Simulation of a Grain Boundary in Zirconia
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Simulation of a grain boundary in zirconia Michael W. Finnis and Anthony T. Paxton Atomistic Simulation Group, Department of Physics, Queen’s University Belfast BT7 1NN, Northern Ireland ABSTRACT Tetragonal zirconia, (t0 –ZrO2 ) a ferroelastic material, readily forms domains with domain boundaries on {011}. For example, by compressing a single crystal along [100] the formation and movement of such domain walls has been demonstrated experimentally. We have made atomistic simulations of a domain wall with a self-consistent tight-binding model which correctly reproduces both the high temperature tetragonal to cubic phase transition exhibited by zirconia, and its low temperature monoclinic phase. We analyse the results of our simulation, in particular the width of the domain wall, in terms of a Landau–Ginzburg theory in which the order parameter measures the degree of tetragonality of the lattice INTRODUCTION Zirconia, ZrO2 , exhibits a high temperature, cubic, fluorite phase which on cooling undergoes a second order phase transition to a tetragonal structure. Figure 1 shows a pseudo merohedral twin in tetragonal zirconia. As a → c the twin plane becomes a symmetry plane of the lattice. Two of the three tetragonal variants are separated by such a twin plane, a domain boundary which is mobile under an applied stress. These properties are the basis of ferroelastic behaviour. Little is known about the detailed atomic structure of the domain boundary. Foitzik and coworkers1 studied it by high resolution electron microscopy and suggested that the region of the boundary is rather wide. One might even postulate a band of cubic material separating the two tetragonal variants. The purpose of the present work is to address this question from both phenomenological and atomistic points of view. From a phenomenological point of view there are two order parameters associated with the cubic to tetragonal phase transition in the fluorite structure, namely the axial c/a ratio, η, and the displacement of the oxygen sublattice, δ. The free energy as a function of these two parameters at finite temperature was recently studied within a self-consistent tight-binding model by Fabris et al.2 They found that within the field of tetragonal stability, for a given axial ratio the free energy is unstable with respect to δ, in the manner of a classic symmetric double well, but the value of δ at the minimum of energy is relatively insensitive to η. At first sight one might expect to need at the very least these two order parameters to describe the structure of the domain boundary at the phenomenological level. The problem with the two bulk order parameters however is that they are not uniquely defined when the symmetry is broken by the interface and the local unit cells are distorted. Fortunately consideration of the crystal structure led us to the conclusion that there is a single order parameter, which we call φ, uniquely defined even as we go through the interface, and which is therefore ideally suited to a phenomenological model.
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