TY - JOUR
T1 - Size dependence of the ferroelectric transition of small BaTiO3 particles
T2 - Effect of depolarization
AU - Shih, Wan Y.
AU - Shih, Wei Heng
AU - Aksay, Ilhan A.
N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 1994
Y1 - 1994
N2 - A theory has been developed to examine the depolarization effect on the ferroelectric transition of small BaTiO3 particles. To reduce the depolarization energy, a crystal would break up into domains of different polarization. In this study, we consider cubic particles with alternating domains separated by 180°domain walls. The depolarization energy and the domain-wall energy were incorporated into the Landau-Ginzburg free-energy density. Assuming a hyperbolic tangent polarization profile across the domain wall, the domain-wall energy and the domain-wall half thickness can be obtained by minimizing with respect to . To account for BaTiO3 not being a perfect insulator, a Schottky space charge layer beneath the particle surface that shields the interior of the crystal from the depolarization field was considered. The equilibrium polarization P and domain width D can be obtained by minimizing the total free-energy density with respect to both P and D. The results of the calculations show that the ferroelectric transition temperature of small particles can be substantially lower than that of the bulk transition temperature as a result of the depolarization effect. Consequently, at a temperature below the bulk transition temperature, the dielectric constant can peak at a certain cube size L. These results agree with the existing experimental observations. Finally, the theory can also be applied to other ferroelectric materials such as KH2PO4 or PbTiO3.
AB - A theory has been developed to examine the depolarization effect on the ferroelectric transition of small BaTiO3 particles. To reduce the depolarization energy, a crystal would break up into domains of different polarization. In this study, we consider cubic particles with alternating domains separated by 180°domain walls. The depolarization energy and the domain-wall energy were incorporated into the Landau-Ginzburg free-energy density. Assuming a hyperbolic tangent polarization profile across the domain wall, the domain-wall energy and the domain-wall half thickness can be obtained by minimizing with respect to . To account for BaTiO3 not being a perfect insulator, a Schottky space charge layer beneath the particle surface that shields the interior of the crystal from the depolarization field was considered. The equilibrium polarization P and domain width D can be obtained by minimizing the total free-energy density with respect to both P and D. The results of the calculations show that the ferroelectric transition temperature of small particles can be substantially lower than that of the bulk transition temperature as a result of the depolarization effect. Consequently, at a temperature below the bulk transition temperature, the dielectric constant can peak at a certain cube size L. These results agree with the existing experimental observations. Finally, the theory can also be applied to other ferroelectric materials such as KH2PO4 or PbTiO3.
UR - http://www.scopus.com/inward/record.url?scp=0000040145&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000040145&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.50.15575
DO - 10.1103/PhysRevB.50.15575
M3 - Article
AN - SCOPUS:0000040145
SN - 0163-1829
VL - 50
SP - 15575
EP - 15585
JO - Physical Review B
JF - Physical Review B
IS - 21
ER -