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What is diffusion?

Diffusion is the movement of atoms between sites in a structure. There are two types: substitutional and interstitial.

Solute atoms that are much smaller than the parent atoms may occupy interstitial sites, and can jump between them.

An atom can also move through the lattice by jumping into an adjacent vacant site. This creates a new vacancy in the position previously occupied by the atom.

In both cases, in order to jump to a different site, the atom must pass through a region of high energy (surmount an energy barrier, q₁) and must therefore possess a minimum (thermal) vibrational energy. The probability of this is given by a Boltzmann expression (exp(-q₁/kT)). The jump frequency is therefore given by this expression times the vibration frequency (Debye frequency). In the case of a substitutional solute, the jump frequency is further reduced by a factor equal to the probability of the adjacent site being vacant, which is (exp(-q₂/kT)), where q₂ is the energy associated with a vacancy. The upshot of this is that, for both types of solute, the diffusion coefficient is given by an expression of the type

although q represents only the energy barrier (q₁) in the case of interstitial solutes, whereas it also includes the effect of the need for an adjacent site to be vacant (q=q₁+q₂) in the case of substitutional solutes (and hence its value is always appreciably higher for such solutes). It’s also common to express q in molar terms, in which case it’s usually written as Q, and the Boltzmann constant k is replaced by the gas constant R.

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