a misfit dislocation

When you try to line up two crystals whose atomic spacings are slightly different, say one has 100 atoms in the same length where the other has 101, they cannot match everywhere. For a while the rows drift steadily out of step, until eventually one crystal has fitted in a whole extra row that the other lacks. At that spot there is an extra half-plane of atoms: a dislocation. A dislocation placed at an interface precisely to absorb this spacing mismatch is a misfit dislocation.

Misfit dislocations are the defining feature of a semicoherent interface. If the two lattices differ in spacing by a fraction delta = (a2 - a1)/a1, and the dislocation Burgers vector has length b, then the misfit dislocations sit a distance D = b/delta apart along the interface. Concrete numbers: a 4 percent misfit (delta = 0.04) with b = 0.2 nm needs a misfit dislocation every D = 0.2/0.04 = 5 nm. Between them the two crystals fit almost perfectly (coherently); each dislocation swallows exactly one row of the mismatch, relieving the elastic strain that a fully coherent interface would have to store.

Misfit dislocations are why a strained epitaxial film relaxes once it grows past a critical thickness, and why a coherent precipitate loses coherency as it coarsens. They are a double-edged sword: they relieve costly elastic strain, but they add their own line energy and, in a semiconductor device, act as electrically active defects that degrade performance. That is why device engineers keep epitaxial layers thin enough to stay coherent and misfit-dislocation-free. Honest note: a misfit dislocation is an ordinary dislocation (usually an edge type) doing a specific job at an interface; it is not a separate species of defect, just a dislocation classified by its role.