An interstitial site is a gap between the atoms of a crystal where a smaller atom can sit. A tetrahedral site lies at the centre of a tetrahedron of four atoms, an octahedral site at the centre of an octahedron of six. The habitability of a site is the radius of the largest sphere that fits in it without pushing the surrounding atoms apart.
Examples
Example 5.21 (Steel)
Carbon, of covalent radius (half the distance in diamond), is too large for the sites of iron without distortion, but much less so in -iron, whose octahedral sites are the largest. Steel is made by dissolving carbon in hot -iron; quenched, the carbon is trapped as the iron returns to a body-centred structure, which it distorts, and the distorted crystal is hard.