Surface Relaxation in Ferroelectric Perovskites: An Atomistic Study
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INTRODUCTION Although there exist several theoretical studies of defects in technologically important perovskites [1, 2, 3], they were devoted mainly to the investigation of point defects. However, any crystalline surface, even perfect, is nothing but 2D defect which may lead to unusual behavior of perovskite films and nanocrystals, including the changes of the thermodynamnic and the kinetic properties of first-order phase transitions. The relaxation of the surface atoms may turn out to be large enough for affecting the thermodynamic parameters characterizing the phase transitions, as compared with their bulk values. In particular, the atomic relaxation nearby the surface of paraelectric SrTi0 3 may result in its ferroelectric reconstruction at the finite temperatures, as suggested in ref. [4]. The aim of this communication is to study in details the surface relaxation of a large (up to ten planes) near-surface region and, on its basis, to demonstrate creation of a considerable polarization induced by a surface in perovskites. We use cubic BaTiO 3 as a prototype. Although ab initio calculations are, known to be efficient in the study of the oxide properties [5], their use is essentially restricted by a relatively small number of surface layers which could be realistically handled. This is why in this paper a simpler, the so-called shell-model technique is used [6]. This approach was previously successfully applied to the investigation of defects in numerous ionic crystals including perovskites [1, 2, 3]. Its advantage is that the shell model is very-well suited for the treatmentof-4he polarization effects which are a central issue of our study.
SIMULATION TECHNIQUE In the present simulations we have studied a periodic two-dimenional slab of BaTi0 3 . 219 Mat. Res. Soc. Symp. Proc. Vol. 459 01997 Materials Research Society
Table 1: Short-range potential parameters for BaTi0
-
O2-
C(eV/A 6) 8.0
p(A) 0.35220
02
877.2
0.38096
9.0
02-
22764.0
0.1490 k(eV/A 2 ) 29.1 65974.0 18.41
43.0
Ion Ba2+ Ti4& 02-
used in our simulations.
A(eV) 1214.4
Interaction Ba 2+ - 02-
Ti4&
3
Y(e) 1.848 -35.863 -2.389
To study the surface relaxation, we have optimized the atomic positions in several (varied from one to ten) [001] surface planes placed into the electrostatic field of the remainder
of the crystal (simulated by six additional planes whose atoms were fixed in their perfect lattice sites). The number of these additional planes was chosen to reach a convergency of the crystalline field in the surface planes. The interatomic interactions are described, as usual, by the core-core, core-shell and shell-shell pair potentials, representing the shell-model (Table 1). In this approach each ion has a charged core and electronic shell. The sum of the core and shell charges is equal to the charge of the corresponding ideal ion. The spring constant k connects the core and the shell of the same ion. The value of this spring coefficient and the shell charge Y are chosen to describe correctly the polarizability a of the io
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