Using an effective Hamiltonian parametrized from first principles, Monte Carlo simulations are performed in order to study the piezoelectric response of in the ferroelectric tetragonal phase as a function of temperature. The effect of an electric field on the phase behavior is also illustrated by a simulation of the transformation of a rhombohedral domain into a tetragonal one under a strong field.
REFERENCES
1.
S.
Wada
, S.-E.
Park
, L. E.
Cross
, and T. R.
Shrout
, J. Korean Phys. Soc.
32
, S1290
(1998
).2.
S.
de Gironcoli
, S.
Baroni
, and R.
Resta
, Phys. Rev. Lett.
62
, 2853
(1989
);F.
Bernardini
, V.
Fiorentini
, and D.
Vanderbilt
, Phys. Rev. B
56
, R10024
(1997
);G. Sághi-Szabó, R. E. Cohen, and H. Krakauer, Phys. Rev. Lett. (in press).
3.
W.
Zhong
, D.
Vanderbilt
, and K. M.
Rabe
, Phys. Rev. Lett.
73
, 1861
(1994
);W.
Zhong
, D.
Vanderbilt
, and K. M.
Rabe
, Phys. Rev. B
52
, 6301
(1995
).4.
A. Garcia and D. Vanderbilt (unpublished).
5.
See, for example, M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectric and Related Materials (Clarendon, Oxford, 1977).
6.
In what follows, Greek subscripts run from 1 to 6 (Voigt scheme).
7.
8.
The relationship between and the strain and polarization correlations can be simply obtained by differentiation of the expression where is the extended Boltzmann factor and is the extended partition function.
9.
A Monte Carlo sweep is completed after each local variable is considered for a “flip attempt” and each component of the homogeneous strain suffers attempted changes, where is the linear size of the simulation box.
10.
Landolt–Börnstein: Numerical Data and Functional Relationships in Science and Technology, New Series, Vol. III/11 (Springer, Berlin, 1989).
11.
For the rhombohedral to orthorhombic to tetragonal to cubic transition sequence, the experimental ’s are, respectively, 187, 278, and 403 K, while the theoretical ones are 197, 230, and 295 K.
12.
See, for example, M. E. Lines and A. M. Glass, op. cit.;
F. Jona and G. Shirane, Ferroelectric Crystals (Pergamon, Oxford, 1962).
13.
These results hint that the transition becomes second-order at zero temperature. Such an interpretation is supported by an analysis of the energy surface of the effective Hamiltonian, showing that the distorted rhombohedral minima coalesce continuously into a tetragonal one with increasing field at 0 K.
This content is only available via PDF.
© 1998 American Institute of Physics.
1998
American Institute of Physics
You do not currently have access to this content.
