a semicoherent interface

A coherent interface keeps its lattices perfectly lined up, but it pays for that with elastic strain, and that strain grows as the two spacings differ or the particle gets bigger. At some point stretching everything into line simply costs too much. Nature then strikes a bargain: let the lattices match over most of the interface, and dump the leftover mismatch into occasional defect lines spaced along the seam. That compromise interface, mostly matched with a regular array of dislocations mopping up the misfit, is a semicoherent interface.

The dislocations that take up the leftover misfit are called misfit dislocations. If the two lattices differ in spacing by a fraction delta, the misfit dislocations sit a distance D = b/delta apart, where b is the Burgers vector. Work it out: a 1 percent misfit (delta = 0.01) with b = 0.25 nm puts a misfit dislocation every D = 0.25/0.01 = 25 nm. Between the dislocations the crystals fit coherently; right at each dislocation the extra half-plane absorbs one row of misfit. So a semicoherent interface is part good-fit, part dislocation, intermediate in energy between coherent and incoherent.

This is the normal state of a moderately mismatched interface: the interface between a growing precipitate and its matrix, or an epitaxial film once it exceeds a critical thickness. The transition coherent to semicoherent to incoherent as a particle coarsens governs how alloys age and lose strength. Honest note: misfit dislocations lower the elastic strain but add their own line energy, so semicoherent is favoured only in a middle range of misfit and size; too little misfit stays coherent, and too much goes incoherent.