Coherent Boundary
Index
A coherent boundary is one for which atomic positions on either side of the boundary are correlated. This is illustrated for a coherent precipitate (yellow) in the top diagram. The lower diagram shows a similar precipitate, but with an incoherent boundary. Atoms in the matrix and the lattice are no longer in register across the interface.

If the atomic spacing in the two regions is different, a coherent boundary will create strain fields in the lattice at the interface. The stresses due to this condition will hamper the movement of dislocations in the material and increase its yield stress. This occurs in precipitation hardened alloy such as the Cu-Al binary alloy where Guinier-Preston zones and q'' precipitates have incoherent boundaries with the (Al)-matrix. 

From: Higgins, "Physical Metallurgy," Arnold (1989)