The Orientation of Domain Walls in Twinned Ferroelectric Crystals

Abstract

Due to the spontaneous deformations of ferroelectric crystals in their ferroelectric phases, twins (domains) may be separated only by those composition planes (domain walls) which satisfy the mechanical compatibility conditions; such planes are in an infinite crystal called permissible walls. A mathematical treatment is proposed which makes it possible to find all permissible walls in any ferroelectric species. It is shown that different types of permissible walls exist: W∞ walls with arbitrary orientation, crystallographically prominent Wf walls, and S walls whose indices depend on PS and the electromechanical coefficients. The orientations of such S walls are necessarily temperature dependent. Two particular domains may be separated by a W∞ wall or by one of two mutually perpendicular permissible walls of Wf and/or S type. In a number of species, however, there are pairs of domains between which no wall is permissible. It is shown that the occurrence of W∞ and Wf walls can be predicted from the symmetry properties of the paraelectric phase. The properties of S walls are discussed in detail. Among the known ferroelectrics, S walls are most likely to exist in MASD and in boracites. The available data on nickel-chlorine boracite suggest that S walls have been observed in this material.