Twinning in strained ferroelastics: Microstructure and statistics

The generation of functional interfaces such as superconducting and ferroelectric twin boundaries requires new ways to nucleate as many interfaces as possible in bulk materials and thin films. Materials with high densities of twin boundaries are often ferroelastics and martensites. In this review, we show that the nucleation and propagation of twin boundaries depend sensitively on temperature and system size. Sudden changes of the domain pattern manifest themselves as avalanches or "jerks" in the potential energy of the sample. At high temperatures, the change of the twin pattern is thermally activated; the probability P to find sudden energy changes of jerks E follows the Vogel-Fulcher statistics P(E) ∼ exp (E/(T - T _VF)), whereas the athermal regime at low temperatures corresponds to power-law statistics P(E) ∼ E ^-ε . We find that the complexity of the pattern is well characterized by the number of junctions between twin boundaries. Materials with soft bulk moduli have much higher junction densities than those with hard bulk moduli. Soft materials also show an increase in the junction density with diminishing sample size. The change of the complexity and the number density of twin boundaries represents an important step forward in the development of "domain boundary engineering," where the functionality of the materials is directly linked to the domain pattern.