# Analyse:Kor/Fragment 066 01

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 Typus BauernOpfer Bearbeiter Graf Isolan Gesichtet
Untersuchte Arbeit:
Seite: 66, Zeilen: 1-19ff
Quelle: Meyer and Vanderbilt 2001
Seite(n): 205426-3, Zeilen: 2-8, 11-29
In addition to the microscopic quantities ρ(r) and ν(r), we assume the slabs to be thick enough that macroscopic quantities like the macroscopic electric field E, the dielectric displacement field D, and the polarization P are also well defined inside the slab. In practice, these fields may be calculated, for example, from unit cell averages of the electrostatic potential and the charge density.

In the case of an applied external electric field Eext perpendicular to the surfaces, the dielectric displacement field D inside the slab is oriented parallel to the z axis and is equal to Eext. The boundary condition of a vanishing external electric field is therefore equivalent to a vanishing dielectric displacement field D inside the slab. fig. [sic] 5.1(a) shows a schematic picture of the planar-averaged potential ν(r) for this situation.

The potential is constant outside the slab, but due to the slab dipole moment m the potential drops by 4πem when going from one side of the slab to the other. At the same time, the polarization P leads to surface charges σ = P ⋅ $\hat n$, which give rise to a huge depolarization field E = D - 4πP = -4πP inside the slab. (Notice, that E does not depend on the thickness of the slab). The contribution of the depolarization field to the total energy is large enough to completely destabilize the bulk FE state. Therefore, relaxing a polarized slab under the boundary condition of a vanishing external electric field will inevitably result in a paraelectric cubic structure [111].

[111] B. Meyer and David Vanderbilt. Ab initio study of BaTiO3 and PbTiO3 surfaces in external electric fields. Phys. Rev. B, 63(20):205426, May 2001.

In addition to the microscopic quantities ρ(r) and ν(r), we assume the slabs to be thick enough that macroscopic quantities like the macroscopic electric field E, the dielectric displacement field D, and the polarization P are also well defined inside the slab. In practice, these fields may be calculated, for example, from unit cell averages of the electrostatic potential and the charge density.6 [...]

In the case of an applied external electric field Eext perpendicular to the surfaces, the dielectric displacement field D inside the slab is oriented parallel to the z axis and is equal to Eext. The boundary condition of a vanishing external electric field is therefore equivalent to a vanishing dielectric displacement field D inside the slab. Figure 1(a) shows a schematic picture of the planar-averaged potential ν(z) for this situation.

The potential is constant outside the slab, but due to the slab dipole moment m the potential jumps by 4πem when going from one side of the slab to the other. At the same time, the polarization P leads to surface charges σ = P·<hat>n</hat>, which give rise to a huge depolarization field E=D-4πPP inside the slab (notice that E does not depend on the thickness of the slab). The contribution of the depolarization field to the total energy is large enough to completely destabilize the bulk FE state.15,16 Therefore, relaxing a polarized slab under the boundary condition of a vanishing external electric field will inevitably result in a paraelectric cubic structure.

6L. Fu, W. Yaschenko, L. Resca, and R. Resta, Phys. Rev. B 60, 2697 (1999).

15M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials (Clarendon Press, Oxford, 1977).

16W. Zhong, R. D. King-Smith, and D. Vanderbilt, Phys. Rev. Lett. 72, 3618 (1994).

 Anmerkungen At the end of the first two paragraphs and in the legend of figure 5.1.a the original paper is given. But nothing hinds at Kor's text being a nearly exact copy of the original one. Mark that the original ν(z) becomes ν(r) in Kor. Sichter (Graf Isolan)