Section 3.3.10.7.5. Twin textures in polycrystalline aggregates

So far, twin textures have been treated independently of their occurrence in `single crystals' or in polycrystalline aggregates. In the present section, the specific situation in polycrystalline materials such as ceramics, metals and rocks is discussed. This treatment is concerned with the extra effects that occur in addition to those discussed in Sections 3.3.10.7.1 to 3.3.10.7.4 above. These additional effects result from the fact that in a polycrystalline material a given crystal grain is surrounded by other grains and thus `clamped' with respect to form and orientation changes arising from mechanical stress, electrical polarization or magnetization. Here, this effect is called `neighbour clamping'.

Two cases of neighbour clamping occur, three-dimensional clamping of grains in the bulk of a sample and two-dimensional clamping at the surface of a sample. In addition, two-dimensional clamping can occur in thin films, either free or epitaxial. The result of this clamping is high elastic stress which is relaxed (`stress relief'; Arlt, 1990) by twinning, in particular by the formation of `shape-preserving' twin textures.

Twinning in a ceramic is of great technical importance for the preparation and optimization of devices such as capacitors, piezoelectric elements and magnets. They often contain ferroelectric or ferromagnetic polycrystalline materials which undergo domain switching in an electric or magnetic field and, hence, can be poled.

In the following, we restrict our considerations to non-metallic ceramics where twinning is generated by a ferroelastic phase transition (e.g. perovskites). It is assumed that the ceramic is formed at temperatures far above the phase transition, which is accompanied on cooling by a considerable spontaneous lattice strain in the low-temperature phase, leading to the formation of non-merohedral twins. Without any formation of twins a considerable change of the grain shapes would occur and cause high inter-grain stress. The main mechanism of stress relaxation (`stress relief') is the formation of a ferroelastic twin texture which preserves the shape of the original (high-temperature phase) grain as far as possible. Note that the twin texture resulting from this `neighbour clamping' is quite different from the twin texture of a free, unclamped grain. In the free grain, only few twin lamellae with usually coherent boundaries are formed, whereas in the clamped grain several twin bands with narrow-spaced twin lamellae of different twin types occur.

In the clamped case, the significant effect of ferroelastic twin formation is the reduction of the elastic energy resulting from the clamping. On the other hand, the formation of new twin interfaces increases the twin-boundary energy. The competition of these effects leads to an energetic balance with a (relative) minimum of the overall energy of the sample. The process of twin formation does not occur sharply at the transition temperature T_c but continues over a considerable temperature range below T_c. The `ideal' state of lowest energy is hardly ever reached due to the rigidity of the original grain structure (which remains rather unchanged) and to the existence of kinetic (coercive) barriers.

The group of materials for which these effects are most typical are the ferroelectric and ferroelastic perovskites, in particular BaTiO₃. A detailed study is provided by Arlt (1990), who also presents extensive model calculations of relevant energy terms, as well as of average domain sizes and widths of twin bands.

Twinning phenomena in polycrystalline metals are treated by Christian (1965, Chapter 8).

Note. As mentioned above in Section 3.3.10.7.1, non-ferroelastic transitions phase transitions cause no spontaneous lattice strain and, hence, the associated merohedral twins cannot act as `stress relief' for a `clamped' twin texture.