Ferroic crystals

Twinned crystals are normally classified according to twin-laws and morphology, or according to their mode of origin, or according to a structural basis, but there is another classification that deserves wider acceptance, one that is based on the tensor properties of the orientation states. An advantage of such a classification is the logical relationship between free energy and twin structures, for it becomes immediately apparent which forces and fields will be effective in moving twin walls. The domain patterns in ferroelectric and ferromagnetic materials are strongly affected by external fields, but there are many other types of twinned crystals with movable twin walls and hysteresis. These materials are classified as ferroelastic, ferrobielastic, and various other ferroic species. As explained in the next section, each type of switching arises from a particular term in the free energy function. Ferroic crystals possess two or more orientation states or domains, and under a suitably chosen driving force the domain walls move, switching the crystal from one domain state to another. Switching may be accomplished by mechanical stress (X), electric field (E), magnetic field (H), or some combination of the three. Ferroelectric, ferroelastic, and ferromagnetic materials are well known examples of primary ferroic crystals in which the orientation states differ in spontaneous polarization (P(s)), spontaneous strain (x(s)), and spontaneous magnetization (I(s)), respectively. It is not necessary, however, that the orientation states differ in the primary quantities (strain, polarization, or magnetization) for the appropriate field to develop a driving force for domain walls. If, for example, the twinning rules between domains lead to a different orientation of the elastic compliance tensor, a suitably chosen stress can then produce different strains in the two domains. This same stress may act upon the difference in induced strain to produce wall motion and domain reorientation. Aizu suggested the term ferrobielastic to distinguish this type of response from ferroelasticity, and illustrated the effect with Dauphine twinning in quartz. Other types of secondary ferroic crystals are listed in Table 16.1, along with the difference between domain states, and the driving fields required to switch between states.