Ferroelectric materials exhibit spontaneous polarization and domain structures below the Curie temperature. In this work the phase field approach has been used to simulate phase transformations and the formation of ferroelectric domain structures. The evolution of phases and domain structures was simulated in ferroelectric single crystals by solving the time dependent Ginzburg-Landau (TDGL) equation with polarization as the order parameter. In the TDGL equation the free energy of a ferroelectric crystal is written as a function of polarization and applied fields. Change of temperature as well as application of stress and electric fields leads to change of the free energy and evolution of phase states and domain structures. In this work the finite difference method was implemented for the spatial description of the polarization and the temporal evolution of polarization field was computed by solving the TDGL equation with an explicit time integration scheme. Cubic to tetragonal, cubic to rhombohedral and rhombohedral to tetragonal phase transformations were modeled, and the formation of domain structures was simulated. Field induced polarization switching and rhombohedral to tetragonal phase transition were simulated.
Volume Subject Area:
Aerospace
1.
Nosek, J., 2000, “Advanced sensors and actuators and their incorporation into micro electromechanical systems”, IEEE International Symposium on Industrial Electronics, Puebla, pp. 540–545.
2.
Hackenberger, W., Rehrig, P.W., Ritter, T., and Shrout, T., 2001, “Advanced piezoelectric materials for medical ultrasound transducers”, IEEE Ultrasonics Symposium (Cat. No.01CH37263), Atlanta, GA, USA, pp. 1101–1104.
3.
Song, G., Gu, H., and Li, H., 2004, “Application of the Piezoelectric Materials for Health Monitoring in Civil Engineering: An Overview”, Engineering Construction and Operations in Challenging Environments Earth and Space 2004: Proceedings of the Ninth Biennial ASCE Aerospace Division International Conference, League City/Houston, TX, United States, pp. 680–687.
4.
McLaughlin
E. A.
Liu
T.
Lynch
C. S.
2004
, “Relaxor ferroelectric PMN-32%PT crystals under stress and electric field loading: I – 32 mode measurements
”, Acta Materialia
, 52
(13)
, pp. 3849
–3857
.5.
McLaughlin
E. A.
Liu
T.
Lynch
C. S.
2005
, “Relaxor ferroelectric PMN-32%PT crystals under stress, electric field and temperature loading: II-33-mode measurements
”, Acta Materialia
, 53
(14)
, pp. 4001
–4008
.6.
Davis
M.
Damjanovic
D.
Setter
N.
2006
, “Electric-field-, temperature-, and stress-induced phase transitions in relaxor ferroelectric single crystals
”, Physical Review B (Condensed Matter and Materials Physics)
, 73
(1, 14115)
, pp. 1
–16
.7.
Yang
W.
Chen
L.-Q.
1995
, “Computer simulation of the dynamics of 180° ferroelectric domains
”, Journal of the American Ceramic Society
, 78
(9)
, pp. 2554
–2556
.8.
Hu
H.-L.
Chen
L.-Q.
1997
, “Computer simulation of 90° ferroelectric domain formation in two-dimensions
”, Materials Science & Engineering A: Structural Materials: Properties, Microstructure and Processing
, A238
(1)
, pp. 182
–191
.9.
Hu
H. L.
Chen
L.-Q.
1998
, “Three-dimensional computer simulation of ferroelectric domain formation
”, Journal of the American Ceramic Society
, 81
(3)
, pp. 492
–500
.10.
Li, Y.L., Hu, S.Y., Liu, Z.K., and Chen, L.Q., 2001, “Phase-field simulation of domain structure evolution in ferroelectric thin films”, Materials Research Society Symposium - Proceedings, Boston, MA, pp. 421–4210.
11.
Li
Y. L.
Hu
S. Y.
Liu
Z. K.
Chen
L. Q.
2002
, “Effect of substrate constraint on the stability and evolution of ferroelectric domain structures in thin films
”, Acta Materialia
, 50
(2)
, pp. 395
–411
.12.
