a twin boundary

A twin boundary is the most special, best-behaved boundary of all. Picture the boundary as a mirror: on one side sits a crystal, and on the other side sits its exact mirror image. The two grains are not randomly misoriented; one is the reflection of the other across the boundary plane, like the two halves of a symmetric butterfly. Because the atoms fit together so neatly at that mirror, a twin boundary carries very little extra energy.

In a coherent twin the atoms sit exactly where BOTH crystals want them: every atom in the boundary plane is shared, bonds are almost undistorted, so the energy is tiny (in copper a coherent twin-boundary energy is only about 20 mJ/m^2, roughly a twentieth of an ordinary grain boundary). In FCC metals the classic twin is a mirror across a {111} plane; in terms of stacking it flips the sequence, so ...ABCABC turns into ...ABCBACBA..., which is why a twin is intimately related to a stacking fault. A coherent twin is the Sigma = 3 coincidence boundary, the lowest-energy misorientation there is. Twins with a slightly tilted, less perfect boundary plane are incoherent and cost more energy.

Twins form by two routes: grown-in annealing twins that appear during heat treatment (very common in brass and other FCC metals), and deformation twins produced when a crystal shears mechanically (important in materials that cannot slip easily, like some titanium and magnesium alloys, and in the mechanical twinning that toughens TWIP steels). Because they are cheap, coherent, and block dislocations, densely twinned metals can be both strong and ductile. Honest note: the flat, straight bands you often see inside grains under the microscope are usually annealing twin boundaries, not ordinary grain boundaries.