
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.

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.

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