Simulating Oxide Interfaces and Heterointerfaces
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Simulating Oxide Interfaces and Heterointerfaces John H. Harding, Dorothy M. Duffy and Duncan J. Harris, Department of Physics and Astronomy, University College London, Gower St, London WC1E 6BT, U.K. ABSTRACT Interfaces can be considered at a variety of length scales. All interfaces except grain boundaries are dielectric interfaces. In many cases, the geometric constraints of matching two lattices must be considered, together with the misfit strains that are often present. Continuum mechanics is useful for tackling such problems. In many cases, however, the local ordering of ions must also be considered. Atomistic simulation is therefore necessary, together with the problems associated with large length scales and long time scales. We discuss a number of examples to illustrate the issues involved and the compromises between different approaches that must be made. INTRODUCTION Real crystals stop somewhere; they have surfaces or interfaces. The region close to the interface has a characteristic structure, different from the bulk. This is associated with an energy. Two definitions of an interface are possible, depending on the reference state. The classic thermodynamic definition due to Gibbs, uses the device of a dividing surface and defines the interfacial energy as the difference between the system with the interface and a system with the same number of atoms but entirely composed of the bulk material (or for a heterointerface, materials). Another quantity, which we shall call the interfacial binding energy (or simply the binding energy) is the energy required to break the system along the interface, to produce the two int is surfaces that are joined to make the interface. There is a simple relation between them: if γ AB the interfacial energy between A and B and γ Asurf , γ Bsurf are the surface energies of the bind int components, then the binding energy is given by E AB = γ AB − (γ Asurf + γ Bsurf ). For surface energies the definitions are equivalent. However, for grain boundaries (and heterointerfaces) they are 6.00
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Boundary energy (Jm-2)
Boundary energy (Jm-2)
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Figure 1. Interfacial energy (left) and binding energy (right) of nickel oxide grain boundaries [1].
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are quite different as can be seen from Figure 1. More important, the definitions correspond to different experiments. The interfacial energy is relevant for experiments like wetting, nucleation, thermal grooving [2]. The binding energy corresponds to a cleavage experiment. All surfaces and heterointerfaces are dielectric boundaries. There will therefore be a strong interaction with a charge (and many defects in oxides are charged) given approximately by E=
εA 16πε 0 ε A R ε A
Q2
−εB + εB
(1)
where Q is the charge, R is the distance from the interface between A and B and ε A , ε B are the dielectric constants of the component materials. This image interaction
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