a self-interstitial
If a vacancy is a missing atom, a self-interstitial is the opposite: an atom of the host metal that has been jammed into a gap between the normal lattice positions — a spot never meant to hold an atom. Picture a tightly packed crowd on a train, then someone forces themselves into the narrow space between two seated rows. Everyone nearby gets shoved and squeezed. That is what a self-interstitial does to the surrounding lattice: it distorts it heavily in all directions.
Because the interstitial gaps in a metal are small and the host atom is full-sized, cramming one in strains the neighbors enormously. This makes a self-interstitial very expensive to create — its formation energy is roughly three to four times that of a vacancy. Feeding that big Qv back into the same Arrhenius law, exp(-Qv/kT), makes the equilibrium concentration of self-interstitials in a normal metal utterly negligible — many orders of magnitude rarer than vacancies. In everyday thermal conditions you can almost ignore them.
So why learn about them? Because they matter enormously under radiation. When a fast neutron or ion knocks an atom clean out of its site, it leaves behind a vacancy and lodges the atom in an interstitial position — a paired vacancy-plus-interstitial defect called a Frenkel defect. This is the fundamental unit of radiation damage in the steels of nuclear reactors and in spacecraft electronics, where accumulated interstitials and vacancies cause swelling, hardening, and embrittlement over years of service.
In an FCC or BCC metal at room temperature the ratio of self-interstitials to vacancies is astronomically small — if vacancies sit at 10^-10, self-interstitials might be near 10^-30. But inside a reactor pressure vessel, a single energetic neutron collision creates a Frenkel pair (one vacancy plus one interstitial) directly, bypassing the thermal statistics entirely.
Thermally almost nonexistent, but radiation makes self-interstitials in bulk — the seed of reactor-steel damage.
Do not confuse a self-interstitial (a host atom out of place) with an interstitial impurity like carbon in iron (a small foreign atom that fits the gap comfortably). The impurity forms a stable solid solution; the self-interstitial is a high-energy defect.