Wang
J.
Shi
S.-Q.
Chen
L.-Q.
Li
Y.
Zhang
T.-Y.
2004
, “Phase-field simulations of ferroelectric/ferroelastic polarization switching
”, Acta Materialia
, 52
(3)
, pp. 749
–764
.13.
Wang
J.
Li
Y.
Chen
L.-Q.
Zhang
T.-Y.
2005
, “The effect of mechanical strains on the ferroelectric and dielectric properties of a model single crystal - Phase field simulation
”, Acta Materialia
, 53
(8)
, pp. 2495
–2507
.14.
Li
Y. L.
Hu
S. Y.
Chen
L. Q.
2005
, “Ferroelectric domain morphologies of (001) PbZr1_x Tix O3 epitaxial thin films
”, Journal of Applied Physics
, 97
(3, 034112)
, pp. 1
–7
.15.
Vanderbilt
D.
Cohen
M. H.
2001
, “Monoclinic and triclinic phases in higher-order Devonshire theory
”, Physical Review B: Condensed Matter and Materials Physics
, 63
(094108)
, pp. 1
–9
.16.
Zhirnov
V. A.
1958
, J. Exptl. Theoret. Phys.
(USSR), 35
, pp. 1175
1175
[Sov. Phys. JETP 1178, 1822 (1959)].17.
Khachaturyan, A.G., 1983, Theory of Structural Transformations in Solids, John Wiley, New York.
18.
Zhang
W.
Bhattacharya
K.
2005
, “A computational model of ferroelectric domains. Part 1: model formulation and domain switching
”, Acta Materialia
, 53
(1)
, pp. 185
–198
.19.
Nambu
S.
Sagala
D. A.
1994
, “Domain formation and elastic long-range interaction in ferroelectric perovskites
”, Physical Review B (Condensed Matter)
, 50
(9)
, pp. 5838
–5847
.20.
Yin
J.
Cao
W.
2000
, “Domain configurations in domain engineered 0.955Pb(Zn1/3Nb2/3)O3-0.045PbTiO3 single crystals
”, Journal of Applied Physics
, 87
(10)
, pp. 7438
–7441
.21.
Abplanalp
M.
Barosova
D.
Bridenbaugh
P.
Erhart
J.
Fousek
J.
Gunter
P.
Nosek
J.
Sulc
M.
2002
“Scanning force microscopy of domain structures in Pb(Zn1/3Nb2/3)O3-8%PbTiO3 and Pb(Mg1/3Nb2/3)O3-29%PbTiO3
”, Journal of Applied Physics
, 91
(6)
, pp. 3797
–3805
.22.
Han
J.
Cao
W.
2003
, “Interweaving domain configurations in [001]-poled rhombohedral phase 0.68Pb(Mg1/3Nb2/3)O3-0.32PbTiO3 single crystals
”, Applied Physics Letters
, 83
(10)
, pp. 2040
–2042
.23.
Streiffer
S. K.
Parker
C. B.
Romanov
A. E.
Lefevre
M. J.
Zhao
L.
Speck
J. S.
Pompe
W.
Foster
C. M.
Bai
G. R.
1998
, “Domain patterns in epitaxial rhombohedral ferroelectric films. I. Geometry and experiments
”, Journal of Applied Physics
, 83
(5)
, pp. 2742
–2753
.24.
Shin
M. C.
Chung
S. J.
Lee
S. G.
Feigelson
R. S.
2004
, “Growth and observation of domain structure of Lead Magnesium Niobate-Lead Titanate Single Crystals
”, Journal of Crystal Growth
, 263
(1–4)
, pp. 412
–420
.25.
Liu
T.
Lynch
C. S.
2003
, “Ferroelectric properties of [110], [001] and [111] poled relaxor single crystals: measurements and modeling
”, Acta Materialia
, 51
(2)
, pp. 407
–416
.
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