Modelling and interaction of needle domains in barium titanate single crystals

Abstract

Needle domains are thin, lamellar domains that can appear as fine lines or stripes in a ferroelectric crystal. They affect the poling, switching, and other properties of ferroelectrics. A model is established to study the stress and electric fields caused by needle domains and their interaction. Considering the electrical and mechanical compatibility conditions at the tip of a needle domain, the fields are represented using equivalent edge dislocations and line charges. Accordingly, the dislocation fields derived by Barnett and Lothe for anisotropic piezoelectric media are employed. A modified Peach-Koehler force and calculations of the total energy due to the needle domains are used to study the formation, interaction and stability of needle patterns, taking full account of the strong anisotropy and electromechanical coupling present. The interaction of pairs of needle domains in an infinite piezoelectric with properties of barium titanate is found to be dominated by the electrostatic terms. This makes comb-like arrays of needle domains unstable if perfectly insulating properties are assumed. By considering redistribution of charge, stable equilibrium states for arrays of needle domains are found; these agree well with experimental observations. The model explains the stability of various observed needle patterns and also how unstable patterns evolve.

Boundary influence on the fields and arrangement of the needle domains in barium titanate single crystals

“…It is found that the minimum potential energy state corresponds to Q ∼ 0.44q − 0.49q for the range of positions explored. This result is consistent with the innite case (no boundaries) studied by Sui and Huber (2020), and justies adopting the eective line charge Q = 0.48q, as in previous work, for subsequent calculations. Note that the potential energy of the pair decreases as they approach the crystal edge at x 1 = 250w.…”

“…However, only position a2 is stable for both needle domains, corresponding to a minimum energy. This stable conguration implies that needles far from the boundary can form a comb structure with the tips aligning on the line x 2 = −x 1 , at 45 • to the x 1 -axis, as in the case of the innte crystal studied by Sui and Huber (2020).…”

“…However, the incompatible jumps in spontaneous polarization and strain near the needle domain tip imply the existence of local stress and electric elds to restore compatibility. The stresses and electric elds due to this kind of needle domain can be approximated as those due to an eective edge dislocation coupled with line charge (Sui and Huber (2020)). As illustrated in Fig.…”

“…Based on the previous study of Sui and Huber (2020), the equilibrium conguration of needle domains is sensitive to the quantity of eective charge at the needle tip. It was found, in the innite case, that there was no stable equilibrium conguration for a pair of parallel similar needle domains if the line charge magnitude Q was greater than 0.73q where q = √ 2p 0 w. A minimum potential energy conguration for two parallel interacting needle domains was found with Q = 0.48q.…”

“…Both material anisotropy and electromechanical coupling are taken into account. The model is used to analyse the behaviour of needle domains in nite crystals with external loads, which is a development from our previous research Sui and Huber (2020). In previous research, we found that, in an innite crystal, needle domain patterns were typically unstable due to strong electric elds near the needle-tips.…”