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How do atoms move between atomic sites?

This is a small cross section of a material. This is a perfect lattice with no defects so the atoms cannot move from site to site.

All the atoms have thermal energy and therefore vibrate about their stable positions.
In a real material there will be defects, such as the vacancies shown. These allow atoms within the structure to move from one atomic site to another.
We can illustrate the idea of an energy barrier, this time using an impurity atom that moves between the gaps in the atomic structure (interstices).

Drag the impurity atom (purple) to see how the potential energy changes

This is the height of the 'energy barrier', Q
The height of the energy barrier, Q, is known as the activation energy. If an atom has enough thermal energy
(> Q), then it can cross over the energy barrier.

We see now that how often diffusion happens in a solid depends on the temperature of the solid. At high temperatures it is more likely for an atom to gain enough thermal energy to move to another site.
This probability of an atom jumping over the energy barrier is determined by Boltzman statistics, and is a function of the height of the energy barrier, Q, and the temperature of the system, T...
P = A exp ( -Q k B T )
Roll over the components of the equation to find out more
Probability of a succesful jump
Height of energy barrier
Boltzmann Constant
Absolute Temperature
Normalisation factor