the vacancy mechanism
How does an atom locked into a rigid crystal actually move, when every neighbouring site is already occupied? The commonest answer is the vacancy mechanism: it waits for a next-door site to fall empty, then hops into it. Picture a nearly full car park, or the sliding-tile puzzle where one empty square lets all the others shuffle — no tile can move except into the gap, and the gap effectively travels the opposite way as tiles fill it. An atom diffuses by trading places with a vacancy, one jump at a time.
For this to work the crystal must contain vacancies, and it always does: above absolute zero a thermal-equilibrium population of empty sites exists (and in ionic ceramics, Schottky disorder or aliovalent doping fixes how many). An atom next to a vacancy needs enough energy to squeeze past its neighbours into the empty site; when it jumps, the vacancy has moved to where the atom was. So the atom's diffusion coefficient depends on two things multiplied together: how many vacancies are available (their concentration) and how easily an atom jumps into one (the migration energy). That is why the activation energy for vacancy diffusion includes both a formation term and a migration term. Substitutional atoms — those sitting on normal lattice sites, including most host cations and anions in a ceramic — move almost exclusively this way.
The vacancy mechanism is the master route for the atoms that build a ceramic's framework, so it governs densification during sintering, cation interdiffusion in solid-state reactions, and high-temperature creep. Its rate is throttled by the vacancy supply: dope a crystal to create more vacancies of the right kind and you can speed the diffusion of the species that rides them — the trick behind many sintering aids and stabilized zirconia. A common misconception is that the atom and the vacancy are somehow separate travellers; they are two views of one event — each atom jump is a vacancy jump in the opposite direction.
In MgO, magnesium ions diffuse by the vacancy mechanism: a Mg2+ hops into a neighbouring cation vacancy, and the vacancy moves the other way. Adding an aliovalent dopant that raises the cation-vacancy population directly speeds Mg diffusion and, with it, sintering.
Vacancy mechanism: an atom moves only by jumping into an adjacent empty site, so the vacancy travels the opposite way — the sliding-tile puzzle of the crystal.
Because the atom needs a vacancy waiting next door, vacancy diffusion is only as fast as the vacancy supply allows. That is why it is slower than interstitial diffusion, and why doping that changes the vacancy concentration is such a powerful lever on firing.