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SCIENCE CHINA Technological Sciences, Volume 59 , Issue 7 : 1059-1064(2016) https://doi.org/10.1007/s11431-016-6080-8

An unconventional phase field modeling of domains formation and evolution in tetragonal ferroelectrics

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  • ReceivedJan 21, 2016
  • AcceptedMay 24, 2016
  • PublishedJun 15, 2016

Abstract

Based on characteristic functions of variants, we developed an unconventional phase field modeling for investigating domains formation and evolution in tetragonal ferroelectrics. In order to develop this computational approach, we constructed the anisotropy energy of tetragonal variants, which is used instead of Landau-Devonshire potential in the conventional phase field method, resulting in that much fewer parameters are needed for simulations. This approach is advantageous in simulations of emerging ferroelectric materials. We employ it to study the formation and evolution of domains in tetragonal barium titanate single crystal, as well as the nonlinear behaviors under cyclical stress and electric field loading. A multi-rank laminated ferroelectric domain pattern, 90° domain switching accompanied by polarization rotation, and 180° domain switching accompanied by move of domain wall are predicted. It is found that the speed of 90° domain switching is slower than that of 180° domain switching, due to both polarization and transformation strain changed in 90° domain switching. It also suggests that large strain actuation can be generated in single crystal ferroelectrics via combined electromechanical loading inducing 90° domain switching. The good agreement between simulation results and experimental measurements is observed.


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11572276 & 11502225), and Hunan Provincial Natural Science Foundation of China (Grant No. 14JJ6015).


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  • Figure 1

    (Color online) (a) A schematic of multi-well structure for stored energy density in tetragonal ferroelectrics, (b) the schematic of anisotropy energy density of variant i.

  • Figure 2

    (Color online) (a) The phase field simulation of ferroelectric domains in tetragonal BaTiO3 crystal in the absence of applied fields, where the white arrows corresponding to polarization vectors, the corresponding variations of (b) characteristic function and (c) polarization P when x2=32, and (d) domains observed in experiment [31].

  • Figure 3

    (Color online) Temporal evolution of ferroelectric domains in tetragonal BaTiO3 crystal under an external stress σ 220 : (a) initial state, (b)–(d) corresponding 50 steps, 80 steps, and final stable state under compressive stress; while (e)–(g) corresponding 50 steps, 80 steps, and final stable state under tensile stress. Note that the white arrows correspond to polarization vectors.

  • Figure 4

    (Color online) Temporal evolution of ferroelectric domains in tetragonal BaTiO3 crystal under an in-plane electric field E 20: (a) initial state; (b) 8 steps; (c) 16 steps, and final stable state. Note that the white arrows correspond to polarization vectors.

  • Figure 5

    (Color online) (a) The simulated stress-average strain curve under a cyclical stress σ2 20 loading and zero electric field, (b) hysteresis loop of average polarization versus applied electric field E 20 for tetragonal BaTiO3 crystals with and without stress loading, and (c)–(d) butterfly loop of average strain versus electric field E20 for tetragonal BaTiO3 crystals with and without stress loading, where the inset in (c) showing the zoomed-in curve for the case without stress loading. The experimental polarization-electric field hysteresis loop [34] shown by squares in (b).

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