Effective intrinsic linear properties of laminar piezoelectric composites and simple ferroelectric domain structures

Abstract

The effective properties of piezoelectric laminates have been analyzed, based on the calculation of internal fields and making use of a simple matrix manipulation method. The results are expressed in a compact notation which is convenient for numerical implementation and at the same time suitable for further analytical treatments. A detailed analysis of fully compatible ferroelectric domain structures shows, that the results for arbitrary piezoelectric laminates can be further simplified and specific property relationships for rank-1 laminates of tetragonal and rhombohedral crystals are derived. The method is finally applied to the analysis of various hierarchical domain structures. Detailed orientation relationships between the particular domains in some important domain pattern are given to make these structures accessible for the presented method. Some numerical results for tetragonal barium titanate illustrate the effects of different domain arrangements on the effective properties.

A Review of Domain Modelling and Domain Imaging Techniques in Ferroelectric Crystals

“…(a) A rank-5 arrangement with average compatibility (b) A simpler, rank-3 arrangement with exact compatibility [41]. …”

Thermodynamic driving force in ferroelectric crystals with a rank-2 laminated domain pattern, and a study of enhanced electrostriction

“…The issues covered in these books, however, are mostly related to physics; the mechanics issues-either continuum mechanics or micromechanics-remain largely untouched. In particular, continuum and thermodynamic models have been developed by Chen and Peercy (1979), Chen (1980), Chen and Marsden (1981), Bassiouny et al (1988), Bassiouny and Maugin (1989), Loge and Suo (1996), Lynch (1998), Cocks and McMeeking (1999), Landis and McMeeking (1999), Kamlah and Tsakmakis (1999), Landis (2002), Schrade et al (2007), Rodel (2007), and Su and Landis (2007), among others. Finite element calculations have been carried out by Kamlah et al (2005), Haug et al (2007), and Pathak and McMeeking (2008) for polycrystals, and phase-field studies have been given by Chen (2002), Zhang and Bhattacharya (2005a, b), Dayal and Bhattacharya (2007), , and Shu et al (2008).…”

Periodic boundary conditions for the simulation of 3D domain patterns in tetragonal ferroelectric material

“…The formation of periodic or nearly periodic patterns of domains is commonly observed; the effect of specimen size and mechanical strain on the formation of such periodic domain patterns has also been widely reported [4,[12][13][14][15]. The spatial distribution of domains affects ferroelectric properties at both fine scale and macroscale [8,11,[16][17][18][19][20][21]. Rödel [21] discussed the dependence of piezoelectric coefficients on the volume fractions of domains, while Weng and Wong [22] showed that the macroscale ferroelectric behaviour is enhanced in certain laminated domain patterns.…”

“…The spatial distribution of domains affects ferroelectric properties at both fine scale and macroscale [8,11,[16][17][18][19][20][21]. Rödel [21] discussed the dependence of piezoelectric coefficients on the volume fractions of domains, while Weng and Wong [22] showed that the macroscale ferroelectric behaviour is enhanced in certain laminated domain patterns. There is great interest in the domain patterns because of the potential to exploit engineered configurations of domains for energy harvesting, actuation, sensing, and memory devices [23][24][25][26][27].…”