

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