a self-interstitial
A self-interstitial is a host atom that has been squeezed into a gap between the normal lattice sites — a place not meant to hold an atom at all. If a vacancy is an empty parking bay, a self-interstitial is a car parked crosswise in the narrow aisle between the bays, jammed where there is really no room. It is the same kind of atom as its neighbours (that is what self means: an atom of the crystal's own element, not a foreign one), just shoved into the wrong sort of spot.
The tight gaps between atoms in a crystal (interstitial sites) are small — much smaller than the atoms themselves in a close-packed metal. Forcing a full-sized host atom into one badly distorts the surrounding lattice, so the energy to form a self-interstitial is large, typically 3 to 4 eV in a metal, three or four times the cost of a vacancy. Plug that into the Boltzmann law n/N = exp(-Q/kT) and the equilibrium number comes out vanishingly small: with Q around 4 eV even a hot metal near melting holds essentially no thermal self-interstitials. So in ordinary heating they are, for practical purposes, absent.
Where self-interstitials come into their own is under irradiation. When a fast neutron or ion knocks an atom clean out of its site, it leaves a vacancy behind and lodges the displaced atom in an interstitial position — a vacancy and a self-interstitial created together as a pair (a Frenkel pair). This is the fundamental unit of radiation damage in reactor steels and electronic materials. The two defects are highly mobile and, if they do not simply recombine, cluster into voids and dislocation loops that swell and embrittle the material — which is why self-interstitials, negligible in a furnace, are central to nuclear materials science.
In reactor pressure-vessel steel, each energetic neutron collision can displace an iron atom, creating a Frenkel pair: a vacancy plus an iron self-interstitial. Over years of service billions of these form; the surviving interstitials and vacancies migrate and cluster, hardening and embrittling the steel — irradiation damage that self-interstitials, absent in ordinary heat treatment, drive.
A self-interstitial is a host atom jammed into a gap; costly to form thermally, but mass-produced by radiation.
Because its formation energy is so much higher than a vacancy's, the thermal self-interstitial population is negligible in metals — do not treat vacancies and self-interstitials as roughly equal in number. In ordinary heating, vacancies dominate overwhelmingly.