an interstitial solid solution

The second way to dissolve one element into another does not replace host atoms at all — it slips the guest atoms into the leftover gaps. Even in a tightly packed crystal, there are small empty pockets between the atoms, called interstitial sites (think of the little spaces between stacked oranges in a crate). If the guest atom is small enough, it can nestle into those pockets without kicking any host atom off its site. That is an interstitial solid solution.

This only works for genuinely small atoms — chiefly carbon, nitrogen, hydrogen, oxygen, and boron — dissolving into a host of much larger atoms. The most important case in all of engineering is carbon in iron, which is what makes steel. Carbon's atomic radius is only about 0.071 nm against iron's 0.124 nm, small enough to squeeze into the interstitial holes of the iron lattice. But even so it is a tight fit, so the amount that dissolves is limited: FCC iron (austenite) can hold up to 2.14 wt% carbon at 1147 degrees C, while BCC iron (ferrite) can hold barely 0.022 wt% at room temperature because its interstitial holes are smaller and awkwardly shaped.

That difference in interstitial capacity between FCC and BCC iron is the hidden engine behind all of steel heat treatment. When you cool carbon-rich austenite, the iron wants to become BCC ferrite, but the ferrite cannot hold the carbon — so the carbon must go somewhere, driving the formation of pearlite, or, if cooled fast enough to trap it, the hard distorted phase martensite. Interstitial solutions also strengthen strongly per atom, because the small atom wedges the lattice apart and clamps down on dislocation motion.