an interstitial solid solution
An interstitial solid solution is a solid mixture in which the guest atoms dissolve not by replacing host atoms but by hiding in the gaps between them. The host lattice keeps every one of its own atoms; the newcomers simply move into the little pockets (interstitial sites) that were empty in the first place. It is like a crowd standing in a grid: instead of anyone leaving to make room, small children squeeze into the spaces between people's feet.
Because the gaps are small, only small solute atoms can dissolve interstitially, and even they fit tightly, so the solubility is usually limited to a few percent at most. The defining example is carbon in iron. In face-centred-cubic iron (austenite) carbon takes the octahedral interstitial holes and can dissolve up to about 2.1 percent by weight at high temperature; in the more tightly packed body-centred-cubic iron (ferrite) the holes are even more cramped and less than 0.02 percent carbon dissolves. That difference in interstitial solubility between the two forms of iron is the physical engine behind the entire iron-carbon phase diagram and the heat treatment of steel.
Interstitial solid solutions matter enormously in engineering precisely because a little goes a long way. Dissolved carbon, nitrogen, hydrogen, or oxygen strains the host lattice and locks up its dislocations, hardening and strengthening the metal far more, atom for atom, than a substitutional solute of similar amount. But there is a price: interstitial hydrogen can embrittle steel, and interstitial oxygen or nitrogen can make otherwise-ductile metals brittle — the same tight squeeze that strengthens can also crack.
Heat plain steel into the austenite range and carbon dissolves interstitially in the FCC iron; cool slowly and the excess carbon, no longer welcome in the low-solubility BCC ferrite, precipitates as iron carbide (cementite). The whole art of steel processing is managing how much carbon stays in interstitial solid solution and how much comes out as a separate phase.
Carbon in iron: up to ~2 percent dissolves interstitially in FCC austenite, but almost none in BCC ferrite.
Interstitial solubility is generally far lower than substitutional solubility, because the gaps are small. Do not expect interstitial solutes to dissolve freely — even carbon, the great example, tops out around 2 percent, and only in the more open FCC iron.