ELSEVIER Thin Solid Films 296 (I997) 76-78 o " (L¢ Atomistic simulation of the [ 001 ] surface structure in BaTiO3 Eugene Heifets a, Simon Dorfman b, David Fuks c, Eugene Kotomin d a Institute of Chemical Physics, University of Latvia, Rainis blvd. 19, Riga, LV-1586 Latvia b Department of Physics, Technion--Israel Institute of Technology, 32000 Haifa, Israel ° Materials Engineering Department, Ben-Gurion University of the Negev, P.O.B. 653, 84105 Beer Sheva, Israel d Institute of Solid State Physics, University of Latvia, Kengara str. 8, Riga, LV-1063 Latvia Abstract We simulate the effect of the surface relaxation on the polarization of the layers of paraeIectric phase in the vicinity of the [001 ] surface in BaTiO3 in the framework of the shell-model potentials. We observe large polarization of ions in the first two layers of the surface. Our simulations confirm the possibility of existence of Ti- and Ba-containing top layers in [001 ] BaTiO3 surfaces. © 1997 Elsevier Science S.A. Keywords: Atomistic simulation; Surface relaxation; Ferroelectrics 1. Introduction The size effect on phase transitions in ferroelectrics is the phenomenon which has been known from the middle of the 1950s [ 1 ]. It has recently attracted much attention because of the development of thin films and composite materials. Large capacity memory devices put this phenomenon into the group of hot topics in modern solid state physics [2]. The discrepancy of experimental results on the influence of the size of thin films or particles of ferroelectrics [ 3] may be affected by the surface preparation of the samples. Although there were some theoretical efforts to study the defects in ferroelectrics (see, for example, Refs. [4-7]) they were devoted mainly to the investigation of point defects, for exam- ple, dopped or undopped bulk materials. At the same time surface represents the defect that may lead to unusual behav- ior of ferroelectrics, which may be realized in the changes of the thermodynamic and kinetic properties of paraelectric- ferroelectric phase transition. The relaxation of the surface may be sufficient in thin films as well as in small particles and may shift the thermodynamic parameters which are usu- ally used in characterization of phase transitions in the film/ particle-based devices. The aim of this paper is to demonstrate the effect of the surface relaxation on the polarization of the layers of paraelectric phase in the vicinity of the [001] sur- face in BaTiO 3. Although the ab initio calculations represent a more consistent procedure in the study of the properties of oxides [ 8] its application is restricted by a relatively small number of surface layers; for this reason we used the shell- model technique [ 9,10 ]. This technique was previously suc- 0040-6090/97/$17.00 © 1997 Elsevier Science S.A. All rights reserved PHS0040-6090 (96) 09348-0 cessfully applied for the investigation of the defects in a lot of ionic crystals including ferroelectric perovskites [4-7]. 2. Method In the present simulation we kept cubic perovskite structure for the bulk of BaTiQ crystal. To study the surface relaxation we optimized the positions of several (from 1 to 10) surface layers situated into the field of the remainder of the crystal. Six additional layers modelled the remainder of the crystal. Ions in these layers were fixed in lattice sites. The number of additional layers was choosen to reach a convergency of the crystal field at the surface layers. The interatomic interaction is choosen in the spirit of core- core, core-shell and shell-shell pair potentials, representing the shell-model. In this approach each ion is represented by charged core and shell. The sum of the core and the shell charges is equal to the charge of the corresponding ideal ion. A spring with elastic coefficient k connects the core and the shell of the same ion. The values of the elastic coefficient k and the shell charges Yhave to be choosen to describe correct polarization of the ion in the crystal: ~= Y2/k (1) Interactions between the cores and between cores and shells of different ions include only Coulombic interaction. At the same time interactions between the shells of different ions besides of Coulombic part can contain the short-range potentials to account for the effects of exchange repulsion of