Fig. 1 An annealed microstructure of an aluminum bronze (Cu-5wt.% Al). Addition of aluminum lowers the stacking fault energy of copper.
Annealing twins are a prominent feature observed in the metallography of face centered cubic (FCC) metals. The formation of the twins is usually associated with the process of grain growth, but twins also form during recrystallization. An example of an annealed aluminum bronze is shown in Fig. 1 and multiple twins can be found in each grain.

Twin boundaries are usually flat and extend across an entire grain. These twin boundaries define a trace of a {111} atomic plane, i.e. the close packed planes in the FCC crystal structure. In some cases the twin is terminated within the grain and a stair step interface is observed consisting of a series of {111} planes.

The formation of a twin is accomplished by changing the atomic stacking sequence of these {111} planes. In the FCC structure, the {111} planes are stacked in a sequence ABCABCABC, which is equivalent to stacking billiard balls to form a pyramid. However, a choice of two positions is possible with the start of each new {111} layer.

The twin interface is where a layer of {111} has been added in the wrong stacking sequence. If the crystal continues to grow as FCC, the stacking sequence would look like ABCABACBA where the stacking sequence is mirror reflected through the center B layer that represents the stacking error or fault.

The formation of a stacking fault costs energy, therefore, crystals with high stacking fault energy do not show many annealing twins whereas low stacking fault energy metals like silver show a very high density of twins. Aluminum is a good example of an FCC material where very few twins are observed in the microstructure.

Fig. 2 A schematic illustration of the ledge structure of a grain boundary produced by termination of (111) planes. Growth of the plane o-p occurs by transferring atoms from ledges a, b, c, etc. to the new plane.
A simple mechanism to explain twin formation is shown in Fig. 2 where the grain at the bottom, D, is growing into grain C along the X direction. Grain growth occurs by the growth of (111) ledges where the atoms are supplied from the locations a, b, c, d, e, f, and g and added to locations h, i, j, k, l and m. Eventually a new layer, o-p, will be added to grain D. New layers are added by the nucleation of a new plane on the existing (111) plane.

The nucleation of a twin occurs when the next layer is added in the wrong stacking sequence and this is often referred to as a "growth accident." The probability of a growth accident is dependent upon the stacking fault energy, the chemical driving force for grain growth (or recrystallization) and the annealing temperature. The probability of nucleating a stacking error is lower for materials that have higher stacking fault energies and increases with both chemical driving force and temperature. An increase in twin density with increasing temperature may seem counter intuitive, but the process of nucleation is a thermally activated process. A more in-depth discussion of the theory may be found in the book "Grain Boundary Structure and Kinetics" published by ASM (1980), pp. 440-443.

As a final comment on twin boundaries, it should be noted that twin boundaries affect deformation and must be included when modeling strength. For example, the Hall-Petch equation is often cited for modeling single-phase alloys where the yield strength (Sy) is inversely related to the square root of the grain diameter, D.

The parameters S0 and k are material specific constants. The measurement of D must include the twin boundaries when using Hall-Petch. However, twins must not be counted when measuring and reporting the ASTM grain size. IH